# 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 $M_H=170\, GeV$?

-

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.

-
Thanks for the answer, but could you please write my name with f? I appreciate. – Rafael Jan 24 '11 at 19:41
Fixed, @Rafael, apologies. I would always write it with a "f" but ten years in the U.S. and interactions with the likes of Raphael Bousso changes some detailed things. – Luboš Motl Jan 26 '11 at 9:25

Nice question. I did notice this "dip" too, but didn't think too much about it. While the explanation seems to be pretty simple:
$M_W \simeq 80\,\mbox{GeV},\quad M_Z \simeq 91\,\mbox{GeV}$

Therefore, around 170 GeV you are below the threshold for ZZ, but above the threshold for WW.

But I also think that this dip tends to be overemphasised on such a graph. First because of the logarithmic scale, and also since the branching ratio is the relative to the full width.

Edit: In response to Luboš Motl's response I'll add two more points:

1. The reference to the original of the plot: hep-ph/9704448
2. In fact, below the threshold it is safe (with 1% accuracy) to assume that one boson is on shell.
-

The branching ratio for a certain channel $i$ is given by the ratio of its partial decay with $\Gamma_i$ and the sum of all partial decay widths:

$$BR(H \rightarrow i) = \dfrac{\Gamma_i}{\sum_j \Gamma_j}$$

where the $\Gamma_i$ depend on the Higgs mass. If a new channel opens up or becomes important (such as the decay to a pair of W bosons at around twice the W boson mass), other channels become less likely, the new channel 'steals' branching ratio from the others.

(An analogy in daily life is the following: finding a cure for heart diseases reducing the probability of dying from a heart attack would increase the risk of dying from other diseases. At the same time, the overall life expectancy would go up. In particle physics, the total width $\Gamma = \sum_j \Gamma_j$ of a resonance is inversely proportional to its mean lifetime, longer living particles have smaller total width).

To illustrate this, here is a plot of the partial and total decay width (values taken from http://arxiv.org/abs/1307.1347 , Tables A.1-14):

You'll notice that the widths for decays to WW (solid blue line) and ZZ (solid red line) increase more rapidly at twice the W and Z mass respectively (note that the y axis is logarithmic) at which point both bosons can be produced on-shell.

-