scholarly journals Solving the Gap Equation of the NJL Model through Iterations: Unexpected Chaos

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 492
Author(s):  
Angelo Martínez ◽  
Alfredo Raya
Keyword(s):  
Magnetic Field ◽  
Iterative Procedure ◽  
Proper Time ◽  
Thermal Bath ◽  
Coupling Constant ◽  
Regularization Scheme ◽  
Gap Equation ◽  
A Value ◽  
Njl Model

We explore the behavior of the iterative procedure to obtain the solution to the gap equation of the Nambu-Jona-Lasinio (NLJ) model for arbitrarily large values of the coupling constant and in the presence of a magnetic field and a thermal bath. We find that the iterative procedure shows a different behavior depending on the regularization scheme used. It is stable and very accurate when a hard cut-off is employed. Nevertheless, for the Paul-Villars and proper time regularization schemes, there exists a value of the coupling constant (different in each case) from where the procedure becomes chaotic and does not converge any longer.

The two-flavor NJL model with two-cutoff proper time regularization

2014 ◽  
Vol 29 ◽  
pp. 1460232 ◽  
Author(s):  
Zhu-Fang Cui ◽  
Yi-Lun Du ◽  
Hong-Shi Zong
Keyword(s):  
Phase Transition ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Proper Time ◽  
Model Parameters ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Regularization Scheme ◽  
Njl Model

In this paper, we use the two-flavor Nambu–Jona-Lasinio model together with the proper time regularization that has both ultraviolet and infrared cutoffs to study the chiral phase transition at finite temperature and zero chemical potential. The involved model parameters in our calculation are determined in the traditional way. Our calculations show that the dependence of the results on the choice of the parameters are really small, which can then be regarded as an advantage besides such a regularization scheme is Lorentz invariant.

scholarly journals NAMBU–JONA–LASINIO MODEL IN CURVED SPACETIME WITH MAGNETIC FIELD

1996 ◽  
Vol 11 (25) ◽  
pp. 2053-2063 ◽  
Author(s):  
B. GEYER ◽  
L.N. GRANDA ◽  
S.D. ODINTSOV
Keyword(s):  
Magnetic Field ◽  
Gravitational Field ◽  
Chiral Symmetry ◽  
Proper Time ◽  
Chiral Symmetry Breaking ◽  
Curved Spacetime ◽  
Njl Model ◽  
Nonzero Curvature ◽  
Curvature Approximation ◽  
The Magnetic Field

We discuss the phase structure of the NJL model in curved spacetime with magnetic field using 1/N-expansion and linear curvature approximation. The effective potential for composite fields [Formula: see text] is calculated using the proper-time cutoff in the following cases: (a) at nonzero curvature, (b) at nonzero curvature and nonzero magnetic field, and (c) at nonzero curvature and nonzero covariantly constant gauge field. Chiral symmetry breaking is studied numerically. We show that the gravitational field may compensate the effect of the magnetic field what leads to restoration of chiral symmetry.

scholarly journals Magnetic field driven enhancement of the weak decay width of charged pions

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Maximo Coppola ◽  
Daniel Gomez Dumm ◽  
Santiago Noguera ◽  
Norberto N. Scoccola
Keyword(s):  
Magnetic Field ◽  
Enhancement Factor ◽  
Uniform Magnetic Field ◽  
Weak Decay ◽  
Significant Suppression ◽  
Decay Constants ◽  
A Value ◽  
Njl Model ◽  
Charged Pions ◽  
The Magnetic Field

Abstract We study the effect of a uniform magnetic field $$ \overrightarrow{B} $$ B → on the decays $$ {\pi}^{-}\to {l}^{-}{\overline{\nu}}_l $$ π − → l − ν ¯ l , where l− = e−, μ−, carrying out a general analysis that includes four π− decay constants. Taking the values of these constants from a chiral effective Nambu-Jona-Lasinio (NJL) model, it is seen that the total decay rate gets strongly increased with respect to the B = 0 case, with an enhancement factor ranging from ∼ 10 for eB = 0.1 GeV2 up to ∼ 103 for eB = 1 GeV2. The ratio between electronic and muonic decays gets also enhanced, reaching a value of about 1 : 2 for eB = 1 GeV2. In addition, we find that for large B the angular distribution of outgoing antineutrinos shows a significant suppression in the direction of the magnetic field.

scholarly journals Exploring the BEC-BCS Crossover in a Cold and Magnetized 2-Color QCD

2017 ◽  
Vol 45 ◽  
pp. 1760066 ◽  
Author(s):  
Dyana C. Duarte ◽  
Pablo G. Allen ◽  
Ricardo L. S. Farias ◽  
Pedro H. A. Manso ◽  
Norberto N. Scoccola
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
External Magnetic Field ◽  
Magnetic Fields ◽  
Regularization Scheme ◽  
Magnetic Catalysis ◽  
Chemical Potentials ◽  
Njl Model

