Studies On The Collisional Energy Loss Of Heavy Quark In A Semi-quark Gluon Plasma

The Lattice Quantum Chromodynamics(QCD)predicts that under extreme condi-tions,hadrons will undergo a deconfinement phase transition and become Quark-Gluon Plasma(QGP).It provides valuable insights into the fundamental structure of hadrons and the properties of strong interactions by studying the properties of QGP.The heavy-flavor quarks are produced during the early stage of high-energy heavy-ion collisions and undergo all the evolution processes of the quark-gluon plasma,and analyzing their energy loss can provide significant information about the QGP.Typically,in the temperature range between the phase transition temperature T_cto 4～5T_c,the QGP is only partially ionized rather than fully,and is therefore referred to as a semi-QGP.Investigations of physical phenomena in the semi-QGP state require the application of effective theories due to the non-perturbative effects,which arise as a result of the asymptotic freedom prop-erty of QCD.In this work,we used the background fields effective theory framework to calculate the energy loss resulting from the scattering of high-energy heavy flavor quarks and partons in the QGP during collisions.We compared our results with those obtained in the absence of a background field,and focused on the impact of the background field on energy loss in the non-perturbative regime.Based on the framework of collisional energy loss proposed by Braaten and Thoma,we studied the contributions of quark-quark and quark-gluon scatterings to collisional energy loss in leading-order approximation.We chose a cutoff parameter q~*and divided the scattering process into the soft regimes and hard regimes.In the hard regime,the presence of the background fields leads to modifications of the parton distribution func-tions in the medium.In the soft regime,we study the impact of the background fields on energy loss by using the resummed propagator with gluon self-energy corrections in the background field.The cutoff parameter q~*is determined by the variational method,and the temperature dependence of the background fields is obtained from the equations of motion of the background fields in the effective theory.Based on these,we calculate the collisional energy loss of charm and bottom quarks at different temperatures.Our results show that the energy loss of heavy quarks in collisions increases as the momentum of the incoming parton increases,while the energy loss caused by hard processes grad-ually becomes dominant.At extremely high energies(v→1),the contribution of hard processes to the total collisional energy loss will reach over～85%.On the other hand,compared to the perturbative theory that does not take into account the background field,the energy loss in the presence of the background field is lower.As the temperature decreases,the suppression of the background field becomes more prominent.Especially when the temperature approaches the phase transition temperature T_c,the introduc-tion of the background field will reduce the heavy-flaver quarks collisional energy loss to～30%of that in the perturbative limit.However,the suppression of energy loss caused by the background field is highly sensitive to temperature.The significant suppression effect only appears in an extremely narrow temperature range above T_c.Our study sug-gests that when the temperature of QGP is higher than twice the critical temperature,the heavy quark collisional energy loss obtained from the effective theory in background fields will approach the results obtained from perturbative theory.