scholarly journals Dependence of the crossover zone on the regularization method in the two-flavor Nambu–Jona-Lasinio model

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 089-103
Author(s):  
José Rubén Morones-Ibarra ◽  
Nallaly Berenice Mata-Carrizal ◽  
Enrique Valbuena-Ordóñez ◽  
Adrián Jacob Garza-Aguirre
Keyword(s):  
Phase Diagrams ◽  
Regularization Method ◽  
Proper Time ◽  
Regularization Methods ◽  
Quark Loop ◽  
End Points ◽  
Regularization Procedure ◽  
Njl Model ◽  
Villars Regularization ◽  
Ultraviolet Regularization

AbstractIn this article, we study the two-flavor Nambu and Jona-Lasinio (NJL) phase diagrams on the T–μ plane through three regularization methods. In one of these, we introduce an infrared three-momentum cutoff in addition to the usual ultraviolet regularization to the quark loop integrals and compare the obtained phase diagrams with those obtained from the NJL model with proper time regularization and Pauli–Villars regularization. We have found that the crossover appears as a band with a well-defined width in the T–μ plane. To determine the extension of the crossover zone, we propose a novel criterion, comparing it to another criterion that is commonly reported in the literature; we then obtain the phase diagrams for each criterion. We study the behavior of the phase diagrams under all these schemes, focusing on the influence of the regularization procedure on the crossover zone and the presence or absence of critical end points.

Light front Hamiltonian for boson form of QED (1 + 1) in Pauli–Villars regularization

2019 ◽  
Vol 34 (21) ◽  
pp. 1950113
Author(s):  
V. A. Franke ◽  
M. Yu. Malyshev ◽  
S. A. Paston ◽  
E. V. Prokhvatilov ◽  
M. I. Vyazovsky
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chiral Condensate ◽  
Light Front ◽  
Coupling Constants ◽  
Hamiltonian Approach ◽  
Chiral Perturbation ◽  
Dimensional Models ◽  
Villars Regularization ◽  
Ultraviolet Regularization

Light front (LF) Hamiltonian for QED in [Formula: see text] dimensions is constructed using the boson form of this model with additional Pauli–Villars-type ultraviolet regularization. Perturbation theory, generated by this LF Hamiltonian, is proved to be equivalent to usual covariant chiral perturbation theory. The obtained LF Hamiltonian depends explicitly on chiral condensate parameters which enter in a form of some renormalization of coupling constants. The obtained results can be useful when one attempts to apply LF Hamiltonian approach for [Formula: see text]-dimensional models like QCD.

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

Analysis of Order of the Sequential Regularization Solutions of Inverse Heat Conduction Problems

1989 ◽  
Vol 111 (2) ◽  
pp. 218-224 ◽  
Author(s):  
E. P. Scott ◽  
J. V. Beck
Keyword(s):  
Heat Conduction ◽  
Regularization Method ◽  
Heat Conduction Problem ◽  
Regularization Parameter ◽  
Inverse Heat Conduction Problem ◽  
Regularization Methods ◽  
Inverse Heat Conduction ◽  
Random Errors ◽  
Internal Temperature ◽  
Inverse Heat Conduction Problems

Various methods have been proposed to solve the inverse heat conduction problem of determining a boundary condition at the surface of a body from discrete internal temperature measurements. These include function specification and regularization methods. This paper investigates the various components of the regularization method using the sequential regularization method proposed by Beck and Murio (1986). Specifically, the effects of the regularization order and the influence of the regularization parameter are analyzed. It is shown that as the order of regularization increases, the bias errors decrease and the variance increases. Comparatively, the zeroth regularization has higher bias errors and the second-order regularization is more sensitive to random errors. As the regularization parameter decreases, the sensitivity of the estimator to random errors is shown to increase; on the other hand, the bias errors are shown to decrease.

scholarly journals A new regularization method for dynamic load identification

2020 ◽  
Vol 103 (3) ◽  
pp. 003685042093128 ◽  
Author(s):  
Linjun Wang ◽  
Yang Huang ◽  
Youxiang Xie ◽  
Yixian Du
Keyword(s):  
Dynamic Load ◽  
Regularization Method ◽  
Inverse Analysis ◽  
Vibration Isolation ◽  
Frame Structure ◽  
Tikhonov Regularization Method ◽  
Strength Analysis ◽  
Regularization Methods ◽  
Load Identification ◽  
Practical Engineering

Dynamic forces are very important boundary conditions in practical engineering applications, such as structural strength analysis, health monitoring and fault diagnosis, and vibration isolation. Moreover, there are many applications in which we have found it very difficult to directly obtain the expected dynamic load which acts on a structure. Some traditional indirect inverse analysis techniques are developed for load identification by measured responses. These inverse problems about load identification mentioned above are complex and inherently ill-posed, while regularization methods can deal with this kind of problem. However, most of regularization methods are only limited to solve the pure mathematical numerical examples without application to practical engineering problems, and they should be improved to exclude jamming of noises in engineering. In order to solve these problems, a new regularization method is presented in this article to investigate the minimum of this minimization problem, and applied to reconstructing multi-source dynamic loads on the frame structure of hydrogenerator by its steady-state responses. Numerical simulations of the inverse analysis show that the proposed method is more effective and accurate than the famous Tikhonov regularization method. The proposed regularization method in this article is powerful in solving the dyanmic load identification problems.

