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Authors
Christoph P. Hofmann
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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 $|qH| ll T^2$.
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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.
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.
We present two-loop results for the quark condensate in an external magnetic field within chiral perturbation theory using coordinate space techniques. At finite temperature, we explore the impact of the magnetic field on the pion-pion interaction in the quark condensate for arbitrary pion masses and derive the correct weak magnetic field expansion in the chiral limit. At zero temperature, we provide the complete two-loop representation for the vacuum energy density and the quark condensate.
Considering the general structure of the two point functions of quarks and gluons, we compute the free energy and pressure of a strongly magnetized hot and dense QCD matter created in heavy-ion collisions. In presence of strong magnetic field we found that the deconfined QCD matter exhibits a paramagnetic nature. One gets different pressure in a direction parallel and perpendicular to magnetic field due to the magnetization acquired by the system. We obtain both longitudinal and transverse pressure, and magnetization of a hot deconfined QCD matter in presence of magnetic field. We have used hard thermal loop approximation (HTL) for heat bath. We obtained completely analytic expression for pressure and magnetization under certain approximation. Various divergences appearing in free energy are regulated using appropriate counter terms. The obtained anisotropic pressure may be useful for magnetohydrodynamics description of a hot and dense deconfined QCD matter produced in heavy-ion collisions.
We investigate the mass spectra of open heavy flavor mesons in an external constant magnetic field within QCD sum rules. Spectral ansatze on the phenomenological side are proposed in order to properly take into account mixing effects between the pseudoscalar and vector channels, and the Landau levels of charged mesons. The operator product expansion is implemented up to dimension-5 operators. As a result, we find for neutral D mesons a significant positive mass shift that goes beyond simple mixing effects. In contrast, charged D mesons are further subject to Landau level effects, which together with the mixing effects almost completely saturate the mass shifts obtained in our sum rule analysis.
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