Today the ATLAS and CMS experiments at CERN’s Large Hadron Collider (LHC) have presented the results of the analysis of all their most recent data. One tricky thing about the Higgs boson is that we do not know what is its mass, and so one needs to look for it in all its possible decay channels. ATLAS and CMS show that there is no Higgs boson with a mass above about 130 GeV and below 115 GeV (it could still be heavier than about 500 GeV but this is not favored by the theory).

Whether the Higgs boson exists or not, the ATLAS and CMS experiments moved today one big step closer to the answer.

Particle physicists call “standard model” our best theory of what are the smallest constituents of matter, and how they interact with each other by exchanging spin 1 particles. This standard model describes successfully and very precisely a wide range of experiments.

There is one problem though: all particles in this standard model are massless! And obviously that’s not correct as we have measured with precision the masses of most elementary particles and they are not zero! There is one way to save our “standard model” and that’s by adding another particle with spin zero: the Higgs boson. What’s special with the Higgs boson is that even in vacuum there is a non zero probability to find one. In the same way that a material below a certain temperature can become spontaneously magnetized, we think that the probability of the Higgs boson to be found in vacuum became non zero early on in the history of the universe and at that moment elementary particles got a mass. In this model the mass of an elementary particle is just a measure of how much the particle interacts with the ever present Higgs bosons in the vacuum.

Some say that not finding the Higgs would be a bigger discovery in itself, and this is true in the sense we would now be sitting with a standard model that predicts all particles to be massless, so our fundamental theory would be wrong. This would force a major rethink and whatever would come out we would have to figure out some important new things about the world we live in.

One way of looking at today’s results is that almost the entire possible mass range has been excluded apart from a small window which goes from 115 GeV to 130 GeV and we expect to cover this difficult region with the 2012 data, so we are really closing in now. One should remember that just about 1.5 year ago before the start of the LHC, most of the range above 115 GeV was unexplored, so a lot of ground was covered in little time.

The second way of looking at today’s results is by peering into the 115 – 130 GeV mass range. Both ATLAS and CMS actually see more collisions in that range than expected without a Higgs boson. Both ATLAS and CMS were expecting to exclude all Higgs masses above 124 GeV but could not do so because of a deviation in the data. That deviation is small but consistent in size with a Higgs boson in this mass range.

In this mass range the main characteristic signal of a Higgs boson signal would be a pair of highly energetic photons (“gamma-gamma”), but it could also decay into a pair of Z bosons (“ZZ”) and to a lesser extent into a pair of W bosons (“WW”). The ATLAS data show an excess in the gamma-gamma channel and an even more modest (but still an) excess in the ZZ and WW channels. These excesses are consistent with a Higgs boson with a mass of 126 GeV. CMS sees a modest but consistent excess in 5 different channels and this occurs at a mass a few GeV lower than the ATLAS excess.

One has to be very careful with statistics. Sometimes things happen even if they are very unlikely, maybe one day you win the lottery even if the chance was one in a million. So that’s the same in high energy physics, when you look at billions of collisions and search just for just a few that look like a Higgs boson decay, there is a chance that you find an excess compatible with a Higgs signal even if there is no Higgs. In the end physicists will call it a discovery only if its probability to be a statistical fluctuation is one in a million or less. Right now we are more like at a one in a thousand…

ATLAS quantified the excess to be 2.8 sigma in the gamma-gamma channel, 2.1 sigma in the ZZ channel and 1.4 sigma in the WW channel, which respectively correspond to approximately 1 chance in 200, 1 chance in 28 and 1 chance in 6. But you would be right to say that the probability of all three happening at the same time is much smaller and this is now 3.6 sigma or about one chance in 10000 (after proper combination and taking into account correlations). The other thing we have to take into account is that ATLAS and CMS are looking in many channels and many different mass intervals and this has the effect of increasing the odds of seeing something unusual just by chance, if we take this into account ATLAS excess is just 2.3 sigma or about 1 chance in 50. Overall the maximum deviation seen by CMS is 2.6 sigma but taking into account that CMS has looked at many channels and many mass intervals then the CMS excess is 1.9 sigma, which represents about chance in 20. So without doing a proper statistical combination the probability of both outcome is about one in a thousand and that’s far from the one in a million we need to claim a discovery. Still it is exciting.

If the excess at 126 GeV really is due to the Higgs boson then the 2012 data (an expected 20fb-1 per experiment ) will allow ATLAS and CMS to definitely prove its existence at this mass. If this is a statisical fluctuation then it will wash away with more data and at the end of 2012 ATLAS and CMS together should be able to exclude the entire Higgs mass range. Whether we exclude completely a Higgs or we are starting to see it, in any case it is pretty exciting. Knowing the Higgs mass and the perspective of measuring its properties and decay channels in detail will be a boost for dark matter searches. This will allow us to tremendously reduce the range of possible models for dark matter. If the Higgs is completely excluded then one of our favourite dark matter theories, namely supersymmetry, will be in danger. But we are not there yet.

Christophe….excellent article. Exciting times!

For the exclusion plot, I was looking for a more in-depth explanation of the ordinate axis. I read the explanation of the plot on ATLAS’ website and not sure I completely understand the sigma variable “Higgs production cross section we exclude”. Can you comment or point me to a reference…..thks

Hi Brett,

This is very confusing actually, there are two different sigmas that refer to two completely different things. In the text I refer to the number of sigmas (2.8, 2.1 …). This is just the width of a normal distribution and has only to do with statistics.

The sigma on the diagram is a different sigma and is the “cross section” which is a unit of area, so sigma can be expressed in cm^-2 or “barn”, see for instance:

http://en.wikipedia.org/wiki/Barn_(unit)

The cross section sigma is related to the probability to produce a particle in a collision, but here let’s assimilate it to the probability for simplicity. So sigma used on the y-axis is the probability to produce a Higgs boson.

Now from the theory of particle physics we can compute from basic principles the value of sigma, given the particle’s properties, in this case a Higgs boson. On the plot sigmaSM is just this probability to produce a Higgs boson computed from the theory.

So when we look at the data and see that the data gives us approximately the same number of collisions as we expect from the background, then we can exclude that the probability to produce a Higgs (sigma) is very large. If sigma was very large, then we should see in data more collisions than the background only count. So by comparing the data and the background prediction you can exclude large values of sigma, it means you can write sigma < UpperLimit with a certain degree of statistical confidence.

If you do not have enough data then perhaps UpperLimit is higher than the cross section you predict for a normal higgs boson (sigmaSM), in that case you are not yet sensitive enough.

So the y-axis of the diagram is sigma/sigmaSM which is the ratio between the actual probability to produce a Higgs in Nature divided by the theoretical probability to produce a Higgs. The diagram shows the exclusion limit on this quantity sigma/sigmaSM. So if the upper limit on sigma/sigmaSM is less than one it means you have excluded that the probability to produce a higgs boson in real life is as large as the one expected from theory. If the limit on sigma/sigmaSM is for instance 0.5 it means that you have excluded the higgs boson even if its probability in nature to be produced was half of what you expect from theory.