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