scholarly journals Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field

2020 ◽  
Vol 101 (7) ◽  
Author(s):  
Aritra Das ◽  
Najmul Haque
Keyword(s):  
Magnetic Field ◽  
Sigma Model ◽  
Neutral Pion ◽  
Pion Mass ◽  
Linear Sigma Model ◽  
Arbitrary Magnetic Field

scholarly journals Magnetic field dependence of the neutral pion mass in the linear sigma model with quarks: The strong field case

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Alejandro Ayala ◽  
José Luis Hernández ◽  
L. A. Hernández ◽  
Ricardo L. S. Farias ◽  
R. Zamora
Keyword(s):  
Magnetic Field ◽  
Field Dependence ◽  
Magnetic Field Dependence ◽  
Sigma Model ◽  
Neutral Pion ◽  
Strong Field ◽  
Pion Mass ◽  
Linear Sigma Model ◽  
Field Case

scholarly journals Magnetic field dependence of the neutral pion mass in the linear sigma model coupled to quarks: The weak field case

2018 ◽  
Vol 98 (11) ◽  
Author(s):  
Alejandro Ayala ◽  
Ricardo L. S. Farias ◽  
S. Hernández-Ortiz ◽  
L. A. Hernández ◽  
D. Manreza Paret ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Field Dependence ◽  
Magnetic Field Dependence ◽  
Sigma Model ◽  
Neutral Pion ◽  
Pion Mass ◽  
Weak Field ◽  
Linear Sigma Model ◽  
Field Case

THE DEPENDENCE OF THE NUCLEON MASS ON THE PION MASS IN THE EXTENDED QUARK SIGMA MODEL

2010 ◽  
Vol 19 (10) ◽  
pp. 2051-2062 ◽  
Author(s):  
M. ABU-SHADY
Keyword(s):  
Sigma Model ◽  
Pion Mass ◽  
Mean Field ◽  
Field Approximation ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
Nucleon Mass ◽  
Field Equations ◽  
Analytic Expressions ◽  
The Mean

The dependence of the nucleon mass on the pion mass is studied in the framework of the extended quark sigma model. We apply the modified quark sigma model to analyze the pion–nucleon sigma term. Analytic expressions are derived using the Feynman–Hellman theorem. The field equations are solved in the mean-field approximation. The results are compared with the CP-PACS group and the cloudy bag model. The results indicate that the extended linear sigma model provides good agreement compared to other models in the mean-field approximation.

scholarly journals Effects of the Tsallis distribution in the linear sigma model

2015 ◽  
Vol 24 (11) ◽  
pp. 1550085 ◽  
Author(s):  
Masamichi Ishihara
Keyword(s):  
Critical Temperature ◽  
Energy Density ◽  
Sigma Model ◽  
Small Deviation ◽  
Pion Mass ◽  
Gibbs Distribution ◽  
Linear Sigma Model ◽  
Chiral Phase ◽  
Tsallis Distribution ◽  
Physical Quantities

The effects of the Tsallis distribution which has two parameters, [Formula: see text] and [Formula: see text], on physical quantities are studied using the linear sigma model in chiral phase transitions. The Tsallis distribution approaches the Boltzmann–Gibbs distribution as [Formula: see text] approaches one. The parameter [Formula: see text] dependences of the condensate and mass for various [Formula: see text] are shown, where [Formula: see text] is called temperature. The critical temperature and energy density are described with digamma function, and the [Formula: see text] dependences of these quantities and the extension of Stefan–Boltzmann limit of the energy density are shown. The following facts are clarified. The chiral symmetry restoration at [Formula: see text] occurs at low temperature, compared with the restoration at [Formula: see text]. The sigma mass and pion mass reflect the restoration. The critical temperature decreases monotonically as [Formula: see text] increases. The small deviation from the Boltzmann–Gibbs distribution results in the large deviations of physical quantities, especially the energy density. It is displayed from the energetic point of view that the small deviation from the Boltzmann–Gibbs distribution is realized for [Formula: see text]. The physical quantities are affected by the Tsallis distribution even when [Formula: see text] is small.

scholarly journals Can a Linear Sigma Model Describe Walking Gauge Theories at Low Energies?

