Martí Ramón

Solano

'AS THE SAYING (OR WHATEVER) GOES': SAYINGS AND PSEUDO-SAYINGS IN THE AMERICAN PRESS

Keywords: introductory phrase, lexicalisation, proverbs, quotations, journalistic discourse

The main objective of this study is to investigate how the phrase 'as the (old) saying goes' is actually used in journalism-especially in the American press-and what types of units it introduces or refers to. We highlight the importance and pervasiveness of this phrase in this type of register as over 10,000 article results have been yielded by the online archives of The New York Times containing the target phrase. We claim that this string is applied to an enormous range of words and phrases going from adjectives, collocations and lexical bundles to actual sayings, proverbs and quotations. Our ultimate objective is to find out, observe and examine modern (and also less modern), popular proverbial phrases that seem to crop up in journalistic discourse.

"As the (old) saying goes"

The epistemological reason for this study lies in the hypothetically high possibility of coming across an important number of set phrases, idioms, sayings, proverbs and other types of sentence-like units such as slogans, catchphrases and so forth being used in combination with the introductory phrase 'as the (old) saying goes'. This phrase can be analysed as a metalinguistic remark or comment on the use of an expression, saying or proverb, or, as it will be shown in what follows, on the use of slang, of a non-standard sense of a word, or to put it in a nutshell, on any deviation from the speaker's "regular" use of language. It could be stated that this phrase has clearly become a reflex response or action among speakers, and particularly among journalists. The variant 'as the old saying goes' is far less used and this is confirmed by a scanty number of 61 occurrences in the online archives of The New York Times. However, we have decided to look into it in order to account for potential differences of choice of target sayings or syntactic structures. Obviously other semantically or pragmatically synonymous expressions such as 'as they say', 'as the proverb says', 'as my grandmother used to say', 'it is true that', 'everybody knows that', etc. are also possible in this context (Mieder, 2004). This phrase is noticeably interpolated or added to the text in which it can have three different positions. It may occupy the head of the phrase, sentence or text, in which case it serves as an introduction, but it can also be inserted inside the actual saying or expression or even occupy a final position, functioning as a sort of coda.

It is worthwhile trying to differentiate and delimit the terms 'saying' and 'proverb', a real challenge and an extremely arduous task since the distinction is undoubtedly rather vague and blurred. A starting point could be what Strässler had to say on the subject in 1982:

"Proverbs and sayings are mostly taken as different types, although there is no difference to be noticed in the OED. A proverb is "a short pithy saying in common use", a saying "something that is said: a dictum, a proverb". The agreed distinction is the free place in a saying (mostly the subject), which is occupied in a proverb." (Strässler, 1982: 16) It is clear that nowadays 'saying' is used as an umbrella term in lexicography to lump together all different types of fixed, idiomatic sentence-like units such as catchphrases, maxims, slogans, adages, aphorisms, clichés, dicta, epigrams, idioms, mottos, proverbs, refrains, quotations, allusions or gambits. Our main concern is to examine the inordinate amount of more or less fixed and more or less idiomatic expressions introduced by this phrase as well as to set out a typology according to frequency and usage. We have decided to focus on one single type of discourse, the media discourse, for the following reasons: firstly, because online newspaper archives constitute an amazingly vast database for lexical and phraseological research and secondly, because this phrase has become a sort of padding, a pet phrase or verbal mannerism especially among journalists.

The phrase can be found, with different levels of frequency, in all sorts of written or spoken genres. For the purposes of this study we have limited our research to the American newspaper The New York Times. It is, on the one hand, the epitome of American journalism and, on the other hand, its online archives go back to the foundation of the newspaper, exactly to 1851, which allows an interesting diachronic comparison as far as uses are concerned and which has proved extremely revealing. Besides all this, these archives allow exact searches when using a combination of words, which is, for the objectives of this investigation, absolutely essential. The fact of not having access to the whole article, or even to a larger linguistic context, has not prevented the finding and retrieval of the searched-for results since sayings or expressions occur systematically in the near context of the target phrase.

Research method

In order to observe and analyse the actual use of this phrase in journalistic discourse we created a corpus of 500 examples including the string 'as the saying goes'. A random sample of 500 occurrences containing this phrase was selected from the online archives of The New York Times out of a total of over 10,000 results yielded by the search engine of this newspaper. It must be stated that the combinations of our target phrase and a saying or pseudo-saying 1 are practically all nonce uses, which shows their extreme lack of institutionalisation or recurrence. The only exception in our corpus is represented by the combination of 'as the saying goes' and the saying A picture is worth a thousand words, with a meagre number of three different tokens.

A second corpus of 61 occurrences was created, following the same procedures as for the main corpus, including the variant form 'as the old saying goes'. All occurrences were then manually analysed for the purpose of typological classification.

Typology

The range of words and phrases introduced or referred to by the target phrase is strikingly varied and heterogeneous. They include adjectives, collocations, fixed non-idiomatic phrases and lexical bundles, idioms, similes and comparisons, conversational formulae, slang words and phrases, substandard lexis, professional jargon, sayings and proverbs, proverb extensions, antiproverbs and quotations. These results prove the high level of lexicalisation of the target phrase, which is used in a wide range of co-occurrences and that, in a great number of cases, should be understood as synonymous with 'as they say', as shown in (1):

(1) That dress for example: it fits perfectly, but it seems to be wearing her 2 , as the saying goes.

Adjectives

At the lower end of the typological range the target phrase is used to introduce or refer to adjectives. This combination shows the highest level of lexicalisation of the target phrase as it accompanies a single-word unit or a compound adjective as in (3). The inverted commas in examples (3) and (5) function as an emphasising or intensifying device, further marking the unfamiliarity or strangeness of the adjective in question but also the personal linguistic stance on the part of the journalist:

(2) An international patent is, as the saying goes, pending.

(3) It is easy to learn to fly in the very stable latest types of machines which, as the saying goes, are "fool-proof."

(4) They were not political, as the saying goes.

It is interesting to notice that some of the examples found date back to the 19 th century and early 20 th century, which accounts for a rather early lexicalisation of this phrase:

(5) […] and he came to the conference "primed," as the saying goes. (17/01/1895) (6) Mr. Shaw's plays, for instance, are not especially moving, as the saying goes. (20/11/1910) (7) He will make it, as the saying goes, snappy. (04/10/1921)

Collocations

Second to adjectives are collocations. These are recurrent word combinations that tend to appear together in texts. The types found in our corpus are noun + verb, verb + noun, adverb + adjective, verb + adjective and verb + adverb collocations, a selection of which is provided in examples from ( 8) to ( 12):

(8) Complications, as the saying goes, ensue.

(9) They remained, as the saying goes, friends. (10) […] when she discovers that her daughter is, as the saying goes, sexually active.

(11) He "felt lucky," as the saying goes, and he knew that he could "get action" without any limit at his favorite game. As with adjectives, an early 20 th -century example as the one in ( 12) seems to corroborate the rather early use of the target phrase in combination with collocations. The unconscious linguistic awareness of the collocational phenomenon is signalled then by the use of the target phrase.

Fixed non-idiomatic phrases and lexical bundles

Fixed-non idiomatic phrases are semantically compositional prepositional or adverbial phrases such as those in ( 13), ( 14) and ( 15) which can also be associated to the target phrase.

On the other hand, lexical bundles are extended collocations, i.e. bundles of words with a tendency to occur together as the one found in (16). In either case it is not idiomaticity or noncompositionality that triggers off the use of the target phrase but rather polylexicality:

(13) In real life, as the saying goes, Hank Wangford is Dr. Sam Hutt, 47, a National Health Service physician who […] (14) Due to popular demand, as the saying goes, Mr. Paul had to scrap plans to hold […] (15) The momentous announcement was received with mixed emotions, as the saying goes.

(16) "Los Angeles had nothing to lose, as the saying goes, so they could make changes like that.

Idioms

This is a very important group from a quantitative point of view. Idioms are usually included in different collections and dictionaries of proverbs in the same way as sayings or proverbs are not rare in dictionaries of idioms 3 :

(19) As the saying goes, it was all Greek to me.

(20) I took up chess because of him when I was pre-teenhe was "all the rage" at the time, as the saying goes.

(21) We preferred to make our own from "scratch", as the saying goes.

(22) He knew the Rogues' Gallery by heart, as the saying goes.

(23) The prohibition issue will not "cut much ice," as the saying goes, in the present campaign.

(24) "Everything is up in the air now, as the saying goes," said the Senator.

(25) […] leaving the task of designing actual sound equipment to practical engineers who, as the saying goes, often fly by the seat of their pants.

Idioms represent the largest group of multi-word units which could be considered closest to the general and popular idea of a 'saying'. It is then not surprising that this type is well represented in our corpus.

Similes and comparisons

Traditional or modern comparative formulae have also been found in combination with the target phrase. They are much less frequent than the previous type but, on the other hand, they represent a closer stance to the general idea of 'saying' or 'proverb' among non-specialist native speakers:

(26) It was created by Marina Polvay, a fine Russian-born cook, and the pie is, as the saying goes, richer than sin.

(27) It was as easy, as the saying goes, as rolling off a log.

The amount of similes of the type white as snow or fresh as a cucumber are remarkably numerous in, for instance, Whiting's Modern Proverbs and Proverbial Sayings. We consider that this lexicographical choice responds to the widespread belief that similes are both sayings and proverbial.

Conversational formulae

Although only two examples have been found in our corpus, informal conversational formulae can be actually and potentially accompanied or introduced by the target phrase: The scant number of hits can be explained by the fact that this type of formula is, for obvious reasons, infrequent in journalistic texts.

Slang, informal or substandard register

Let us examine the words in bold type in the following examples:

(30) Maybe we, black and white, just didn't want it bad enough, as the saying goes.

(31) That, as the saying goes, is a hell of a note.

(32) The plot, however, creaks, as the saying goes, and the two really capable juvenile leads… (33) As the saying goes, something had clicked. Zoe hit the last toss squarely, and the purple ball […] (34) In the technology world, Mr. Swartz is kind of a big deal, as the saying goes.

(35) Grove Strangler in his triumphant summer tour, wrapped his two hands around the windpipe of an opponent who was, as the saying goes, dissing him.

(36) There are wealthy people, usually elderly ones, and estates that have, as the saying goes, money to burn. (29/07/1894) (37) "As the saying goes, 'Head 'em up, move 'em out.' (38) Well, we will know more later, as the saying goes.

This type clusters together various deviant or sub-standard uses of words as well as slang words and expressions. In (30) the informal use of the adjective bad in lieu of the adverb badly activates the use of the target phrase. As for (32) and ( 33) it is the special informal meaning of the verbs creak and click respectively that makes them 'special' and therefore appropriate for the metalinguistic remark. The use of substandard English is conscious and conspicuous in ( 37) and ( 38) and the target phrase serves in both examples as a sort of personal excuse on the part of the journalist.

