Flavor-nonsinglet axial Ward identity with equal quark masses (${\partial }_{\mu }{A}_a^{\mu }=m{P}_a,A_a^{\mu }=\bar{q}{\gamma }^{\mu }{\gamma }_5{\tau }_{a}q/2$)

For the Dirac equation with two equal quark masses $m$, the equations for $q$ and $\bar{q}$ give the divergence of the nonsinglet axial current as $im\bar{q}{\gamma }_5{\tau }_{a}q=m{P}_a$. The color chiral anomaly is absent in this nonsinglet identity because the quark flavor generator is traceless. Equivalently, the mass term in the Hamiltonian is $m\int S{d}^{3}x$, and the nonsinglet axial charge algebra of quark densities gives ${\dot{Q}}_{5,a}=m\int P_a{d}^{3}x$.