Chiral Symmetry Restoration at Nonzero Temperature in the SU(3) \times SU(3) Linear Sigma Model

D.H. Rischke (RIKEN-BNL); J. Schaffner-Bielich (RIKEN-BNL); J.T. Lenaghan (Yale University)

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Chiral Symmetry Restoration at Nonzero Temperature in the SU(3) \times SU(3) Linear Sigma Model

J.T. Lenaghan (Yale University), D.H. Rischke (RIKEN-BNL), J. Schaffner-Bielich (RIKEN-BNL)

Nuclear Theory · Submitted 4 Apr 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Taking the experimental values for the meson masses, however, the transition is crossover.

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arXiv IDnucl-th/0004006 (version 1)

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CitationD.H. Rischke (RIKEN-BNL), J. Schaffner-Bielich (RIKEN-BNL), J.T. Lenaghan (Yale University). "Chiral Symmetry Restoration at Nonzero Temperature in the SU(3) \times SU(3) Linear Sigma Model." arXiv:nucl-th/0004006 (2000). https://pith.science/paper/NSFGB5LQ

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We study patterns of chiral symmetry breaking at zero temperature and its subsequent restoration at nonzero temperature within the $SU(3)_{r} \times SU(3)_{\ell}$ linear sigma model. Gap equations for the masses of the scalar and pseudoscalar mesons and the non-strange and strange quark condensates are systematically derived in the Hartree approximation via the Cornwall-Jackiw-Tomboulis formalism. In the chiral limit, the chiral symmetry restoring transition is found to be first order, as predicted by universality arguments. Taking the experimental values for the meson masses, however, the transition is crossover. The absence of the $U(1)_A$ anomaly is found to drive this transition closer to being first order. At large temperatures, the mixing angles between octet and singlet states approach ideal flavor mixing.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study patterns of chiral symmetry breaking at zero temperature and its subsequent restoration at nonzero temperature within the $SU(3)_{r} \times SU(3)_{\ell}$ linear sigma model.	contribution 0.98	0.85	0.07	asserted 0.63
s1	Gap equations for the masses of the scalar and pseudoscalar mesons and the non-strange and strange quark condensates are systematically derived in the Hartree approximation via the Cornwall-Jackiw-Tomboulis formalism.	method 0.98	0.94	0.04	asserted 1.00
s2	In the chiral limit, the chiral symmetry restoring transition is found to be first order, as predicted by universality arguments.	result 1.00	0.83	0.21	asserted 1.00
s3	Taking the experimental values for the meson masses, however, the transition is crossover.	result 1.00	0.87	0.42	asserted 1.00
s4	The absence of the $U(1)_A$ anomaly is found to drive this transition closer to being first order.	result 0.70	0.89	0.10	asserted 1.00
s5	At large temperatures, the mixing angles between octet and singlet states approach ideal flavor mixing.	result 1.00	0.84	0.08	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 0.87.

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Original abstract

We study patterns of chiral symmetry breaking at zero temperature and its subsequent restoration at nonzero temperature within the $SU(3)_{r} \times SU(3)_{\ell}$ linear sigma model. Gap equations for the masses of the scalar and pseudoscalar mesons and the non-strange and strange quark condensates are systematically derived in the Hartree approximation via the Cornwall-Jackiw-Tomboulis formalism. In the chiral limit, the chiral symmetry restoring transition is found to be first order, as predicted by universality arguments. Taking the experimental values for the meson masses, however, the transition is crossover. The absence of the $U(1)_A$ anomaly is found to drive this transition closer to being first order. At large temperatures, the mixing angles between octet and singlet states approach ideal flavor mixing.

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4 later papers by other authors are listed below: 1 used its method or tool, 2 used its data or values and 1 compared its own results with it.

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Used this paper's expressions, derived via the partially conserved axial current relation, for the expectation values and source terms.

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States the same result 1 paper

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These values agree approximately with those of a linear sigma model without a logarithmic coupling, as studied by Lenaghan, Rischke, and Schaffner-Bielich (LRS) in Ref. [ref] .

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