We study the BEC-BCS crossover in the presence of an external magnetic field for a two color NJL model with diquark interactions, giving special attention to the regularization scheme. We found a inverse magnetic catalysis on the critical chemical potentials, both for BEC phase transition and the BEC-BCS crossover for small values of magnetic fields, and a magnetic catalysis for large [Formula: see text].

scholarly journals Thermal conductivity in 3D NJL model under external magnetic field

2003 ◽  
Vol 33 (4) ◽  
pp. 397-411 ◽  
Author(s):  
E. J. Ferrer ◽  
V. P. Gusynin ◽  
V. de la Incera
Keyword(s):  
Magnetic Field ◽  
Thermal Conductivity ◽  
External Magnetic Field ◽  
Njl Model

Studies on proper time regularization and the QCD chiral phase transition

2019 ◽  
Vol 34 (01) ◽  
pp. 1950003
Author(s):  
Yu-Qiang Cui ◽  
Zhong-Liang Pan
Keyword(s):  
Phase Transition ◽  
Small Parameter ◽  
Effective Mass ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Proper Time ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Njl Model ◽  
The Difference

We investigate the finite-temperature and zero quark chemical potential QCD chiral phase transition of strongly interacting matter within the two-flavor Nambu–Jona-Lasinio (NJL) model as well as the proper time regularization. We use two different regularization processes, as discussed in Refs. 36 and 37, separately, to discuss how the effective mass M varies with the temperature T. Based on the calculation, we find that the M of both regularization schemes decreases when T increases. However, for three different parameter sets, quite different behaviors will show up. The results obtained by the method in Ref. 36 are very close to each other, but those in Ref. 37 are getting farther and farther from each other. This means that although the method in Ref. 37 seems physically more reasonable, it loses the advantage in Ref. 36 of a small parameter dependence. In addition, we also, find that two regularization schemes provide similar results when T [Formula: see text] 100 MeV, while when T is larger than 100 MeV, the difference becomes obvious: the M calculated by the method in Ref. 36 decreases more rapidly than that in Ref. 37.

scholarly journals Strange quark stars within proper time regularized ( 2+1 )-flavor NJL model

2020 ◽  
Vol 101 (6) ◽  
Author(s):  
Cheng-Ming Li ◽  
Shu-Yu Zuo ◽  
Yan Yan ◽  
Ya-Peng Zhao ◽  
Fei Wang ◽  
...  
Keyword(s):  
Strange Quark ◽  
Proper Time ◽  
Quark Stars ◽  
Njl Model

scholarly journals Rb, Rc and New Physics: An Updated Model Independent Analysis

1997 ◽  
Vol 12 (04) ◽  
pp. 723-742 ◽  
Author(s):  
P. Bamert
Keyword(s):  
Standard Model ◽  
Neutral Current ◽  
New Physics ◽  
Low Energy ◽  
Coupling Constant ◽  
A Value ◽  
Independent Analysis ◽  
The Standard Model ◽  
Necessary And Sufficient ◽  
Do So

We analyze LEP and SLC data from the 1995 Summer Conferences as well as from low energy neutral current experiments for signals of new physics. The reasons for doing this are twofold: first to explain the deviations from the Standard Model observed in Rb and Rc and second to constrain nonstandard contributions to couplings of the Z0 boson to all fermions and to the oblique parameters. We do so by comparing the data with the Standard Model as well as with a number of test hypotheses concerning the nature of the new physics. These include nonstandard [Formula: see text]-, [Formula: see text]- and [Formula: see text]-couplings as well as the couplings of the Z0 to fermions of the entire first, second and third generations and universal corrections to all up- and down-type quark couplings (as can arise see for example in Z' mixing models). We find that nonstandard [Formula: see text] couplings are both necessary and sufficient to explain the data and in particular the Rb anomaly. It is not possible to explain Rb, Rc and a value of the strong coupling constant consistent with low energy determinations invoking only nonstandard [Formula: see text]- and [Formula: see text]-couplings. To do so one has to have also new physics contributions to the [Formula: see text] or universal corrections to all [Formula: see text] couplings.

EFFECTS OF TEMPERATURE-DEPENDENT COUPLING CONSTANT EVOLUTION ON THE UNIFICATION SCALE

1987 ◽  
Vol 02 (07) ◽  
pp. 479-485 ◽  
Author(s):  
K. ENQVIST ◽  
K. KAJANTIE
Keyword(s):  
Gauge Coupling ◽  
Coupling Constants ◽  
Thermal Bath ◽  
Coupling Constant ◽  
Temperature Dependent ◽  
Cosmological Context ◽  
Effects Of Temperature

We discuss how the evolution of gauge coupling constants is affected by a thermal bath, the existence of which is natural to assume in a cosmological context. The temperature dependent renormalization prescription induced by the thermal bath can cause sizeable effects, and the unification scale is shifted from the value computed from the coupling constant evolution in vacuum.

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