Professional jargon

The awareness of a certain type of jargon phraseology or parlance is also a triggering factor for the use of the target phrase. Examples are numerous and varied and the expressions involved tend to be powerful and vivid. Although we have found examples related to different professional fields and technical domains, most of them are proper either to business or to sports:

(39) Executives of the American Motors Corporation are not trying, as the saying goes, to lose money on each sale, but make it up in volume.

(40) There is a widespread perception that, as the saying goes, in good times you should advertise, but in bad times you must.

(41) Inflation, as the saying goes, is caused by too much money chasing too few goods.

(42) I never thought I'd be wishing for inflation, but as the saying goes, "inflation maims, deflation kills." (43) Still, nervous investors may prefer to stick with investments that can be valued, as the saying goes, by letting the market decide.

(44) As the saying goes, real estate is all about location, location, location.

(45) For now, both players were on serve, as the saying goes.

(46) As the saying goes in baseball, both games were hotly contested… (47) Letting the ball do a lot of running, as the saying goes in soccer, and playing with more heart, the Irish proved more effective for the greater part… (48) A point guard often has the ball when the shot clock is short, as the saying goes in the league.

(49) He won the next diamond and "went into the tank," as the saying goes.

The expressions in bold type in examples from (39) to (44) are characteristic of the business, finance, marketing and real estate milieus. Examples from (45) to (49) show expressions used in different sports. The phrase 'go into the tank' is used in poker and means 'to think very hard about your next play'. A 'shot-clock' is a timer designed to increase the pace, and consequently the score, in games such as basketball. The expression 'when the short-clock is short' thus speaks for itself.

Sayings and proverbs

This is the most important type both quantitatively and qualitatively. Apart from traditional proverbs and sayings-which, in general, do not abound-, there seems to be an inexhaustible amount of more or less modern proverbs which illustrate the vitality and strength of multiword units in American journalistic discourse:

(52) As the saying goes, "Hurt me twice, shame on me." (53) "Much honor, many enemies," as the saying goes.

(54) As the saying goes: Nobody ever beats the river.

(55) As the saying goes, if you can remember the 1960s you probably weren't there.

(56) As the saying goes, after sex all animals are sad.

(57) As the saying goes, it takes a lot of beer to make a little wine, meaning that more than a few […] (58) Knowledge is power, as the saying goes.

(59) As the saying goes, life is like a revolving door.

(60) As the saying goes "Genius is 1% inspiration and 99% perspiration."

(61) As the saying goes, nothing focuses the mind like one's own hanging.

(62) When it comes to Sarah Bernhardt, as the saying goes: you can dip a frog in honey but it doesn't mean I'll eat it.

(63) Sex sells, as the saying goes, and, according to most studies, the number […] (64) "War, as the saying goes, is too important to be left to the generals.

(65) But as the saying goes, the more things change, the more they stay the same.

(66) As the saying goes, "If Mohammed won't come to the mountain […]

(67) If patriotism is the last refuge of scoundrels, as the saying goes, then […] (68) Culture leads politics, as the saying goes. (77) "As the saying goes, 'There is no sinner without a future and no saint without a past,'" Mr.

Dodd said.

(78) "Successful people are too busy, as the saying goes, to take care of the chickens."

The phrase in (60) is "[a]ttributed to Thomas Alva Edison, U.S. inventor and businessman [and q]uoted in the Washington Post 10 May 1915." (Yale Book of Quotations 2006: 226). The origin of the phrase in ( 64) is to be found in a quotation also attested in the Yale Book of Quotations:

War is too important to be left to the generals. Attributed to the French Prime Minister Georges Clemenceau (1841Clemenceau ( -1929)). La guerre! C'est une chose trop grave pour la confier à des militaries.

"War is too serious a matter to entrust to military men" (YBQ 2006: 158)

Extended proverbs

A traditional proverb is reinterpreted by extending its meaning by means of a comment or a remark:

(79) As the saying goes: To err is human, but it takes a computer to really foul things up.

(80) As the saying goes, "when it comes to schools, there's no place like home 4 !" (81) Comparisons, as the saying goes, are odious, but sometimes unavoidable.

(82) As the saying goes, the way to a man's heart is through his stomach, and that is especially true for cyclists.

(83) As the saying goes, every dark cloud has a silver lining, and so it is with bad contracts.

(84) Life is short and so am I, as the saying goes.

These extended proverbs can have, as in (82), a restrictive effect. In (84) it is rather a matter of syllepse and humoristic effect.

Antiproverbs

Antiproverbs-the manipulation of a traditional proverb by means of lexical substitutionrepresents an important means of achieving stylistic effect in journalistic discourse. This phenomenon is related to the unfreezing or destabilization of fixed expressions and idioms (Moon 1998: 40):

(85) It was, as the saying goes, lust at first sight, a lust that turned to love. (< love at first sight).

(86) "Yes, he has been accused of being a terrorist, although, as the saying goes, one man's terrorist is another man's freedom fighter." (< One man's meat is another man's poison).

(87) But good news is good news, as the saying goes, and especially may it be said… (< No news is good news).

Quotations and catchphrases

An important number of examples in our corpus correspond to quotations and catchphrases.

No distinction is made in the speakers' mind concerning these two different varieties as

shown in examples from ( 90) to ( 94):

(90) As the saying goes, "when it comes to schools, there's no place like home!" (91) "Plaintiff has been, as the saying goes, 'hoist by his own petard, ' and this attempt […] (92) "As the saying goes, it was all Greek to me." (93) "This is a positive sign, but as the saying goes, we will wait and see."

(94) It's true, as the saying goes, that she married Paul Gibson, the New York Yankees pitcher, for better or for worse, but not necessarily for lunch.

The quotations in ( 91) and ( 92) are attributed to William Shakespeare, according to the Dictionary of Word and Phrase Origins (1990: 113;105), whereas that in ( 93) is attributed to Daniel Defoe as registered in the Oxford Dictionary of Catchphrases (2003: 300).

The following quotation from the Oxford Dictionary of Catchphrases explains the origin of the phrase "I married him for better or worse but not for lunch":

"A play on one of the traditional Christian wedding vows, that has become a catchphrase among women's groups and organizations in the USA and the UK, used with reference to adjusting to married life after a husband's retirement, or the onset of memory loss or senility. The exact origins of the phrase are uncertain, but it was popular in both countries by the early 1960s. It has been ascribed to both the Duchess of Windsor, who used it when noting her husband would lunch on his own while she went about her business, as well as to Hazel Weiss, who uttered the line in 1960, after her husband, George Weiss, retired as manager of the New York Yankees." (Oxford Dictionary of Catchphrases, 2003, p. 155)

"As the old saying goes"

Only 61 occurrences corresponding to this phrase have been found in our corpus. Interestingly enough, this variant phrase tends to occupy the initial position as illustrated in the following examples:

(95) As the old saying goes, a rising tide lifts all boats.

(96) As the old saying goes, two minds are better than one.

(97) As the old saying goes, in vino veritas.

(98) As the old saying goes, he who seeks revenge had best dig two graves, one for his victim and one for himself.

(99) As the old saying goes, providence moves slowly but the devil always hurries.

(100) As the old saying goes, "A picture is worth a thousand words."

These results demonstrate that this variant phrase has not gone through the same process of lexicalisation as the target phrase 'as the saying goes' and thus keeps its original meaning, as in (97), even though some of the sayings may be not as old as thought as illustrated in ( 95) and (98).

Frequency of use

A search carried out on the 20 September 2001 on <http//:www.google.com> yielded interesting results as far as frequency of use is concerned. Table 1 shows a selection of proverbs, sayings and quotations found in our corpus ranging from extremely high frequency to nonce-forms: Life is like a revolving door.

65,400

War is too important to be left to the generals.

28,600

After sex all animals are sad.

9,020

Genius is 1% inspiration and 99% perspiration.

8,330

If you can remember the 1960s you probably weren't there. 584

Nobody ever beats the river. 59

Much honor, many enemies. 1

Nothing focuses the mind like one's own hanging. 1

Conclusions

The results of our research show that the phrase 'as the saying goes' has undergone a process of lexicalisation and is used, in numerous cases, as synonymous with 'as they say'. It occupies several positions in the sentence and actually introduces or refers to an extremely wide range of words, word combinations and phrases. On the contrary, the variant 'as the old saying goes' tends to be used as un introducer 5 and refers, in a high proportion, to regular or traditional sayings and proverbs. Examples of the non-standard or lexicalised use of the phrase 'as the saying goes' have been found as early as the mid-1800s in American journalism, especially in the business and sports sections. This phrase is triggered by the linguistic awareness of speakers and represents an example of a metalinguistic comment or remark. It should be noted the high correlation between the choice of the initial position and the use of traditional or modern proverbs. However, there is no substantial evidence concerning institutionalised links between the target phrase and certain proverbs or sayings.

The use of introductory formulae remains a research strategy to pinpoint and retrieve modern proverbs or even nonce proverbs as well as more or less famous quotations that will (or will not) eventually become proverbial.

Notes

1.

As a working definition, the term 'pseudo-saying' corresponds here to any word, word combination or phrase taken by the speaker or writer as a saying or proverb but not actually being one. These include quotations, slogans, catchphrases, slang words or expressions, etc. 2.

We have highlighted in bold the items (either single words or phrases) introduced or referred to by the target phrase.

3.

Let us mention that the proverb Fools rush in where angels fear to tread is listed together with fool's gold or live in a fool's paradise in the Collins Cobuild Dictionary of Idioms. Hell hath no fury like a woman scorned makes part of the nomenclature of the Oxford Dictionary of Idioms and is included under the headword hell.

4.

This phrase is originally a "[l]ine from the 1939 film The Wizard of Oz, starring Judy Garland as Dorothy, a young girl who finds herself lost in Oz and longing for home." (Oxford Dictionary of Catchphrases, p. 291) 5

For other introducers see František Čermák's "Text Introducers of Proverbs and Other Idioms" (see references).

  (19/03/1905) (12) He talks easily, as the saying goes, but his readiness in that line has […] (03/07/1921)

( 28 )

 28 Whether you choose a sleek catamaran, teak schooner, teeny trimaran, or a windsurf board or kiteboards, as the saying goes: Just do it! (29) As the saying goes, forget it.

( 69 )

 69 If, as the saying goes, there are no atheists in foxholes, there […] (70) As the saying goes, money goes to money. (71) As the saying goes: "Better to remain silent and be thought a fool than to speak and remove all doubt." (72) As the saying goes, "quality is a journey, not a destination." (73) "As the saying goes, from the bitter comes sometimes the sweet," Rabbi Spielman said. (74) Or as the saying goes, "God looks after fools, drunkards and the United States." (75) "Talk, as the saying goes, is cheap." (76) No guts, no galaxy, as the saying goes around Battletech Center.

