Transactional versus Relational Customer Orientation: Developing a Segmentation Tool in the French Banking Industry An exploratory study

The authors conduct an exploratory study in order to develop a measurement scale of customers' transactional/ relational orientation. The study is implemented in the context of French industry in both B.-to-C. and B.-to-B. environments. They show that transactional/ relational orientation can be measured following four dimensions: affective, technical, shortterm and long-term dimensions. This scale is the first in this field and further research is necessary in order to improve its applications and functions. Moreover, this work remains limited in application to the French banking industry.

develop a measurement scale of customers' transactional/ relational orientation. The study is implemented in the context of French industry in both B.-to-C. and B.-to-B. environments. They show that transactional/ relational orientation can be measured following four dimensions: affective, technical, shortterm and long-term dimensions. This scale is the first in this field and further research is necessary in order to improve its applications and functions. Moreover, this work remains limited in application to the French banking industry.

Introduction

"I don't call them and they don't call me" (Barnes, 1997, p.771). Such a statement was the surprising answer to a question relating to good relationships in the B.-to C. banking industry.

This example shows that customers may have different definitions of what a 'good relationship' constitutes. Indeed, one would expect this customer to consider that a good relationship is one with frequent interaction.

Such an example illustrates the fact that customers may react differently to the same type of relationship. Therefore, customers' segmentation should be based on attitudes towards relationships. This would help providers to better allocate their resources (time, money, interface employees, etc.), concentrating their relationship efforts on relational oriented customers (versus transactional oriented ones). Unfortunately, little empirical research has been conducted in this field to help providers to segment their customers. In 1997, Bendapudi & Berry still write "given the lack of research in this area, it is currently not possible to segment customers on the basis of their receptivity to relationship maintenance".

Over the last twenty years, research in relationship marketing has focused mainly on suppliers' customer orientation (e.g., SOCO scale by Saxe and Weitz, 1982) and on customers' relational benefits (e.g., [START_REF] Gwinner | Relational Benefits in Services Industries: The Customer's Perspective[END_REF]. Only little research has been undertaken in order to define the customer orientation (transactional vs. relational). Relational benefits usually represent the customer's aims when entering a relationship. Since all customers do not wish to engage in a close relationship [START_REF] Barnes | Closeness, Strength, and Satisfaction: Examining the Nature of Relationships between Providers of Financial Services and their Retail Customers[END_REF], it would be interesting to study the customer relational orientation: the latter represents the customer's willingness to enter a relationship and to develop it with a long-term perspective.

The first indications of the distinction between relational and transactional orientation are due to [START_REF] Macneil | The New Social Contract, An Inquiry into Modern Contractual Relations[END_REF] and [START_REF] Jackson | Build Customer Relationships that Last[END_REF]. [START_REF] Macneil | The New Social Contract, An Inquiry into Modern Contractual Relations[END_REF] underlines the difference between relational contracts and discrete contracts while [START_REF] Jackson | Build Customer Relationships that Last[END_REF] considers business transactions versus business relations. Usually, authors study the relational/ transactional customer orientation in three different approaches: (1) considering customer personality and global attitude towards the relationship [START_REF] Perrien | The Meaning of Relationship Marketing: A Pilot Study[END_REF], Ricard & Perrien 1996); (2) considering consequences of the relationship such as psychological, social, and economic benefits [START_REF] Gwinner | Relational Benefits in Services Industries: The Customer's Perspective[END_REF]; (3) considering contextual elements such as service characteristics -importance, involvement, quality, complexity- [START_REF] Berry | Relationship Marketing of Services -Growing Interest, Emerging Perspectives[END_REF].

The three approaches show that the relational orientation construct can be measured either by its consequences or by its antecedents. Our paper will focus on the latter.

The customer relational orientation may be perceived as a multidimensional construct: the first dimension is a functional/affective orientation continuum (e.g., [START_REF] Beatty | Customer-Sales Associate Retail Relationships[END_REF]; the second one is a short-term/ long-term orientation continuum (e.g., [START_REF] Macneil | The New Social Contract, An Inquiry into Modern Contractual Relations[END_REF]. The first dimension is represented by tangible elements (economic outcomes of a transaction, such as price) versus emotional elements (psychological variables) -e.g., [START_REF] Grönroos | Service Management and Marketing, Managing the Moment of Truth in Service Competition[END_REF][START_REF] Hakansson | International Marketing and Purchasing of Industrial Goods[END_REF]-. The second one is characterized by the customer's time orientation. Transactional customers tend to be more short-term and function-oriented, and relational ones tend to be more long-term and affective oriented.

The banking industry represents a good field of research, because of the intangibility of services and of the frequency of interpersonal interactions. The authors are developing a customer orientation scale in two different banking contexts: B-to-C and B-to-B relationships.

Such a scale will allow us to draw conclusions primarily on the generalization of the construct.

The first section of this paper will present a literature review. Two types of research will be explored: (1) research studying suppliers' customer orientation and customer relational benefits (without segmenting the population) and ( 2) theoretical research introducing the segmentation between relational and transactional customers theoretically. In the second section, a presentation of the scale's development and of our methodology will be outlined in details (A set of 15 items has been developed and was tested in the two contexts). Finally, the authors will analyze and discuss the results and conclusions.

I. Literature Review

I.1. Lack of customer segmentation...

I.1.a. Suppliers' customer orientation: the SOCO scale

The adoption of the marketing concept is quite an old phenomenon. The marketing concept is a business philosophy which holds that long-term profitability is best achieved by focusing the coordinated activities of the organization towards satisfying the needs of particular market segment(s) [START_REF] Gray | Developing a Better Measure of Market Orientation[END_REF]. However almost no literature helps identify these market segments.

The adoption of this concept was first reported in industrial sales in the sixties (Saxe & Weitz, 1982). Years later, it achieved important success in the service industry.

One of the most famous works in this field has been conducted by Saxe & Weitz (1982) with the SOCO (Customer orientation of salespeople) scale. These authors measure the degree to which a salesperson engages in customer-oriented selling (i.e., the degree to which salespeople implement the marketing concept by trying to help their customers make purchase decisions that will satisfy their needs). They demonstrate that highly customer-oriented salespeople avoid taking actions, which might dissatisfy customers. Saxe & Weitz (1982) have identified six dimensions defining the customer orientation of salespeople: (1) A desire to help customers make wise purchase decisions; (2) helping customers assess their needs; (3) offering products that will satisfy those needs; (4) describing products accurately; (5) avoiding deceptive or manipulative influence tactics; (6) avoiding the use of high pressure.

In their conclusion, Saxe & Weitz (1982) suggest studying the relationship between customer orientation and customer satisfaction. They also suggest investigating the 'psychology' of salespeople.

Three years later, [START_REF] Michaels R | Measuring Customer Orientation of Salespeople: A Replication with Industrial Buyers[END_REF] extended Saxe and Weitz's work. In fact, they noticed that the SOCO scale was implemented with samples of salespeople who assess their own customer orientation and they believe it is more appropriate to implement the SOCO scale with customers themselves (Michaels & Day, 1985 , p.443). Using this scale, customers are able to assess the degree of customer orientation of salespeople with whom they deal.

Studies on market orientation have extended such work. Further research integrates the customer orientation into a more global concept: the firm's market orientation. [START_REF] Kohli | Market Orientation: The Construct, Research Propositions and Managerial Implications[END_REF] define market orientation as the generation of market intelligence, the dissemination of such intelligence, and the organization-wide responsiveness to it. [START_REF] Narver | The Effect of Market Orientation on Business Profitability[END_REF] complement this definition with three behavioral components: customer orientation, competitor orientation, and interfunctional coordination. In summary, market orientation studies concentrate on the coordination and the management of the 4P's in order to make the companies more responsive in meeting customer needs [START_REF] Gray | Developing a Better Measure of Market Orientation[END_REF]. However, they are conducting an internal approach and they fall to investigate what the customer truly needs. Such an approach is opposed to customer-based marketing as it is described in the following section.

