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_\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.