QCD chiral transition,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mi>A</mml:mi></mml:msub></mml:math>symmetry and the dirac spectrum using domain wall fermions

Buchoff, Michael I.; Cheng, Michael; Christ, Norman H.; Ding, Heng-Tong; Jung, Chulwoo; Karsch, Frithjof; Lin, Zhen; Mawhinney, Robert D.; Mukherjee, Swagato; Petreczky, Péter; Renfrew, Dwight; Schroeder, Chris; Vranas, P.; Yin, H.

doi:10.1103/physrevd.89.054514

Cited by 122 publications

(202 citation statements)

References 39 publications

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“…This is because we assume that the coefficient c A is fixed, and does not vary with temperature. This is clearly unphysical, as seen in lattice simulations [5], and as we discuss in Sec. (V F).…”

Section: Chiral Matrix Model At Nonzero Temperature a Complete Modelmentioning

confidence: 92%

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Chiral matrix model of the semi-QGP in QCD

Pisarski¹,

Skokov²

2016

Phys. Rev. D

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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

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Section: Chiral Matrix Model At Nonzero Temperature a Complete Modelmentioning

confidence: 92%

“…At present, for QCD with 2 + 1 light flavors, these simulations provide us with results, near the continuum limit, for the behavior of QCD in thermodynamic equilibrium [1][2][3][4][5][6][7][8][9][10][11][12][13]. Most notably, that there is a chiral crossover at a temperature of T χ ∼ 155 ± 9 MeV.…”

Section: Introductionmentioning

confidence: 99%

Chiral matrix model of the semi-QGP in QCD

Pisarski¹,

Skokov²

2016

Phys. Rev. D

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“…where P J are Legendre polynomials, θ is the scattering angle and T I is a particular combination involving Aðs; t; uÞ [defined in (4)] which gives the scattering amplitude at given isospin I, with tðs; cos θÞ, uðs; cos θÞ in the c.m. frame.…”

Section: Partial Wave Analysis and Unitaritymentioning

confidence: 99%

“…Moreover, chiral partners in the scalar-pseudoscalar sector are understood through degeneration of correlators and susceptibilities [26], something which is also directly seen in lattice data [4,5]. The role of the f 0 ð500Þ state for chiral restoration could become more complicated if its possible tetraquark component is also considered at finite temperature [27].…”

Section: Introductionmentioning

confidence: 99%

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Large-Npion scattering at finite temperature: Thef0(500)and chiral restoration

2016

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We consider the OðN þ 1Þ=OðNÞ nonlinear sigma model for large N as an effective theory for lowenergy QCD at finite temperature T, in the chiral limit. At T ¼ 0 this formulation provides a good description of scattering data in the scalar channel and dynamically generates the f 0 ð500Þ pole, the pole position lying within experimental determinations. Previous T ¼ 0 results with this model are updated using newer analysis of pion scattering data. We calculate the pion scattering amplitude at finite T and show that it exactly satisfies thermal unitarity, which had been assumed but not formally proven in previous works. We discuss the main differences with the T ¼ 0 result, and we show that one can define a proper renormalization scheme with T ¼ 0 counterterms such that the renormalized amplitude can be chosen to depend only on a few parameters. Next, we analyze the behavior of the f 0 ð500Þ pole at finite T, which is consistent with chiral symmetry restoration when the scalar susceptibility is saturated by the f 0 ð500Þ state, in a second-order transition scenario and in accordance with lattice and theoretical analysis.

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