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To incorporate the effect of gluons on the evolution dynamics of the quarkmatter produced in relativistic heavy-ion collisions, we extend the 3-flavorNambu-Jona-Lasinio (NJL) transport model to include the contribution from thePolyakov loops. Imbedding the resulting pNJL partonic transport model in anextended multiphase transport (extended AMPT) model, we then study the ellipticflow splittings between particles and their antiparticles in relativisticheavy-ion collisions at RHIC-BES energies. We find that a weak quark vectorinteraction in the partonic phase is able to describe the elliptic flowsplitting between protons and antiprotons in heavy-ion collisions at$\sqrt{s_{NN}}=7.7$ to 39 GeV. Knowledge on the quark vector interaction isuseful for understanding the equation of state of quark matter at large baryonchemical potentials and thus the location of the critical point in the QCDphase diagram.

Elliptic flow splittings in the Polyakov-looped Nambu-Jona Lasinio transport model