Spin-isospin Kondo effects for ${\Sigma }_c$ and ${\Sigma }_c^{\ast }$ baryons and $\bar{D}$ and ${\bar{D}}^{\ast }$ mesons

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.

Comments: 28 pages, 7 figures