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

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Int School Advanced Studies
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We derive the formal Ward identities relating pseudoscalar susceptibilities and quark condensates in three-flavor QCD, including consistently the 77-n' 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 SU(3) framework and the large-Nc 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.
Open Access, © The Authors, 2016. Article funded by SCOAP3. © Int School Advanced Studies. We thank Z.H. Guo for helpful discussions. Work partially supported by research contracts FPA2011-27853-C02-02 (spanish “Ministerio de Ciencia e Innovación"), FPA2014-53375- C2-2-P (spanish “Ministerio de Economía y Competitividad"). We also acknowledge the support of the EU FP7 HadronPhysics3 project, the Spanish Hadron Excellence Network (spanish “Ministerio de Economía y Competitividad" contract FIS2014-57026-REDT), the DFG (SFB/TR 16, “Subnuclear Structure of Matter") and the UCM-Banco de Santander contract GR3/14 910309.
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