Magnetically induced QCD Kondo effect

TL;DR

This paper proposes a new type of QCD Kondo effect induced by strong magnetic fields, where Landau quantization leads to dimensional reduction and a finite density of states, resulting in characteristic scattering behavior in high-density quark matter.

Contribution

It introduces a novel magnetically induced QCD Kondo effect mechanism leveraging Landau quantization effects in strong magnetic fields.

Findings

Demonstrates the Kondo effect in a strong magnetic field via scattering amplitude analysis.

Estimates the Kondo scale as proportional to the magnetic field strength and coupling constants.

Shows the role of Landau quantization in enabling the effect in high-density quark matter.

Abstract

The "QCD Kondo effect" stems from the color exchange interaction in QCD with non-Abelian property, and can be realized in a high-density quark matter containing heavy-quark impurities. We propose a novel type of the QCD Kondo effect induced by a strong magnetic field. In addition to the fact that the magnetic field does not affect the color degrees of freedom, two properties caused by the Landau quantization in a strong magnetic field are essential for the "magnetically induced QCD Kondo effect"; (1) dimensional reduction to 1+1-dimensions, and (2) finiteness of the density of states for lowest energy quarks. We demonstrate that, in a strong magnetic field $B$, the scattering amplitude of a massless quark off a heavy quark impurity indeed shows a characteristic behavior of the Kondo effect. The resulting Kondo scale is estimated as $\Lambda_{\rm K} \simeq \sqrt{e_qB}\ \alpha_{s}^{1/3} {\rm{exp}}\{-{4}\pi/N_{c} \alpha_{s} {\rm{log}}( 4 \pi/\alpha_{s}) \}$ where $\alpha_{s}$ and $N_c$ are the fine structure constant of strong interaction and the number of colors in QCD, and $e_q$ is the electric charge of light quarks.