Feynman diagram for ##\mu^+\mu^-## production in ##p\bar{p}## reaction

[Nirmal Padwal]

Homework Statement

Remembering that helicity is conserved at high energies,
a) Draw a typical diagram for $\mu^+ \mu^-$-pair production, with an invariant mass around 30 GeV, in unpolarised $p\bar{p}$ collisions.
b) Derive an expression for the angular distribution (with respect to the $\bar{p}$ direction) of $\mu^+$ in the $\mu^+\mu^-$, centre-of-mass system.
(Hint: You will need to look up the appropriate $d^j_{m'm}$ rotation matrix elements)

Relevant Equations

1) $d^1_{11} = \frac{1}{2}(1+\cos\theta)$
2) $d^1_{-11} = \frac{1}{2}(1-\cos\theta)$

I was able to solve b) but I am confused for a). I understand that in the proton-antiproton collision, only two quarks (one from proton and other from anti-proton) can be combined to get a virtual photon that in turn creates muon and anti-muon. I don't understand what would happen to the other quarks? Since single quarks cannot exist independently, I think maybe they combine to form mesons. Is that correct? But which meson? If I take $u$ and $\bar{u}$ from $p$ and $\bar{p}$ respectively (please check the feynman diagram below), I am still left with $u,d,\bar{u},\bar{d}$. Do they combine to give two $\pi^0$s or $\pi^+\pi^-$?

 

[topsquark]

Homework Statement:: Remembering that helicity is conserved at high energies,
a) Draw a typical diagram for $\mu^+ \mu^-$-pair production, with an invariant mass around 30 GeV, in unpolarised $p\bar{p}$ collisions.
b) Derive an expression for the angular distribution (with respect to the $\bar{p}$ direction) of $\mu^+$ in the $\mu^+\mu^-$, centre-of-mass system.
(Hint: You will need to look up the appropriate $d^j_{m'm}$ rotation matrix elements)
Relevant Equations:: 1) $d^1_{11} = \frac{1}{2}(1+\cos\theta)$
2) $d^1_{-11} = \frac{1}{2}(1-\cos\theta)$

I was able to solve b) but I am confused for a). I understand that in the proton-antiproton collision, only two quarks (one from proton and other from anti-proton) can be combined to get a virtual photon that in turn creates muon and anti-muon. I don't understand what would happen to the other quarks? Since single quarks cannot exist independently, I think maybe they combine to form mesons. Is that correct? But which meson? If I take $u$ and $\bar{u}$ from $p$ and $\bar{p}$ respectively (please check the feynman diagram below), I am still left with $u,d,\bar{u},\bar{d}$. Do they combine to give two $\pi^0$s or $\pi^+\pi^-$?
View attachment 323288

It's not so much a matter of which happens, it's a matter of which is more likely. I haven't checked the tables but I would suspect that both versions are about equally probable

-Dan