Magnetic test of chiral dynamics in QCD

TL;DR

This paper investigates how strong magnetic fields affect chiral mesons and quark condensates in QCD, showing that the condensate grows quadratically then linearly with magnetic field strength, aligning with lattice data.

Contribution

It extends chiral theory to include quark degrees of freedom under strong magnetic fields, providing explicit estimates of condensate growth that differ from previous predictions.

Findings

Quark condensate grows quadratically with eB for eB < 0.2 GeV^2.

Condensate grows linearly with eB for higher magnetic fields.

Results agree with recent lattice QCD data, contrasting with chiral perturbation theory predictions.

Abstract

Strong magnetic fields in the range $ eB\gg m^2_\pi $ effectively probe internal quark structure of chiral mesons and test basic parameters of chiral theory, such as $\lan\bar q q\ran, f_\pi$. We argue on general grounds that $\lan\bar q q\ran$ should grow linearly with $eB$ when charged quark degrees of freedom come into play. To make explicit estimates we extend previously formulated chiral theory, including quark degrees of freedom, to the case of strong magnetic fields and show that the quark condensate $|\lan \bar q q\ran|_{u,d}$ grows quadratically with $eB$ for $eB\la 0.2$ GeV$^2$ and linearly for higher field values. These results agree quantitatively with recent lattice data and differ from $\chi PT$ predictions.