Magic Mixing Angles for Doubly Heavy Baryons

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_\rm q+j_\rho\right)=\left(J, \^4l_\lambda/^2l_\lambda\\right) for a doubly heavy baryon in the standard \rho-\lambda configuration, where \boldsymbolj_\ell=\boldsymboll_\lambda+\boldsymbols_\rm q, \boldsymbols_\rho=\boldsymbols_\rm Q1+\boldsymbols_\rm Q2, and \boldsymbolj_\rho=\boldsymbols_\rho+\boldsymbolL_\rho. We point out that when we calculate decays of doubly heavy baryons, we need to consider decays of magically mixed states, such as (1S1p)1/2^-, (1S1p)3/2^- and so on.