Conversion of neutron stars to 2 + 1 flavor Nambu–Jona-Lasinio quark stars as a mechanism for gamma-ray bursts

2017 ◽  
Vol 32 (37) ◽  
pp. 1750209
Author(s):  
Xiao-Yu Shu ◽  
Yong-Feng Huang ◽  
Hong-Shi Zong
Keyword(s):  
Phase Transition ◽  
Gamma Ray ◽  
Chemical Potential ◽  
Proper Time ◽  
Mean Field ◽  
Gamma Ray Bursts ◽  
Compact Stars ◽  
Relativistic Mean Field ◽  
Quark Stars ◽  
Njl Model

The phase transition from a neutron star to a quark star and its relation to gamma-ray bursts are investigated. A new model: the 2 + 1 flavor Nambu–Jona-Lasinio (NJL) model with the method of proper-time regularization (PTR) is utilized for the quark phase; while the Relativistic Mean Field (RMF) theory is used for the hadronic phase. The process of phase transition is studied by considering the chemical potential, paying special attention to the phase transition point and the emergence of strange quark matter. Characteristics of compact stars are illustrated, and the energy release during the phase transition is found to be [Formula: see text] erg.

scholarly journals SYMMETRY-PRESERVING LOOP REGULARIZATION AND RENORMALIZATION OF QFTs

2004 ◽  
Vol 19 (29) ◽  
pp. 2191-2204 ◽  
Author(s):  
YUE-LIANG WU
Keyword(s):  
Regularization Method ◽  
Proper Time ◽  
Dimensional Regularization ◽  
Energy Scale ◽  
Lagrangian Formalism ◽  
Quantum Field Theories ◽  
Characteristic Energy ◽  
Interaction Terms ◽  
Dimensional Interaction ◽  
Time Formalism

A new symmetry-preserving loop regularization method proposed in Ref. 1 is further investigated. It is found that its prescription can be understood by introducing a regulating distribution function to the proper-time formalism of irreducible loop integrals. The method simulates in many interesting features to the momentum cutoff, Pauli–Villars and dimensional regularization. The loop regularization method is also simple and general for the practical calculations to higher loop graphs and can be applied to both underlying and effective quantum field theories including gauge, chiral, supersymmetric and gravitational ones as the new method does not modify either the Lagrangian formalism or the spacetime dimension of original theory. The appearance of characteristic energy scale Mc and sliding energy scale μs offers a systematic way for studying the renormalization-group evolution of gauge theories in the spirit of Wilson–Kadanoff and for exploring important effects of higher dimensional interaction terms in the infrared regime.

Krein regularization of quantum chromodynamics

2015 ◽  
Vol 30 (26) ◽  
pp. 1550126 ◽  
Author(s):  
B. Forghan ◽  
M. R. Tanhayi
Keyword(s):  
Hilbert Space ◽  
Quantum Chromodynamics ◽  
Regularization Method ◽  
Negative Norm ◽  
Self Energy ◽  
Villars Regularization ◽  
Krein Regularization

In this paper, we use Krein regularization to study certain standard computations in quantum chromodynamics (QCD). In this method, the auxiliary modes[Formula: see text]— those with negative norms[Formula: see text]— are employed to calculate the quark self-energy, vacuum polarizations and vertex functions. We explicitly show that after making use of these modes and by taking into account the quantum metric fluctuation for the problems at hand, the conventional results can indeed be reproduced; but with the advantage of finite answers which require fewer mathematical procedures. An obvious merit of this approach is that the theory is naturally renormalized. The ultraviolet (UV) divergences disappear due to the presence of negative norm state, similar to the Pauli–Villars regularization method. We compare the answers of Krein regularization with the results of calculations which have been done in Hilbert space.

Proper time regularization at finite quark chemical potential

2016 ◽  
Vol 31 (14) ◽  
pp. 1650086 ◽  
Author(s):  
Jin-Li Zhang ◽  
Yuan-Mei Shi ◽  
Shu-Sheng Xu ◽  
Hong-Shi Zong
Keyword(s):  
Phase Transition ◽  
Chemical Potential ◽  
Chiral Limit ◽  
Proper Time ◽  
Quark Confinement ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Njl Model ◽  
Potential Case ◽  
Chiral Susceptibility

In this paper, we use the two-flavor Nambu–Jona-Lasinio (NJL) model to study the quantum chromodynamics (QCD) chiral phase transition. To deal with the ultraviolet (UV) issue, we adopt the popular proper time regularization (PTR), which is commonly used not only for hadron physics but also for the studies with magnetic fields. This regularization scheme can introduce the infrared (IR) cutoff to include quark confinement. We generalize the PTR to zero temperature and finite chemical potential case use a completely new method, and then study the chiral susceptibility, both in the chiral limit case and with finite current quark mass. The chiral phase transition is second-order in [Formula: see text] and [Formula: see text] and crossover at [Formula: see text] and [Formula: see text]. Three sets of parameters are used to make sure that the results do not depend on the parameter choice.

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.

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