Vector meson spectral function and dilepton production rate in a hot and dense medium within an effective QCD approach

Abstract

The properties of the vector meson current-current correlation function and its spectral representation are investigated in details with and without isoscalar-vector interaction within the framework of effective QCD approach, namely Nambu-Jona-Lasinio (NJL) model and its Polyakov Loop extended version (PNJL), at finite temperature and finite density. The influence of the isoscalar-vector interaction on the vector meson correlator is obtained using the ring resummation known as the Random Phase Approximation (RPA). The spectral as well as the correlation function in PNJL model show that the vector meson retains its bound property up to a moderate value of temperature above the phase transition. Using the vector meson spectral function we, for the first time, obtained the dilepton production rate from a hot and dense medium within the framework of PNJL model that takes into account the nonperturbative effect through the Polyakov Loop fields. The dilepton production rate in PNJL model is enhanced compared to NJL and Born rate in the deconfined phase due to the suppression of color degrees of freedom at moderate temperature. The presence of isoscalar-vector interaction further enhances the dileption rate over the Born rate in the low mass region. Further, we also have computed the Euclidean correlation function in vector channel and the conserved density fluctuation associated with temporal correlation function appropriate for a hot and dense medium. The dilepton rate and the Euclidean correlator are also compared with available lattice data and those quantities in PNJL model are found to agree well in certain domain.

Dilepton and photon production in the presence of a nontrivial Polyakov loop

“…We emphasize that the equality between our results and the PNJL model [99] is valid only to leading order. In both cases, at leading order dilepton production is only a function of the Polyakov loop and the temperature.…”

“…In this instance, identities similar to eq. (3.23) hold for a n a (E) and a n a (E) separately, and are again equal to those in the PNJL model, [57,58,99]. )…”

“…We can also make contact with results from Polyakov Nambu-Jona-Lasino (PNJL) models [56][57][58], especially with the computation of dilepton production by Islam, Majumder, Haque, and Mustafa [99]. To do so we need a simple identity.…”

“…In the PNJL model calculation done in ref. [99], Im Π R 00 is given in eq. (4.36), and Im Π R ii by eq.…”

“…[99] and by Satow and Weise [105]. There is a relatively mild dependence on the quark masses, apart from obvious kinematical constraints, such as the energy of the photon has to be greater than twice the quark mass.…”