Determination of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:msub><mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="normal">A</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>restoration from pion and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mm

We analyze the restoration pattern of the members of the scalar and pseudoscalar meson nonets under chiral Oð4Þ and Uð1Þ A symmetries. For that purpose, we exploit QCD Ward identities (WI), which allow one to relate susceptibilities with quark condensates, as well as susceptibility differences with meson vertices. In addition, we consider the low-energy realization of QCD provided by Uð3Þ chiral perturbation theory (ChPT) at finite temperature to perform a full analysis of the different correlators involved. Our analysis suggests Uð1Þ A partner restoration if chiral symmetry partners are also degenerated. This is also confirmed by the ChPT analysis when the light chiral limit is reached. Partner degeneration for the I ¼ 1=2 sector, the behavior of I ¼ 0 mixing and the temperature scaling of meson masses predicted by WI are also studied. Special attention is paid to the connection of our results with recent lattice analyses.

Section: Introductionmentioning

confidence: 93%

Chiral and U(1)A restoration for the scalar and pseudoscalar meson nonets

Nicola

Elvira

2018

“…Nevertheless, the latter limit is meant to be reached at a much higher temperature than chiral restoration, as seen, for instance, in the degeneration of screening masses [35]. The four correlators (34) and (35) have been actively investigated in lattice and theoretical analyses to study partner degeneracy [5,[22][23][24][25]27,36,37].…”

Section: Consequences For Chiral Symmetry Restorationmentioning

confidence: 99%

“…For instance, at T ¼ 0 χ π P ¼ Oðm −1 Þ and χ l S ¼ OðlogmÞ [2,32], the r.h.s. of (22) should scale at least as 1=m at zero temperature.…”

Section: E Comments On the Wi Relating Two And Three Point Functionsmentioning

confidence: 99%

See 1 more Smart Citation

Patterns and partners for chiral symmetry restoration

Nicola

Elvira

2018

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 Oð4Þ vs Oð4Þ × Uð1Þ A . The degeneracy of chiral partners for all scalar and pseudoscalar meson nonet members is studied through their corresponding correlators. Around chiral symmetry degeneration of Oð4Þ partners, our analysis predicts that Uð1Þ A partners are also degenerated. Our analysis also leads to I ¼ 1=2 scalar-pseudoscalar partner degeneration at exact chiral restoration and supports ideal mixing between the η-η 0 and the f 0 ð500Þ-f 0 ð980Þ mesons at Oð4Þ × Uð1Þ 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 Uð1Þ A restoration for future lattice and model analyses.

“…The chiral matrix model can be considered as a generalization of Polyakov loop models, as first proposed by Fukushima [34][35][36][37][38][39][40]; see also [41]. In a Polyakov loop model, the gauge fields are integrated out to obtain an effective model of the Polyakov loop and hadrons.…”

Section: Introductionmentioning

confidence: 99%

Chiral matrix model of the semi-QGP in QCD

Pisarski¹,

Skokov²

2016

Previously, a matrix model of the region near the transition temperature, in the "semi"-Quark Gluon Plasma, was developed for the theory of SU (3) gluons without quarks. In this paper we develop a a chiral matrix model applicable to QCD by including dynamical quarks with 2 + 1 flavors. This requires adding a nonet of scalar fields, with both parities, and coupling these to quarks through a Yukawa coupling, y. Treating the scalar fields in mean field approximation, the effective Lagrangian is computed by integrating out quarks to one loop order. As is standard, the potential for the scalar fields is chosen to be symmetric under the flavor symmetry of SU (3) L × SU (3) R × Z(3) A , except for a term linear in the current quark mass, m qk . In addition, at a nonzero temperature T it is necessary to add a new term, ∼ m qk T 2 . The parameters of the gluon part of the matrix model are identical to that for the pure glue theory without quarks. The parameters in the chiral matrix model are fixed by the values, at zero temperature, of the pion decay constant and the masses of the pions, kaons, η, and η . The temperature for the chiral crossover at T χ = 155 MeV is determined by adjusting the Yukawa coupling y. We find reasonable agreement with the results of numerical simulations on the lattice for the pressure and related quantities. In the chiral limit, besides the divergence in the chiral susceptibility there is also a milder divergence in the susceptibility between the Polyakov loop and the chiral order parameter, with critical exponent β − 1. We compute derivatives with respect to a quark chemical potential to determine the susceptibilities for baryon number, the χ 2n . Especially sensitive tests are provided by χ 4 − χ 2 and by χ 6 , which changes in sign about T χ . The behavior of the susceptibilities in the chiral matrix model strongly suggests that as the temperature increases from T χ , that the transition to deconfinement is significantly quicker than indicated by the measurements of the (renormalized) Polyakov loop on the lattice. * pisarski@bnl.gov † vskokov@bnl.gov 2