Magic mixing angles for doubly heavy baryons

Abstract

We study the so-called magic mixing angles for doubly heavy baryons. Defining that a magic mixing angle rotates states with definite ${}^{2S+1}(l_{\lambda }{)}_J$ to make them heavy-quark symmetric states, we derive the magic mixing angle only in the case $L_{\rho }=0$ between the heavy quark symmetric states with quantum numbers $\left(J,j_{\ell }\right)$ and the states with $\left(J,s_q+j_{\rho }\right)=\left(J,{\{}^4{l}_{\lambda }{/}^2{l}_{\lambda }\}\right)$ for a doubly heavy baryon in the standard $\rho -\lambda$ configuration, where ${\vec{j}}_{\ell }={\vec{l}}_{\lambda }+{\vec{s}}_q$, ${\vec{s}}_{\rho }={\vec{s}}_{Q1}+{\vec{s}}_{Q2}$, and ${\vec{j}}_{\rho }={\vec{s}}_{\rho }+{\vec{L}}_{\rho }$. We discuss how this mixing angle affects model building for a doubly heavy baryon.

6 pages, 1 figure