Wave Functions of the Proton Ground State in the Presence of a Uniform Background Magnetic Field in Lattice QCD

TL;DR

This study investigates how a uniform magnetic field influences the quark wave functions within the proton's ground state using lattice QCD, revealing minimal distortion but notable elongation along the field axis.

Contribution

It provides the first detailed lattice QCD analysis of proton wave functions under a background magnetic field, highlighting diquark clustering and distribution elongation effects.

Findings

Diquark clustering is observed in the proton.

Magnetic field causes elongation of quark distributions along the field axis.

Overall distortion of distributions is small even at large fields.

Abstract

We calculate the probability distributions of quarks in the ground state of the proton, and how they are affected in the presence of a constant background magnetic field. We focus on wave functions in the Landau and Coulomb gauges. We observe the formation of a scalar u-d diquark clustering. The overall distortion of the quark probability distribution under a very large magnetic field, as demanded by the quantisation conditions on the field, is quite small. The effect is to elongate the distributions along the external field axis while localizing the remainder of the distribution.