• Open Access

Pole and screening masses of neutral pions in a hot and magnetized medium: A comprehensive study in the Nambu–Jona-Lasinio model

Bingkai Sheng, Yuanyuan Wang, Xinyang Wang, and Lang Yu
Phys. Rev. D 103, 094001 – Published 7 May 2021

Abstract

In this work, we investigate not only the pole masses but also the screening masses of neutral pions at finite temperature and magnetic field by utilizing the random phase approximation (RPA) approach in the framework of the two-flavor Nambu–Jona-Lasinio model. And two equivalent formalisms in the presence of a magnetic field, i.e., the Landau level representation and the proper-time representation (PTR), are applied to obtain the corresponding analytical expressions of the polarization functions (except the expressions for the pole masses in the PTR). In order to evaluate the applicable region of the low-momentum expansion (LME), we compare the numerical results within the full RPA (FRPA) with those within the reduced RPA, i.e., the RPA in the LME. It is confirmed that the pole masses of π0 in the FRPA suffer a sudden mass jump at the Mott transition temperature when in the presence of external magnetic field, the Mott transition temperature is catalyzed by the magnetic field. And by analyzing the behaviors of the directional sound velocities of π0, which are associated with the breaking of the Lorentz invariance by the heat bath and the magnetic field, we clarify the two problems existing in previous literatures: one is that the transverse sound velocities in the medium are always larger than unity and thus violate the law of causality on account of the noncovariant regularization scheme, and the other is that the longitudinal sound velocities are identically equal unity at finite temperature on account of the limitation of the derivative expansion method used.

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  • Received 19 October 2020
  • Accepted 8 April 2021

DOI:https://doi.org/10.1103/PhysRevD.103.094001

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Nuclear PhysicsParticles & Fields

Authors & Affiliations

Bingkai Sheng1, Yuanyuan Wang1, Xinyang Wang2,*, and Lang Yu1,†

  • 1College of Physics, Jilin University, Changchun 130012, People’s Republic of China
  • 2Department of Physics, Jiangsu University, Zhenjiang 212013, People’s Republic of China

  • *wangxy@ujs.edu.cn
  • yulang@jlu.edu.cn

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Vol. 103, Iss. 9 — 1 May 2021

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