Why Does the Higgs Boson Prefer to Decay into W Bosons Over Z Bosons?

[kelly0303]

Hello! In the (famous) plot I attached we have the branches ratios for the Higgs decay for different Higgs masses. I am sure that sitting down and doing the Feynman diagram calculation (to 1 or 2 next to leading order?) I will get these curves. But I am a bit confused about the physics intuition behind the decay to W and Z. The coupling between Z and Higgs is bigger than the coupling between W and Higgs (by a factor of $\frac{1}{(cos{\theta_w})^2}$). Yet the branching ratio for Higgs to WW is almost double that Higgs to ZZ for a wide range of energies. Of course the mass of the Z is higher so the phase space is smaller in this case, compared to W, but I wouldn't expect that a 10GeV difference to create such a big effect on the branching ratio, especially at big Higgs masses where a 10GeV difference should be almost insignificant. Is there a physical intuition as to why is this happening or it's just math and renormalization group stuff, without an actual deep physical meaning? What I mean by this is: could someone, knowing all the parameters involved, but without actually calculating the Feynman diagrams, predict that the branching ratio to W will be bigger than to Z? Thank you!

 

[mfb]

At low masses (below both WW and ZZ threshold) the mass difference leads to a large difference in branching ratios. Then you get a narrow region where WW can be on-shell while ZZ has to be off-shell, that region is completely dominated by WW. Afterwards both WW and ZZ are important. The Higgs cross section working group has tables, the ratio of WW to ZZ approaches 2.0 at high Higgs mass. That makes me think it might be a simple counting thing in some way. W⁺W^- vs. W^-W⁺?

 

[Vanadium 50]

that makes me think it might be a simple counting thing in some way. W+W- vs. W-W+?

Yes.

One level deeper, it's the sum of the squares of Clebsch-Gordon coefficients that happen to be 1/3, 1/3 and 1/3.