( 88 )

 88 Nothing succeeds like failure, as the saying goes. (< Nothing succeeds like success).

( 89 )

 89 As the saying goes, the President proposes and Congress disposes. (< Man proposes and God disposes).

Table 1 .

 1 A selection of proverb, sayings and quotations and number of results in the World Wide Web

	Proverbs, sayings and quotations	Google hits
	Knowledge is power.	7,680,000
	Sex sells.	2,340,000

As a working definition, the term 'pseudo-saying' corresponds here to any word, word combination or phrase taken by the speaker or writer as a saying or proverb but not actually being one. These include quotations, slogans, catchphrases, slang words or expressions, etc.

We have highlighted in bold the items (either single words or phrases) introduced or referred to by the target phrase.

Let us mention that the proverb Fools rush in where angels fear to tread is listed together with fool's gold or live in a fool's paradise in the Collins Cobuild Dictionary of Idioms. Hell hath no fury like a woman scorned makes part of the nomenclature of the Oxford Dictionary of Idioms and is included under the headword hell.

This phrase is originally a "[l]ine from the 1939 film The Wizard of Oz, starring Judy Garland as Dorothy, a young girl who finds herself lost in Oz and longing for home." (Oxford Dictionary of Catchphrases, p. 291)

For other introducers see František Čermák's "Text Introducers of Proverbs and Other Idioms" (see references).

Curriculum vitae

Ramón Martí Solano is a lecturer at the Department of English, University of Limoges, France. He teaches, at undergraduate level, English for Specific Purposes. He read Spanish and English at the University of Seville, Spain, and did an MA in Anglo-Germanic Philology in the same institution. He has worked as a Spanish exchange teacher at the University of Harvard, USA, and at Joseph Chamberlain College in Birmingham, UK.

He has also been a lecturer in Spanish at the Paris School of Political Sciences and a lecturer in English at the University of Poitiers, France. His main field of research is phraseology and his doctoral thesis dealt with variation and innovation of phraseological units in the British press. Other research interests include paremiology, lexical semantics, corpus linguistics, lexicography, linguistic awareness, language variation and discourse analysis. He has collaborated as a proof-reader in the project "Widespread Idioms in Europe and Beyond: A Cross-linguistic and Cross-cultural Research Project". He is a member of the European Society of Phraseology (Europhras) and of the International Association of Paremiology (AIP-IAP). He has published several articles on paremiology, phraseology, word-formation, discourse analysis and lexicography in Spanish, French, and English.


Natalia I Vargas-Cuentas
email: natalia.i.vargascuentas@ieee.org

Avid Roman-Gonzalez
email: roman-gonzalez@ieee.org

THE SPACE TECHNOLOGY TO SOLVING SOCIETAL ISSUES IN BOLIVIA: AN OVERVIEW

Aerospace development for a country represents their technological level, development capacity, and their sovereignty. The development of the aerospace industry brings technology that the society use in the daily lives. The technology initially developed to explore the universe is the same that today we use in our daily lives.

Today we can see that the South American countries, including Bolivia, are showing strong economic growth, and this leads to a higher rate of development and increased investment in new technologies. For example in recent years, it has seen as many governments in South America, have decided to invest in space systems. These space systems have different applications, among them we can mention, remote sensing technology for disaster management, urban planning improvement, environmental assessment, telecommunications systems.

In the space technology field, Bolivia is developing its expertise with the creation of the Bolivian Space Agency (ABE), the launch of its first telecommunications satellite Túpac Katari (TKSat-1), the training of Bolivian professionals, and the creation of two ground stations. Other important thing is that the Bolivian Space Agency announced the country's willingness to purchase another satellite soon.

In that context, the present research wants to show how our communication satellite has opened a great opportunity for our rural communities through the integration into their life new technologies of information and communication. Because, thanks to our satellite, over 1000 telecentres were installed in remote rural communities that never had direct access to telecommunications services. In these telecentres, thousands of Bolivians have, for the first time, the possibility of connecting to the world and somehow reduce the difference gap between the rural area and the urban area.

The country knows that in this new era, we must move from being a country that dependent from others, to become a country applying the learned concepts. It is necessary to become a country with the capacity to do research activities and to be able to develop its technology because it has the human resource to meet this challenge and we need to offer a chance to inspire people and bring to their attention the potential and benefits of the space sector.

I. INTRODUCTION

Currently in the Latin American region there has been an increase in the rate of the acquisition of new aerospace technologies, especially remote sensing technology, which can have diverse applications, such as monitoring and response to natural disasters, urban growth planning, agriculture, border monitoring and many more applications. [START_REF] Roman-Gonzalez | Tecnología Aeroespacial en el Mundo[END_REF] [START_REF] Roman-Gonzalez | The UNSAAC Activities in Aerospace Development[END_REF] For its part, Bolivia has acquired a communications satellite that was launched in 2013. [START_REF] Vargas-Cuentas | Promotion of Aerospace Technology in Bolivia[END_REF] The country's satellite project not only seeks to improve telecommunications coverage throughout Bolivia, but also seeks to promote the development of rural areas, promote the inclusion of remote communities and reduce the gap of social differences in Bolivia, on the other hand seeks to encourage the growth of future professionals in satellite technologies and ensure this future the development of aerospace technologies in the country.

In order to understand the evolution of space technology and its impact on Bolivian society, it is necessary to describe the space and ground segment of the TKSat-1 satellite project, also we need to describe the promotion activities of the space technology that have been carried out in Bolivia, for the other hand we need to describe the presence of the Space Generation Advisory Council in Bolivia and its main functions.

On the other hand, we need to specify the emerging opportunities that have arisen directly from the impact of the beginning of the development of space technology in Bolivia, such as the installation of rural integral telecentres, the creation of educational channels in open signal, the emergence of training opportunities for Bolivian professionals in areas related to aerospace technology and the emergence of remote sensing technology and its future applications in Bolivia.

Finally, it is important to take into account the future projects that will be developed in the country, such as the participation of a team of students in the NASA Human Exploration Rover Challenge, on the other hand another group of students has raised the creation of CEBLI launch centre.

Bolivia has its eyes on the horizon, its plans seek to improve the future of the country and have a technological sovereignty, for this it understands that it must give tools to its students and professionals, beginning by diminishing the social differences, and integrating the remote communities and use the space technology to solve societal issues in Bolivia.

II. DEVELOPMENT OF AEROSPACE

TECHNOLOGY IN BOLIVIA As we said before aerospace technology brings development to the country that invests in this field; you can meet social inclusion objectives, military control, management of mining areas, pollution monitoring, deforestation monitoring, etc.

With the recent growth of development in the area of aerospace technology and the new possibilities of starting a small-scale space mission; countries like Bolivia without access to space before, have leapt to the aerospace era and now have access to space in many ways. For example, by carrying out various individual projects or by establishing agreements with other nations, including public or private investment.

Since 2010, with the creation of the Bolivian Space Agency (ABE), Bolivia has started a "Space Era". In this new era our country launch of its first telecommunications satellite Túpac Katari (TKSat-1), which was launched on December 20 of 2013, with the training of Bolivian professionals on the Great Wall Industrial Corporation (CIGM), and the creation of ground stations in the cities of La Paz and Santa Cruz for management and monitoring of TKSat-1. [START_REF] Vargas-Cuentas | Promotion of Aerospace Technology in Bolivia[END_REF] A. Telecommunications satellite TKSat-1 The TKSat was built, launched and put into orbit for the Great Wall Industrial Corporation, was launched on December 20, 2013, from the Xichang Satellite Launch Center, using a Long March 3 B / E rocket and started its full operations on April 1, 2014.

It is located in a geostationary orbit, on the plane of terrestrial Ecuador, 87.2 ° W longitude and 36000 km high above the surface of the Earth. Some technical information of TKSat-1:

Table 1: Technical information TKSat-1. Source: Bolivian Space Agency (ABE)

The dimensions of TKSat-1 are: 2.36 m x 2.1 m x 3.6 m and its weight is 5100 kg. This satellite has a capacity for the bands C, Ku, and Ka, it consists of 30 channels [START_REF] Viles | Ku band satellite antenna position control and monitoring system[END_REF] on the C / Ku / Ka bands and will operate on three frequencies: This communication satellite increased mobile service coverage throughout the Bolivian territory to reach rural and remote locations where it was not possible to achieve with terrestrial telecommunications networks, such as optical fiber or microwave. In May 2016, The Bolivian Space Agency has obtained a license to provide telecommunications services directly to the public in rural areas of our country.

B. Amachuma and La Guardia Earth Stations

The terrestrial segment of the Bolivian satellite consists in two earth stations which are located in two different cities of Bolivia.

The earth station of Amachuma is the main station of the TKSat-1 and is located in the city of El Alto in the department of La Paz, at a height of four thousand meters above sea level. In this station, a teleport has also been implemented, which allows the provision of telecommunications services to various public and private clients. On the other hand the earth station of La Guardia is the second earth station of the TKSat-1 and is located in the department of Santa Cruz to a height of 500 meters above sea level.

C. Promotion of the Aerospace Technology in the Country

Bolivia is proud because it achieves the primary objective of the country which is being a country applying the academic theory, a country with the capacity to do research activities, to be able to develop its own technology.

Currently, it is necessary that students, professionals, and the general public, are aware of the importance of space technology in Bolivia, the impact that is taking the new projects of the Bolivian Space Agency and also know all the future plans for space technology in our country.

Taking this into account, it is necessary the promotion and development of aerospace technology in students, professionals and the general public of Bolivia, in this sense it has organized the First and Second Bolivian Congress in Aerospace Technology -ABC (Aerospace Bolivian Conference).

The first conference ABC 2014 was held from Wednesday, July 23th through Friday, July 25th, 2014 at the Military School of Engineering -EMI -Campus Irpavi in the beautiful city of La Paz -Bolivia.

The second conference ABC 2016 was held from Wednesday, July 27th through Friday, July 29th, 2016 at the same place of the first one. [START_REF] Sarli | South American Space Era[END_REF] This congress, at both years, had the support of various public institutions, private companies and various Bolivian and foreign universities.

Mainly had the support of the Military School of Engineering (Escuela Militar de Ingeniería -EMI) and of the Cultural Cooperation Section of the Embassy of France in Bolivia, who were co-organizers of the conference.

This event was organized for students and professionals to promote interdisciplinary understanding of aerospace systems, their underlying science and technology, and their applications to government and commercial endeavours. The Aerospace Bolivian Conference had the participation of national and international keynotespeakers from countries like France, Germany, Russia, United States, Netherlands, Brazil, Uruguay, Ecuador, Paraguay, Peru, and Bolivia.

The topics of the conference were: Ground station design, test radiation on EEE components, space monitoring applications, propulsion systems for satellites, nano-satellites, analog astronaut missions and the use of remote sensing for the study of water resources.