I.1.b. Customers' relational benefits

In marketing literature, benefits of long-term relationships are studied primarily from the firm's perspective. In fact, it is commonly recognized that continuous relationships lead to repurchasing, low levels of customer turnover, decrease of costs, positive word of mouth, and finally increase of profits (e.g., [START_REF] Berry | Relationship Marketing of Services -Growing Interest, Emerging Perspectives[END_REF]Reichfeld & Sasser, 1990). However, more recently, research in relationship marketing has also focused on customers' relational benefits. [START_REF] Gwinner | Relational Benefits in Services Industries: The Customer's Perspective[END_REF] examine the benefits customers receive as a result of engaging in long term relational exchanges with service firms. Findings from two studies across three categories of services indicate that consumer relational benefits can be categorized into three distinct types of benefits: (1) social benefits: beyond the benefits of the basic service, customers search for fraternization and likable relationships. Therefore, they are looking for certain personal recognition; (2) psychological benefits: they are often linked with comfort, feelings of security and particularly trust or confidence in the provider; (3) customization benefits: the final category of relational benefits relates to customization of the offered service. For regular customers, many service providers may tailor their services to meet particular needs. In some cases, this may be perceived by customers as preferential treatment. It also includes economic benefits such as discounts or price breaks. In addition to monetary benefits, non-monetary, and timesaving benefits were identified by the authors.

Finally, these findings indicate that psychological (or confidence) benefits are the most important to consumers within all three categories of services. Social benefits are the second most important and customization benefits are perceived as the least important benefit for customers.

Overall, in summary, research in relationship marketing has focused on suppliers' customer orientation (e.g. SOCO scale) as well as on the consequences of relationships for customers, (i.e. on customers' relational benefits). Customer segmentation, based on their relational versus transactional orientation, has not been researched in these research projects.

I.2. The emergence of customer segmentation ...

Segmentation based on customers relational versus transactional orientation has only been studied empirically once at present, but it is not a new concept. Indeed, [START_REF] Macneil | The New Social Contract, An Inquiry into Modern Contractual Relations[END_REF] and [START_REF] Lovelock | Classifying Services to Gain Strategic Marketing Insights[END_REF] referred to it for the first time 20 years ago.

When segmenting customer into relational versus transactional oriented ones, authors usually use two different approaches: (1) an approach based on contextual elements such as relationship or service characteristics and (2) another one based on psychological elements such as a customer's personality and his/her global attitude towards the relationship.

I.2.a. Segmentation based on contextual elements

As early as 1985, Jackson claimed that "relationship marketing (...) can be extremely beneficial when it is relevant, but can also be costly and ineffective when it is not". Indeed, a relationship strategy is not necessarily valuable or interesting for all customers. In 1986, Jackson distinguishes two possible customer behavior schemes or models: She calls the first one the "distribution model". In this scheme, the customer who regularly buys a certain type of product can easily switch from one provider to another. The relationship exit costs are very low for the customer. Therefore, he has freedom to purchase from several providers. This kind of customer has a short-term vision of relationships and focuses on immediate results.

"Business transaction" is, according to Jackson, a well-adapted system for this type of customer. The second behavior scheme described by Jackson is opposite the first. It implies that the relationship exit costs are so high that the customer is dependent on his major provider. He has, therefore, a vision of a continuous, long-term relationship and reaps long term results and benefits. "Business relation" is thus a well-adapted system for this type of customer. [START_REF] Jackson | Construisez des relations durables avec voc clients![END_REF] implicitly makes the distinction between relational customers (in favor of business relations) and transactional ones (in favor of business transactions). She bases this distinction on contextual elements, which are the business relationship exit cost levels.

In a theoretical paper, dated 1997, Bendapudi and Berry study the customers' motivations for maintaining relationships with service providers. The authors focus on the idea of relationship exit costs to explain the customer's attitude towards the relationship; furthermore, they add the level of the customer's dedication. They attempt to understand customer's motivations from an economic perspective (explaining continuance in terms of the costs and benefits of staying in the relationship versus leaving it) as well as the psychological perspective (focusing on the affective responses of a party in the relationship and on his/her dedication level). When a customer is dedicated to a relationship, he is less inclined to seek other alternatives and less receptive to competitors' offers. Therefore, we can hypothesize that dedicated customers are more relational oriented while others are more transactional. As shown in table 1, [START_REF] Bendapudi | Customers' Motivations for Maintaining Relationships with Service Providers[END_REF] identify four combinations of motivation: (1) customers with a low level of dedication and constraints (they are unlikely to perceive the need for stable relationships and are transactional oriented); (2) customers with a low-level of dedication but with high levels of constraints (the relationship may persist because there are no alternatives for these transactional customers); (3) customers with a high-level of dedication and low-levels of constraints (they represent fundamentally relational oriented customers) ; (4) customers with a high-level of dedication and constraints (in this chart, they represent fundamentally relational oriented customers or may rationalize their constraints by dedication). [START_REF] Bendapudi | Customers' Motivations for Maintaining Relationships with Service Providers[END_REF] implicitly make the difference between relational and transactional customers using various levels of dedication and constraints. However, the authors consider that constraints come from dependence, while dedication comes from both trust and dependence. Therefore, in order to determine the relational orientation of customers, the researchers rely on contextual elements such as the relationship characteristics (trust, dependence) and not solely on customers' personalities.

While [START_REF] Jackson | Construisez des relations durables avec voc clients![END_REF] and [START_REF] Bendapudi | Customers' Motivations for Maintaining Relationships with Service Providers[END_REF] segment customers on the basis of relationship characteristics (exit costs/level of constraints and dedication linked with dependence and trust), [START_REF] Berry | Relationship Marketing of Services -Growing Interest, Emerging Perspectives[END_REF] argues about service characteristics. "For continuously or periodically delivered services that are personally important, variable in quality, and/or complex, many customers will desire to be 'relationship customers'. High involvement services also hold relationship appeal to customers. Medical, banking, insurance and hairstyling services illustrate some (or all) of the significant characteristics -importance, variability, complexity and involvement -that would cause many customers to desire continuity with the same provider, and customized service delivery". [START_REF] Berry | Relationship Marketing of Services -Growing Interest, Emerging Perspectives[END_REF] evokes relational oriented customers using service characteristics but does not talk about transactional oriented ones.

In summary, when segmenting customers into relational versus transactional oriented ones, some authors use an approach based on contextual elements such as relationship characteristics (exit costs, level of constraints, dedication, trust and dependence) or service characteristics (importance, complexity, etc.). However, others use a different approach based on the customer's personality and his/her global attitude towards the relationship.

I.2.b. Segmentation based on customer's personality

Perrien & Ricard (1995) examine B.-to-B. relationships in the banking industry. After a qualitative study, the authors notice that two variables may moderate the development of a relationship strategy: (1) company's size (small firms seem to be less attractive than big firms) and (2) customer's personality (bankers admit that they cannot control this characteristic).

Ricard & Perrien (1996) make the difference between relational and transactional people in order to better allocate the bank resources. For this segmentation, they rely on the customer's personality and on his/her global attitude towards the relationship.

As with [START_REF] Perrien | The Meaning of Relationship Marketing: A Pilot Study[END_REF], [START_REF] Beatty | Customer-Sales Associate Retail Relationships[END_REF] study customer-sales associate retail relationships. They segment customers on the basis of their motivations. Hence, some customers are motivated in their purchases by social elements, (such as discussions, friendship, etc.), while others are more preoccupied by functional elements (such as product attributes, efficient and rapid purchases, etc.). The first category of clients is then considered as relational; the second one is more transactional oriented.

