Resummed Gluon Propagator And Debye Screening Effect In A Constant Background Field

One of the most important goal in high-energy nuclear physics is to explore a new form of matter,the so-called Quark Gluon Plasma(QGP),which has been predicted by finite temperature lattice Quantum Chromodynamicsis(QCD).Due to the non-neutrality of color charge,QGP cannot be directly observed.Therefore,the suppression of heavy quarkonia caused by the reduction of the in-medium interactions between quark and antiquark,pro-vides the possibility to learn physical properties of QGP.On the one hand,the interactions between quarks and antiquarks induced by the exchanged gluons can be described by gluon propagators.In the QGP,the self-energy function which accounts for the interactions be-tween the exchanged gluons and medium partons,plays an important role.It corrects the bare gluon propagators and results in screening effects that affect the binding of quarkonium.Therefore,studying the resummed gluon propagators with self-energy contribution can pro-vide important information for understanding the properties of heavy quarkonia in QGP.On the other hand,at the asymptotically high temperature,we can rely on the perturbation QCD,while non-perturbative physical effects can not be neglected in the“semi”-QGP re-gion,from the critical temperature T_c to about 4~5T_c.Based on the Lattice simulations of the Polyakov loops,their values are non-zero,but less than unity which can be described by introducing non-zero background field.In order to investigate screening effect in the“semi”-QGP region,we focus on the resummed gluon propagators with non-zero background field and study the influence of non-zero background field on the properties of quarkonia.The double line basis has been widely used to compute the resummed gluon propagators in non-zero background field.Because of the transversality of the gluon self-energy in Lorentz space,the Lorentz structure of the gluon propagator is analogous to that in the perturbative QGP with zero background field.Due to the over-completeness of the double line basis,the propagator of each diagonal gluon cannot be uniquely determined.However,multiplied by a projection operator,the propagators for diagonal gluons are uniquely obtained after summing over the color indices and the result exhibits a highly non-trivial dependence on the background field.For an arbitrary background field,we take SU(2)and SU(3)as an example to discuss the static limit of the obtained resummed propagators which gives us an insight into the screening effects in the background field.In general,introducing non-zero holonomy merely amounts to modifications on the perturbative screening mass m Dand the resulting heavy-quark potential,which remains the standard Debye screened form,is always deeper than the screened potential in the perturbative Quark-Gluon Plasma.Therefore,a weaker screening,thus a more tightly bounded quarkonium state can be expected in a holonomous plasma.In addition,both the diagonal and off-diagonal gluons become distinguishable by their modified screening masses MDand the tem-perature dependence of the ratio MD/T shows a very similar behavior as that found in lattice simulations.