Diquarks and nucleons under strong magnetic fields in the NJL model

M Coppola,N N Scoccola,D Gomez Dumm

doi:10.1103/physrevd.102.094020

Abstract

We study the description of nucleons and diquarks in the presence of a uniform strong magnetic field within the framework of the two-flavor Nambu-Jona--Lasinio (NJL) model. Diquarks are constructed through the resummation of quark loop chains using the random phase approximation, while nucleons are treated as bound quark-diquark states described by a relativistic Fadeev equation, using the static approximation for quark exchange interactions. For charged particles, analytical calculations are performed using the Ritus eigenfunction method, which properly takes into account the breakdown of translation invariance that arises from the presence of Schwinger phases. Within this scheme, for definite model parametrizations we obtain numerical predictions for diquark and nucleon masses, which are compared with Chiral Perturbation Theory and Lattice QCD results. In addition, numerical estimations for nucleon magnetic moments are obtained.

Highlights

In recent years, a significant effort has been devoted to the study of the properties of strongly interacting matter under the influence of strong magnetic fields
As done in Ref. [16], we take the parameter set m0 1⁄4 5.66 MeV, Λ 1⁄4 613.4 MeV, and GΛ2 1⁄4 2.250, which corresponds to a constituent quark mass M 1⁄4 350 MeV and a quark-antiquark condensate hffi 1⁄4 ð−243.3 MeVÞ3. This parametrization properly reproduces the empirical values of the pion mass and decay constant in vacuum, mπ 1⁄4 138 MeV and fπ 1⁄4 92.4 MeV. It provides a very good agreement with the results from lattice quantum chromodynamics (QCD) quoted in Ref. [30] for the normalized average ff condensate ΔΣðBÞ up to jeBj ≃ 1 GeV2 [16]
We have explored the effect of a strong external uniform magnetic field on diquark and nucleon masses

Summary

Introduction

A significant effort has been devoted to the study of the properties of strongly interacting matter under the influence of strong magnetic fields (see, e.g., [1,2,3], and references therein) This is mostly motivated by the realization that large magnetic fields might play an important role in the physics of the early Universe [4], in the analysis of high-energy noncentral heavy ion collisions [5], and in the description of physical systems such as magnetars [6]. Existing analyses are based either in the predictions of effective models or in the results obtained through lattice QCD (LQCD) calculations Most of these works have been focused on the properties of light mesons. To deal with low-energy QCD, various theoretical approaches have been followed, e.g., Nambu– Jona-Lasinio (NJL)-like models [7,8,9,10,11,12,13,14,15,16,17,18,19], quark-meson models [20,21], chiral perturbation theory (ChPT) [22,23,24], path integral Hamiltonians [25,26], effective chiral confinement Lagrangian approaches [27,28], and QCD sum rules [29]

Objectives

Results

Conclusion