Mixing angle between ${}^3{P}_1$ and ${}^1{P}_1$ in HQET

Abstract

Some claim that there are two independent mixing angles ($\theta =35.3^{\circ }$, $-54.7^{\circ }$) between ${}^3{P}_1$ and ${}^1{P}_1$ states of heavy-light mesons in heavy quark symmetric limit, and others claim there is only one ($\theta =35.3^{\circ }$). We clarify the difference between these two and suggest which should be adopted. General arguments on the mixing angle between ${}^3{L}_L$ and ${}^1{L}_L$ of heavy-light mesons are given in HQET and a general relation is derived in heavy quark mass limit as well as that including the first order correction in $1/m_Q$.

Comments: 6 pages, 1 table