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

TL;DR

This study investigates the magnetic susceptibility of the QCD vacuum at zero and finite temperatures using lattice QCD simulations, revealing diamagnetic behavior and temperature-dependent polarization changes across the confinement transition.

Contribution

It provides the first detailed lattice QCD determination of magnetic susceptibilities for different quark flavors at physical masses, including continuum and finite size effects.

Findings

Magnetic susceptibilities are negative, indicating diamagnetism.

Susceptibility values for u, d, s quarks at zero temperature are quantified.

Polarization decreases sharply around the QCD transition temperature.

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 tree-level Symanzik improved gauge action and N_f=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 T>0 and at T=0, using different lattice spacings. Finite size effects are studied by using various spatial lattice volumes. The magnetic susceptibilities \chi_f reveal a diamagnetic behavior; we obtain at zero temperature \chi_u=-(2.08 +/- 0.08) 1/GeV^2, \chi_d=-(2.02 +/- 0.09) 1/GeV^2 and \chi_s=-(3.4 +/- 1.4) 1/GeV^2 for the up, down and strange quarks, respectively, in the MSBar 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.