Kondo effect of ${\overline{D}}_s$ and ${\overline{D}}_s^{*}$ mesons in nuclear matter

We study the Kondo effect for ${\overline{D}}_s$ and ${\overline{D}}_s^{*}$ mesons as impurity particles in nuclear matter. The spin-exchange interaction between the ${\overline{D}}_s$ or ${\overline{D}}_s^{*}$ meson and the nucleon induces the enhancement of the effective coupling in the low-energy scattering in the infrared region, whose energy scale of singularity is given by the Kondo scale. We investigate the Kondo scale in the renormalization group equation at nucleon one-loop level. We furthermore study the ground state with the Kondo effect in the mean-field approach, and present that the Kondo scale is related to the mixing strength between the ${\overline{D}}_s$ or ${\overline{D}}_s^{*}$ meson and the nucleon in nuclear matter. We show the spectral function of the impurity when the Kondo effect occurs.

Figure 1

The diagrams at nucleon one-loop level. The single (double) solid line indicates the propagator of the nucleon (${\overline{D}}_s^{(*)}$ meson).

Figure 2

A schematic figure of the spectral function of impurities for (i) $v=0$, (ii) $\left|v\right|\ll \delta$, and (iii) $\left|v\right|\gg \delta$ for $\delta ={\delta }^1+{\delta }^2$. Widths are indicated in the figure. There are degeneracies in the $\delta$-like peak and the broad peak, respectively, as denoted by $(\times 2)$ in (i).