In the same way, Sheaves & Barnes (1996) consider that "a relationship begins only when both parties are interested in forming a relationship. (...) a customer has to be willing to enter the relationship. (...) a firm risks alienating customers if it tries to force a relationship with customers who do not want one, and there may very well be customers who just do not want a relationship or whose definition of a relationship does not match that of the firm". The authors admit that different individuals may have different needs in a relationship; this being a permanent feature of their personality and not only an occasional one. Some customers avoid intimacy while others seek out intimacy with other people and wish to have a close, personal relationship with a firm and its employees. The implication is that the first group of customers is more transactional oriented while the second one is more relational oriented. [START_REF] Barnes | Closeness, Strength, and Satisfaction: Examining the Nature of Relationships between Providers of Financial Services and their Retail Customers[END_REF], who examined the nature of relationships between providers of financial services and their retail customers, also states that "not all customers wish to engage in close relationships". Barnes' quantitative study shows that the relationship between a customer and his bank depends on three factors: (1) the customer's attitude and psychological view of the relationship (intimacy, emotion, strength, intensity, etc.); (2) how the relationship is conducted (content, frequency of interactions, interpersonal contacts, etc.); (3) characteristics of the customer (various demographic and socioeconomic factors). [START_REF] Barnes | Closeness, Strength, and Satisfaction: Examining the Nature of Relationships between Providers of Financial Services and their Retail Customers[END_REF] shows empirically that some long term and/or satisfied customers do not develop close relationships with their bank because they are transactional oriented individuals. As his predecessors, Barnes supports the idea of segmenting markets based on the type of relationship that the customer desires.

Finally, [START_REF] Garbarino | The Different Roles of Satisfaction, Trust and Commitment in Customer Relationships[END_REF] study the relationships of satisfaction, trust and commitment to component satisfaction attitudes and future intentions for the customers of a New York off-Broadway repertory theater company. They consider that "customers vary in their relationships with a firm on a continuum from transactional to highly relational bonds".

The authors show empirically that, for low-relational customers (individual ticket buyers and occasional subscribers), overall satisfaction is the primary mediating construct between the component attitudes and future intentions. For highly relational customers (consistent subscribers), trust and commitment, rather than satisfaction, are the mediators between component attitudes and future intentions. Hence, customers vary in their reactions and relationships with the same service or organization. [START_REF] Garbarino | The Different Roles of Satisfaction, Trust and Commitment in Customer Relationships[END_REF] implicitly suggest that customers' relational versus transactional orientation is therefore based on their own individual personality.

In summary, instead of basing customers' segmentation on relationship and/or service characteristics, [START_REF] Perrien | The Meaning of Relationship Marketing: A Pilot Study[END_REF]), Ricard & Perrien (1996), [START_REF] Beatty | Customer-Sales Associate Retail Relationships[END_REF],

Sheaves & Barnes (1996), [START_REF] Barnes | Closeness, Strength, and Satisfaction: Examining the Nature of Relationships between Providers of Financial Services and their Retail Customers[END_REF] as well as Garabarino & Johnson (1999) rely principally -explicitly or implicitly -on the personality of the customer and the general attitude toward the relationship. We will examine this view in our research.

I.3. Definition of the transactional versus relational customer orientation

Our literature review has shown the development of a need to measure the customer's relational orientation. The following figure summarizes this evolution: All the authors cited above describe implicitly or explicitly the difference between relational versus transactional relational customer orientation, but most of this research is theoretical.

The authors justify the existence of this behavior in different manners (using contextual elements or psychological factor such as customer's personality). They do not give neither a clear definition of this concept nor any way to measure it. [START_REF] Garbarino | The Different Roles of Satisfaction, Trust and Commitment in Customer Relationships[END_REF] give a very succinct definition of relational orientation, classifying customers by differences in their contractual relations (e.g., subscribers or individual theater ticket buyers). In doing so, they draw on [START_REF] Macneil | The New Social Contract, An Inquiry into Modern Contractual Relations[END_REF] and [START_REF] Dwyer | Developing Buyer-Seller Relationships[END_REF]'s previous work.

We propose a more extended definition of relational orientation, based on its antecedents.

Indeed, there are three different manners of measuring a construct: its antecedents, its manifestation, or its consequences. The choice of measuring the concept by its antecedents may be risky, since we need to make sure that we do not forget a dimension.

The customer relational orientation may be perceived as a multidimensional construct: the first dimension is a functional/affective orientation continuum; the second one is a short-term/ long-term orientation continuum.

The first dimension is represented by tangible elements (economic outcomes of transactions such as price) versus emotional elements (psychological variables) -e.g., [START_REF] Grönroos | Service Management and Marketing, Managing the Moment of Truth in Service Competition[END_REF][START_REF] Hakansson | International Marketing and Purchasing of Industrial Goods[END_REF]-. The second one is characterized by the customer's time orientation.

Transactional customers should be more short-term and functional oriented and relational ones should be more long-term and affective oriented. We will return to these dimensions in the scale development presentation. B. field has been defined in this study as organizations with less than 8.000.000 Euros of turnover. These organizations are quite small and decision-making power is assumed to be centralized in the hands of one or a few people at most. These structures are between individuals (for whom the decision process is quite similar) and organizations (for whom the aims are similar). Moreover, the question of SME relational orientation has never been studied. Currently, it is therefore not possible to say that all SMEs representatives are relational oriented or not. Our study will be the first in this field. Conclusions may not be relevant to larger organizations. Nevertheless, it is very important to know this segment in more details as it represents the greatest potential for bank development on the French market.

Short-term

Moreover, Webster (1984) states that there are two kinds of needs which guide the buyer's behavior: personal needs which motivate behavior, and social needs which define the kinds of activities which are acceptable in a social situation. We voluntarily focus on the first type of needs for the reasons explained above.

II.2. Hypothesized scale dimensions

We first developed the scale on literature elements and on an exploratory phase (where 13 dyads were interviewed: 13 SMEs representatives and their bank account managers). The exploratory phase aimed at better understanding the relationship between bank account managers and SME representatives. 43 items were generated for our scale.

Ricard (1995) has done some interesting work in measuring the "sensitivity to a relational approach". She bases her work on [START_REF] Moriarty R | The Management of corporate banking Relationships[END_REF] and [START_REF] Jackson | Construisez des relations durables avec voc clients![END_REF]. Her measuring method is very simple (4 items) and takes into account two dimensions5 . The first one is the importance given by the customer to service quality and relationship quality. The second one is the importance with regards to financial concerns (service fees and interest rates). We consider this scale as a milestone for our scale development. We did not include the interest rate item in our work. In the B.-to-B. context it would have been more relevant to discuss credit conditions (cf. our exploratory phase). Also, on the B.-to-C. market, interest rates concern only a small percentage of the population. Such an element is considered to be more closely linked with exit barriers.

As we have stated previously, two dimensions emerge from the literature examination. The first one is a temporal dimension: [START_REF] Macneil | Contracts: Adjustment of Long-term Economic Relations Under Classical, Neoclassical and Relational Contract Law[END_REF][START_REF] Macneil | The New Social Contract, An Inquiry into Modern Contractual Relations[END_REF] differentiates discrete transactions from relational exchanges along several key dimensions. However, the most important one is linked to the fact that relational exchange develops over long periods of time. In consequence, relational oriented people will highly value long-term perspectives and transactional ones will prioritize current events [START_REF] Bendapudi | Customers' Motivations for Maintaining Relationships with Service Providers[END_REF]. Webster (1984) also emphasizes the importance of time writing that "buyer-seller relationships in industrial marketing develop in the purchasing decision process and continue through negotiation of the sale and consummation of the transaction to post-sales service and repeat orders. (p.52)".

Time orientation can be captured through different measurements such as the importance given to loyal behaviors, stability orientation, and opportunity orientation (which is a shortterm strategy). It was not possible to use the length of the relationship to measure relational orientation since we can consider that somebody entering a new relationship may be relational. He/she could have stayed 20 years in a previous relationship.

