In Perkins's Introduction to High Energy Physics, the author obtained the spin of neutral pions from the decay [tex]\pi^0 → 2\gamma[/tex] He argued that the z-component of the total photon spin in the above decay can have the value [itex]S_z=0[/itex] or [itex]2[/itex]. If [itex]s_\pi=1[/itex], then only [itex]S_z=0[/itex] is possible, and the two-photon amplitude must behave under rotation like [itex]P_1^m(\cos \theta)[/itex] with [itex]m=0[/itex]. Why does the orbit angular momentum [itex]l=1[/itex] in his reasoning? Acually I do not understand why only [itex]S_z=0[/itex] is possible. Since if there is a [itex]l_z[/itex], then [itex]S_z[/itex] can be both 0 and 2.