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Abstract
We calculate the gluon self-energy using quark energy projectors in a general quark-gluon plasma. By separating the quark field into positive- and a negative-energy modes, the quark loop constructed with the same mode is always convergent, and the divergence appears only in the mixed loop with different modes and is medium independent. After removing the divergence in vacuum, we obtain the one-loop gluon self-energy at finite temperature, chemical potential, and quark mass without approximation. With the method of quark-loop resummation, we calculate nonperturbatively the gluon Debye mass and thermodynamic potential. In the limit of small gluon momentum in comparison with temperature, chemical potential, and quark mass, our calculation comes back to the known HTL/HDL results in literature.
Highlights
As an often used method in theoretical calculations, one introduces energy projectors to divide the quark field into positive- and negative-energy modes, and any Feynman diagram is separated into two groups: the pure fraction constructed from the same modes, and the mixed fraction contructed from the two modes [55,56,57,58,59,60,61]
The one-loop diagram plays a crucial role in nonperturbative calculations of QCD, like the approaches of hard thermal loop resummation (HTL) [83,84,85,86,87,88] and hard dense loop resummation (HDL) [89]
Like extremely high temperature or high baryon density, the divergence is properly removed in HTL and HDL [90,91,92]
Summary
The properties of QCD matter at finite temperature and chemical potential, especially the deconfinement and chiral symmetry phase transitions [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] and their realization in high-energy nuclear collisions [27,28,29,30,31,32,33,34,35,36,37,38,39] and compact stars [40,41,42,43,44,45,46,47,48,49,50,51,52,53,54], have been widely studied for decades. Like extremely high temperature or high baryon density, the divergence is properly removed in HTL and HDL [90,91,92]. Divergence problem in the calculation of the in-medium one-loop gluon self-energy at finite temperature, chemical potential, and quark mass, using the quark energy-projector method. We will see that the divergence appears only in the mixed loop and is medium independent It does not change the thermodynamic properties relative to the vacuum and can be directly removed.
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