[Paper Review] The compressibility of quark matter under strong magnetic field in the NJL model

Li Yang, Xin-Jian Wen|arXiv (Cornell University)|Nov 18, 2021

High-Energy Particle Collisions Research66 references5 citations

TL;DR

This paper investigates the compressibility of two-flavor quark matter under strong magnetic fields using the SU(2) Nambu-Jona-Lasinio (NJL) model. It reveals that compressibility decreases with increasing chemical potential and temperature, leading to a stiffer equation of state, while magnetic fields induce anisotropic compressibility with distinct longitudinal and transverse behaviors. A key result is the inverse proportionality of longitudinal compressibility to both magnetic field strength and chemical potential squared under the lowest Landau level approximation at zero temperature.

ABSTRACT

The compressibility of magnetized quark matter is investigated in the SU(2) NJL model. The increases of the chemical potential and the temperature can reduce the compressibility, and lead to the much stiffer equation of state. The variation of the compressibility with the magnetic field will depend on the phase region. Due to the anisotropic structure, the compressibility is different in the directions parallel and perpendicular to the field. The discontinuity of longitudinal compressibility with the chemical potential and the temperature captures the signature of a first-order chiral phase transition and the crossover at high temperature. Moreover, the magnetic-field-and-temperature running coupling would have an important effect on the position of the phase transition. Under the lowest landau level approximation at zero temperature, the longitudinal compressibility has a direct inverse proportional relation to the magnetic field strength and the chemical potential square as $\kappa^\parallel_{\mathrm{LLL},\chi}\propto1/(eB \mu^2)$.

Motivation & Objective

• To study the compressibility of two-flavor quark matter in the presence of strong magnetic fields.
• To examine the effects of finite temperature and chemical potential on compressibility and equation of state stiffness.
• To investigate the anisotropic nature of compressibility due to magnetic field-induced Landau level quantization.
• To explore the role of magnetic-field- and temperature-dependent coupling in phase transition dynamics.
• To determine the analytical behavior of compressibility in the lowest Landau level regime at zero temperature.

Proposed method

• The SU(2) NJL model is employed to describe quark matter under strong magnetic fields, incorporating quark self-energy corrections via the mean-field approximation.
• The thermodynamic potential is calculated using the Magnetic Field Independent Regularization (MFIR) scheme based on the Hurwitz-Riemann zeta function to handle divergences.
• Quark condensates are decomposed into vacuum, magnetic field, and medium contributions, with Landau level quantization explicitly included.
• The longitudinal and transverse compressibilities are derived from the second derivative of the thermodynamic potential with respect to pressure.
• The lowest Landau level (LLL) approximation is applied at zero temperature to analytically derive the compressibility behavior.
• Numerical analysis is performed across varying magnetic fields, chemical potentials, and temperatures to map phase transitions and compressibility evolution.

Experimental results

Research questions

• RQ1 How does the compressibility of quark matter vary with increasing chemical potential and temperature in the presence of a strong magnetic field?
• RQ2 What is the origin of anisotropy in compressibility, and how do longitudinal and transverse components differ?
• RQ3 How does the magnetic field influence the phase transition structure, particularly in terms of first-order transitions and crossovers?
• RQ4 What analytical relation governs the longitudinal compressibility in the lowest Landau level limit at zero temperature?
• RQ5 How do magnetic-field- and temperature-dependent couplings affect the location and nature of chiral phase transitions?

Key findings

• The compressibility decreases with increasing chemical potential and temperature, leading to a stiffer equation of state.
• The longitudinal compressibility in the lowest Landau level approximation at zero temperature follows an inverse proportionality: κ∥_LLL,χ ∝ 1/(eBμ²).
• Transverse compressibility (κ⊥) is significantly larger than longitudinal compressibility (κ∥), with the difference diminishing at higher chemical potentials.
• A discontinuity in longitudinal compressibility with respect to chemical potential and temperature signals a first-order chiral phase transition.
• The inclusion of magnetic-field- and temperature-dependent coupling shifts the position of the chiral phase transition, affecting the critical behavior.
• The anisotropic compressibility arises from Landau level quantization, with distinct responses along and perpendicular to the magnetic field direction.