Macneil (1980) also emphasizes the importance given to primary personal relations in relational exchanges. In contrast, transactional people are more focused on technical quality (Gronroos, 1990). This concept was hypothesized as being the second dimension moving from outcome oriented people to process oriented people: outcome oriented people value the technical quality (the "what") and process oriented people value the functional quality (the "how" in Gronroos' terminology). [START_REF] Bendapudi | Customers' Motivations for Maintaining Relationships with Service Providers[END_REF] note the importance of the psychological perspective in the relationship. Some authors such as [START_REF] Ganesan | Determinants Of Long-Term Orientation In Buyer-Seller Relationships[END_REF] speak about the affective desire for a relationship to continue and last over a long period of time.

Both the affective and the technical dimensions of the industrial buyer-seller relationship clearly demonstrate that industrial marketing and selling strategies must often be directed towards individual customer organizations and not to mass markets (Webster, 1984). Such evidence indicates a need for personalization of the service delivered to the customer.

III.3. Scale development

We followed Churchill's recommendations for developing measurements of our marketing constructs [START_REF] Churchill | A Pardigm for Developing Better Measures of Marketing Constructs[END_REF].

Four faculty experts judged the relevance of the items to the definition given to the relational orientation. They had to state if they considered the item (1) highly relevant to the concept,

(2) relevant to the concept or (3) irrelevant to the concept. We rejected all of the items having two or more negative evaluations (i.e., irrelevant to the concept).

At first, we tried adapting existing scales to our context (translation from English to French as well as adaptation to the bank industry context). But these scales did not pass the expert examination. For instance, to measure the customer's opportunism orientation (included in the short-term orientation), we adapted a scale proposed by Dwyer & Oh (1987) 6 . This scale was not considered "politically correct" in the French banking industry context.

Seven items came from an adaptation and translation into French of a scale developed by Williams and Spiro (1985) 7 . This scale was developed to measure the affective dimension of customer relational orientation as seen by the seller. This scale was also judged irrelevant to our research context.

Since we could not find any other useful scale, we used our exploratory work to generate complementary items. Two strategies were implemented: when possible, we directly imitated the customer's verbatim. When this was not possible, we reformulated ideas furnished by the customers during our qualitative interviews and identified in the content analysis. The method allowed us to develop an extra 31 items.

We then conducted qualitative pretests on a focus group composed of two former SME representatives, two former bank account managers, as well as on one current SME representative (face-to-face interview 8 ). The scale (along with a complementary 6 α=0.79 7 α=0.89 8 We went to see this person twice, in order to validate changes.

questionnaire) was also sent to three SME representatives for comments and completion of the data. Lastly, representatives from the bank we are working with validated the scale.

Using the experts' judgment and the qualitative pretests, 12 items were included in the first version of the scale plus three items proposed by [START_REF] Perrien | The Meaning of Relationship Marketing: A Pilot Study[END_REF]. As previously stated, the fourth item representing the importance given to interest rates was not included in the analysis. In the B to B questionnaire, this item referred to credit conditions. A qualitative analysis of 30 face-to-face interviews shows that credit condition importance depends primarily on companies' financial health (lack or excess of funds). In more detail: two items represented short-term orientation and three others long-term orientation9 ; three items were originally dedicated to the affective aspect of this dimension and three others to the technical side; and three items were included in the scale which originally come from Ricard's work (1995). These items consider the importance of service quality, of relationship quality, and of prices of service fees in a bank's evaluation.

The same scale was used for both B.-to-B. and B.-to-C. research projects. Nevertheless, some words were changed for synonyms in order to fit with each context common vocabulary.

One item was deleted before the statistical analysis because the interviewers noted some problems in administering the question. In addition, the percentage of non-response was quite high for this particular question. This item was inspired from Ricard's work (1995) and dealt with the issue of meeting his/her bank account manager for reasons other than business.

Respondents often interpreted the question as surprising and negatively viewed it as tempting collision. One must note that all of the interviews, in the B.-to-B. research project, were conducted in a very large city and its close suburbs. Such characteristics may explain the lack of understanding for this question. The phenomena may be more prevalent in smaller towns.

II.4. Results

II.4.1. Exploratory factor analysis

Exploratory factor analysis is useful in scale development. This first step is highly recommended by DeVellis (1995) and [START_REF] Churchill | Marketing Research: Methodological Foundations[END_REF]. It constitutes a good technique for reducing a large number of indicators to a more manageable set. "It is particularly useful as a preliminary analysis in the absence of sufficiently detailed theory about the relations of the indicators to the underlying constructs" (Gerbing & Anderson, 1988, p. 189). A typical usage of exploratory factor analysis is to factor an overall set of items and then construct scales on the basis of the resulting factors loadings. [START_REF] Churchill | A Pardigm for Developing Better Measures of Marketing Constructs[END_REF] also suggests that factor analysis can be used to suggest dimensions. The second scale did not start at "Not important at all" because qualitative pretests had shown that nobody would choose this answer.

II

Factor analysis

The factor analysis (SPSS 8.0) used 117 questionnaires. We originally had 138 questionnaires but 21 of them included non-responses. We chose to eliminate them instead of taking the average answer on the item ('exclude cases listwise') as the remaining number was still sufficient to implement the analysis (> to 5xN, N = number of items in the original scale).

In order to insure the relevance of the method used in our data, two tests were conducted:

• Firstly, we used the Kaiser, Mayer & Aklin's test to check if a factorial analysis was relevant. The result must be between .5 and 1. We calculated .723. • Secondly, Barlett's test was conducted and showed significance.

We used a factor analysis (principal component analysis) in order to derive a small number of items and to maximize the explained variance [START_REF] Darpy | La procrastination du consommateur: Une contribution à l'explication du report d'achat[END_REF].

Since the dimensions were hypothesized as dependent, we had recourse to an oblimin rotation.

After 5 iterations, the pattern matrix was acceptable, as well as the communalities -since all the factors were higher than .5 as recommended by Evrard & al. (1993)-. All of the results are presented in Annex 2.

Dimensions

DIMENSION 1 (QS, QR, A2) 11Items brought together by this component deal with quality, the importance of the role played by the bank account manager, and his/her personality. The emphasis is placed on the relationship. This dimension is linked to affectivity in the relationship. The presence of the service quality in this dimension is easily explained by the fact that interviewees perceived service as something delivered by a person. Because of the intangibility of service, they identified service delivery as the person rendering the service. The third component regroups items related to the customer's short-term orientation. This dimension represents the importance given by customers to competition and the sensitivity to promotions. Customers who have a high score in this dimension are those who highly value more short-term benefits.

DIMENSION 4 (T3, F1, LT3) This fourth component is the most difficult to interpret. At first glance, they seem to be very inconsistent with each other. But if we consider their possible links, this component has some relevance. Without item F1, it could mean that loyalty programs are a way to get personalized service. Considering now all three items: F1 is related to service fees; usually customers become members to get better prices or other advantages. This remark was often mentioned in the interviewers' comments. Moreover, a qualitative analysis of the interviews shows that a majority of respondents considered membership as a long term-commitment. This long-term commitment is for them a sine qua non condition to be known by the bank and its employees, which is in itself a condition in obtaining tailored services.

Scale reliability

Cronbach's alphas are fine for the three first dimensions (cf. Table 2). The fourth dimension is less satisfactory.

Nunnally (1967) suggests that in the early stages of basic research, reliabilities of .5 or .6 are sufficient. We are slightly below this recommended level for the fourth dimension. This is not very surprising since this dimension is the most difficult to interpret. .4037 without item F1

Scale validity

They are two types of validity: nomological and trait validities (Peter, 1981).

Trait validity:

Convergent validity: it is not possible to measure any convergent validity since we did not have any other similar scale measuring the same construct. Further investigation is needed in order to test discriminant validity.

Nomological validity:

It is based on the "explicit investigation of constructs and measures in terms of formal hypothesis derived from theory; [… it is] primarily 'external' and entails investigating both the theoritical relationship between different constructs and the empirical relationship between measures of those constructs" (Peter, 1981, p. 135).

In order to guarantee this validity, we asked different experts to evaluate the relevance of items to the constructs.

II

Factor analysis

The factor analysis (SPSS 8.0) used 75 questionnaires.

