# Spin-isospin Kondo effects for $\Sigma_{c}$ and $\Sigma_{c}^{\ast}$ baryons and $\bar{D}$ and $\bar{D}^{\ast}$ mesons

## TL;DR

This paper investigates the Kondo effect involving $ ext{Sigma}_c$, $ ext{Sigma}_c^*$ baryons and $ar{D}$, $ar{D}^*$ mesons in nuclear matter, revealing how spin and isospin exchanges enhance the effect and proposing a mapping between vacuum and nuclear matter states.

## Contribution

It provides a detailed analysis of the Kondo effect for heavy baryons and mesons in nuclear matter, highlighting the role of combined spin and isospin exchanges and extending symmetry considerations.

## Key findings

- Spin and isospin exchange interactions magnify the Kondo effect.
- Existence of solutions under extended SU(4) symmetry.
- Conjecture of a mapping from vacuum to nuclear matter states.

## Abstract

We study the Kondo effect for a $\Sigma_{c}$ ($\Sigma_{c}^{\ast}$) baryon in nuclear matter. In terms of the spin and isospin ($\mathrm{SU}(2)_{\mathrm{spin}} \times \mathrm{SU}(2)_{\mathrm{isospin}}$) symmetry, the heavy-quark spin symmetry and the S-wave interaction, we provide the general form of the Lagrangian for a $\Sigma_{c}$ ($\Sigma_{c}^{\ast}$) baryon and a nucleon. We analyze the renormalization equation at the one-loop level, and find that the coexistence of spin exchange and isospin exchange magnifies the Kondo effect in comparison with the case where the spin-exchange interaction and the isospin-exchange interaction exist separately. We demonstrate that the solution exists for the ideal sets of the coupling constants, including the $\mathrm{SU}(4)$ symmetry as an extension of the $\mathrm{SU}(2)_{\mathrm{spin}} \times \mathrm{SU}(2)_{\mathrm{isospin}}$ symmetry. We also conduct a similar analysis for the Kondo effect of a $\bar{D}$ ($\bar{D}^{\ast}$) meson in nuclear matter. On the basis of the obtained result, we conjecture that there could exist a "mapping" from the heavy meson (baryon) in vacuum onto the heavy baryon (meson) in nuclear matter.