Pseudoscalar susceptibilities and quark condensates: chiral restoration and lattice screening masses

Abstract

We derive the formal Ward identities relating pseudoscalar susceptibilities and quark condensates in three-flavor QCD, including consistently the $\eta$-${\eta }^{\prime }$ sector and the $U_A(1)$ anomaly. These identities are verified in the low-energy realization provided by ChPT, both in the standard $SU(3)$ framework for the octet case and combining the use of the $U(3)$ framework and the large-$N_c$ expansion of QCD to account properly for the nonet sector and anomalous contributions. The analysis is performed including finite temperature corrections as well as the calculation of $U(3)$ quark condensates and all pseudoscalar susceptibilities, which together with the full set of Ward identities, are new results of this work. Finally, the Ward identities are used to derive scaling relations for pseudoscalar masses, which explain the behavior with temperature of lattice screening masses near chiral symmetry restoration.

20 pages, 6 figures

References in corpus (4)

• The QCD transition temperature: results with physical masses in the continuum limit II.
• The QCD phase transition with physical-mass, chiral quarks
• Meson screening masses from lattice QCD with two light and the strange quark
• Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD

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