Abstract
We present and analyze a new set of Ward Identities which shed light on the distinction between different patterns of chiral symmetry restoration in QCD, namely $O(4)$ vs $O(4)\times U(1)_A$. The degeneracy of chiral partners for all scalar and pseudoscalar meson nonet members are studied through their corresponding correlators. Around chiral symmetry degeneration of $O(4)$ partners, our analysis predicts that $U(1)_A$ partners are also degenerated. Our analysis also leads to $I=1/2$ scalar-pseudoscalar partner degeneration at exact chiral restoration, and supports ideal mixing between the $\eta$-$\eta^\prime$ and the $f_0(500)$-$f_0(980)$ mesons at $O(4)\times U(1)_A$ restoration, with a possible range where the pseudoscalar mixing vanishes if the two transitions are well separated. We test our results with lattice data and provide further relevant observables regarding chiral and $U(1)_A$ restoration for future lattice and model analyses.
Highlights
Chiral symmetry restoration is a prominent feature of the QCD phase diagram, realized in lattice simulations and presumably in matter formed after a heavy ion collision
As we will detail below, another signal of chiral restoration would be the degeneration of chiral partners, due to the crossover nature of the transition, different chiral-restoring observables may lead to different transition temperatures
We have performed an analysis based on Ward Identities of several quantities relevant for the understanding of the pattern of chiral symmetry restoration and the degeneration of the corresponding partners under Oð4Þ and Uð1ÞA symmetries
Summary
Chiral symmetry restoration is a prominent feature of the QCD phase diagram, realized in lattice simulations and presumably in matter formed after a heavy ion collision. In the m =ms → 0þ limit (light chiral limit), all chiral restoration effects are enhanced, i.e., the quark condensate decreases, the scalar susceptibility peak increases [6], and the degeneration of chiral partners becomes more noticeable, with transition temperatures approaching the same. The restoration of Uð1ÞA affects the chiral transition order for three flavors [9], as well as the behavior near the critical end point at finite temperature and baryon density [10]. The idea that Uð1ÞA partners can degenerate in an ideal chiral-restoring scenario was suggested in [16] and corroborated in [17] through an analysis of spectral properties of the QCD quark propagator. In that work, π − a0 and other Uð1ÞA symmetry partners degenerate asymptotically, but their difference is still sizable near the point where π − σ degeneracy occurs.
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