Chiral scalar spinor overlap (${\bar{u}}_R{u}_L=m_{\mathrm{spinor}}$)

A Lorentz scalar Dirac bilinear connects opposite chiralities. In the stated on-shell normalization ${\bar{u}}_R{u}_L=m_{\mathrm{spinor}}$, whereas ${\bar{u}}_L{u}_L=0$. Such an overlap verifies the allowed Lorentz structure but does not determine an independent coefficient multiplying a different mass operator.