Magnetic field-induced gluonic (inverse) catalysis and pressure (an)isotropy in QCD

Abstract

Abstract:We study the influence of strong external magnetic fields on gluonic and fermionic observables in the QCD vacuum at zero and nonzero temperatures, via lattice simulations with N f = 1+1+1 staggered quarks of physical masses. The gluonic action density is found to undergo magnetic catalysis at low temperatures and inverse magnetic catalysis near and above the transition temperature, similar to the quark condensate. Moreover, the gluonic action develops an anisotropy: the chromo-magnetic field parallel to the external field is enhanced, while the chromo-electric field in this direction is suppressed. We demonstrate that the same hierarchy is obtained using the Euler-Heisenberg effective action. Conversely, the topological charge density correlator does not reveal a significant anisotropy up to magnetic fields eB ≈ 1 GeV 2 . Furthermore, we show that the pressure remains isotropic even for nonzero magnetic fields, if it is defined through a compression of the system at fixed external field. In contrast, if the flux of the field is kept fixed during the compression -which is the situation realized in the lattice simulation -the pressure develops an anisotropy. We estimate the quark and gluonic contributions to this anisotropy, and relate them to the magnetization of the QCD vacuum. After performing electric charge renormalization, we obtain an estimate for the magnetization, which indicates that QCD is paramagnetic.

Quark-Gluon Plasma in an External Magnetic Field

“…The magnetic susceptibility C r 2 is positive for temperatures above the transition, which means that the quark-gluon plasma exhibits a paramagnetic behavior to lowest (linear) order in the magnetic field. Paramagnetism in the quarkgluon plasma has been also previously found in other lattice studies [7,9].…”

Hadronic vacuum polarization and muong−2from magnetic susceptibilities on the lattice

“…We also tested stochastic wall sources to obtain Π(0) as the second moment of a momentum projected current-current correlation function and found that it can compete with the accuracy of the homogeneous susceptibility for a sufficiently large number of random sources. It is interesting to note that 0 can also be obtained via stochastic wall sources at finite temperatures, giving direct access to the renormalized magnetic susceptibility 0 ( ) − 0 ( = 0) that enters the QCD equation of state at finite magnetic fields [48,55,56,58,71,72] . FIG.…”

The magnetic susceptibility in QCD

“…The only divergences that do not cancel in the difference ∆ f are the B−dependent ones and it can be show that such divergences are temperature independent (see e.g. [7,8]). Motivated by this result and by the physical observation that we are interested in the magnetic properties of the thermal medium and not in those of the…”