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BOAS

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## Homework Statement

Neutral vector mesons with ##J^{PC} = 1^{−−}## include the ##\phi## (mφ = 1020 MeV), ##J/\psi## (mJ/ψ = 3100 MeV), and ##\Upsilon## (mΥ = 9460 MeV), with quark content ss¯, cc¯, and b ¯b respectively. The decays of these mesons go largely to hadronic final states (jets), but there are non zero branching ratios to leptonic states via the process: qq¯ → γ → l+l-.

(a) Draw a Feynman diagram for the leptonic decay of a neutral vector meson, qq¯ → γ → l+l−, labelling all particles and coupling strengths.

(b) Show that the decay widths of the φ, J/ψ, and Υ to (all) leptonic states can be given approximately by the ratios: φ : J/ψ : Υ = 2 : 8 : 3.

(c) Compare the ratios of leptonic decay widths estimated in part (b) against experimental data as is found in the PDG (http://pdg.lbl.gov) and comment on the validity of your estimate.

## Homework Equations

## The Attempt at a Solution

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I have done parts (a) and (c) of this question, but am struggling to do part (b).

I think that these decays to leptonic states are governed by the EM interaction, and thus the interaction strength at each vertex in the Feynman diagrams should be ##\sqrt{\alpha}##.

I have also noticed that only the ##\Upsilon## is able to decay into a ##\tau^+ \tau^-## since they are so massive.

How do I go about calculating a decay width here?

I have been trying to read around the subject, but most of the material online seems to rely on QFT and other things I have not studied.

Any help would be greatly appreciated!

Thanks