Proton-Antiproton Annihilation

[Skatch]

Homework Statement

A proton and antiproton at rest in an S-state annihilate to produce $$\pi$$⁰$$\pi$$⁰ pairs. Show
that this reaction cannot be a strong interaction.

Homework Equations

I interpret this problem as:

p + p_bar -> $$\pi$$⁰ + $$\pi$$⁰

The Attempt at a Solution

If this were a strong interaction, Parity should be conserved, yes? I think that in the annihilation
described above, parity is not being conserved.But really, my first question is, am I interpreting it correctly? Is the annihiliation producing $$\pi$$⁰ + $$\pi$$⁰?
Or is it producing $$\pi$$⁰ + $$\pi$$⁰ + $$\pi$$⁰ + $$\pi$$⁰? Not sure what they mean by "$$\pi$$⁰$$\pi$$⁰ pairs".Then my next question is, what is the Parity of p_bar?

 

[Skatch]

Okay, so I think I've come to the conclusion that the Parity of the antiproton is -1.
I read that, in general, P(fermion * antifermion) = -1, and since proton's parity is +1, I'm
going to conclude that parity of the antiproton is -1.

Okay, so total parity on the left hand side of the equation is 0.

But I still don't know if I'm interpreting the problem correctly. Is the annihilation producing:

$$\pi$$⁰ + $$\pi$$⁰ ?

$$\pi$$⁰ + $$\pi$$⁰ + $$\pi$$⁰ + $$\pi$$⁰ ?

$$\pi$$⁰$$\pi$$⁰ ?

$$\pi$$⁰$$\pi$$⁰ + $$\pi$$⁰$$\pi$$⁰ ?

Pardon the ignorance here. I'm taking this Nuclear Physics class despite not meeting some
of the pre-reqs. I'm a math major that was just interested in the material, so I'm a bit
behind.

Thanks for any help.