Quark fluctuations and anisotropic confinement in magnetic fields

TL;DR

This paper investigates how external magnetic fields influence the string tension in QCD by combining quasi-particle and collective treatments, comparing results with lattice data, and exploring the effects of magnetic fields through dielectric functions and effective quark masses.

Contribution

The study introduces a combined approach using 1/Nc-expansion and Wilson's strong coupling expansion to analyze magnetic field effects on QCD string tension, aligning with lattice results.

Findings

Qualitative trends match lattice QCD with small parameter C_B.

Quantitative agreement achieved with C_B ≈ 0 and strong coupling α_S ≈ 5.

String tension behavior explored from weak to strong magnetic fields.

Abstract

We study the string tension $\sigma$ of quantum chromodynamics (QCD) in external magnetic fields $B$ by combining the quasi-particle treatments for quarks with the collective treatments for gluons. We utilize the 1/Nc-expansion (Nc: number of colors) and the framework of Wilson's strong coupling expansion at long distance, and compare the resulting string tensions with the lattice data. The effects of magnetic fields are taken into account through the dielectric functions, which are evaluated from the one-loop polarization due to light flavor quarks with $B$-dependent effective masses $M_{\rm f}(B)\ ({\rm f}=u,d,s)$. All Landau levels are adopted in the calculations so that we can explore the string tensions from weak to strong magnetic fields. For the effective quark masses, we use a simple parameterization: $M_{\rm f}(B) = M_{\rm f}(0) + C_B |q_{\rm f}B|^{1/2}$ with $q_{\rm f}$ the electric charge of a given flavor and $C_B$ an adaptive parameter. We find that the parameter $C_B$ needs to be small, $C_B \lesssim 0.05$, to qualitatively reproduce the trends of lattice QCD results for $0 \leq |eB| \lesssim 1.5\, {\rm GeV}^2$. The quantitative agreement is found for $C_B \simeq 0$ and the strong coupling $\alpha_S \simeq 5$ in the infrared.