Gluon condensates in a cold quark–gluon plasma

Abstract

The quark gluon plasma which has been observed at RHIC is a strongly interacting system and has been called sQGP. This is a system at high temperatures and almost zero baryon chemical potential. A similar system with high chemical potential and almost zero temperature may exist in the core of compact stars. Most likely it is also a strongly interacting system. The strong interactions may be partly due to non-perturbative effects, which survive after the deconfinement transition and which can be related with the non-vanishing gluon condensates in the sQGP. In this work, starting from the QCD Lagrangian we perform a gluon field decomposition in low ("soft") and high ("hard") momentum components, we make a mean field approximation for the hard gluons and take the matrix elements of the soft gluon fields in the plasma. The latter are related to the condensates of dimension two and four. With these approximations we derive an analytical expression for the equation of state, which is compared to the MIT bag model one. The effect of the condensates is to soften the equation of state whereas the hard gluons significantly increase the energy density and the pressure.

The quark gluon plasma equation of state and the expansion of the early Universe

“…The model presented below was proposed in [24] and it was applied to study the cold and dense quark gluon plasma in the inner core of neutron stars [25]. In [24] we start from the QCD Lagrangian and split the gluon field into low and high momentum modes.…”

Strongly coupled quark gluon plasma in a magnetic field

“…where B QCD is our equivalent of the bag constant given by B QCD ≡ 9 φ 0 4 /136 and m G is the dynamical gluon mass given by m G 2 ≡ 9 μ 0 2 /32, where μ 0 is an energy scale associated with A 2 , which is the gluon condensate of dimension two [1]:…”

“…It is also reasonable to assume that the yet untested cold quark gluon plasma, which presumably exists in the core of dense stars, is also a strongly interacting system. In [1] we developed a mean field approach to the cold sQGP, which is inspired in the old relativistic mean field Walecka model. As in that model, because of the strong coupling and the large number of fermion sources, the vector boson is assumed to behave as a classical field.…”

“…Due to the strongly repulsive interaction of the vector field our EOS is much harder than the MIT one. The details of the derivation can be found in [1], where we discuss these approximations. In a subsequent paper, Ref.…”

“…In a subsequent paper, Ref. [2], we have applied our EOS [1] to the calculation of the structure of compact quark stars. We found that the inclusion of gluon interaction creates pressure and energy density large enough to generate stars wiht masses and radii consistent with the most recent astrophysical observations.…”