Magnetically induced QCD Kondo effect

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 ${\mathrm{\Lambda }}_{\mathrm{K}}\simeq \sqrt{e_{q}B}{\alpha }_s^{1/3}\exp \{-4\pi /N_c{\alpha }_s\log (4\pi /{\alpha }_s)\}$ 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.

Figure 1

Dispersions of massless quarks in the LLL with right and left handed chiralities are shown in the $k^0-k^3$ plane where the magnetic field is imposed in the third ($z$) direction. The signs $\pm$ stand for the eigenvalues of the spin in the $z$ direction.

Figure 2

The tree diagram. Solid and double solid lines are massless and heavy quarks, respectively.

Figure 3

One-loop diagrams (a) a box diagram, (b) a crossed diagram.

Figure 4

Self-energy diagram of the heavy quark.

Figure 5

Leading order contribution to Fig. 4.

Figure 6

Next to leading order contribution to Fig. 4, corresponding to the box diagram.