The Kaiser, Mayer & Aklin's test was .699, and the Bartlett's test showed significance.

We also used in this context a factor analysis (principal component analysis) as well an oblimin rotation (on the assumption of dependence between the different dimensions).

After 3 iterations, the pattern matrix was acceptable as well as the communalities. All of the results are presented in Annex 3. The importance given by customers to competition, to sensitivity to promotions as well as the importance of the bank account manager are included in this third dimension. They represent the short-term aspect of the scale. In fact, to ask for more information, to be sensitive to promotions or to consider the account manager as non essential mean that the customer is not so far attached to the bank and to its employees.

Dimensions

DIMENSION 4 (LT1, LT2, T3, A3)

This dimension reflects stability. It includes the attachment to the account manager, the propensity to loyalty, the willingness to get personalized service and the importance of a good relationship. All these elements characterize a long-term commitment of the client.

Scale reliability

Cronbach's alphas are satisfying for all four dimensions (Cf.

Scale validity

The same criteria as for the B.-to-B. context have been applied.

III. Discussion

This study is a first step in the elaboration of a transactional / relational orientation scale.

Instead of having two dimensions, it appears that we have four (short-term, long-term, affective and functional). Indeed, when we have a look at scatterplots, we see that the affective dimension is not totally exclusive from the technical one, and that the short-term orientation is not totally exclusive from the long-term one. Therefore, they are not two ends of the same continuum.

The four dimensions are the same in both contexts but do not exactly bring together the same items. These differences reflect some characteristics of each context. In summary, the four dimensions obtained in both contexts are close to what was expected.

These dimensions can be interpreted in the same way even if they do not contain exactly the same items. This difference does not mean that private clients are more relational than professional ones (or conversely) but mean that they have different definitions of what a relational or a transactional orientation is. The main conclusion is that we need two different tools reflecting these differences. Indeed, it appears that SME representatives give value to relationships but are more rational than private customers.

IV. Further research…

This work needs further research. First of all, it needs a confirmatory analysis. AMOS would allow this work, but we need to collect more data in order to have larger samples.

At present, it is still too early to develop a norm, strictly defining who is relational and who is not. Our samples are too small and it is only the first development of such a scale. In the short-term, we will use the scale in the following way: we will only use two groups in our studies. The first group will be composed of the third of the sample having the smallest score on the scale. The second group will be composed of the third of the sample having the highest score on the scale. In this way, it will be possible to identify and analyze differences in behaviors due to relational/ transactional orientation.

However, using this method, we do not take into account people who are not strictly relational or strictly transactional. In fact, we consider, in our research, customers orientation as a personality characteristic based on their affective, technical and time orientations; then, it is not a rational and simple concept. Some individuals may be relational for a particular banking product or service and transactional for another one. Therefore, further empirical research should be conducted to study this third group of customers.

As we can see, this study shows that not everybody is relational oriented. This may be true in

  Figure 1 -A need for an intrument to measure relational orientation

Figure 2 -

 2 Figure 2 -Relational orientation dimensions

  .4.1.a. Field 1: Business-to-Business Context Data was collected from 138 face-to-face interviews. The interviews were one hour long since this study was part of a larger research program. All of the items were presented in the middle of the questionnaire. Therefore, there was no lassitude effect in the answers.A scale was shown to respondents as follows 10 :

  brings together items related to technical characteristics. Products and financial services are prevalent to human aspects of the relationship. In other words, transactions are only based on products and services. DIMENSION 3 (CT1, CT2)

  mailed to a large French bank customers all around the country. 93 questionnaires were returned. 18 of them included non-responses. They were eliminated from the factor analysis. The questions related to the 'relational versus transactional orientation scale' were part of a broader questionnaire. The Likert scale used in the B.-to-B. context was also proposed to the B.-to-C. segment.

  by this component deal with the bank account manager's personality and the customer's propensity to discuss with his/her bank account manager. Both items strongly reflect the affective dimension of the scale: they are closely linked with the individuals' personality characteristics and with interactions. DIMENSION 2 (QS, F1) This component regroups two items related to service quality and service fees. They reflect the technical dimension of the scale. Indeed, service quality in the B.-to-C. French banking industry context is considered as a basic element and not as a "plus". Service fees naturally represent a technical characteristic. DIMENSION 3 (CT1, CT2, T2)

  B.-to-C. customers seem to be more human relation oriented while B.-to-B. customers appear to be more rational. For instance, the items which characterize the long-term dimension in the B.-to-C. context seem to be stronger than the ones characterizing the B.-to-B. environment. Moreover, items LT1, LT2 and A3 in the B.-to-C. study reflect the individuals personality whereas items T3, F1 and LT3 in the B.-to-B. research project represent more the relationship functioning. Concerning the short-term dimension, results are quite similar: items CT1 and CT2 are included in both contexts. This dimension has an extra item in the B.-to-C context: T2. This reinforce the short-term aspect of the dimension. The technical dimension of the scale is different from one context to the other. B.-to-C. customers give more attention to service quality and service fees. B.-to-B. clients base more their evaluation on the basic offer of the bank and on the role (essential or not) played by the bank account manager. Items QS and F1 (B.-to-C.) focus on the exchange process while items T1 and T2 (B.-to-B.) focus on the exchange object. In fact, T1 and T2 reflect the prevalence of the basic offer of the bank on the intervention of the account manager. Finally, as well as for the long-term dimension, items representing the affective dimension in the B.-to-C. context seem to be stronger than the ones in the B.-to-B. environment. Indeed, item A1, relating to propensity to discuss with the account manager, reinforce this affective aspect. Comments collected during the interviews may explain the presence of the QS item in the B.-to-B. context: SME representatives very often assimilated service quality to relationship quality.

Table 1 .

 1 Implications of constraints and dedication for relationship marketing

		Level of dedication
		Low	High
	Low	Objective : Relationship	Objective : Relationship
		formation	stability
	Level of constraints
	High	Objective : Relationship	Objective : Relationship
		enhancement	nurturing

Source : Bendapudi et Berry (1997) -Simplified scheme

Table 2 -

 2 Cronbach's alphas

	Dimension	α
	1	.6943
	2	.5238
	3	.5869
	4	.4706	.4690 without item LT3

Table 3

 3

	)

  They represent small organisations where the decision-making power is centralised in the hands of one or two persons. Another area for further research is to study customers' orientation with a sample of larger companies. Results may be different.Finally, this research has been conducted in the French banking industry, which certainly presents some particular national characteristics. It could be interesting to conduct it in the banking industry of others countries. Cultural differences may affect the relational versus transactional orientation of customers. It could be also possible to conduct this study in other fields of research such as insurance or any other service sectors. People may react differently according to the used service.Nevertheless, this work is a first step in the evaluation of relational/transactional orientation. Such an evaluation is of importance in both B.-to-B. and B.-to-C. contexts in a managerial perspective. Indeed, it will allow the segmentation of marketing strategies -and particularly relationship marketing strategies -according to customer's expectations as well as a better allocation of resources. Therefore, it represents a valuable segmentation tool.

	ANNEX 1 -SELECTED ITEMS
	Dimension Variable	B.-to-B. context items	Variable	B.-to-C. context items
	Affective	• QS	• When you evaluate your
			bank, the service quality is…
			(not very important;
			extremely important)?
		• QR	• When you evaluate your
			bank, the relationship quality
			is… (not very important;
			extremely important)?
		• A2	• For us, our bank account
			manager's personality is at
			least as important as the
			bank's customer services

the B.-to-B. context because we took in our samples only SME's.

Does not exist?

Grönroos' terminology (1990)

The exploratory phase as well as the study on SMEs have been conducted by Prim, for more information, please contact this author.

α=0.7 for the first dimension and 0.57 for the second one.

The number of items was limited since the questionnaire including this scale was long (one hour in length).

Translated from French

Items are presented in annex 1.

Items are presented in Annex 1.