2018 ◽  
Vol 175 ◽  
pp. 08024 ◽  
Author(s):  
Andrew Gasbarro
Keyword(s):  
Sigma Model ◽  
Gauge Theories ◽  
Pion Mass ◽  
Effective Field ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Lattice Data ◽  
Conformal Window ◽  
Quark Masses ◽  
Low Energies

In recent years, many investigations of confining Yang Mills gauge theories near the edge of the conformal window have been carried out using lattice techniques. These studies have revealed that the spectrum of hadrons in nearly conformal ("walking") gauge theories differs significantly from the QCD spectrum. In particular, a light singlet scalar appears in the spectrum which is nearly degenerate with the PNGBs at the lightest currently accessible quark masses. This state is a viable candidate for a composite Higgs boson. Presently, an acceptable effective field theory (EFT) description of the light states in walking theories has not been established. Such an EFT would be useful for performing chiral extrapolations of lattice data and for serving as a bridge between lattice calculations and phenomenology. It has been shown that the chiral Lagrangian fails to describe the IR dynamics of a theory near the edge of the conformal window. Here we assess a linear sigma model as an alternate EFT description by performing explicit chiral fits to lattice data. In a combined fit to the Goldstone (pion) mass and decay constant, a tree level linear sigma model has a Χ2/d.o.f. = 0.5 compared to Χ2/d.o.f. = 29.6 from fitting nextto-leading order chiral perturbation theory. When the 0++ (σ) mass is included in the fit, Χ2/d.o.f. = 4.9. We remark on future directions for providing better fits to the σ mass.

scholarly journals Chiral phase transition within the linear sigma model in the Tsallis nonextensive statistics based on density operator

2019 ◽  
Vol 28 (04) ◽  
pp. 1950020 ◽  
Author(s):  
Masamichi Ishihara
Keyword(s):  
Phase Transition ◽  
Sigma Model ◽  
Pion Mass ◽  
Free Particle ◽  
Chiral Condensate ◽  
Linear Sigma Model ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Nonextensive Statistics ◽  
Particle Approximation

We studied the chiral phase transition for small [Formula: see text] within the Tsallis nonextensive statistics of the entropic parameter [Formula: see text], where the quantity [Formula: see text] is the measure of the deviation from the Boltzmann–Gibbs statistics. We adopted the normalized [Formula: see text]-expectation value in this study. We applied the free particle approximation and the massless approximation in the calculations of the expectation values. We estimated the critical physical temperature, and obtained the chiral condensate, the sigma mass, and the pion mass, as functions of the physical temperature [Formula: see text] for various [Formula: see text]. We found the following facts. The [Formula: see text]-dependence of the critical physical temperature is [Formula: see text]. The chiral condensate at [Formula: see text] is smaller than that at [Formula: see text] for [Formula: see text]. The [Formula: see text]-dependence of the pion mass and that of the sigma mass reflect the [Formula: see text]-dependence of the condensate. The pion mass at [Formula: see text] is heavier than that at [Formula: see text] for [Formula: see text]. The sigma mass at [Formula: see text] is heavier than that at [Formula: see text] for [Formula: see text] at high physical temperature, while the sigma mass at [Formula: see text] is lighter than that at [Formula: see text] for [Formula: see text] at low physical temperature. The quantities which are functions of the physical temperature [Formula: see text] and the entropic parameter [Formula: see text] are described by only the effective physical temperature defined as [Formula: see text] under the approximations.

scholarly journals Long way to Ricci flatness

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jin Chen ◽  
Chao-Hsiang Sheu ◽  
Mikhail Shifman ◽  
Gianni Tallarita ◽  
Alexei Yung
Keyword(s):  
Sigma Model ◽  
Ultra Violet ◽  
The Other ◽  
Target Space ◽  
Linear Sigma Model ◽  
Close Relative ◽  
Two Dimensional ◽  
World Sheet ◽  
Ricci Flat ◽  
The World

Abstract We study two-dimensional weighted $$ \mathcal{N} $$ N = (2) supersymmetric ℂℙ models with the goal of exploring their infrared (IR) limit. 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) are simplified versions of world-sheet theories on non-Abelian strings in four-dimensional $$ \mathcal{N} $$ N = 2 QCD. In the gauged linear sigma model (GLSM) formulation, 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) has N charges +1 and $$ \tilde{N} $$ N ˜ charges −1 fields. As well-known, at $$ \tilde{N} $$ N ˜ = N this GLSM is conformal. Its target space is believed to be a non-compact Calabi-Yau manifold. We mostly focus on the N = 2 case, then the Calabi-Yau space is a conifold. On the other hand, in the non-linear sigma model (NLSM) formulation the model has ultra-violet logarithms and does not look conformal. Moreover, its metric is not Ricci-flat. We address this puzzle by studying the renormalization group (RG) flow of the model. We show that the metric of NLSM becomes Ricci-flat in the IR. Moreover, it tends to the known metric of the resolved conifold. We also study a close relative of the 𝕎ℂℙ model — the so called zn model — which in actuality represents the world sheet theory on a non-Abelian semilocal string and show that this zn model has similar RG properties.

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