1. 1 CONFINING INTERQUARK POTENTIALS FROM NON ABELIAN GAUGE THEORIES COUPLED TO DILATON Mohamed CHABAB LPHEA, FSSM Cadi- Ayyad University Marrakech, Morocco MENU2004@ Sep. 02, Beijing

2. 2 Part I Quark Confinement  Low energy effective models: Color dielectric models Constituent models Dual Landau-Ginzburg Model Extension of Gauge theories  Dilatonic dof Dilatonic Yang-Mills theories with stable, finite energy solutions also, Dilaton dof  Topological structure of the vacuum

3. 3 Our work: derivation of a new family of confining interquark potentials Recall: Dilaton is an hypothetical scalar particle string theory & Kaluza-Klein theories spectrum strength of the gauge coupling Dick Model (97’) new confinement generating mechanism V (r) = Coulomb phase+ Confining phase With main features of QCD: quark confinement Objective: String inspired effective theory

4. 4 >> The model Consider the general Lagrangian, point like static Coulomb source coupling function: In string theory In Cornwall-Soni In Dick model

5. 5 (important formula) The equations of motion,

6. 6 The interquark potential is then, Note that, ( the chromo-electric field) (the effective charge) Quark confinement if: r  lim r F -1 (  (r)) = finite

7. 7 The equation becomes: >> Solving the equations of motion: fix two of (new)

8. 8 Large distance behavior of  (r) - solution in the asymptotic regime - Therefore the potential >> Family of confining interquark potentials if >> Moreover, if Criterion of Seiler

9. 9 These phenomenological potentials gained a theoretical basis Some specific values of n, Cornell potential Song-Lin & Motyka-Zalewski potentials Turin potential Martin’s potential Confinement in our model appears for nn, 1 1 3 

10. 10 Conclusion Popular phenomenological potentials gained credibility since they emerge from a low energy effective theory String inspired effective gauge theory Massive dilaton and new coupling function found a family of electric solutions Confinement in our model appears for nn, 1 1 3 

11. 11 Part II Spectroscopy

12. 12 where For statesof orbital angular momentum l, define the reduced radiale wave function: Then, the equation becomes,

13. 13 Procedure of SLET: Shift the origin of the coordinate x And expand:

14. 14 Our equation resembles 1d anharmonic oscillateur then the meson mass is

15. 15 Dick interquark potential V D (r) ANALYSIS: Five inputs parameters m c, m b, m, f, a s

16. 16 Word average experimental value and We obtain For:

17. 17 m and f free parameters in our analysis Best fit with the experimental data :

18. 18 energy levels RESULTS energy levels

19. 19 energy levels

20. 20 Some references R. Dick, Eur. Phys. J. C 6, 701 (1999); Phys. Lett. B 397, 193 (1997). * R. Dick, L. P. Fulcher, Eur. Phys. J. C 9, 271 (1999). * M. Chabab et al.; Eur. Phys. J. C 13, 543 (2000). * M. Chabab et al., Class. Quant. Gravity 18, 5085 (2001). * M. Chabab and L. Sanhaji; (hep-th/ 0311096). (to appear in Phys. Rev. D) * T. Barakat and M. Chabab, hep-ph/0101056