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We analyze the helicity conservation following from the axial Ward identityfor the massless fermion. We discuss the pair production of a fermion, $\ell$,and an anti-fermion, $\bar{\ell}$, from the annihilation process of photons,$\gamma$'s and conclude that the chirality production is prohibited in anyannihilation process of on-shell $\gamma$'s. We demonstrate this selection rulein the tree-level process of $\gamma+\gamma\to \ell+\bar{\ell}$. We nextconsider the off-shell effect on the chirality production in the presence ofthe background magnetic field. We point out that the particle conversionprocess under the magnetic field induces the polarization of an incident$\gamma$, which can also be interpreted intuitively from the helicityconservation.

Implications of the helicity conservation for on-shell and off-shell chirality production