Dilepton Yields from Brown-Rho Scaled Vector Mesons Including Memory Effects

Abstract

Brown-Rho scaling, which has been strongly discussed after recent NA60 data was presented, is investigated within a nonequilibrium field theoretical description that includes quantum mechanical memory. Dimuon yields are calculated by application of a model for the fireball, and strong modifications are found in the comparison to quasi-equilibrium calculations, which assume instantaneous adjustment of all meson properties to the surrounding medium. In addition, we show results for the situation of very broad excitations. [6,7,8,9], have an important influence on the final dilepton yields, especially for dropping mass scenarios. This lead to the conclusion that an analysis of which scenario describes the data correctly demands the proper inclusion of memory effects. The aim of this work is to clarify how the inclusion of memory affects the dimuon yields from Brown-Rho scaled vector mesons. The validity of standard equilibrium calculations depends on the strength of these effects.We consider two mass parameterizations: The temperature and density dependent one used by Rapp et al. [10] assuming a constant gauge coupling g in the vector meson dominance (VMD) -coupling, and one motivated by the renewed version of Brown-Rho scaling discussed in [11,12]:with a modified gauge coupling g * , in such a way that g * is constant up to normal nuclear density n 0 , while from then on m * ρ /g * is taken to be constant [13]. This parameterization is not valid close to T c because it does not take the meson mass to zero at the critical point. However, Brown and Rho argue [11,12] that because lattice calculations show that the pole mass of the vector mesons does not change appreciably up to T = 125 MeV, the parameterization using [1 − (T /T c ) n ] d (with positive d and integer n) overestimates the mass shift. They find temperature dependent effects to be an order of magnitude smaller than the density dependent effects, and hence suggest to concentrate on the density dependent part.We also wish to study the effect of finite memory for a mass shift following this parameterization and ignore its shortcomings for the moment. Furthermore, Brown and Rho point out that due to the violation of VMD, which accounts for most of the shape of the dilepton spectrum (see [11,12] and [14]), the overall dilepton production in dense matter should be reduced by a factor of 4 compared to Rapp's calculations, which we do not take into account here.We compare the usual approach [18], where the dilepton rate is given by the well known equilibrium formulawith invariant mass, to the nonequilibrium formalism, in which the propagators of the ρ-meson and the virtual photon are calculated using the general nonequilibrium formulas. The dilepton rate for a spatially homogeneous but time dependent system is given by [4]:. (4) In its derivation we treated transverse and longitudinal modes equally, which is adequate for our purposes. D < γ T is the transverse virtual photon propagator, and satisfies the generalized fluctuation dissipation relationwith all t...

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