The Hadron Collider Physics conference starts today in Paris and we eagerly await updates for various searches including the Higgs. 5/fb of luminosity have been collected in each experiment but it is too soon for the analysis of the full data to be out and this week we are only expecting results at 2/fb to be shown (but surprises are always possible) Indeed ATLAS have recently revealed updates for three of the diboson Higgs channels at 2/fb in conference notes and other conferences. These do not make much difference but an update to the diphoton search would be worth seeing. It has so far only been shown by ATLAS at 1/fb. CMS have only released results at 1.6/fb for the main Higgs decay modes so they are even more overdue for updates.
While we are waiting for that we can look forward to next year when results for 5/fb will be revealed, probably in March. When the results are combined we will see 10/fb and here is a plot showing the expected significance at that level. This is for 10/fb at CMS which can be taken as a good approximation for the ATLAS+CMS combination at 5/fb for each.
From this you can see that they expect at least 4 sigma significance all the way from 120 GeV to 550 GeV, which suggests that a good clear signal for the Higgs is almost certain if it exists, but not so fast. There are a couple of caveats that should be added.
Firstly the WW decay channels have been very good for excluding the Higgs over a wide mass range. Here is the viXra combined plot using 2/fb of ATLAS data and 1.5/fb from CMS.
This is only a rough approximation to what would be produced if they did an official version because it assumes a flat normal distribution uses a linear interpolation for CMS points and ignores any correlations.
Within those limitations we get an exclusion from 140 GeV to 218 GeV with a broad excess around 2 sigma extending all the way from 120 GeV to 160 GeV. A Standard Model Higgs in this region would only have a width of a few GeV and no bump of the sort is seen, so what does it mean? ATLAS and CMS will probably need to consider this question for a long time before agreeing to approve results like this with more data along with a suitable explanation. For now you should just bear in mind that this plot suffers from large backgrounds and poor energy resolution due to the use of missing energy to identify the two neutrinos. These effects have been worsened by high pile-up this year. I suspect that this channel will have to be used only where it provides a 5 sigma exclusion and should be left out when looking for a positive signal.
For this reason I have added a red line to the projected significance plot above showing the expected significance for just the diphoton plus ZZ to 4 lepton channels. These decay modes have very good energy resolution because the photons and high energy leptons (electrons and muons) are detected directly with good clarity and are not effected by pile-up. I think that the best early signal for the Higgs boson will be seen in a combination of these channels alone. The projected significance plot shows that with the data delivered in 2011 we can expect a signal or exclusion at a level of significance ranging from about 3 sigma to 6 sigma in the mass range of 115 GeV to 150 GeV where the Higgs boson is now most likely to be found.
Does this mean that we will get at least a 3 sigma “observation” for the Higgs by March? No, not quite. There is one other obvious caveat that is often forgotten when showing these projected significance plots. These are only expected levels of significance and like everything else they are subject to fluctuations. Indeed, given twenty uncorrelated mass points we should expect fluctuations of up to 2 sigma over the range. How could this affect the result? The next plot illustrates what this could mean assuming an expected significance of 4 sigma
In this plot the green line represents the expected level for a positive signal of a standard model Higgs, while the gred line represents the level where there is no Higgs. The data points have error bars at the size you will get when you expect a 4-sigma level of significance. So point A shows where the bars are expected to sit if the SM Higgs exists at a given mass value and point B shows where the bars are expected if there is no Higgs. If they get observed data in these locations they will be able to claim a 4-sigma observation or exclusion, but remember that fluctuations are also expected. Point C show what happens when the Higgs is there but an unlucky one sigma fluctuation reduces the number of observed events. The result is a reduced significance of three sigmas. Likewise point D shows an unlucky one sigma fluctuation when there is no Higgs which still gives a healthy three sigma exclusion. But remember that we expect fluctuations of up to two sigma somewhere in the range. Point E shows what happens when a Higgs is there but an unlucky two sigma fluctuations hits that mass point, and point F shows what happens when there is no Higgs with an unlucky two sigma fluctuation. The points are the same, corresponding to either a two sigma signal or a two sigma exclusion. We have already seen some points that look just like this at the summer conferences. This is why the CERN DG has cautiously promised to identify or exclude the Higgs only by the end of 2012 and not by the end of 2011. More optimistically we can also hope for some lucky fluctuations. If they fall at the mass where the Higgs actually lives we will get a 6 sigma discovery level signal like point G instead of merely a 4-sigma observation.
It’s a simple point and my explanation is a little too long-winded, but I think this had too be said clearly before the next results come out in case people do not see what they thought they should have expected to see. With another year of data 10/fb becomes (perhaps) 40/fb and 4 sigma becomes 8 sigma. Even with unlucky 2 sigma fluctuations they will be left with 6 sigma signals. The results will probably be good enough to claim discoveries even for the individual experiments and some individual decay channels, but for this year’s data there could still be a lot of ambiguity to mull over.