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

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.