Magnetic susceptibility of QCD at zero and at finite temperature from the lattice

Abstract

The response of the QCD vacuum to a constant external (electro)magnetic field is studied through the tensor polarization of the chiral condensate and the magnetic susceptibility at zero and at finite temperature. We determine these quantities using lattice configurations generated with the treelevel Symanzik improved gauge action and = 1 + 1 + 1 flavors of stout smeared staggered quarks with physical masses. We carry out the renormalization of the observables under study and perform the continuum limit both at > 0 and at = 0, using different lattice spacings. Finite size effects are studied by using various spatial lattice volumes. The magnetic susceptibilities reveal a spin-diamagnetic behavior; we obtain at zero temperature = −(2.08 ± 0.08) GeV −2 , = −(2.02 ± 0.09) GeV −2 and = −(3.4 ± 1.4) GeV −2 for the up, down and strange quarks, respectively, in the MS scheme at a renormalization scale of 2 GeV. We also find the polarization to change smoothly with the temperature in the confinement phase and then to drastically reduce around the transition region.* Corresponding author. gergely.endrodi@physik.uni-r.de 1 Employing physical quark masses in the simulation and extrapolating the results to the continuum limit, as was done in Refs. [5][6][7], proved to be essential. Studies where these ingredients are missing produce qualitatively different results, namely an increasing ( ) function [8,9]. A possible explanation for this discrepancy and a comparison to effective theories was given recently in Ref. [7].

Modification of theBmeson mass in a magnetic field from QCD sum rules

“…However, for other types of interpolating currents [such as the vector mesons ϒð1SÞ or B Ã ], the contribution from the hqσ 12 qi condensate may enter explicitly in the OPE and must be considered. With this possibility in mind, we remark that there are already lattice results for this quantity in the presence of a magnetic field [34]. The nonperturbative contribution to the correlator that comes from using the propagator in Eq.…”

Successes and failures of a more comprehensive hard wall AdS/QCD

“…Values of c u in the literature vary from 0.96 to 1.04 for lattice QCD computations [27][28][29], while c u 1.4 is a typical value obtained from radiative meson decays [35,36]. Sum rule approaches in QCD which can also be applied in conjunction with ideas of holography lead to c u 2 − 2.15 [32,34] while the resonance sum rules of [41] require c u = 4.…”

“…It has been calculated in QCD using a variety of theoretical tools [30][31][32][33] and most recently has been studied using holographic methods [19,34,41]. It has also been the subject of several lattice QCD computations [27][28][29].…”

Perturbative renormalization of staggered fermion operators with stout improvement: Application to the magnetic susceptibility of QCD

“…[8,12], we measure the magnetic susceptibilities χ f at zero temperature for the up, down and strange quarks in the MS scheme at a renormalization scale of 2 GeV. The magnetic susceptibilities at T = 0 are negative, indicating the spin-diamagnetic nature of the QCD vacuum.…”