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Authors
Prabal Adhikari
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We study the topological susceptibility and the fourth cumulant of the QCD vacuum in the presence of a uniform, background magnetic field in two-and-flavor QCD finding model-independent sum rules relating the shift in the topological susceptibility due to the background magnetic field to the shift in the quark condensates, and the shift in the fourth cumulant to the shifts in the quark condensates and susceptibilities.
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We reconsider the problem of calculating the vacuum free energy (density) of QCD and the shift of the quark condensates in the presence of a uniform background magnetic field using two-and-three-flavor chiral perturbation theory ($chi$PT). Using the free energy, we calculate the degenerate, light quark condensates in the two-flavor case and the up, down and strange quark condensates in the three-flavor case. We also use the vacuum free energy to calculate the (renormalized) magnetization of the QCD vacuum, which shows that it is paramagnetic. We find that the three-flavor light-quark condensates and (renormalized) magnetization are improvements on the two-flavor results. We also find that the average light quark condensate is in agreement with the lattice up to $eB=0.2 {rm GeV^{2}}$, and the (renormalized) magnetization is in agreement up to $eB=0.3 {rm GeV^{2}}$, while three-flavor $chi$PT, which gives a non-zero shift in the difference between the light quark condensates unlike two-flavor $chi$PT, underestimates the difference compared to lattice QCD.
Considering the strong field approximation we compute the hard thermal loop pressure at finite temperature and chemical potential of hot and dense deconfined QCD matter in lowest Landau level in one-loop order. We consider the anisotropic pressure in the presence of the strong magnetic field i.e., longitudinal and transverse pressure along parallel and perpendicular to the magnetic field direction. As a first effort, we compute and discuss the anisotropic quark number susceptibility of deconfined QCD matter in lowest Landau level. The longitudinal quark number susceptibility is found to increase with the temperature whereas the transverse one decreases with the temperature. We also compute the quark number susceptibility in the weak field approximation. We find that the thermomagnetic correction to the quark number susceptibility is very marginal in the weak field approximation.
While the partition function for QCD in a magnetic field $H$ has been calculated before within chiral perturbation theory up to two-loop order, our investigation relies on an alternative representation for the Bose functions which allows for a clear-cut expansion of thermodynamic quantities in the chiral limit. We first focus on the pion-pion interaction in the pressure and show that -- depending on magnetic field strength, temperature and pion mass -- it may be attractive or repulsive. We then analyze the thermodynamic properties in the chiral limit and provide explicit two-loop representations for the pressure in the weak magnetic field limit $|qH| ll T^2$.
We show that the nonlocal two-flavor Nambu--Jona-Lasinio model predicts the enhancement of both chiral and axial symmetry breaking as the chiral imbalance of hot QCD matter, regulated by a chiral chemical potential $mu_5$, increases. The two crossovers are reasonably close to each other in the range of $mu_5$ examined here and the pseudocritical temperatures rise with $mu_5$. The curvatures of the chiral and axial crossovers for the chiral quark chemical potential approximately coincide and give $kappa_5 simeq - 0.011$. We point out that the presence of $mu_5$ in thermodynamic equilibrium is inconsistent with the fact that the chiral charge is not a Noether-conserved quantity for massive fermions. The chiral chemical potential should not, therefore, be considered as a true chemical potential that sets a thermodynamically stable environment in the massive theory, but rather than as a new coupling that may require a renormalization in the ultraviolet domain. The divergence of an unrenormalized chiral density, corr{coming from zero-point fermionic fluctuations,} is a consequence of this property. We propose a solution to this problem via a renormalization procedure.
We have computed the chiral susceptibility in quark-gluon plasma in presence of finite chemical potential and weak magnetic field within hard thermal loop approximation. First we construct the massive effective quark propagator in a thermomagnetic medium. Then we obtain completely analytic expression for the chiral susceptibility in weak magnetic field approximation. In the absence of magnetic field the thermal chiral susceptibility increases in presence of finite chemical potential. The effect of thermomagnetic correction is found to be very marginal as temperature is the dominant scale in weak field approximation.
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