MENDED CHIRAL SYMMETRY AND THE LINEAR SIGMA MODEL IN ONE-LOOP ORDER

1992 ◽  
Vol 07 (06) ◽  
pp. 497-505 ◽  
Author(s):  
M.D. SCADRON
Keyword(s):  
Chiral Symmetry ◽  
Decay Width ◽  
Sigma Model ◽  
Chiral Limit ◽  
Radiative Decays ◽  
Linear Sigma Model ◽  
Loop Order

It is shown that the linear σ-model in one-loop order in the chiral limit recovers meson masses mπ=0, mσ=2mqk (NJL), [Formula: see text] (KSRF), along with couplings [Formula: see text] (VMD universality) and Weinberg’s mended chiral symmetry decay width relation Γσ=(9/2)Γρ. The linear σ-model combined quark and meson loops also properly predict the radiative decays π0→2γ, π→evγ and δ0(983)→2γ.

CHIRAL SYMMETRY RESTORATION IN THE LINEAR SIGMA MODEL

1992 ◽  
Vol 03 (05) ◽  
pp. 993-1009 ◽  
Author(s):  
H. MEYER-ORTMANNS ◽  
H.-J. PIRNER ◽  
A. PATKÓS
Keyword(s):  
Chiral Symmetry ◽  
Sigma Model ◽  
Chiral Limit ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Gradual Change ◽  
Chiral Symmetry Restoration ◽  
Meson Octet ◽  
First Order Transition ◽  
Experimental Values

We report on results about the mass sensitivity of chiral symmetry restoration in the linear sigma model. For masses of the pseudoscalar meson octet which are close to the experimental values, we observed only a gradual change in the order parameters, when the temperature was changed. To estimate the size of the first order transition region around the chiral limit, we have varied the mass input for the tree level parametrization in several ways. The point with realistic meson masses turned out to lie well inside the crossover region.

scholarly journals DYNAMICAL GENERATION OF THE GAUGED SU(2) LINEAR SIGMA MODEL

1995 ◽  
Vol 10 (03) ◽  
pp. 251-266 ◽  
Author(s):  
R. DELBOURGO ◽  
M. D. SCADRON
Keyword(s):  
Sigma Model ◽  
Decay Constant ◽  
Chiral Limit ◽  
Linear Sigma Model ◽  
Coupling Constant ◽  
Vector Coupling ◽  
Dynamical Generation ◽  
Meson Coupling ◽  
Quark Level ◽  
The Masses

The fermion and meson sectors of the quark-level SU(2) linear sigma model are dynamically generated from a meson–quark Lagrangian, with the quark (q) and meson (σ, π) fields all treated as elementary, having neither bare masses nor expectation values. In the chiral limit, the masses are predicted to be mq = fπg, mπ = 0, mσ = 2mq, and we also find that the quark–meson coupling is [Formula: see text], the three-meson coupling is [Formula: see text] and the four-meson coupling is λ = 2g2 = g′/fπ, where fπ ≃ 90 MeV is the pion decay constant and Nc = 3 is the color number. By gauging this model one can generate the couplings to the vector mesons ρ and A1, including the quark–vector coupling constant gρ = 2π, gρππ, gA1ρπ and the masses mρ ~ 700 MeV, [Formula: see text]; of course the vector and axial currents remain conserved throughout.

scholarly journals Chiral symmetry restoration at finite temperature in the linear sigma-model

1994 ◽  
Vol 321 (1-2) ◽  
pp. 66-74 ◽  
Author(s):  
D. Metzger ◽  
H. Meyer-Ortmanns ◽  
H.-J. Pirner
Keyword(s):  
Chiral Symmetry ◽  
Finite Temperature ◽  
Sigma Model ◽  
Linear Sigma Model ◽  
Chiral Symmetry Restoration

scholarly journals SYMMETRIES AND AMBIGUITIES IN THE LINEAR SIGMA MODEL WITH LIGHT QUARKS

2006 ◽  
Vol 21 (04) ◽  
pp. 339-347 ◽  
Author(s):  
E. W. DIAS ◽  
B. HILLER ◽  
A. L. MOTA ◽  
M. C. NEMES ◽  
M. SAMPAIO ◽  
...  
Keyword(s):  
Chiral Symmetry ◽  
Sigma Model ◽  
Decay Constant ◽  
Linear Sigma Model ◽  
Pion Decay ◽  
Radiative Corrections ◽  
Pion Decay Constant ◽  
Renormalization Procedure

We investigate the role of undetermined finite contributions generated by radiative corrections in an SU (2)× SU (2) linear sigma model with quarks. Although some of such terms can be absorbed in the renormalization procedure, one such contribution is left in the expression for the pion decay constant. This arbitrariness is eliminated by chiral symmetry.

scholarly journals Degeneracy Patterns of Chiral Companions at Finite Temperature

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1400
Author(s):  
Juan M. Torres-Rincon
Keyword(s):  
Chiral Symmetry ◽  
Nuclear Physics ◽  
Degrees Of Freedom ◽  
Sigma Model ◽  
Smooth Transition ◽  
Linear Sigma Model ◽  
Spontaneous Breaking ◽  
Low Energies ◽  
Effective Theories ◽  
Chiral Partner

Chiral symmetry represents a fundamental concept lying at the core of particle and nuclear physics. Its spontaneous breaking in vacuum can be exploited to distinguish chiral hadronic partners, whose masses differ. In fact, the features of this breaking serve as guiding principles for the construction of effective approaches of QCD at low energies, e.g., the chiral perturbation theory, the linear sigma model, the (Polyakov)–Nambu–Jona-Lasinio model, etc. At high temperatures/densities chiral symmetry can be restored bringing the chiral partners to be nearly degenerated in mass. At vanishing baryochemical potential, such restoration follows a smooth transition, and the chiral companions reach this degeneration above the transition temperature. In this work I review how different realizations of chiral partner degeneracy arise in different effective theories/models of QCD. I distinguish the cases where the chiral states are either fundamental degrees of freedom or (dynamically-generated) composed states. In particular, I discuss the intriguing case in which chiral symmetry restoration involves more than two chiral partners, recently addressed in the literature.

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