D. Space Generation Advisory Council in Bolivia

The Space Generation Advisory Council is a global non-governmental, non-profit organization in support of the United Nations Programme on Space Applications. This network aims to represent university students and young space professionals to the United Nations, space agencies, industry, and academia in fields like international space policy issues.

SGAC is responsible for injecting the new generation point of view into international space policy creation introducing youth opinion in the United Nations through its observer status in the United Nations Committee on the Peaceful Uses of Outer Space (COPUOS) SGAC -Bolivia is proud because is helping with the main objective of the country and is taking giant steps in their mission to promote knowledge of space science in the young students and professionals with the organization of different space activities in Bolivia. Thanks to the presence of the SGAC in Bolivia volunteers and young students and professionals have been able to benefit from participation in events organized in the country with reference to aerospace technologies and their applications, which has been able to give them a wider vision and better opportunities for their academic and professional life.

III. EMERGING OPPORTUNITIES

The space activities and the technology involved in its development is, for our country, a tool that generates new and emerging opportunities to find a way to solve different social problems that afflict us.

A. Rural satellite telecentres Thanks to TKSAT-1 over 1000 telecentres were installed in remote rural communities that never had direct access to telecommunications services, in these telecentres, thousands of Bolivians have for the first time a window to the world and integrate into their life new technologies of information and communication.

Telecentres are public places of free access, where computers with Internet and other technologies can be used to help the development of digital skills in the population. [START_REF] Hallberg | Telecentros en Bolivia: la atención en las mujeres[END_REF] For the correct operation, each telecentres is equipped with different subsystems, the most important are: subsystem of energy (AC or DC), network and Internet access subsystem, satellite TV subsystem and computer equipment subsystem.

Each telecentre is equipped with five computer equipment, a television, a printer, a VSAT antenna, a Wi-Fi router, chairs and desks among others. We can see in the following figure a map of the distribution of all these equipment in the environment of the telecentre. The installation of this telecentres in remote areas of the country has increased notably, in 2006 Bolivia just had 17 telecentres, but this number increased and reached 1673 telecentres in the year 2015. In addition in the following years until nowadays, 1500 new telecentres have been added in order to include more rural populations in the project. [START_REF] Crespo | Políticas en tecnologías de la información y la comunicación en el nuevo contexto social y educativo en Bolivia[END_REF] In addition, distant populations in the country have benefited from telephone, Internet and satellite television, before this 1.2 million people never had access to these services. The authorities of rural communities and neighbourhood councils have been very involved in the implementation of the telecentres in their community and in a joint work with the Municipal Government have defined the rules of use and operating hours of each telecentre.

It has been defined that in school hours the use must be a priority for students in the community, so schools can request the telecentre room to provide a class in that environment.

Any user under the age of 12 who uses the telecentre outside of class hours must be accompanied by their parents or guardians.

The use of telecentre equipment should be requested half an hour before and can be used for one hour maximum unless there is availability of equipment and space in the telecentre. On the other hand, training has been implemented to prepare the people in charge of the management, care and maintenance of the telecentre.

Evaluation materials and small practices have also been developed that can be developed by the users during their visits to the telecentre. These practices are aimed at providing them with the necessary tools to use the telecentre equipment and to measure the evolution of their digital abilities over time. It is important to mention that this project is in direct coordination with the Ministry of Education and essentially seeks to improve the access and quality of education in Bolivia.

The project includes the creation of two television channels, the first one will be oriented to offer contents of ongoing training and the second channel will be oriented to complement the content of our educational system.

Both channels will have technological and scientific content, designed as much for students, as for teachers and parents. [9] The signal from these television channels can be accessed at the TKSat-1 telecentres or from any home by acquiring a satellite antenna and by visiting the ABE website for detailed installation instructions.

The initiative of these education channels arises due to a great problem in the country, which shows that there is a large population of students living in rural areas that cannot attend school because of the long distance they must travel to access to an educational centre close to their communities.

The open signal educational channels will serve to specialize teachers from all over the country, to provide training tools to parents who must educate their children at home and finally to awaken in young students a vocation for technology and science, giving children and youth throughout Bolivia the same opportunities for access to education.

C. Training of professionals in Aerospace

Applications In 2016 the Bolivian Space Agency, in conjunction with the Universidad Mayor de San Andres (UMSA), developed a postgraduate course in Satellite Communication Systems, this program would have Bolivian lecturers specialized on the Great Wall Industrial Corporation (CIGM) in China, thus being a technology transfer for future generations of professionals. This project is the first specialized study program in Space Applications in the country.

For the other hand, the Bolivian government has understood that we must be a country with the capacity to do research activities and to develop our technology.

That is why Bolivia with help of the Bolivian Space Agency is starting with the training of young professionals, with programs that aim to provide scholarships for master and doctorate in various fields, such as aeronautics and aerospace engineering and others that are of importance to scientific and technological sovereignty.

Two of the main programs who provide scholarships in the aerospace field are:

1) Project "100 Study Scholarships for Scientific and Technological Sovereignty," this program of the Bolivian government through the Ministry of Education awards outstanding Bolivian students with 100 annual scholarships to study postgraduate programs in universities of all the world, this project aims to support the training of scientists for the development of strategic areas of the country. In the area of aeronautics and space, masters programs are offered in aeronautical engineering and aerospace engineering. [START_REF]El gobierno promulga decreto supremo que otorga becas de postgrado a profesionales con excelencia académica[END_REF] 2) Scholarships of the China Scholarship Council (CSC) and the Regional Centre for Space Science and Technology Education in Asia and the Pacific (RCSSTEAP), through the Bolivian Space Agency grants scholarships to Bolivian professionals for Master programs in Space Technology Applications (MASTA) and a Doctoral Program on Space Technology Applications (DOCSTA), to be held at Beijing University of Aeronautics and Astronautics Beihang University (BUAA) in China. [START_REF]MASTA and DOCSTA programs[END_REF] Some of the specialization programs are Remote Sensing and Geo-Information Systems (RS & GIS), Global Navigation Satellite Systems (GNSS), Space Law and Policy and Micro-Satellite Technology. The first step that must be taken to carry out this project is to train Bolivian professionals in the processing of satellite images, which will allow the Bolivian State to have the capacity to use space technology in order to contribute to national development through satellite information.

Recently in 2015 the Bolivian Space Agency and the French company THALES signed an agreement for the inauguration of an experimental laboratory to train operators in the processing of satellite images that help training and image detection of natural disasters and agricultural fields. [START_REF] Boliviana | Observación de la Tierra[END_REF] Currently, the Image Processing Laboratory of the Bolivian Space Agency (LPAIS), has presented satellite images with a basic processing, for the analysis and interpretation of certain phenomena, such as: The urban growth of the most important cities of the country such as La Paz , El Alto, Cochabamba and Santa Cruz; forest fires in the eastern regions of the country; the monitoring of climate change and its effect in the Bolivian Andes, and finally the image processing for the monitoring of droughts and landslides in some areas of Bolivia.

The Bolivian state has considered a list of interests of the applications of Remote Sensing, including the following: monitoring biodiversity and environment, mining and geology, epidemiology, agriculture, drought monitoring, flood monitoring, water resources, forest fires, landslides and city planning. This course will be a technology transfer for the formation of future generations of professionals and it will be a way of transmit all the theory learned in foreign universities to students and young professionals of the country.

The space launch centre INTI was born in 2015 by a group of approximately 20 university students and volunteer engineers who began to enter the research and implementation of aerospace technology in Bolivia, as they know the need of our country to enter in the space race. [START_REF] Cebli | Centro Espacial Base de Lanzamientos -INTI[END_REF] This research group plans in the near future to present some prototypes of its investigations, among them we can mention the development of a nanosatellite in real-scale named "killa" and several rocket prototypes built to scale by the researchers of the centre, the main rocket prototype is called "chaska chinkay". Source: CEBLI Another future project is the formation of a 100% Bolivian team to compete in the NASA Human Exploration Rover Challenge to be held in the city of Huntsville, Alabama, United States on March 30 -April 1, 2017, at the U.S. Space & Rocket Centre. [START_REF] Razón | Equipo de la UMSA participa en competencia de la NASA con prototipo de explorador lunar[END_REF] The main objective of this challenge is encouraging in young students the research and development of new technology for future mission planning and crewed space missions to other worlds. For achieving the main objective of the challenge the groups need to design, construct and test technologies for mobility devices to perform space exploration in different environments.

VI. CONCLUSIONS AND RECOMMENDATIONS

 Bolivia must develop more space technology dissemination activities to awaken the motivation in young students to specialize in the space technology and its applications.  It is necessary to begin to support the development of a nano-satellite project to form abilities in students and professionals and thus to have a sovereign access to the space.  More scholarships should be encouraged and created for the specialization of Bolivian professionals in areas related to space technology abroad, which this we can ensure a technological transfer of everything learned during the training.  Research and use of Remote Sensing technology should be further exploited and encouraged, as its applications can be very useful for different areas of the country.

Fig. 1 :

 1 Fig. 1: Area of coverage of the different bands of TKSat -1. Source: Bolivian Space Agency (ABE)

Fig. 2 :

 2 Fig. 2: Amachuma Earth Station Source: Bolivian Space Agency (ABE)

Fig. 3 :

 3 Fig. 3: Main organizers of the Aerospace Bolivian Conference. Source: ABC 2016

Fig. 4 :

 4 Fig. 4: Aerospace Bolivian Conference Source: ABC 2016 Finally the conference had the presence of representatives of major companies specializing in aerospace technology as TIMA Laboratory, The National Center for Scientific Research of France (CNRS), THALES Alenia Space, Airbus Space and Defense (ASTRIUM) and Arianespace, they developed a technology fair, where the event sponsoring companies shown their work, services and/or products offered to the general public.

Fig. 5 :

 5 Fig. 5: Regional Coordinator and National Point of Contacts Bolivia. Source: SGAC

Fig. 6 :

 6 Fig. 6: Map of a telecentre. Source: Bolivian Space Agency (ABE)

Fig. 7 :

 7 Fig. 7: Satellite communication scheme of the telecentres. Source: Bolivian Space Agency (ABE)

Fig. 8 :

 8 Fig. 8: Operation of telecentres in the country.Source: Bolivian Space Agency (ABE)

Fig. 9 :

 9 Fig. 9: Integral satellite telecentres. Source: Bolivian Space Agency (ABE) Each telecentre, or also called community technology centre, has the main objective to promote social and community development through the use of technologies to provide the opportunity for development to groups and communities in situations of rural technological backwardness. At the same time, it seeks to create economic opportunities for the population and promotes the creation of contacts between communities. [8] B. Development of educational television channels The Bolivian Space Agency, in its role of management of the satellite project, wants to use the information, communication and development technologies provided by our communications satellite, is for this reason that has proposed to create television channels with educational content in open signal.It is important to mention that this project is in direct coordination with the Ministry of Education and essentially seeks to improve the access and quality of education in Bolivia.

