Magnetically induced QCD Kondo effect

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.