Magnetic test of chiral dynamics in QCD

Abstract

Strong magnetic fields in the range $eB\gg m_{\pi }^2$ effectively probe internal quark structure of chiral mesons and test basic parameters of chiral theory, such as $\text{lan}\bar{q}q\text{ran},f_{\pi }$. We argue on general grounds that $\text{lan}\bar{q}q\text{ran}$ 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 $|\text{lan}\bar{q}q\text{ran}{|}_{u,d}$ grows quadratically with $eB$ for $eB\text{la}0.2$ GeV${}^2$ and linearly for higher field values. These results agree quantitatively with recent lattice data and differ from $\chi PT$ predictions.

Comments: 14 pages,1 figure