  D. Arising of the remote sensing technology Bolivia has outlined a binational cooperation agreement with Peru to exchange knowledge and experiences in the implementation of telecommunications and earth observation satellites.

Fig. 10 :

 10 Fig. 10: Land classification map of Santa Cruz. Source: LPAIS-ABE These research areas have been selected taking into account the priorities of the Bolivian State to achieve the country's primary objective of promoting sustainable development, reducing socio-economic gaps and ensuring the well-being of the population.

Fig. 11 :

 11 Fig. 11: CEBLI (Space launch centre INTI).Source: CEBLI


Yu Chen

Eric Fleury

Backbone-based Scheduling for Data Dissemination in Wireless Sensor Networks with Mobile Sinks


J Orloff

Could a γ Line Betray the Mass of Light Dark Matter?

We 1 compute the pair annihilation cross section of light dark matter scalar particles into two photons, and discuss the detectability of the monochromatic line associated with these annihilations.

Introduction

The need for Cold Dark Matter (DM) to describe and understand how structures in the universe hold together, has become increasingly pressing with the impressive amout of observational data collected in the last ten years. Alternatives to DM, like modifications of gravity, are being put to critical and maybe fatal test by recording maps of gravitational lensing. Indeed, the separation recently observed in colliding clusters between the (maybe modified) gravitational deviation of light and the normal matter that causes it, seems very contrived with modified gravity, and very natural if collisionless DM is the main source of gravity. Questions about the nature of DM and its non-gravitational detection are therefore more relevant than ever.

In this context, the precise determination by INTEGRAL/SPI 2 of the characteristics of the 511 keV line emitted in our galaxy is intriguing. Indeed, it implies wihtout any doubt that the central bulge of our galaxy is a strong source of positrons. Astrophysical sources like Low Mass X-ray Binaries (LMXB) and Type 1a Supernovae (SN1A) 3 cannot naturally explain why this source is at the same time steady, extended and absent in the disk. On the contrary, production of positrons through DM annihilation is naturally steady and concentrated in the bulge where the DM density increases: a fit of the needed DM density profile can even be attempted 4 , yielding a reasonable NFW profile ρ(r) ∼ r -1 for DM annihilation at rest, in opposition to a less reasonable ρ ∼ r -2 for DM decay.

In order to maximize the electron-positron annihilation channel, such DM must be light (LDM) 5,6 , at least below muon pair threshold: m dm < 100 MeV. More constraining upper bounds can be obtained by a careful study of final state radiation processes (dm dm ⋆ → e + e -γ) and positron anihilation in flight, both producing continuous gamma ray spectra which increase with m dm . From the first, m dm < 35 MeV is obtained 7 , and m dm < 20 MeV from comparing the second with error bars on the measured spectra. On the other hand, m dm should be higher than 2 MeV to avoid spoiling nucleosynthesis 8 , and higher than 10 MeV if there is a significant coupling to neutrinos which can alter supernova explosions 9 , but such is not necessarily the case. 1

A fairly unique viable model satisfying all the above constraints contains scalar DM particles with m dm ∼ 10 MeV, annihilating at rest in the galactic bulge into e + e -pairs via t-channel exchange of heavy (> 100 GeV) fermions F e . Given the large local DM abundance inferred from the rotation curve, the annihilation cross-section yielding the observed positron source is however too small to explain a correct relic density inferred e.g. from cosmic microwave background measurements. A further light vector particle can then be invoked to mediate an s-channel annihilation process: being velocity dependent, this process becomes dominant in the early universe and can independently be adjusted to the relic density.

If correct, such a model 5 would profoundly alter the road to unification in particle physics. It therefore seems important to look for other experimental cross-checks. The simplest and most convincing one would be the discovery of another gamma ray line, from the process dm dm ⋆ → γγ. In the following, we show 1 this line is anavoidable in such a model, estimate its intensity, and discuss its observability.

Dark matter annihilation cross section into two photons

The model considered is specified by the Lagrangian L = ψFe (c r P L + c l P R )ψ e φ dm + h.c where P R,L are the chiral projectors (1 ± γ 5 )/2. The relevant annihilation diagrams are box-diagrams containing 1, 2 or 3 heavy fermions F e . Assuming that dm = dm ⋆ (which fixes the circulation of arrows), there are 6 diagrams, taking into account permutation of the 2 photon external legs.

From naive power counting, each box is logarithmically divergent. However, gauge invariance dictates a result proportional to F 2 µν rather than A 2 µ . This requires 2 powers of external momenta, so that the integrand must in fact converge like d 4 k/k 6 for large loop momenta k. In the limit m Fe ≫ m e,dm (relevant due to LEP and other collider/accelerator constraints), the contribution of momenta larger than m Fe is ∼ 1/m 2 Fe . The leading 1/m Fe term can thus be safely obtained by expanding the integrand in powers of 1/m Fe and keeping only the first term.

m 2 F ) ⇔ L ef f = 1 m Fe φ * dm φ dm ψe (a + ibγ 5 )ψ e
This corresponds to "pinching" the box with one F e into a triangle involving only electrons and an effective dm-dm-e-e coupling given bywith the real couplings a, b given by a + ib = c * l c r . For this set-up, computing the cross-section is a loop-textbook exercise for which we find:

σ γγ v r = α 2 (2π) 3 m 2 Fe m 2 e m 2 dm × b 2 |2C 0 m 2 dm | 2 + a 2 |1 + 2C 0 (m 2 e -m 2 dm )| 2 .
C 0 is a function of m e and m dm given by the Passarino-Veltman scalar integral. For m dm > m e , this function develops an imaginary part corresponding to the formation of a real 2

e + e -pair subsequently annihilating into 2 photons, and giving the largest contribution for masses above 1 MeV. For m dm ≪ m e , C 0 behaves as [-1/(2m 2 e ) + m 2 dm /(3m 4 e )], so that both terms of the cross section behave as m 2 dm /(m e m Fe ) 2 . This limit is relevant to estimate the effect of heavier particles than the electron in the loop. For example, the contribution of the τ lepton could be significant if the corresponding couplings (a τ , b τ ) are larger than ≈ (m τ /m dm ) × (a e , b e ) × (m Fτ /m Fe ) (with m dm < m τ ), i.e. if they scale at least like usual Yukawa couplings. Since an independent detailed analysis is required to check whether or not such couplings can pass particle physics constraints, we prefer giving a conservative estimate based on the electron contribution only. The latter cannot be turned off without losing the 511 keV line signal. It therefore constitutes a safe lower bound for assessing the detectability of the line at E γ = m dm .

Within the pinch approximation, the cross-section relevant for the origin of the 511 keV emission is:

σ 511 v r = β e 4πm 2 Fe a 2 β 2 e + b 2
with β e = 1 -m 2 e /m 2 dm , which indeed for b = 0 reduces to the expression used 4 for large m Fe . After careful comparison with SPI data, Ascasibar et al. 4 found

σ 511 v r = 2.6 10 -30 m dm MeV 2 cm 3 /s.
The γγ annihilation cross-section is then also determined by this measurement in terms of the ratio of annihilation branching ratios:

η . = σ γγ σ 511 = α 2 2π 2 β e m 2 e m 2 dm a 2 |1 + 2 (m 2 e -m 2 dm )C 0 | 2 + b 2 |2m 2 dm C 0 | 2 a 2 β 2 e + b 2 (1)
As announced, this ratio cannot vanish, whatever the value of a/b, so that a minimum γγ flux is guaranteed. As m dm approaches m e from above, the ratio increases like β -3 e for a pure scalar coupling (b = 0) and like β -1 e for an axial one (a = 0). The ratio decreases almost linearly with the dark mater mass for m dm > 1 MeV. In the table below, we give typical values of the ratio η for the most conservative case (i.e. a = 0, β -1 e ): m dm (MeV) : 0.52 1 5 20 η(a = 0) : 8.8 10 -5 1.4 10 -5 3.6 10 -6 8. 1 10 -7 Notice that the simple guess 10 applied to the case of decaying DM

η guess ≈ α 2 m 2 dm 2π 2 m 2 e β 3 e
increases instead of decreasing with m dm . For a typical mass of 10 MeV, this guess overestimates the monochromatic flux by a factor 635 with respect to our result (Eq.1). As we will see in the next section, such a factor is crucial to the line observability.

Detectability of the monochromatic line

A few experiments have already scanned the energy range above the electron mass. The instruments on board of INTEGRAL for example have been designed to survey point-like objects as well as extended sources over an energy range between 15 keV-10 MeV. The instrument INTEGRAL/SPI itself is a spectrometer designed to monitor the 20 keV-8 MeV range with excellent energy resolution. Therefore a legitimate question is whether or not the line E γ = m dm could have been (or could be) detected by the same instrument that has unveiled the 511 keV signal. This essentially depends on the ratio η as given above, and on the background. The 511 keV emission has been measured with a ∼ 10% precision 11 to be

I 511 = 6.62 × 10 -3 ph cm -2 s -1 sr -1
inside a region that extends over 350 • < l < 10 • in longitude and |b| < 10 • in latitude. If this emission originates from a NFW distribution of LDM species around the galactic center with a characteristic halo radius of 16.7 kpc, the signal from the inner 5 • is found 4 to be

I 511 (5 • ) = 1.8 × 10 -2 ph cm -2 s -1 sr -1 ,
once the SPI response function is taken into account and the instrumental background is properly modeled. If the positron propagation is negligible, then the map of the 511 keV emission should correspond to that of the LDM annihilations. Within this approximation, we expect the spatial distributions of both the 511 keV and the two-gamma ray lines to be identical and their intensities to be related by the ratio η:

I γγ (θ γγ ) = η θ 511 θ γγ I 511 (θ 511 ) (1 -3f /4) .
This expression is approximately valid as long as the angular radii θ γγ and θ 511 of the regions monitored by the gamma-ray spectrometer are small. In what follows, the fraction f of positrons forming positronium has been taken 4 equal to 93%. This is in perfect agreement with the positronium fraction later derived 12 , i.e. f P s = 0.92 ± 0.09. The monochromatic line flux φ γγ (< θ γγ ) = π θ 2 γγ I γγ (θ γγ ) has been plotted in Fig. 1 in the case of the LDM model with F exchange and assuming a NFW profile. The angular radius θ γγ = 8 • corresponds to the field of view of the satellite. For typical LDM masses in the MeV range, the expected flux is about three orders of magnitude below the claimed INTEGRAL/SPI line sensitivity 13 (which is about 2.5 × 10 -5 ph cm -2 s -1 after 10 6 seconds). An unrealistic exposure of 30,000 years would thus be required in order to detect the E = m dm line. When the LDM species is degenerate in mass with the electron, the flux is only a factor of 25 below the SPI detection limit (assuming a pure scalar coupling b=0). As long as the mass difference m dm -m e does not exceed 0.1 MeV, it is roughly comparable with the expected 478 keV line signal emitted by Novae 14 , that is about ∼ 10 -7 ph cm -2 s -1 .

