Mixing angle between $^3P_1$ and $^1P_1$ in HQET

TL;DR

This paper clarifies the conflicting claims about the number of mixing angles between $^3P_1$ and $^1P_1$ states in heavy-light mesons within HQET, providing theoretical arguments and relations in the heavy quark limit.

Contribution

It resolves the debate on whether one or two mixing angles are relevant in heavy-light meson states and offers a theoretical framework for understanding these angles in HQET.

Findings

Clarifies the difference between one and two mixing angle claims.

Derives a general relation for mixing angles in the heavy quark limit.

Includes first order $1/m_Q$ corrections in the analysis.

Abstract

Some claim that there are two independent mixing angles ($\theta = 35.3^\circ$, $-54.7^\circ$) between $^3P_1$ and $^1P_1$ 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 $^3L_L$ and $^1L_L$ 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 $1/m_Q$.