Abstract
We derive some exact results concerning the anomalous U(1)$_A$ symmetry in the chirally symmetric phase of QCD at high temperature. We discuss the importance of topology and finite-volume effects on the U(1)$_A$ symmetry violation characterized by the difference of chiral susceptibilities. In particular, we present a reliable method to measure the anomaly strength in lattice simulations with fixed topology. We also derive new spectral sum rules and a novel Banks-Casher-type relation. Through our spectral analysis we arrive at a simple alternative proof of the Aoki-Fukaya-Taniguchi "theorem" on the effective restoration of the U(1)$_A$ symmetry at high temperature.
Highlights
Finite temperature [4],1 the U(1)A symmetry could be effectively restored at the level of mesonic two-point correlation functions [5]
The U(1)A problem at finite temperature has been studied intensively in first-principles lattice QCD simulations [14, 15], but a consensus is not reached yet: effective restoration of the U(1)A symmetry was reported in simulations with overlap fermions [16] and domain-wall fermions [17,18,19,20], whereas a violation of the U(1)A symmetry was reported in simulations using staggered fermions [21,22,23,24] and domainwall fermions [25]
Contrary to our assumption that fA = 0 for T > Tc, Aoki at al. [13] claim that, under certain assumptions, the violation of the U(1)A symmetry is invisible in correlation functions of scalar and pseudoscalar quark bilinears for T > Tc in two-flavor QCD. (This claim does not generalize to the vector-axial-vector sector, as we discussed in section 2.) There are two key assumptions in their analysis
Summary
We write down the most general QCD partition function for T > Tc in terms of quark masses and derive general expressions for the chiral susceptibilities and topological susceptibility based on the method of [15, 26]. Our arguments here are based on symmetries of QCD and a systematic expansion in terms of a small parameter m/T 1, and are fully under theoretical control. We elucidate the contributions of topology and finite-volume effects to the violation of the U(1)A symmetry (characterized by the difference of two-point functions χπ − χδ to be defined below), and discuss possible implications for lattice QCD simulations. We will concentrate on two-flavor QCD below
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