SPI sensitivity is limited by the instrumental background that arises mostly from cosmic rays impinging on the apparatus and activating the BGO scintillator. On the contrary, the absolute sensitivity of an ideal instrument is purely limited by the gammaray continuum background. This emission has been recently estimated 11 I BG (E) = 1.15 × 10 -2 E -1.82 ph cm -2 s -1 sr -1 MeV -1 , inside the central region that extends over 350 • < l < 10 • in longitude and |b| < 10 • in latitude. The energy E is expressed in units of MeV.

We thus estimate the significance Σ ≡ signal/ √ background for the LDM line to emerge above this background (assuming it is isotropic) to be

Σ = √ π θ 511 I 511 (θ 511 ) (1 -3f /4) η S 0 T 0 I BG ∆E 0 ,
with S 0 the surface of the detector, T 0 the exposure time, I BG the above-mentionned continuum background intensity and ∆E 0 the energy resolution. The significance Σ (displayed as a function of the dark particle mass in Fig. 1 for a surface of 1 m 2 , an exposure duration of T 0 = 1 year and an energy resolution of 0.1%) indicates that those values would theoretically allow to extract the minimal guaranteed signal computed at 3 standard deviations above background for all relevant LDM masses below 30 MeV.

There is nothing to be gained by narrowing the angular aperture θ γγ because, for the assumed NFW profile, the signal increases linearly with this angular radius, as does the square root of an isotropic background.

In contrast, note that the monochromatic line should be extremely narrow: its width is expected to be about a few eV which experimentally is very challenging if one compares it with the present SPI sensitivity that is about 10 -3 at MeV energies. At lower energies, there are nevertheless instruments, e.g. X-ray CCD, bolometers, Bragg spectrometers which are able to resolve eV widths. A significant improvement on the resolution ∆E 0 at higher energies would probably be necessary in order to reach a large enough significance and ensure detection. Indeed, an effective surface of 1m 2 might be hard to attain in space.

Next generation instruments such as AGILE/(super AGILE) or GLAST, which in principle could be more promising, will probably be limited by the energy range that they are able to investigate. Future instruments might nevertheless be able to see this line if their energy resolution and sensitivity are improved by a large factor with respect to SPI present characteristics.

Maybe a better chance to detect this line is to do observations at a high latitude and a longitude slightly off the galactic centre. In this case, indeed, the background should drop significantly (the density of dark clouds has been measured recently 15 ) but the line flux may decrease by a smaller factor.

Figure 1 :

 1 Figure 1: Left: flux of the monochromatic E γ = m dm line from a 8 degree cone around the galactic center. Right: significance of the monochromatic E γ = m dm line above the continuum background for one year of observation with an ideal detector of 1 m 2 and a 10 -3 energy resolution.

Acknowledgement

It is a pleasure to thank the organisers for the most enjoyable and stimulating conference.


M Ericson

G Chanfray

Constraints on nuclear matter properties from QCD susceptibilities

Keywords: Pacs: 24, 85, +p 11, 30, Rd 12, 40, Yx 13, 75, Cs 21, 30, -x

Constraints on nuclear matter properties from QCD susceptibilities

M. Ericson, G.

Introduction

The spectrum of scalar-isoscalar excitations is quite different in the vacuum and in the nuclear medium. In the second case it includes low lying nuclear excitations and also two quasi-pion states, i.e., pions dressed by particle hole-excitations. All these lie at lower energies than the vacuum scalar excitations which start at 2 m π . We have shown in previous works [1,2,3] that this produces a large increase of the magnitude of the scalar QCD susceptibility over its vacuum value. We have expressed the origin of this increase as arising from the mixing of the nuclear response to a scalar probe coupled to nucleonic scalar density fluctuations into the QCD scalar response.

It is natural to investigate also the reciprocal problem of the influence of the QCD scalar response to a probe which couples to the quark density fluctuations on the ordinary nuclear scalar response of nuclear physics, which is the object of the present work. We will study this influence not only for what concerns the nuclear excitations but also for a single nucleon for which only nucleonic excitations are involved. If this influence indeed exists, does it lead to non-trivial observable consequences ? We will show that this is the case, with one main application. It is the possibility to infer medium effects in the propagation of the scalar meson which binds the nucleus from QCD results, such as the lattice ones on the evolution of the nucleon mass with the pion mass.

Our article is organized as follows. In section 2 we illustrate the mixing notion of the nuclear response into the QCD one, and vice-versa in the framework of a nuclear chiral model with a scalar and vector meson exchange. We show that this mutual influence also exists at the nucleonic level. In section 3 we discuss the influence of the quark structure of the nucleon on the scalar response of nuclear physics in a framework which also incorporates confinement effects.

2 Mutual influence of the scalar QCD response and nuclear physics response

Study in a nuclear chiral model

We first remind how the usual nuclear physics response to a scalar field enters in the QCD susceptibility. For this, following ref. [1], we start from the expression of the modification of the quark condensate in the nuclear medium, ∆ qq (ρ) = qq (ρ) -qq vac . We first use, as in ref. [1], its expression for a collection of independent nucleons :

∆ qq (ρ) = Q S ρ S , (1)
where ρ S is the nucleon scalar density. We have introduced the scalar charge of the nucleon, Q S = σ N /2 m q , which represents the scalar number of quarks of the nucleon. The susceptibility of the nuclear medium, χ A S , is the derivative of the quark scalar density with respect to the quark mass. We define it in such a way that it represents a purely nuclear contribution with the vacuum susceptibility substracted off :

χ A S = ∂∆ qq(ρ) ∂m q µ = ∂(Q S ρ S ) ∂m q µ . (2)
Here the derivatives are taken at constant chemical potential. This expression contains two terms. One arises from the derivative of Q S , which by definition is the free nucleon QCD scalar susceptibility, χ N S = ∂Q S /∂m q . The second one involves the derivative of the nucleon density ρ S . This last contribution is itself built of two pieces, one involves antinucleon excitations and is small [1]. The other one involves, as shown in ref. [1], the nuclear response Π 0 = -2M N p F /π 2 . In this case it is the free Fermi gas one since no interactions between nucleons have been introduced. The result of this derivation is summarized in the following equation:

χ A S = ρ S χ S N + 2 Q 2 S Π 0 . (3)
It says that the nuclear susceptibility is, as expected, the sum of a term arising from the individual nucleon response, i.e., from the nucleonic excitations, and of a term linked to the nuclear excitations. This decomposition survives the introduction of the interactions between the nucleons, as will be shown next. The previous result has been generalized in ref. [2] to an assembly of nucleons interacting through a scalar and a vector meson exchanges, working at the mean field level as in relativistic mean field theories. The original point with respect to standard relativistic theories is that, following our suggestion of ref. [4], the nuclear scalar field is identified with a scalar field of the linear sigma model. Rather than the sigma field, chiral parner of the pion, this is a chiral invariant, denoted S, associated with the chiral circle radius. Nevertheless the nuclear scalar field influences the condensate. Ignoring pion loops the distinction between the two scalar fields, the chiral invariant nuclear one and the non chiral invariant sigma one, wil be ignored. In ref. [2], the condensate was obtained as the derivative of the grand potential with respect to the quark mass (Feynman-Hellmann theorem) and the susceptibility as the derivative of the condensate, both being taken at constant chemical potential. The result for the susceptibility, as given in ref. [2], reads :

χ S = ∂ qq ∂m q µ ≃ -2 qq 2 vac f 2 π ∂ S ∂c µ . (4)
S ≡ f π + s is the expectation value of the chiral invariant scalar field and c = f π m 2 π is the symmetry breaking parameter of the model used in [2]. The quantity ∂ S/∂c µ was shown in ref. [2] to be related to the in-medium sigma propagator :

∂ S ∂c µ = -D * σ (0) = 1 m * 2 σ - g 2 S m * 2 σ Π S (0) 1 m * 2 σ ( 5
)
where Π S (0) is the full RPA scalar polarization propagator and m * σ is the in-medium sigma mass, obtained from the second derivative of the energy density with respect to the order parameter :

m * 2 σ = ∂ 2 ε ∂s 2 = V ′′ (s) + ∂ (g S ) ∂s ρ S = m 2 σ 1 + 3s f π + 3 2 s f π 2 (6)
where the potential V responsible for the spontaneous symmetry breaking is the standard quartic one of the linear sigma model,

V = (m 2 σ /2) (s 2 + s 3 /f π + s 4 /(4f 2 π ))
. At this stage the nucleons are sructureless and hence we ignore the medium renormalization of g S , i.e. we take g S to be independent of s. The mean scalar field s being negative, the term linear in s lowers the sigma mass by an appreciable amount (≃ 30 % at ρ 0 ). This is the chiral dropping associated with chiral restoration [5] and arising from the 3σ interaction as depicted in fig 1 .  Since we are interested only in the medium effects the vacuum value of the quantity ∂ S/∂c µ = 1/m σ 2 has to be subtracted off in eq. ( 5) and the purely nuclear suceptibility, χ A S , writes :

χ A S = 2 qq 2 vac f 2 π 3 s/f π + 3 2 (s/f π ) 2 m * 2 σ + g 2 S m * 2 σ Π S (0) 1 m * 2 σ . (7)
We see that χ A S receives two types of contributions, the second denoted as (χ A S ) nuclear being proportionnal to the full RPA scalar response Π S (the response to the scalar nuclear field is g 2 S Π S ). The corresponding proportionality factor r between this second contribution and g 2 S Π S writes, to leading order, i.e., neglecting the medium modification of the sigma mass :

r = (χ A S ) nuclear g 2 S Π S (0) = 2 qq 2 vac f 2 π m 4 σ ≃ 2 (Q s S ) 2 g 2 S ( 8
)
where we have introduced the nucleon scalar charge Q s S from the scalar field, defined below. In the sigma model the free nucleon sigma commutator is the sum of two contributions, one arising from the pion cloud, which depends on the mean value of the squared pion field, i.e., on the scalar number of pions in the nucleonic cloud. In the mean field approximation where pion loops are ignored this term does not appear. The other one, Q s S , arises from the scalar meson [6,7,8]. It is linear in the σ field :

Q s S = σ s N 2m q = - qq vac f π d 3 r N|σ( r)|N = - qq vac f π g S m 2 σ (9)
which establishes relation (8) if we ignore the in-medium modification of Q s S , i.e., the difference beween m * σ and m σ . We now turn to the first part of χ A S which depends on the mean scalar field s. We will show that it provides an information on the nucleon susceptibility. For this we investigate the low density limit of eq. ( 7). In this case, s reduces to s = -g S ρ S /m 2 σ , and we can ignore the term in s2 as well as the difference beween m * σ and m σ . In this limit the first term in the expression (7) of χ A S is linear in the density. In the decomposition of eq. ( 3) for χ A S , it obviously belongs to the individual nucleon contribution, ρ S χ N S , to the nuclear susceptibility. Writing the linear term explicitly in eq. ( 7) we deduce the free nucleon scalar susceptibility from the scalar field, (χ N S ) s :

