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 $^{2S+1}(l_λ)_J$ to make them heavy-quark symmetric states, we derive the magic mixing angle only in the case $L_ρ=0$ between the heavy quark symmetric states with quantum numbers $\left(J, j_\ell\right)$ and the states with $\left(J, s_q+j_ρ\right)=\left(J, \{^4l_λ/^2l_λ\}\right)$ for a doubly heavy baryon in the standard $ρ-λ$ configuration, where $\vec j_\ell=\vec l_λ+\vec s_q$, $\vec s_ρ=\vec s_{Q1}+\vec s_{Q2}$, and $\vec j_ρ=\vec s_ρ+\vec L_ρ$. We discuss how this mixing angle affects model building for a doubly heavy baryon.