How π 0 → γ γ changes with temperature

Self Cite

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

Section: Behavior Of the Order Parametersmentioning

confidence: 99%

Chiral matrix model of the semi-QGP in QCD

Pisarski¹,

Skokov²

2016

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“…The renormalization of π a and f π comes from the tadpole corrections to the pion propagator and the π 0 γγ vertex, which is well known (see [27] and Refs. therein),…”

mentioning

confidence: 99%

“…In order to do that, on should calculate expectation values of the currents and renormalize the pion fields and pion decay constant f π by considering tadpole diagrams coming from the quartic (in π a ) terms of the pion Lagrangian [11,27]. Given that the pion loops in tadpoles are excited thermally with the Bose-Einstein occupation numbers, the renormalization constant for the pion fields, δ Zπ = 1 − π r /π, will be proportional to…”

mentioning

confidence: 99%

Temperature dependence of the chiral vortical effects

Kalaydzhyan

2014

We discuss the origins of temperature dependence of the axial vortical effect, i.e. generation of an axial current in a rotating chiral medium along the rotation axis. We show that the corresponding transport coefficient depends, in general, on the number of light weakly interacting degrees of freedom, rather than on the gravitational anomaly. We also comment on the role of low-dimensional defects in the rotating medium, and appearance of the chiral vortical effect due to them.

“…on temperature has been investigated by various authors [8][9][10][11]. It is well understood that though the anomaly, which drives the decay, is temperature independent, nonetheless the amplitude does depend on T through the phase space or through the modification of the thermal quark propagators in evaluating explicitly the triangle diagram.…”

Section: Introductionmentioning

confidence: 99%

“…It is well understood that though the anomaly, which drives the decay, is temperature independent, nonetheless the amplitude does depend on T through the phase space or through the modification of the thermal quark propagators in evaluating explicitly the triangle diagram. In particular, [10,11] consider temperature effects in the Wess-ZuminoWitten (WZW) effective Lagrangian which incorporates the anomaly. The coefficient of the anomalous term corresponding to 0 !…”

Section: Introductionmentioning

confidence: 99%

Neutral pion decay in dense Skyrmion matter

Kalloniatis

Park

2005

We study the density dependence of the decay π 0 → γγ using the Skyrme Lagrangian to describe simultaneously both the matter background and mesonic fluctuations. The classical ground state configuration has different chiral properties depending on the skyrmion density, which is reflected in the physical properties of pion fluctuating on top of the classical background. This leads to large suppression at high density of both photo-production from the neutral pion and the reverse process. The effective charges of π ± are also discussed in the same framework.