(χ N S ) s = -2 qq 2 vac f 3 π 3 g S m 4 σ , (10)
which is negative. The existence of a contribution to the nucleon susceptibility from the scalar field as given by the expression 10 is a new information provided by this study with interacting nucleons. We have obtained it from the low density expression of χ A S . Another way to derive it is from the derivative with respect to the quark mass of the scalar charge Q s S of eq. ( 9) :

(χ N S ) s = ∂Q s S ∂m q = ∂ ∂m q - qq vac f π g S m 2 σ . (11)
Using the fact that, in the model, qq vac /f π does not depend on m q , only the derivative of the sigma mass with respect to m q enters which, according to the Feynman-Hellmann theorem, is linked to the sigma commutator, σ σ , of the σ. In the linear sigma model the derivative with respect to the quark mass is replaced by the derivative with respect to the symmetry breaking parameter, c = f π m 2 π , keeping the other original parameters of the model, λ and v, constant. The result is :

σ σ = m q ∂m σ ∂m q = 3 2 m 2 π m σ . (12)
When inserted in eq. ( 11), it leads for (χ N S ) s to the expression of eq. ( 10). We have seen that the nuclear part of the susceptibility is related to the nuclear response to the scalar field by the relation 8. Similarly we will show the nucleonic piece of the susceptibility, (χ N S ) s , is related to the scattering amplitude of the scalar meson on the nucleon. Indeed, in the expression(6) of m * 2 σ there is a term linear in density which is obtained from the low density expression :

3 s m * 2 σ ≃ -(3 g S /f π ) ρ S .
This term represents an optical potential for the scalar meson propagation. The corresponding σN scattering amplitude, T σN , which can also be evaluated directly from the graph of fig. 1, is equal to :

T σN = -3 g S /f π . (13)
N σ σ σ We are now in a situation to relate the nucleon scalar susceptibility (eq. ( 10)) to the sigma-nucleon amplitude of eq. ( 13), with the result :

r ′ = (χ N S ) s T σN = 2 (Q s S ) 2 g 2 S . (14)
We observe that the proportionality factor between T σN and (χ N S ) s which is 2 (Q s S ) 2 /g 2 S , is identical to the one which involves the purely nuclear excitations. The quantity g S which appears in the present factor is due to the σNN coupling constant. Adding now the two effects from the nucleonic and nuclear excitations the total QCD scalar susceptibility of the nuclear medium (vacuum value substracted) can therefore be related to the total response, T A , to the nuclear scalar field through :

χ A S = 2 (Q s S ) 2 g 2 S T A (15)
where the two members include both the individual nucleon contribution and the one arising from the nuclear excitations,with :

T A = ρ S T σN + g 2 S Π S . (16)
The last term on the r.h.s. represents the influence of the Born part of the σN amplitude (in-medium corrected in particular for the Pauli effect) while the first piece arises from the non-Born part linked to nucleonic excitations.

Connection with lattice data

Since we have introduced QCD quantities such as the QCD scalar response, it is now interesting to connect our results to lattice simulations of the evolution of the nucleon mass with the pion mass, equivalently the quark mass. At present they do not cover the physical region but only the region beyond m π ≃ 400 MeV and in order to reach the physical nucleon mass an extraplolation has to be performed. The pion cloud contribution to the nucleon self.energy has a non-analytic behavior in the quark mass, preventing a polynomial expansion in this quantity. For that reason Thomas et al [9] have separated out this contribution. This is done in a model dependent way with different cut-off forms for the pion loops (gaussian, dipole, monopole) with an adjustable parameter Λ. They expand the remaining part in terms of m 2 π as follows:

M N (m 2 π ) = a 0 + a 2 m 2 π + a 4 m 4 π + Σ π (m π , Λ). ( 17
)
The best fit value of the parameter a 4 which fixes the susceptibility shows little sensitivity to the shape of the form factor, with a value a 4 ≃ -0.5 GeV -3 , while a 2 ≃ 1.5 GeV -1 (in a previous work [10] smaller values of a 2 and a 4 were given : a 2 ≃ 1 GeV -1 and a 4 ≃ -0.23 GeV -3 ). From the expansion of eq. ( 17) we can therefore infer the nonpionic pieces of the sigma commutator and of the susceptibility :

σ non-pion N = m 2 π ∂M ∂m 2 π = a 2 m 2 π + 2 a 4 m 4 π ≃ 29 MeV . ( 18
)
It is largely dominated by the a 2 term. The corresponding value for

a 2 ≃ 1 GeV -1 is σ non-pion N = 20
MeV . In turn the nucleon susceptibility is :

χ N,non-pion S = 2 qq 2 vac f 4 π ∂ ∂m 2 π σ non-pion N m 2 π = qq 2 vac f 4 π 4 a 4 ≃ -5.4 GeV -1 (19)
The non-pionic susceptibility is found with a negative sign, as expected from the scalar meson term. In ref. [9] however, the negative sign is interpreted differently. It is attributed to possible deviations from the Gellman-Oakes-Renner (GOR) relation which links quark and pion masses. Here instead we assume the validity of the GOR relation.

It is then interesting to test if the empirical values from the lattice are compatible with our previous linear sigma model results. We thus tentatively make the following identifications :

Q s S = - qq vac f π g S m 2 σ = σ non-pion N (2 m q ) ≃ - qq vac f π a 2 = -2.4, (20)
with 2 m q = 12 MeV (taking a 2 ≃ 1 GeV -1 one would get Q s S = 1.66). It is interesting to translate this number into the value of the mean scalar field in the nuclear medium which, to leading order in density, is :

-s = g s ρ S m 2 σ = Q s S f π ρ S qq vac = σ non-pion N (2 m q ) f π ρ S qq vac = a 2 + a 4 m 2 π f π ρ S . (21)
At normal density the value is |s(ρ 0 )| ≃ 21 MeV , compatible with nuclear phenomenology.

The second identification concerns the susceptibility. Identifying the value of the linear sigma model with the lattice one, we should have :

(χ N S ) non-pion = - 2 (Q s S ) 2 g 2 S 3 g S f π = qq 2 vac f 4 π 4 a 4 (22)
which, using the relation (20) between a 2 and Q s S leads to :

-a 4 = 3 2 (σ non-pion N ) 2 g S f π m π 4 ≃ 3 2 a 2 2 g S f π = 3 g S f π a 2 2 = 3.5 GeV -3 , (23)
much larger than the lattice value, -a 4 = 0.5 GeV -3 . For a 2 ≃ 1 GeV -1 one gets -a 4 ≃ 1.2 GeV -3 , also larger than the corresponding lattice value (0.23 GeV -3 ). Thus the linear σ model leads to a too large absolute value of the nucleon scalar susceptibility. We remind at this stage that it also fails in another respect, concerning the saturation properties of nuclear matter. The 3σ coupling present in this model, which lowers the sigma mass in the medium, prevents saturation to occur and produces the collapse [START_REF] Kerman | Second High Energy Heavy Ion Summer Study[END_REF]. Said differently the sigma nucleon scattering amplitude, T σN , of the model is too attractive. In fact what we have shown in this work is that the two problems are linked since we have found that T σN and (χ N S ) s are related. These two failures are coherent. Some mechanism must be at work to introduce in both a suppression effect. In a previous work [2] we have invoked the quark meson coupling model (QMC) [START_REF] Guichon | [END_REF]13] and confinement as a source of cancellation. Indeed, for three valence quarks confined in a bag of radius R, Guichon [14] derived (χ N S ) bag ≃ + 0.25 R ≃ 1 GeV -1 , (for R = 0.8 f m). Contrary to the other components which are negative (of paramagnetic nature), it has a positive sign (of the diamagnetic type, linked to quark-antiquark excitations). In ref ( [2]) we have introduced phenomenologically in the nucleon mass evolution of the linear sigma model a parameter, κ N S which embodies the scalar response of the nucleon from confinement:

M * N = M N + g S s + 1 2 κ N S s2 (24)
It allows a proper description of the saturation properties on nuclear matter.It is then natural to extend the linear sigma model description so as to incorporate effects arising from confinement.

Illustration in a hybrid model of the nucleon

We now want to generalize our previous results so as to incorporate the confinement aspect. In the following we will introduce a model of the nucleon proposed in ref. [15] which is intermediate between the two extreme pictures : the bag one and the Nambu-Jona-Lasinio (NJL) one which generates a linear sigma model. We will study both the scalar susceptibility of the nucleon and the scattering amplitude of the scalar field on the nucleon and their relation. In this framework we retain two concepts that were contained in our previous approach in the linear sigma model : (i) the nuclear scalar field is identified with the chiral field associated with the quark condensate and (ii) part of the nucleon mass originates from this condensate. This model consists in the following. Three constituant quarks moving in a non-perturbative vacuum are kept together by a central force which mimicks confinement and the effect of the color string tension. The mass M of the constituants quarks originates from the chiral condensate as in the NJL model. The nucleon mass is not 3M but, because of the confining force, becomes 3E(M) where the M dependence is fixed by the type of force. For illustration we take for simplicity a harmonic force of the form: ((K/4)(1 + γ 0 ) r 2 , which leads to analytical results. With this particular potential the nucleon mass is :

M N = 3 E = 3 M + 3 2 K E + M . (25)
It is increased as compared to the value, 3M, for three independent constituant quarks. Although oversimplified the model gives an intuitive picture of the role played by confinement. Since we assume that the nuclear scalar field is related to the quark condensate, the presence of the mean scalar field in the medium which modifies the condensate with respect to its vacuum value also affects the mass M. The derivative, ∂M/∂s, has a nonvanishing value, given by the NJL model,

∂M ∂s = g q = M f π . ( 26
)
The nucleon scalar charge, Q S , writes :

Q S = 3 2 ∂E ∂m q = 3 2 ∂E ∂M ∂M ∂m q (27) with : ∂E ∂M = c S = E + 3M 3E + M . ( 28
)
As E > M, c S < 1, the nucleon scalar charge is reduced as compared to a collection of three independent quarks. The nucleon scalar susceptibility, χ N S , given by the next derivative, is composed of two terms arising respectively from the derivative of c S and from that of ∂M/∂m q :

χ N S = ∂Q S ∂m q = 3 2 ∂c S ∂M ∂M ∂m q 2 + c S ∂ 2 M ∂ 2 m 2 q with: ∂c S ∂M = 24 (E 2 -M 2 ) (3E + M) 3 . ( 29
)
Notice that this last derivative is positive since E > M and that it vanishes in the absence of confining force, when E = M. Therefore the first part of the expression of χ N S represents the part of the susceptibility originating in confinement and, as in QMC, it is positive. We find in the susceptibility written in eq. ( 29) the double aspect of the mass, part arising from the constituant quark mass, i.e., from the condensate and part from confinement. The expression (29) can descibe the two extreme situations. In the MIT bag model the confined quarks are the current ones, M = m q , the second term of the susceptibility disappears, only the confinement part enters. In the NJL model instead where the constituant quarks are unconfined, E = M, c S = 1 and only the second term survives.

