On the axial $U(1)$ symmetry at finite temperature

Abstract

We study the $U(1{)}_A$ anomaly in two-flavor lattice QCD at finite temperature with the Möbius domain-wall Dirac operator. We generate gauge configurations in the temperature range $(0.9,1.2)T_c$ on different physical volumes, $L=$ 2--4 fm, and lattice spacings. We measure the difference of the susceptibilities of the flavor non-singlet scalar ($\ddot{I}{‡}_{\hat{I}}´$) and pseudoscalar ($\ddot{I}{‡}_{\ddot{I}}€$) mesons. They are related by an axial $U(1)$ transformation and the difference vanishes if the axial $U(1)$ symmetry is respected. We identify the source of axial $U(1)$ symmetry breaking at finite temperature in the lowest eigenmodes, for the observable $\ddot{I}{‡}_{\ddot{I}}€-\ddot{I}{‡}_{\hat{I}}´$. We then reweight the Möbius domain-wall fermion partition function to that of the overlap-Dirac operator to fully recover chiral symmetry. Our data show a significant discrepancy in the results coming from the Möbius domain-wall valence quarks, the overlap valence quarks on our DWF configurations and the reweighted ones that have full chiral symmetry. After recovering full chiral symmetry we conclude that the difference $\ddot{I}{‡}_{\ddot{I}}€-\ddot{I}{‡}_{\hat{I}}´$ shows a suppression in the chiral limit that is compatible with an effective restoration of $U(1{)}_A$ at $T\gtrsim T_c$ in the scalar meson channels.

7 pages, 3 figures. Proceedings of the The 33rd International Symposium on Lattice Field Theory, 2015 Kobe. arXiv admin note: text overlap with arXiv:1412.5703