Chiral properties of (2+1)-flavor QCD in strong magnetic fields at zero temperature

TL;DR

This study uses lattice QCD to explore how magnetic fields affect meson properties, chiral condensates, and decay constants in (2+1)-flavor QCD at zero temperature, revealing monotonic and nonmonotonic behaviors and scaling laws.

Contribution

It provides the first detailed lattice QCD analysis of chiral and meson properties under strong magnetic fields, including scaling behaviors and corrections to chiral relations.

Findings

Neutral meson masses decrease and saturate with increasing magnetic field.

Charged meson masses show nonmonotonous behavior in magnetic fields.

Observed $qB$ scaling of certain meson properties and chiral condensates.

Abstract

We present lattice QCD results for masses and magnetic polarizabilities of light and strange pseudoscalar mesons, chiral condensates, decay constants of neutral pion, and neutral kaon in the presence of background magnetic fields with $eB$ ranging up to around 3.35 GeV$^2$ ($\sim70~M_\pi^2$) in the vacuum. The computations were carried out in (2+1)-flavor QCD mostly on $32^3 \times 96$ lattices using the highly improved staggered quark action with $M_{\pi} \approx $ 220 MeV at zero temperature. We find that the masses of neutral pseudoscalar mesons monotonously decrease as the magnetic field strength grows and then saturate at a nonzero value, while there exists a nonmonotonous behavior of charged pion and kaon masses in the magnetic field. We observe a $qB$ scaling of the up and down quark flavor components of neutral pion mass, neutral pion decay constant as well as the quark chiral condensates at 0.05 $\lesssim eB\lesssim$ 3.35 GeV$^2$. We show that the correction to the Gell-Mann-Oakes-Renner relation involving the neutral pion is less than 6% and the correction for the relation involving neutral kaon is less than 30% at $eB\lesssim$ 3.35 GeV$^2$. We also derive the Ward-Takahashi identities for QCD in the magnetic field in the continuum formulation including the relation between integrated neutral pseudoscalar meson correlators and chiral condensates.