For what concerns the coupling constant, g S , of the nucleon to the scalar field, it is given by the derivative of the nucleon mass with respect to the mean scalar field s:

g S = 3 ∂E ∂s = 3 ∂E ∂M ∂M ∂s = 3 c S g q . ( 30
)
The nucleon response to the scalar field originating in confinement, κ N S , follows from the eq. ( 24) as the second derivative of the nucleon mass with respect to the scalar field :

κ N S = 3 ∂ 2 E ∂s 2 = 3 ∂c S ∂M ∂M ∂s 2 . ( 31
)
The ratio, r m , between the part of the nucleon scalar susceptibility due to confinement and κ N S is

r m = 1 2 ( ∂M ∂mq ) 2 ( ∂M ∂s ) 2 = 2 Q 2 S g 2 S , (32)
the same ratio, r, as was previously found in the linear sigma model. While the quantity κ N S represents the effect of the nucleon internal quark structure, there is another component of the σN amplitude, which is the tadpole term , T σN , an effect of the mexican hat chiral potential. For each constituant quark the tadpole amplitude is t σN = -3 g q /f π . As the scalar number of constituant quarks is 3 c S , the tadpole amplitude for the nucleon writes T σN tadpole = -3 g S /f π , the same expression as in the linear sigma model. This quantity should be compared to the other component of the susceptibility,

3 2 c S ∂ 2 M ∂ 2 m 2 q
. We define r ′ m as the corresponding ratio through :

3 2 c S ∂ 2 M ∂m 2 q = r ′ m - 3 g S f π . (33)
In the semi-bosonized version of the NJL model we have :

∂M ∂m q = -2 g q qq vac f π m 2 σ ( 34
)
and

∂ 2 M ∂m 2 q = - 2 g q qq vac 2 f 3 π m 4 σ (35)
in such a way that the ratio r ′ m becomes :

r ′ m = 2 qq 2 vac f 2 π m 4 σ = 2 Q 2 S g 2 S ≡ r m . (36)
Since the same ratio applies to the two parts, r ′ m ≡ r m , it can be factorized when we add the two pieces of the susceptibility so as to obtain the relation

χ N S = r m κ N S + r ′ m - 3 g S f π = 2 Q 2 S g 2 S T total N ( 37
)
which thus also holds in the presence of confinement. Adding the nuclear excitations contribution (term in Π S ) on both sides of the above equation once multiplied by the density we recover the relation (7) between the nuclear values χ A S and T A . Numerically we have chosen a value of the ratio E/M ≃ 2.1, which leads to a reasonable value for g A and gives c S ≃ 0.7. It results in a value of the dimensionless parameter C = (f π /2g S ) κ N S ≃ 0.1, while the value needed to account for the saturation properties is C ≃ 1 [16]. In fact the nuclear phenomenology requires a strong suppression of the tadpole term in the σN amplitude (total cancellation occurs for C = 1.5). On the other hand the lattice results also require a nearly total cancellation of the nucleon scalar susceptibility from the scalar meson by the effect of confinement. For us the two cancellations have a unique origin and description since the total susceptibility and the total σNamplitude are related. The condition for a total cancellation between the two components of χ N S , as approximately required by the phenomenology, writes

∂c S ∂M - c S 2g q f π = 0, (38)
which should approximately hold for the physical value of M, but is not fulfilled with our particular form of c S where the second part dominates. Even if our particular model fails to account for the numerical value of C it has the merit to confirm the validity of the relation between the QCD response and the one to the nuclear scalar field in a situation where confinement enters. The relation (37) is indeed general and does not depend on the particular form of E(M).

Applications to nuclear physics

We can now turn to the quantitative applications of the relation (37) between T total N and the scalar susceptibility. The last quantity is known from the lattice expansion. On the other hand the scalar charge which enters the relation (37) is also determined by this expansion. Therefore the only model dependent quantity to determine the amplitude, T total N , from the lattice expansion is g S but this is only a moderate uncertainty. The important point is that the resulting value of T total N is small. The resulting medium effects in the propagation of the nuclear scalar field can be written, using the eq. ( 37) and ( 19), as :

-D -1 s = m 2 σ + g 2 S 2 Q 2 S χ N S ρ S ≈ m 2 σ + g 2 S 2 a 4 a 2 2 ρ S ; (39)
Numerically, at normal nuclear density, and for a value of the coupling constant g S = 10, the second term on the rhs of the second equation takes the value 0.06 GeV 2 (a similar value is found for the other set of parameters a 2 and a 4 ). For a sigma mass of m σ = 0.75 GeV , this represents at ρ 0 only a 6% decrease of the mass, much less that the chiral dropping alone and in much better agreement with the nuclear phenomenology [2,16]. At this stage, conceptual questions naturally arise. As the lattice parameter a 4 is very small one may conclude that QCD effects related to the nucleon quark substructure and chiral symmetry are simply not visible in nuclear physics as they annihilate each other. This conclusion is however erroneous. They strongly show up at the level of the three-body forces, playing an important role in the saturation mechanism, as explained below. For that purpose we introduce a new scalar field u = s + (κ N S /2g S ) s 2 in such a way that the expression of the in-medium nucleon effective mass reduces to a simpler form according to :

M * N (ū) = M N + g S s + 1 2 κ N S s2 ≡ M N + g S ū. ( 40
)
Expressed in term of the u field, the chiral mexican hat potential takes the form :

V chiral = V = m 2 σ 2 s 2 + s 3 f π + s 4 4 f 2 π = m 2 σ 2 u 2 + u 3 f π (1 -2C) + u 4 4 (1 -8C + 20C 2 ) .
(41) In the formulation with the u field the three body forces are contained in the u 3 term :

V three-body = m 2 σ 2 ū3 f π (1 -2C). ( 42
)
We remind the definition of C = (κ N S f π )/(2g S ). As ū < 0, this force is repulsive for C > 1/2, which is actually the case. Without confinement, i.e., C = 0, the chiral potential alone leads to attractive 3-body forces. The important point is that the balance between the effects of the chiral potential and of confinement are not the same in the propagation of the scalar field and in the three body forces. In the first case the amplitude T total N which governs the sigma self-energy is

T total N = 3 g S /f π + κ N S = (3g S /f π ) (1 -2C/3
), while in the three body forces the combination is 1 -2C. With C of the order unity, a strong cancellation occurs in T total N while there is an overcompensation in the three body potential which becomes repulsive. The existence of repulsive three body forces in relativistic theories is strongly supported by the nuclear phenomenology [17,18]. Using the eq. ( 19),(20) and (37), we can express C in terms of the lattice parameters :

C = 3 2 - g S f π a 2 2 a 4 ≃ 1.3, (43)
which leads to

V three-body = - m 2 σ 2 ū3 f π g S f π a 2 2 a 4 + 2 (44)
Notice that since a 4 is small the term 2 dominates the parenthesis on the r.h.s. The equation of motion gives ū ≃ -g S ρ S /m 2 σ . Numerically, for the phenomenological value C = 1, the contribution of the three-body forces to the energy per nucleon is :

E A three-body = V three-body ρ 20 ρ ρ 0 2 , MeV. (45)
With the lattice value. C = 1.3, the result is ≃ 50% larger.

In the QMC approach of ref. [START_REF] Guichon | [END_REF]13], the chiral aspect is not considered and hence the higher order terms in the mexican hat potential are absent. The three-body potential originates only from confinement through the nucleon scalar response :

V three-body = m 2 σ 2 ū3 f π (-2C QM C ). (46)
Comparing the expressions (42) and ( 46), one sees that, numerically, our phenomenological value C ≃ 1 is equivalent to C QM C = 0.5, which is close to the actual value of the QMC model.

Conclusion

In summary we have studied in this work the interplay between the two nuclear responses to probes which couple either to nucleon or to quark scalar density fluctuations. We have found that the two responses are reflected in each other. The scaling coefficient involves the nucleon scalar charge. Both responses incorporate the individual nucleon contributions to the nuclear response in such a way that our result holds not only at the level of the nuclear excitations but also for the nucleonic ones. The response of a nucleon to the nuclear scalar field is linked to its QCD scalar susceptibility. We have first established this results in the linear sigma model, adopting the view that the scalar field is the chiral invariant scalar field of this model, in which case it is linked to the quark condensate.

However the linear sigma model has serious shortcomings, first in nuclear physics where it makes nuclear matter collapse instead of saturate. In QCD as well it fails to account for the value of the nucleon scalar susceptibility, for which it predicts too large a magnitude as compared to the lattice result. In our views the two problems are not distinct but they are automatically linked and we have attributed them to the absence of confinement in the description. In a second step we have improved our approach to incorporate this effect. For the nucleon we have adopted a hybrid image of three constituant quarks sitting in a non perturbative vacuum and kept together by a confining potential. The nucleon mass thus originates in part from the quark condensate and in part from confinement. We have retained the concept that the nuclear scalar field has a relation to the scalar field associated with the chiral quark condensate. In this situation the presence of the nuclear scalar mean field affects the condensate and hence the constituant quark mass. We have shown that, in this model, the relation between the scalar meson self-energy and the nucleon QCD scalar susceptibility remains the same as in the linear sigma model.

The existence of relations between nuclear physics parameters (such as the opticel potential for the propagation of thr scalar field, the three-body potential) and those of QCD opens the possibility of a description of the properties of nuclear matter using as inputs the parameters of the lattice expansion of QCD. We have adopted this approach in ref. ([16]) and it has been successful. With parameters close to those provided by the lattice expansion we have been able to reproduce the saturation properties of nuclear matter. This coherence, which it is not a priori acquired, suggests the validity of such an approach. It supports the idea that a part of the nucleon mass originates in the quark condensate and that the nuclear scalar field plays a role in the restoration of chiral symmetry in nuclei. We have found, both in the lattice expansion results and in the nuclear phenomenology, the need for a strong cancellation of the chiral effects by confinement in the sigma propagation. It follows that the sigma mass remains stable in the medium. Confinement nevertheless shows up very neatly in the three body potential where it dominates the attractive chiral effects, giving rise to repulsive three-body forces.

Figure 1 :

 1 Figure 1: Contribution to the sigma-nucleon scattering amplitude responsible for the lowering of the sigma mass in the medium.