PETER P.J. (1981), Construct Validity: A Review of Basic Issues and Marketing Practices, Journal of Marketing Research, Vol. 18, pp. 133-145. REICHHELD F. & SASSER E. (1990-91), Les clients d'hier font les profits de demain, Harvard/L'Expansion, Hiver. RICARD L. & PERRIEN J. (1996), Les facteurs explicatifs et normatifs d'une approche relationnelle: La perception des clients organisationnels, Association Française de Marketing, Vol.12, Poitiers. RICARD L. (1995), Les facteurs explicatifs et normatifs d'une approche relationnelle, PhD Dissertation, Université du Québec à Montréal, Canada. SAXE R. & WEITZ B.A. (1982), The SOCO Scale: A Measure of the Customer Orientation of Salespeople, Journal of Marketing Research, Vol.19, August , pp. 343-351. SHEAVES D.E. & BARNES J.G. (1996), The Fundamentals of Relationships : An Exploration of the Concept to Guide Marketing Implementation, Advances in Services Marketing and Management, Vol.5, pp.215-245. WEBSTER F.E. (1984), Industrial Marketing Strategy, John Wiley and Sons, 2 nd Ed. WILLIAMS K.C. & SPIRO R.L. (1985), Communication Style in the Salesperson-Consumer Dyad, Journal of Marketing Research, Vol. 12, November, pp. 434-442.

Component correlation matrix


Jean-Marc Richard
email: j-m.richard@ipnl.in2p3.fr

Exotic hadrons and Steiner-tree confinement * †

Keywords: numbers: 12.38.Aw, 12.39.-x, 14.20.Pt, 14.40.Rt Quark dynamics, exotic hadrons, Steiner trees

After a brief review on exotic hadrons, some recent results are presented about multiquarks bound by a minimal path that generalizes the linear potential in quarkonium.

I. INTRODUCTION

The pentaquark episode is probably over, though some indications persist about possible exotic baryons [1,2]. It started with a speculation guided by chiral dynamics [3], and a search by Nakano [4], against the fashion of that time. The announcement in 2003 of positive results created a wave of investigations. Experimental groups realized they had data on tapes, that nobody had the curiosity to analyze. Theorists also discovered that instead of refining the estimate of the properties of ordinary hadrons, they could use their tools for looking at exotic configurations. Nowadays, the multiquark dynamics is studied by lattice QCD, sum rules, and even AdS/QCD.

For years, the possibility of multiquarks was mainly discussed in the framework of constituent models already fitting ordinary mesons and baryons. There is a non-trivial technical difficulty when the number of quarks increases from N = 2 or N = 3 to N > 3. But the main problem consists of extrapolating the interaction towards a domain where new color coupling can be envisaged. In the past, the most current recipe consisted of a pairwise interaction with color factors. This is justified for the short-range part, but not for the confining part, except when (N -1) of the constituents are closely clustered far from the N th one. More realistic models have been proposed for many years, and they are now supported by lattice QCD. The linear interaction in quarkonium, understood as a flux tube of minimal length, is generalized as a Steiner-tree linking the constituents through the minimal path. I shall present a review of the recent results obtained using this new confining interaction.

II. BINDING MECHANISMS FOR MULTIQUARKS

a. Duality The first serious argument in favor of multiquark hadrons was an indirect one, in the context of duality. For a review, see, e.g., [5]. To get consistency in the description of hadronic reactions, a duality principle was imposed relating s-channel and t-channel exchanges. In baryon-antibaryon scattering, the partners of ordinary mesons are mesons made of two quarks and two antiquarks, preferentially coupled to baryon-antibaryon pairs. In the late 70s and the 80s, such new mesons were tentatively seen in proton-antiproton experiments, but none of baryonium candidates were confirmed in further experiments using better antiproton beams.

b. Light scalar mesons For light mesons, especially scalars, creating a quark-antiquark pairs does not cost more than providing the existing pair with an orbital excitation [6,7]. This was the beginning of the saga of scalar mesons, which also includes flavor excitation, hybrids, glueballs and various mixing schemes among them. This subject has been discussed in many contributions to this conference.

c. Chromomagnetism In QED, the Breit-Fermi term V SS ∝ i<j δ(r ij ) σ i .σ j accounts for the observed hyperfine splittings (for the positronium and other positronic atoms, the annihilation diagram also contributes). The analog in QCD reads [8] V SS ∝ i<j δ(r ij ) λi . λj σ i .σ j , considered either phenomenological, or given by one-gluon-exchange. There is also a 1/(m i m j ) dependence that reduces the effect for heavy quarks.

At first sight, the color factor λi . λj simply induces a factor 1/2 for baryons as compared to mesons, and helps to fit the data. However, when combined with the spin factor, it gives a remarkable coherence in some configurations, as first noted by Jaffe [9]. In the SU(3) f limit, the expectation value λ i .λ j σ i .σ j is twice larger for (uuddss) with spin J = 0 than for the ΛΛ dissociation threshold. For comparison, remember that the positronium molecule experiences a Coulomb potential i<j g ij /r ij with the same cumulated strength g ij = -2 as for its threshold made of two positronium atoms. In pure spin-spin model without color, V SS ∝ σ i .σ j , a J = 0 tetraquark would receive a cumulated strength i<j σ i .σ j = -6, whereas each scalar meson of its threshold experiences i<j σ i .σ j = -3, and thus there would be no obvious excess of attraction.

The di-lambda was first estimated to be deeply bound, since the orbital matrix element δ(r ij ) was assumed to be the same as for ordinary baryons. This assumption, and that of SU(3) f symmetry, turn out to give too optimistic estimates. The various corrections work against the stability of the di-lambda [10][11][12][13].

Other configurations receive a coherent attraction of chromomagnetic forces [14], in particular, the 1987-vintage version of the pentaquark [15][16][17]. But, again, it turns out very difficult to build a realistic wave function that gives enough short-range correlation for all pairs. d. Hadronic molecules It has been often stressed that the conventional strong interactions, which build the deuteron out of two nucleons, can produce other bound states or resonances. There are many contributions to this conference. In particular, a DD * composite was predicted, mainly due to one-pion-exchange. See the review [18] for references to the original papers. So, when the X(3872) was discovered, it was greeted as a success for this approach. Unfortunately, some of the latest measurements suggest a radial excitation of charmonium, and there is no obvious way to combine the two pictures consistently (see the section on mixing).

In the past, we learned to be careful with the molecular interpretation of the hidden-charm states. When higher ψ resonances were found, theorists were puzzled by the anomalies in the relative decay rates into DD, D * D + c.c. and D * D * , and a molecular interpretation was suggested [19] (see, also, [20]). But the branching ratios were later understood from the node structure of the decaying states [21][22][23].

FIG. 1: Left: Mixing of (D D) and (cc) in a simple local model. The solid lines represent the reduced radial wave function for the main (D D) and the small (cc) components, as obtained from an actual coupled-channel calculation. The dashed lines correspond to the naive mixing scheme of Eq. ( 1), with neighboring unperturbed states, and θ adjusted to reproduce the same normalization for (cc). Note that the coupled-channel calculation does not produce any node in the (cc) sector. Units are GeV 1/2 for u(r) and GeV -1 for r. Right: Reduced radial wave functions for the (cc) (blue) and (D D) (red) components in the same coupled-channel model, for the ground-state (dotted lines), first (dashed lines) and second (solid lines) excitations.

e. Mixing dynamics This is a current trend in the physics of hadrons: if a first model describes satisfactorily some properties of a hadron, but fails for others that are accounted for by a second model, a tantalizing improvement of the picture consists of writing the wave function as

ψ = cos ϑ ψ 1 + sin ϑ ψ 2 , (1)
and this can be extended as to include more components. This game has been played endlessly for scalar states involving radial excitations, hidden strangeness, glueballs and hybrids. In the case of the X(3872), ψ 1 could be a DD * +c.c. molecule, and ψ 2 a charmonium cc(2P ) with the same quantum numbers and a radial excitation. However, the dynamics of coupled channels dictates that if cos ϑ ψ 1 is the leading term, the small admixture sin ϑ ψ 2 is not very much governed by the diagonal interaction in the second channel. Instead it is given by a folding of the leading component and the transition operator. In particular, if the former is nodeless and the latter smooth, a node hardly appears in ψ 2 .

