What is the ratio of the partial widths of the decay of the Higgs boson into the bound state of b quark and b anti quark and c quark and C anti quark
The Attempt at a Solution
Me and my friend disagree on the answer. I believe it should be the ratio of the masses of the particles and my friend believes it should be the ratio of the masses squared.
My reasoning is if you construct a Feynman diagram for this process then there is only one vertex and therefore one factor of coupling in the amplitude. The amplitude is proportional to the partial width and the mass is proportional to the coupling - therefore with everything else being constant the ratio results in the ratio of masses.
Their argument is that I'm missing a vertex from my diagram and you can't just have a Higgs boson propogate and decay without something creating it first. Hence another factor of the coupling would be introduced and by a similar argument you'd result in a ratio of mass squared.
Suffice to say were both abit confused. Any help greatly appreciated.