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CONFINING INTERQUARK POTENTIALS FROM NON ABELIAN GAUGE THEORIES COUPLED

TO DILATON

Mohamed CHABABLPHEA, FSSM

Cadi- Ayyad UniversityMarrakech, Morocco

MENU2004@ Sep. 02, BeijingMENU2004@ Sep. 02, Beijing

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Part I

Quark Confinement Low energy effective models:

• Color dielectric models • Constituent models • Dual Landau-Ginzburg Model

Extension of Gauge theories Dilatonic dofDilatonic Yang-Mills theories

with stable, finite energy solutions

also, • Dilaton dof Topological structure of the vacuum

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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

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>> The model Consider the general Lagrangian,

point like static Coulomb source

coupling function:

In string theory

In Cornwall-Soni

In Dick model

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(important formula)

The equations of motion,

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The interquark potential is then,

Note that,

( the chromo-electric field)

(the effective charge)

Quark confinement if:r lim r F-1( (r)) = finite

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The equation becomes:

>> Solving the equations of motion:

fix two of

(new)

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Large distance behavior of (r)

- solution in the asymptotic regime -

Therefore the potential

>> Family of confining interquark potentials if

>> Moreover, if Criterion of Seiler

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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 forn , 113

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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 forn , 113

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Part II Spectroscopy

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where

For statesof orbital angular momentum l,

define the reduced radiale wave function:

Then, the equation becomes,

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Procedure of SLET: Shift the origin of the coordinate

x

And expand:

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Our equation resembles

1d anharmonic oscillateur

then the meson mass is

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Dick interquark potential VD(r)

ANALYSIS: Five inputs parameters

mc, mb, m, f, as

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Word average experimental value

and

We obtain

For:

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

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energy levels

RESULTS

energy levels

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energy levels

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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