The  -Meson Mass Shift in Medium Using a Chiral Effective Lagrangian

Abstract

The restoration of chiral symmetry has recently become one of the central issues related to the quark-gluon plasma (QGP). In a high temperature, high density environment, such as that created in the Relativistic Heavy Ion Collider (RHIC), the QCD vacuum condensate is dissolved, and therefore it is believed that a phase transition to QGP is realized. The order parameter characterizing the transition is the chiral quark condensate qq . The reduction of qq is regarded as the partial restoration of chiral symmetry in QCD.It is suggested that the mass shift of the light vector mesons (ρ, ω, φ · · ·) is one way to experimentally detect the restoration of chiral symmetry in medium. The mass shift of light vector mesons is believed to be directly experimentally observable through the production of vector mesons in media (nuclei) and detecting lepton pairs, which themselves decay. Among light vector mesons, the φ-meson is a useful probe for finding the signal of its mass shift, because of its small width.The purpose of this paper is to show that a shift of vector meson masses, in particular the φ-meson mass m * φ , can occur even in ordinary nuclear media at zero temperature prior to the critical point of the QGP phase transition, using an effective theory. Adopting effective chiral quark dynamics as effective theories, we investigate the possibility for the vector meson mass to become light.The model is treated for the one-loop level. The results reveal a density dependence of the masses to decrease in medium, as a result of the decrease of the chiral quark condensate. We also analyze the physical reason of this meson mass shift. We can use f K /f π to eliminate one more parameter, m 8 or m 0 . If we use the relation m 8 /m 0 = 1/(2f K /f π − 1), 24) together with the experimental value f K /f π = 113/92.4 = 1.22, we obtain m 8 /m 0 = 0.69, which is 15% larger than the value assumed in this paper.at