Undergrad How often would a ϕ meson decay to a electron-positron pair?

[imgamedeving]

TL;DR

If a J/ψ decays to an electron-positron pair 5% of the time, how often would a ϕ
meson decay to a electron-positron pair?

I know the mass of J/ψ to be 3097 mev and the mass of phi to be 1018 mev. I know that J/ψ decays to electron and positron 5% of the time. I also know the full width of j/psi to be 0.092mev and that the phi meson lives 50 times longer than J/ψ
. My professor claims that if I am given that info and can draw the feynman diagrams for both interactions then it should be possible to make an estimate on how often the phi meson decays to electron-positron pair too. But I dont understand how this can done.I have drawn both diagrams (c-cbar or s-sbar to electron and positron with photon boson between). I also know the following formulas:

total width = \hbar / \tau where tau is the decay time of the particle. I also know that the branching fraction is given as:

BF = partial width / total widthIm not sure how one could estimate the branching fraction of phi to electron-positron pair.

 

[Vanadium 50]

My professor claims ,,, But I dont understand

And when you told him you didn't understand, what did he say?

If you are more interested in the answer, you can look it up: pdp.lbl.gov.

 

[mfb]

and that the phi meson lives 50 times longer than J/ψ

You might want to check that.