by Tommaso Dorigo

Four years ago, the Higgs boson was officially declared an established subnuclear particle. With that announcement, an over 40 years long search finally reached its conclusion. But that day, July 4th 2012, also marked the start of a new epoch: the one of Higgs boson studies.

What we know about the Higgs boson, four years into the Higgs studies era, is a lot. We know, for instance, that its mass is of 125 GeV, give or take less than half a GeV. We are quite confident that it has null spin and positive parity, as expected by the Standard Model. And we know that the particle does decay similarly to what we predict.

However, there is much more that we still do not yet know about the newest elementary particle in town. We have founded reasons to believe that the Standard Model is not complete, and that it needs to be expanded to be consistent. So, as all other attempts have failed to provide hints of new physics, maybe it is through Higgs boson physics that we will eventually glimpse at what lies beyond.

The 2016 data taking curve is the steep yellow one. 

The Large Hadron Collider is delivering 13 TeV proton-proton collisions at an increased pace to the ATLAS and CMS experiments this year (see figure to the right: the 2016 data taking curve is the steep yellow one), and physicists are ready to look at the resulting new datasets to further improve our knowledge of the Higgs. Personally, one of the things I will be very happy to see with the new data is an improved measurement of the natural width of the Higgs boson.

What is the natural width? It is a fundamental property of elementary as well as composite subnuclear particles, determining the speed of their disintegration. The larger the width, the faster is the decay of the particle. If we measure the Higgs boson width and find out it is larger than what the Standard Model predicts, that would be an indirect, but very clean proof of the existence of new physics in the phenomenology of the Higgs boson: it would imply that new, that is yet unknown particles can “couple” to the Higgs boson, making its decay faster than expected.

Curiously, we can measure the Higgs boson width despite the fact that it is very small. The predicted value is just 4 MeV – a thirty-thousandth of its mass value. If we had an infinite precision detector we could measure it directly by looking at the spread of masses of the Higgs bosons we find in the data; unfortunately, the resolution on the Higgs mass is over 100 times larger than the natural width, so that kind of measurement is undoable. It’s just as if you wanted to measure the thickness of a human hair with a ruler. Good luck with it.

What comes to our rescue is that finite width effects in the Higgs boson width manifest themselves at high mass. The Higgs boson often decays to a pair of Z bosons, and one of the two is forced to have a mass quite smaller than its nominal value (as the Z mass is 91 GeV and the Higgs weighs 125 GeV, one of the two Z bosons needs to be “off mass-shell” for the decay to take place). Now, particles do not like to be off mass-shell -they like to “resonate” at their correct mass value. So the resonance shape of the Higgs boson gets deformed by the relative probability of the Z bosons to be far, or less far, from their own nominal mass. You can check for yourself the effect in the graph below.

Cross section versus invariant mass for Higgs decay to four leptons (red) compared to background processes. While the signal is larger than the backgrounds only around 125 GeV, there is a significant contribution at high masses, due to the top-pair hump. 

As you see, rather than just a narrow peak at 125 GeV, the Higgs mass distribution (red curve) has this funny tail at high mass; not only is there this turn-on-like enhancement at 182 GeV – twice the Z mass: there is also a further enhancement at twice the top quark mass, due to the same kind of effect. The Higgs would love it to decay to a top-antitop quark pair, and so the very fact that a top-antitop pair is a possible decay final state if the Higgs has a mass of 350 GeV enhances the probability that a Higgs boson gets such a unnaturally high mass value.

The reader (yes, the only one who survived up to this point of this post) be warned: the above is a simplification. In truth the resonance shape is created by subtle interference effects, and it is by no means trivial to understand. However, the basic points outlined above give an idea of the reason of the funny multi-humped structure. For an experimentalist, the shape gives a chance to search for off mass-shell Higgs bosons, and from their presence or absence an indirect measurement of the Higgs boson width can be extracted, as the width crucially affects the actual mass shape.

I do hope that ATLAS and CMS will present updates on their width measurements at ICHEP 2016, an international conference which will take place in Chicago in August.That would certainly be a great new contribution to Higgs physics.