Wednesday, 23 October 2019

quantum field theory - Shape of the Higgs branching ratio to ZZ


I've been looking at the, now very popular, graph of the SM Higgs decay branching ratios:




You see that the ZZ branching ratio has a funny dip around the $170\, GeV$, very different from the WW counterpart. It's true that graphs with Z will always have the $\gamma$ interference and, perhaps, this is the cause for this funny shape. However, the value of the mass for which this happens is not something that I can intuitively explain.


Given that I have no idea of the right answer, let me ask: What causes this dip in the $H\rightarrow ZZ$ branching ratio around $M_H=170\, GeV$?



Answer



The dip of the ZZ branching ratio - and all other branching ratios except for the WW branching ratio - near 170 GeV is caused by the increase of the total width (decay rate) at those masses. And the total width (decay rate) around 170 GeV increases exactly because the Higgs decays to the WW final states start to become possible. Because the total width goes up, the ratio of a (non-WW) partial width and the total width goes down - and this ratio is what we call the branching ratio.


Kostya wrote almost the same thing. But I want to emphasize a subtle point: note that in your graph, the branching ratio to WW is nonzero already from Higgs masses at 80 GeV or so. Similarly, the branching ratio to ZZ is nonzero from 90 GeV. How can a 90 GeV Higgs decay to two Z's, each of which has mass close to 90 GeV? Doesn't it violate energy conservation?


The answer is that the graph shows the decays to off-shell particles, not the final states. A Higgs boson may decay to one virtual and one real Z-boson. The virtual particle continues in its decay. To check this hypothesis, note that all decay channels in the graph are composed out of two particles. The actual final states of the decay will often include (many) more than two particles.


When the Higgs mass exceeds two times the mass of the W-bosons, the total width genuinely goes up because there's suddenly a lot of new "phase space" of the final states.


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