A toy model illustrating this property is an S-wave analogue of the X(3872) system, with a (DD) (the difference between D and D * is ignored) channel weakly bound by a Yukawa potential, and a (cc) channel with a standard Coulomb-plus-linear potential, such that before mixing, the threshold is at 3.8 GeV, (DD) at 3.77 GeV and ψ(2S) at 3.57 GeV. The mixing is crudely mimicked by a local interaction with a Gaussian shape. The mass of the (DD) is slightly shifted (more details will be given elsewhere), and the wave function acquires a (cc) component, displayed in Fig. 1, which is nodeless.

The current belief is that the eigenstates mix unchanged, dominantly by affinity of neighboring unperturbed energies, once a gate is open between the two channels. This is inspired by the denominator in the first order correction to a wave function within perturbation theory, namely, in a obvious notation,

φ i = φ (0) i + j =i φ (0) i |V |φ (0) i E (0) i -E (0) j φ (0) i + • • • (2)
However, the node structure of the φ (0) i sometimes gives more drastic constraints. Another example is S-D mixing in ordinary charmonium dynamics. It is almost ever considered that ψ(1D) preferentially mixes with ψ(2S) which is very close. But when one actually computes the small S-wave admixture in ψ(1D) using an explicit tensor force with suitable regularization, one finds a nodeless radial function for the admixed S-component in the ψ(3770). Note that S-D mixing can be calculated analytically for the muonium (µ + e -) and the approximations can be tested there. In the above model, the ground-state has two nodeless components, with the (cc) one dominating. The second state has two nodes, one in the main (cc) channel, and another in the small (D D) admixture, as seen in Fig. 1. The third one has no nodes. Many variants are possible, if the parameters are modified.

Back to X(3872), the ψ(2S) to ψ(1S) ratio of radiative decays has to be studied within a consistent picture involving probably several Fock-space components, cc, ccq q, etc. This requires a modeling of the transition operator creating of annihilating a pair of light quarks, and a few calculations.

A consistently-managed mixing scheme can give interesting results. An example is the celebrated Cornell picture of (cc), supplemented by coupling to real of virtual D ( * ) D ( * ) (including D s ) decay channels [23]. Before the discovery of the η c (2s), this model predicted a substantial reduction of the ψ(2s)η c (2s) splitting [24], as compared to simple potential models. The same effect could explain why the Υη b splitting is slightly larger than estimated by most authors, if the reduction due the meson-meson channels is than for J/ψη c . Other interesting treatments of the configuration mixing can be found, e.g., in [25][START_REF] Bali | 27 th Int. Symp. Lattice Field Theory[END_REF][START_REF] Matheus | [END_REF].

f. Diquark clustering The concept of diquark is very useful in several branches of particle physics, for instance to analyze the baryon-to-meson ratio in multiparticle production. It has been introduced rather early in spectroscopy, see, e.g., Ref. [28] for a review. However, some of the pioneering works are sometimes ignored in recent rediscoveries of the diquarks. A first problem to which diquarks provide a sufficient solution, is why Regge trajectories (squared mass M 2 vs. spin J) are linear with the same slope for baryons as for mesons. For two-body systems, the linear character is reproduced in many pictures, e.g., H 2 = (m 2 + p 2 i ) 1/2 + λr 12 . Thus the equality of slopes comes automatically if the quark-diquark baryons, [q -(qq)], are the partners of the quark-antiquark mesons, [qq]. However, it is not necessary to introduce diquarks by hand to obtain the equality of slopes. In the symmetric quark model, the baryon analogue of

H 2 reads H 3 = (m 2 + p 2 i ) 1/2 + V 3 , where V 3 is λ r ij /2
or the Y -shape potential (discussed below). The Hamiltonian H 3 , for the large angular momentum, gives linear Regge trajectories for baryons, with the same slope as mesons. There is a dynamical clustering, or, say, a spontaneous breaking of symmetry when J increases [29], as illustrated in Fig. 2.

The best argument in favor of the quark-diquark model comes perhaps from the problem of missing resonances. In a recent review on baryons [30], very few states are tentatively interpreted with both degrees of freedom (i.e., Jacobi variables x and y) excited. On the other hand, many states predicted in the three-quark model are not observed, and this was the subject of contributions to this Conference. The most striking state with double FIG. 2: Schematic picture of a rotating baryon at low angular momentum J and higher J.

excitation in the three-quark model is

Ψ = x × y exp[-a (x 2 + y 2 )/2] , (3)
(here in the case of harmonic interaction, but a state with the same symmetry exists for other confining potentials). For experts, it is named the [20, 1 + ] multiplet. Its fully antisymmetric orbital function, with N = 2 degrees of excitation, is associated with an antisymmetric spin-isospin wave function, and an antisymmetric color wave function. It is absent in the quark-diquark picture. Experimentally, it is not (yet?) seen.

If the diquark model is taken seriously, it can be extrapolated outside the framework of baryon spectroscopy. We have seen that the late baryonium states have been described as a diquark and an antidiquark. More recently, cq or cs diquarks and the associated antidiquarks were introduced to describe the X, Y or Z states seen in the hidden-charm spectrum. See, e.g., [31]. The light pentaquark was also described as [(qq) -(qq)q] [32].

Obviously, the Pandora box syndrome becomes threatening here too. In particular, three diquarks can well build a dibaryon. It should be checked whether in models describing the Y mesons as (cs) -(cs), the configuration (cs) 3 is not below the threshold for (sss) + (ccc), since it would be embarrassing to pay the price of a very exotic dibaryon to explain the Y meson. Years ago, a light dibaryon (or "demon deuteron" ) was shown to be a consequence of the diquark model [33]. 1g. Flavor symmetry breaking and chromoelectric binding We adopt here the language of potential models but we believe that the results are much more general. The main advantage of potential models is the possibility of switching on or off some contributions to single out the most effective one for binding.

A remarkable property of the spin-independent interaction among quarks is flavor independence, which induces interesting symmetry breaking effects.

Remember that symmetry breaking tends to lower the ground-state energy. The simplest example is h = p 2 + x 2 + λ x in one-dimensional quantum mechanics, with a ground state energy e(λ) = 1λ 2 /2 which is always below e(0). But this is very general. If

H(λ) = H even + λ H odd , (4)
the variational principle applied to H(0) with the even ground state Ψ(0) of H even as trial wave function gives

E(λ) ≤ Ψ(0)|H(λ)|Ψ(0) = E(0) . (5)
One can apply this result to few-body systems with a variety of symmetries for which the labels "odd" and "even" make sense, in particular particle identity and charge conjugation.

But stability is a competition between a configuration with collective binding and another configuration where the system is split into separate decay products. The threshold also benefits from the symmetry breaking, and very often more! In this case, stability deteriorates, though the energy of the compound configuration decreases. For instance, consider the barely bound (e + , e + , e -, e -) molecule, or any rescaled version with the electron mass replaced by another mass µ, and move to configurations involving two different masses. Then it is observed, and proved, that:

• for (M + , m + , M -, m -): binding deteriorates and is lost for M/m 2.2 [34],

• for (M + , M + , m -, m -): the binding is improved.

