Holographic rho mesons in an external magnetic field

TL;DR

This paper uses a holographic QCD model to study how a uniform magnetic field affects rho mesons, revealing differences in up- and down-flavor responses, and predicts a critical magnetic field for rho meson condensation.

Contribution

It introduces a holographic approach to analyze rho mesons in magnetic fields, incorporating chiral magnetic catalysis and refining predictions of the critical magnetic field for condensation.

Findings

Up- and down-flavor branes respond differently to magnetic fields.

Critical magnetic field for rho meson condensation is increased to 1.1 m_rho^2.

Chiral magnetic catalysis raises constituent quark masses with magnetic field.

Abstract

We study the rho meson in a uniform magnetic field eB using a holographic QCD-model, more specifically a D4/D8/Dbar8 brane setup in the confinement phase at zero temperature with two quenched flavours. The parameters of the model are fixed by matching to corresponding dual field theory parameters at zero magnetic field. We show that the up- and down-flavour branes respond differently to the presence of the magnetic field in the dual QCD-like theory, as expected because of the different electromagnetic charge carried by up- and down-quark. We discuss how to recover the Landau levels, indicating an instability of the QCD vacuum at eB = m_rho^2 towards a phase where charged rho mesons are condensed, as predicted by Chernodub using effective QCD-models. We improve on these existing effective QCD-model analyses by also taking into account the chiral magnetic catalysis effect, which tells us that the constituent quark masses rise with eB. This turns out to increase the value of the critical magnetic field for the onset of rho meson condensation to eB = 1.1 m_rho^2 = 0.67 GeV^2. We briefly discuss the influence of pions, which turn out to be irrelevant for the condensation in the approximation made.