What is the significance of neutral pions' spin in high energy physics?

[karlzr]

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

 

[mfb]

How do you get an l_z with two photons flying back to back in z-direction? I can imagine how you get l_x and l_y.

 

[karlzr]

How do you get an l_z with two photons flying back to back in z-direction? I can imagine how you get l_x and l_y.

What about the total angular momentum l=1? This is the real issue that bothers me.

 

[mfb]

I think the idea is that you get the total spin as combination of the photon spin ($S_z=0$) and the angular momentum (in a different direction, therefore $s_\pi \geq S_z$). But that is a bit speculative.

 

[andrien]

photon's mass is zero.the spin component along z-axis can be only +1 or -1.Since it still behaves like boson(integral spin),you should use the same rotation rotation matrix for m=0.If s=1,for pion then of course,0 is the only possible value.