# Two questions about the Higgs decay mode graph

I have two questions reading this graph which shows the Higgs decay mode: I know the mass of Higgs bosons is measured to be around 125 GeV, which is the solid line on the graph, so I wonder why could the mass on the x-axis become other values other than the measured results, and why are we interested in different Higgs masses?

Another question is why there's no data for the Higgs decay into 4 leptons, on the graph?

Thanks for the help!

• It would be good to add a reference for the figure. Apr 26, 2022 at 23:33
• @Andrew Thanks for the answer! The figure comes from page 18 of this talk: cds.cern.ch/record/2772949/files/ATL-PHYS-SLIDE-2021-268.pdf
– IGY
Apr 26, 2022 at 23:58
• Thanks. Just skimming it, I would guess that the way this plot was used was to say something like "you can see that at a Higgs mass of 125 GeV, many branching ratios are simultaneously large, which means we can do lots of consistency tests to look for physics beyond the Standard Model." In other words, in the context of the talk, I suspect the plot was just motivation. I am not sure what the original context of the plot was, though (since the plot has a date of 2013, years before this 2021 talk was given). Apr 27, 2022 at 0:03
• @Andrew Thank you so much :)
– IGY
Apr 27, 2022 at 0:05
• There is plenty of stuff on 4 l modes on the next page, (3), indeed.... Apr 27, 2022 at 0:06

Based on the date (2013), I assume this figure was made before the Higgs was discovered or its mass was published. The curves are based on a theoretical calculation of the various branching ratios as a function of the Higgs mass within the Standard Model. If the branching ratios are also measured then this would be a way to measure the Higgs, or at least one can check the consistency of the measured Higgs mass and branching ratios, with the Standard Model prediction.

There is not a direct coupling between the Higgs and 4 leptons in the Standard Model. I believe the decay process you have in mind is $$H\rightarrow ZZ \rightarrow 4\ell$$ (Higgs decays to two $$Z$$ bosons which decay to a set of 4 leptons, either electrons or muons). (As @joseph h mentions in the comments, there are also other decay modes that lead to 4 leptons, like $$H\rightarrow WW \rightarrow 4\ell$$ and $$H\rightarrow t\bar{t}\rightarrow 4\ell$$). The four leptons are stable enough to be directly detected. However, I believe this plot is showing direct decays of the Higgs into other particles, ignoring the future decays that will occur before the final products are seen in a detector.

I can't be 100% sure about what message this plot was intended to send without additional context, though (like, what paper was it published in).

• Good. +1. There's also the $H\rightarrow WW\rightarrow 4l$ and $H\rightarrow t\bar t\rightarrow 4l$ second order contributions. The direct decay particles are usually the $W$, $Z$ and heavier quarks $(c,t,b)$. Apr 27, 2022 at 0:07
• @josephh Thanks, I added these as well. Apr 27, 2022 at 0:09
• My memory from a decade ago is a little hazy, but I remember seeing figures with these curves before the 2012 announcement that a Higgs candidate had been observed at CERN. I remember being surprised, based on this figure, that the two- photon channel was where the discovery happened, because that channel is so low down in the branching ratio hierarchy.
– rob
Apr 27, 2022 at 1:07
• I was, as a person from a different branch of physics, surprised there is any branching to photons at all. But it is obviously not at tree level. Apr 27, 2022 at 8:06
• @VladimirFГероямслава Right. For example you can have a one loop diagram with a top quark in the loop, one external Higgs line, and two external photon lines. Apr 27, 2022 at 8:43