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CONFINING INTERQUARK POTENTIALS FROM NON ABELIAN GAUGE THEORIES COUPLED TO DILATON

CONFINING INTERQUARK POTENTIALS FROM NON ABELIAN GAUGE THEORIES COUPLED TO DILATON Mohamed CHABAB LPHEA, FSSM Cadi- Ayyad University Marrakech, Morocco. MENU2004@ Sep. 02, Beijing. Part I. Quark Confinement  Low energy effective models: Color dielectric models

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CONFINING INTERQUARK POTENTIALS FROM NON ABELIAN GAUGE THEORIES COUPLED TO DILATON

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  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. 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. Objective: String inspired effective theory With main features of QCD: quark confinement • 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 Our work: derivation of a new family of confining interquark potentials

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

  5. The equations of motion, (important formula)

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

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

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

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

  11. Part II Spectroscopy

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

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

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

  15. ANALYSIS: Five inputs parameters mc, mb, m, f, as Dick interquark potential VD(r)

  16. Word average experimental value and We obtain For:

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

  18. energy levels energy levels RESULTS

  19. energy levels

  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

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