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 ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{K}}\ensuremath{\simeq}\sqrt{{e}_{q}B}{\ensuremath{\alpha}}_{s}^{1/3}\mathrm{exp}{\ensuremath{-}4\ensuremath{\pi}/{N}_{c}{\ensuremath{\alpha}}_{s}\mathrm{log}(4\ensuremath{\pi}/{\ensuremath{\alpha}}_{s})}$ where ${\ensuremath{\alpha}}_{s}$ 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.