In accord with Heisenberg’s uncertainty principle, short-lived particles have uncertain mass. So the Higgs boson, which gives mass to other particles, is uncertain about its own mass. New results from the CMS experiment at the CERN LHC have started to tell us how uncertain

The Higgs boson was discovered because it makes a bump. Specifically, when we measured the masses of lots of pairs of photons produced in collisions at the Large Hadron Collider at CERN, we found they clustered around the mass of 125 GeV. This is the sign that a new particle, with a mass corresponding to that 125 GeV, was being produced. Cheers, fizzy wine and Nobel Prizes (almost) all round.

But it would be very good to know how tightly clustered about 125 GeV those events were, for the following reason.

Embedded in quantum mechanics is the concept of complementary variables. These are quantities that are subject to Heisenberg’s uncertainty principle. Thus, since momentum and position are complementary, you cannot know both the position and the momentum of a particle with total precision. The more you know about the momentum, the less you know about the position, and vice-versa.



The same applies to energy and time. And this has a consequence for particle masses, since mass is essentially energy (E = mc²). If a particle is stable, it lives for ever without decaying, and in a sense it is not localised in time. This is true of an electron, for example. From measuring it, we learn nothing about the time it was produced. However, its mass is very precisely known and has no spread of values.

For a particle like the Higgs boson, which decays quickly, the situation is different. The existence of a Higgs is tightly constrained in time, because its life is so short. Because of this, its mass has an intrinsic spread – the "width" of the boson. The faster it decays, the wider the bump.



This is great because it means that if you can measure the width of the bump, you can check how many different ways the Higgs is decaying; even if it decays to particles you can't see, these decays will influence the width, making it wider because it will decay faster. Since there are many new theories where the Higgs can decay to exotic new-and-possibly-invisible particles, they would predict a wider Higgs boson bump, and we could test them this way – even if the decays they predict are invisible!



Unfortunately our detectors are not perfect, and they smear the mass peak too, introducing a width that is nothing to do with Heisenberg, and which is much bigger than any theoretically expected value for the intrinsic width.



A very interesting new result from the CMS experiment, based on a clever idea from Fabrizio Caola and Kirill Melnikov of Johns Hopkins University, has nevertheless managed to evade this problem, and constrain the Higgs width to about four times the width expected in the Standard Model – much better than I thought it could be done, and with great potential for the next run of the LHC, when we will have still more data.



It works like this.



One of the ways the Higgs boson can decay is to two Z bosons, which then decay to two leptons each. Plotting the combined mass of these leptons gives a bump. Here's the plot, and the red bump is the Higgs signal.



Facebook Twitter Pinterest CMS ZZ-to-four-leptons mass distribution Photograph: CMS/CERN

You can see that the bump is not standing on a simple, flat background. The blue distribution, which is the non-Higgs background, has an interesting shape. Especially, look at the bump around 200 GeV. This occurs because the mass of the Z boson is 91 GeV. So for four-lepton masses below twice this mass – 182 GeV – the Z bosons cannot have their most probable mass. They are somewhere off to the side of their own "mass width" distributions.



If we consider the contribution from the Higgs boson, then at 125 GeV the Higgs has the right mass but the Z bosons don't. At 182 GeV the Z bosons have the right mass but the Higgs doesn't. The enhancement at 182 GeV means that there is still a significant contribution from the Higgs even at quite high masses, a long way above 125 GeV. Top quarks can also be produced with the right mass at some point, and further enhance this (the top quark has a mass of about 173 GeV).



CMS compare the mass distribution at high masses to the distribution around 125 GeV. By simulating the effect of a very wide Higgs they can use their data to set a much tighter limit on the maximum width of the Higgs boson than would be possible by trying to measure it directly. We now know (with 95% confidence) that the Higgs width is less than 17.4 MeV, which is 4.2 times the expected width for the Standard Model Higgs (4.15 MeV).Still plenty of room for weird new, currently invisible Higgs decays, but much less room than there was before. Plus this technique looks to me to be rather promising for the next LHC run, when we will have even more four-lepton events, and can hopefully measure the width even if it is as narrow as 4.15 MeV.

I find it really interesting and impressive how much information one can squeeze out of data, once you actually have some … Well done CMS, Caola and Melnikov*.

* And, (27/3/2014) as has been pointed out to me, Kauer, Passarino and others who contributed to the development of this method.



Jon Butterworth’s book, Smashing Physics, is out on 22 May. You can order it now!