But the Coulomb character matters little. What is important, is that the potential does not change when the masses are varied. Hence, a similar behavior is observed for any fourbody problem with flavor independence. The splitting (the potential V is assumed to be symmetric under charge conjugation, and independent of the masses)

H(M, M, m, m) = H(µ, µ, μ, μ) + 1 4M - 1 4m (p 2 1 -p 2 2 + p 2 3 -p 2 4 ) , (6)
implies for the ground state

E(M, M, m, m) ≤ E(µ, µ, μ, μ) , 2 µ -1 = M -1 + m -1 , (7)
but, meanwhile, the threshold energy remains constant, as (M, m) and (µ, μ) have the same reduced mass. So the stability is improved. Explicit quark-model calculations have been carried out to illustrate how this favorable symmetry breaking works with flavor-independent potentials. The corresponding fourbody problem is rather delicate, as most other four-body problems. Remember that after Wheeler's proposal in 1945 (the paper was published somewhat later [35]) that the positronium molecule might be stable, a first numerical investigation by Ore [36] concluded that the system is likely unstable, but the following year, Hylleraas and the same Ore published a beautiful analytic proof of the stability [37].

In current quark models, the main conclusion is that binding a doubly-flavored tetraquark requires a large mass ratio, usually (bbq q) or (bcq q). However, a more sophisticated calculation by Janc and Rosina [38] found (ccq q) barely bound. See, e.g., [39] for a detailed survey of the situation.

III. STEINER-TREE MODEL OF CONFINEMENT

It should be acknowledged, however, that these early constituent-model calculations suffer from a basic ambiguity: how to extrapolate from mesons towards multiquarks. The usual recipe is

V = - 3 16 i<j λ(c) i . λ(c) j v(r ij ) , (8)
which is presumably justified for the short-range part, but not for the long-range part, except for very peculiar spatial configurations. In (8), the normalization is such that v(r) is the quark-antiquark interaction in ordinary mesons. Strictly speaking, ( 8) holds for a pairwise interaction with color-octet exchange. Clearly color-singlet exchange cannot contribute to confinement, otherwise everything would be confined together, but color-singlet exchange can contribute to short-range terms. Moreover, there are very likely three-body and multibody forces in baryons and multiquarks.

In the case of baryons, it was suggested very early [40,41] that the potential generalizing the linear confinement of mesons is

V Y = σ min J 3 i=1 r iJ . (9)
This was often rediscovered in the context of models (adiabatic bag, flux tubes), or in studies dealing with the strong-coupling regime of QCD [42]. Estimating the baryon energies and properties with the potential ( 9) is a very interesting 3-body problem. However, the results differ little from these obtained using the color-additive rule, which for baryons reduces to the "1/2" rule, namely

V 3 = σ 2 (r 12 + r 23 + r 31 ) . (10)
This Y -shape interaction has been generalized to tetraquarks. At first, this looked as an astute guess, but it was later endorsed by detailed lattice QCD [43], including the interplay between flip-flop and connected Steiner tree. See, also, [44] for a study within AdS/QCD. The confining potential reads

U = min {d 13 + d 24 , d 14 + d 23 , V 4 } , V 4 = min s 1 ,s 2 ( v 1 s 1 + v 2 s 1 + s 1 s 2 + s 2 v 3 + s 2 v 4 ) , (11)
corresponding schematically to the flux tubes in Fig. 3.

A first study of the tetraquark spectrum with this potential concluded to the "absence of exotics" [45], but a re-analysis by Vijande et al. [46] with a better wave function, indicated that this potential, if alone, and free of constraints due to the Pauli principle, gives stability for the equal-mass case (qq q q), and improved stability for the flavor asymmetric (QQq q). It remains to analyze how this stability survives antisymmetrization, short-range terms in the potential, relativistic effects and spin-dependent corrections. This is however, very encouraging.

Two developments came. First, a better understanding (at least by physicists) of the Steiner trees, with efficient algorithms [47] to compute them, and novel inequalities [48]. For instance, in a Steiner tree, a set of point can be replaced by its associated torroïdal domain, For instance, in the baryon Y -problem, the continuous minimization over the location of the Steiner point s can be replaced by a discrete maximization: the desired Y -shape length, sv 1 + sv 2 + sv 3 in Fig. 4 is the largest of the two distances sw 3 and st 3 , where the points w 3 and t 3 , named the Melznak points or torroïdal domain of {v 1 , v 2 }, form an equilateral triangle with v 1 and v 2 .

FIG. 4: The continuous minimization over the location of s is replaced by the discrete maximum max { sw 3 , st 3 }, where w 3 and t 3 make an equilateral triangle with the quarks v 1 and v 2 . Here, V 3 = sv 1 + sv 2 + sv 3 = v 3 w 3 . The symmetry restoration is reminiscent of the construction of Napoleon's theorem.

This property, and the interesting symmetry restoration (even for an asymmetric triangle, the flux tubes from the junction to the quarks make 120 • angles in Fig. 3) are related to the theorem by Napoleon (see Fig. 4): if one starts from an asymmetric triangle v 1 v 2 v 3 and builds an external equilateral triangle such as v 1 v 2 w 3 along each side, the centers of these auxiliary triangles form an equilateral triangle.

The analogue for a planar tetraquark is

V S = s 1 v 1 + s 1 v 2 + s 2 v 3 + s 2 v 4 = w 12 w 34 , (12)
and is illustrated in Fig. 5: the length of Steiner tree linking the quarks v 1 and v 2 to the antiquarks v 3 and v 4 via the junctions s 1 and s 2 is he distance between the two Melznak points w 12 and w 34 .

In space, one gets the problem pictured in [48]: the auxiliary points w 12 and w 34 are located on a circle of axis v 1 v 2 (resp. v 3 v 4 ), and estimating the minimal Steiner tree can be shown to be equivalent to finding the maximal distance between the two circles [48]. This is a standard problem in computer-assisted geometry, as applied, e.g., in the cartoon industry.

Then you can derive inequalities on the Hamiltonian, and recover rigorously in some limiting cases the stability established by numerical methods.

The disappointing observation, however, is that the dynamics is dominated by the simple flip-flop term, and the most interesting connected Steiner tree plays a relatively minor role.

The exercise can be repeated for the pentaquark, using the linear model with minimal cumulated length, A simple variational calculation gives stability at least for (qqqqq), and (Qqqqq) and (qqqqQ) where m(Q) ≫ m(q) [49]. The other mass configurations remain to be studied.

V P = min(V ff , V St ) , V ff = min i [r 1i + V Y (r j , r k , r ℓ )] , V St = connected
This proliferation of stable states in the minimal-length model becomes embarrassing. Very likely, the dibaryon will also be found stable. If one believes into this confinement, this means that the role of the neglected effects should be investigated with care, in particular, the short-range part of the interaction (Coulomb-like forces) and the antisymmetrization of identical quarks. If the constraint of antisymmetrization turns out the main obstacle to multiquark stability, then exotic hadrons have to be searched in configurations with quarks of different flavors.

IV. CONCLUSIONS

The problem of multiquark binding is now addressed very seriously with QCD sum rules, Lattice QCD and even AdS-QCD. These ambitious but delicate approaches have first confirmed some results that were previously obtained empirically, such as the Steiner-tree structure of the linear term of the quark interaction in the static limit.

The constituent quark model remains a valuable tool of investigation, to detect the most interesting configurations and to analyze the role of the different pieces of the dynamics. In the case of mesons or baryons, the constituent models have been refined over the years, to include relativistic effects, coupling to the continuum, etc. The case of multiquark is of course much more delicate, with the mixing of confined channels and hadron-hadron components probably more crucial to build a reliable wave function.

On the experimental side, it is hoped that the future collider experiments will devote a reasonable amount of time to search for exotics with heavy flavor. As shown by B factories, there is a very good potential of discoveries in hadron physics within experiments primarily designed for studying other aspects of particle physics.

FIG. 3 :

 3 FIG. 3: Confinement of mesons and baryons, and tetraquarks. The minimum over the quark permutations gives the flip-flop potential. For the tetraquarks, the minimum is taken of the flipflop (left) and Steiner tree (right) configurations

  Steiner tree , (13) the latter, V St , being shown in Fig.6(left).

FIG. 5 :FIG. 6 :

 56 FIG.5:The length of the Steiner tree is the distance between the vertices making an external triangle in the quark and in the antiquark sector.

There is an error in[33] about the quantum numbers of the orbital wave function, but this does not remove the issue of dibaryons in diquark models.