Meson Potential Energy in a Non-Conformal Holographic Model

We study the meson potential energy in a non-conformal model at both zero and finite temperature via gauge/gravity duality. This model consists of five-dimensional Einstein gravity coupled to a scalar field with a non-trivial potential. Interestingly, at both zero and finite temperature we find that the relative meson potential energy can be considered as a measure of non-conformality of the theory. At zero temperature we show that parameters of the Cornell potential, i.e. Coulomb strength parameter $κ$ and constant $C$ depends on the energy scale $Λ$ that breaks conformal symmetry and the difference between the number of degrees of freedom of UV and IR fixed points $ΔN$ while QCD string tension $σ_s$ just depends on the $Λ$. At finite temperature we see that there is a melting length $l_{m\ell}$ where beyond that the meson dissociates in the plasma and by increasing $Λ$ the value of $l_{m\ell}$ increases while its value decreases by increasing the temperature.

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