scholarly journals Degeneracy Patterns of Chiral Companions at Finite Temperature

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1400
Author(s):  
Juan M. Torres-Rincon

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.

2016 ◽  
Vol 31 (36) ◽  
pp. 1650199 ◽  
Author(s):  
Alejandro Ayala ◽  
Jorge David Castaño-Yepes ◽  
J. J. Cobos-Martínez ◽  
Saúl Hernández-Ortiz ◽  
Ana Julia Mizher ◽  
...  

We use the linear sigma model coupled to quarks, together with a plausible location of the critical end point (CEP), to study the chiral symmetry transition in the QCD phase diagram. We compute the effective potential at finite temperature and density up to the contribution of the ring diagrams, both in the low and high temperature limits, and use it to compute the pressure and the position of the CEP. In the high temperature regime, by comparing to results from extrapolated lattice data, we determine the model coupling constants. Demanding that the CEP remains in the same location when described in the high temperature limit, we determine again the couplings and the pressure for the low temperature regime. We show that this procedure gives an average description of the lattice QCD results for the pressure and that the change from the low to the high temperature domains in this quantity can be attributed to the change in the coupling constants which in turn we link to the change in the effective degrees of freedom.


2013 ◽  
Vol 22 (11) ◽  
pp. 1350077 ◽  
Author(s):  
TRAN HUU PHAT ◽  
NGUYEN TUAN ANH ◽  
PHUNG THI THU HA

We study systematically various types of phase transitions in nuclear matter at finite temperature T and baryon chemical potential μ based on the extended linear sigma model with nucleon degrees of freedom. It is shown that there are three types of phase transitions in nuclear matter: the chiral symmetry nonrestoration (SNR) at high temperature, the well-known liquid–gas (LG) phase transition at sub-saturation density and the Lifshitz phase transition (LPT) from the fully-gapped state to the state with Fermi surface. Their phase diagrams are established in the (T, μ)-plane and their physical properties are investigated in detail. The relationship between the chiral phase transition and the LG phase transition in nuclear matter is discussed.


1997 ◽  
Vol 12 (29) ◽  
pp. 5325-5357 ◽  
Author(s):  
A. P. Balachandran ◽  
S. Vaidya

There are numerous examples of approximately degenerate states of opposite parity in molecular physics. Theory indicates that these doubles can occur in molecules that are reflection-asymmetric. Such parity doubles occur in nuclear physics as well, among nuclei with odd A ~ 219–229. We have also suggested elsewhere that such doubles occur in particle physics for baryons made up of cbu and cbd quarks. In this article, we discuss the theoretical foundations of these doubles in detail, demonstrating their emergence as a surprisingly subtle consequence of the Born–Oppenheimer approximation, and emphasizing their bundle-theoretic and topological underpinnings. Starting with certain "low energy" effective theories in which classical symmetries like parity and time reversal are anomalously broken on quantization, we show how these symmetries can be restored by judicious inclusion of "high-energy" degrees of freedom. This mechanism of restoring the symmetry naturally leads to the aforementioned doublet structure. A novel byproduct of this mechanism is the emergence of an approximate symmetry (corresponding to the approximate degeneracy of the doubles) at low energies which is not evident in the full Hamiltonian. We also discuss the implications of this mechanism for Skyrmion physics, monopoles, anomalies and quantum gravity.


1997 ◽  
Vol 50 (1) ◽  
pp. 199 ◽  
Author(s):  
Hiroshi Toki ◽  
Shoichi Sasaki ◽  
Hiroko Ichie ◽  
Hideo Suganuma

Confinement and spontaneous chiral symmetry breaking are the most fundamental phenomena in quark nuclear physics, where hadrons and nuclei are described in terms of quarks and gluons. The dual Ginzburg–Landau (DGL) theory contains monopole fields as the most essential degrees of freedom. Their condensation in the vacuum is modelled to describe quark confinement in strong connection with QCD. We then demonstrate that the DGL theory is able to describe the spontaneous breakdown of chiral symmetry.


1992 ◽  
Vol 03 (05) ◽  
pp. 993-1009 ◽  
Author(s):  
H. MEYER-ORTMANNS ◽  
H.-J. PIRNER ◽  
A. PATKÓS

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.


1994 ◽  
Vol 321 (1-2) ◽  
pp. 66-74 ◽  
Author(s):  
D. Metzger ◽  
H. Meyer-Ortmanns ◽  
H.-J. Pirner

2006 ◽  
Vol 21 (04) ◽  
pp. 339-347 ◽  
Author(s):  
E. W. DIAS ◽  
B. HILLER ◽  
A. L. MOTA ◽  
M. C. NEMES ◽  
M. SAMPAIO ◽  
...  

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.


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