On the Parity Degeneracy of Baryons

The gross features of the observed baryon excitation spectrum below 2 GeV are well explained if the spectrum generating algebra of its intrinsic orbital angular momentum states is o (4) ⊗ su (2)I. The spins of the resonances are obtained through the coupling of a Lorentz bi-spinor {1/2,0} ⊕ {0,1/2} to a multiplet of the type {j,j} in its O(4)/O(3) reduction. The parities of the resonances follow from those of the O(3) members of the {j,j} multiplets. In this way relativistic SL (2,C) representations are constructed. For example, the first S11, P11, and D13 states with masses around 1500 MeV fit into the {1/2,1/2} ⊗ [{1/2,0} ⊕ {0,1/2}] representation. The observed parities of the resonances correspond to natural parities of the {1/2,1/2} states. The second P11, S11, D13 — together with the first P13, F15, D15, and (a predicted) F17-resonances, centered around 1700 MeV, are organized into the {3/2,3/2} ⊗ [{1/2,0} ⊕ {0,1/2}] representation. We argue that the members of the {3/2,3/2} multiplet carry unnatural parities and that in this region chiral symmetry is restored. In the N(939)→ N(1650) transition the chiral symmetry mode is changed, and therefore, a chiral phase transition is predicted to take place.

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FIRST AND SECOND ORDER PHASE TRANSITIONS IN MAXWELL–CHERN–SIMONS THEORY COUPLED TO FERMIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x96000365 ◽

1996 ◽

Vol 11 (04) ◽

pp. 777-822 ◽

Cited By ~ 3

Author(s):

KEI-ICHI KONDO

Keyword(s):

Phase Transition ◽

Chiral Symmetry ◽

Dyson Equation ◽

Second Order ◽

Spontaneous Breaking ◽

Simons Theory ◽

Chiral Phase ◽

Chiral Phase Transition ◽

Chern Simons ◽

Chern Simons Theory

In the Maxwell–Chern–Simons theory coupled to Nf flavors of four-component fermions (or an even number of two-component fermions), we construct the gauge-covariant effective potential written in terms of two order parameters which are able to probe the breakdown of chiral symmetry and parity. In the absence of the bare Chern–Simons term, we show that the chiral symmetry is spontaneously broken for fermion flavors Nf below a certain finite critical number [Formula: see text] while the parity is not broken spontaneously. This chiral phase transition is of the second order. In the presence of the bare Chern–Simons term, on the other hand, the chiral phase transition associated with the spontaneous breaking of chiral symmetry is shown to continue to exist, although the parity is explicitly broken. However, it is shown that the existence of the bare Chern–Simons term changes the order of the chiral transition into the first order, no matter how small the bare Chern–Simons coefficient may be. This gauge-invariant result is consistent with that recently obtained through the Schwinger–Dyson equation in the nonlocal gauge.

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Restoration of chiral symmetry in cold and dense Nambu-Jona-Lasinio model with tensor renormalization group

Journal of High Energy Physics ◽

10.1007/jhep01(2021)121 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Shinichiro Akiyama ◽

Yoshinobu Kuramashi ◽

Takumi Yamashita ◽

Yusuke Yoshimura

Keyword(s):

Phase Transition ◽

Renormalization Group ◽

Chiral Symmetry ◽

Chiral Condensate ◽

Dense Region ◽

Chiral Phase ◽

Chiral Phase Transition ◽

First Order ◽

Anisotropic Tensor ◽

Fermion Action

Abstract We analyze the chiral phase transition of the Nambu-Jona-Lasinio model in the cold and dense region on the lattice, developing the Grassmann version of the anisotropic tensor renormalization group algorithm. The model is formulated with the Kogut-Susskind fermion action. We use the chiral condensate as an order parameter to investigate the restoration of the chiral symmetry. The first-order chiral phase transition is clearly observed in the dense region at vanishing temperature with μ/T ∼ O(103) on a large volume of V = 10244. We also present the results for the equation of state.

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LOW-MOMENTUM PION ENHANCEMENT INDUCED BY CHIRAL SYMMETRY RESTORATION

International Journal of Modern Physics A ◽

10.1142/s0217751x04016490 ◽

2004 ◽

Vol 19 (03) ◽

pp. 341-346

Author(s):

PENGFEI ZHUANG

Keyword(s):

Phase Transition ◽

Chiral Symmetry ◽

Finite Temperature ◽

Pion Production ◽

Dense Matter ◽

Chiral Symmetry Restoration ◽

Chiral Phase ◽

Chiral Phase Transition ◽

Symmetric Phase

The thermal and nonthermal pion production by sigma decay and its relation with chiral symmetry restoration in a hot and dense matter are investigated. The nonthermal decay into pions of sigma mesons which are popularly produced in chiral symmetric phase leads to a low-momentum pion enhancement as a possible signature of chiral phase transition at finite temperature and density.

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e+e− MODES AND U(1) SPONTANEOUS CHIRAL SYMMETRY BREAKING: A CASE STUDY

Modern Physics Letters A ◽

10.1142/s0217732392002627 ◽

1992 ◽

Vol 07 (34) ◽

pp. 3237-3244

Author(s):

KLAUS STEININGER

Keyword(s):

Phase Transition ◽

Symmetry Breaking ◽

Chiral Symmetry ◽

Chiral Symmetry Breaking ◽

Heavy Ion ◽

Particle Spectrum ◽

Chiral Phase ◽

Chiral Phase Transition ◽

Ion Collisions

Motivated by evidence for a chiral phase transition in strong coupling lattice QED we calculate the two-particle spectrum of the broken QED phase. This is done in the framework of a Nambu and Jona-Lasinio model with U(1) symmetry including chiral symmetry and symmetry breaking properties of QED. The second order chiral phase transition behavior in our model and in lattice QED are in excellent agreement. We then present a detailed analysis of the spectra of the e+e− modes in the broken phase. We examine whether these modes have any possible relationship to the narrow e+e− resonances found in soft heavy ion collisions at GSL. Our answer is negative.

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A TOY MODEL TO STUDY THE PEAK OF CHIRAL SUSCEPTIBILITY AND CHIRAL PHASE TRANSITION AT FINITE TEMPERATURE

Modern Physics Letters A ◽

10.1142/s0217732312501568 ◽

2012 ◽

Vol 27 (27) ◽

pp. 1250156

Author(s):

YU-QING ZHOU ◽

DONG KE ◽

HONG-TAO FENG

Keyword(s):

Phase Transition ◽

Chiral Symmetry ◽

Finite Temperature ◽

Chiral Condensate ◽

Sharp Peak ◽

Chiral Phase ◽

Chiral Phase Transition ◽

Chiral Susceptibility ◽

Increasing Temperature

In this paper, the chiral susceptibility and fermion chiral condensate are investigated in the same framework for Dyson–Schwinger equation. We show that, with the rise of temperature, the susceptibility gives a sharp peak where the chiral symmetry restores. The appearance of the peak and restoration at the same temperature suggests that the peak of chiral susceptibility can be treated as the hint for the restoration of chiral phase transition with the increasing temperature.

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