Spinor Operator Giving Both Angular Momentum and Parity

In heavy quark effective theory, heavy mesons which contain a heavy quark (or antiquark) are classified by $s_l^{pi_l}$, i.e., the total angular momentum $s_l$ and the parity $pi_l$ of the light quark degrees of freedom around a static heavy quark. In this case, however, one needs to separately estimate the parity other than the angular momentum of a light quark to describe heavy mesons. A new operator $K$ was proposed some time ago by two of us (T.M. and T.M.). In this Letter, we show that the quantum number $k$ of this operator is enough to describe both the total angular momentum of the light quark degrees of freedom and the parity of a heavy meson, and derive a simple relation between $k$ and $s_l^{pi_l}$.