Signal to Expected Signal at LHC

We know with great precision what kind of signature a Standard Model Higgs of a given mass should have at LHC. Knowing how much data has been collected at LHC, we also know what level of statistical significance we should expect to be seeing by now at LHC if there is a Higgs boson at a given mass.

At 4.5/fb, we have:

119 GeV: 3 sigma
144 GeV: 6 sigma
240 GeV: 4.5 sigma
500 GeV: 4 sigma

Significance increases by about a third if the sample size is doubled by combining data from both experiments.

Given the information presented a month or two ago at the summer conferences, we can be pretty confident that we are not seeing SM Higgs boson signals of sufficient significance to match the theoretical prediction at 144 GeV-500 GeV. These mass ranges are sufficiently "brightly lit" that a real signal in these mass ranges would have been clear much earlier than now.

If we aren't seeing 3 sigma results from individual experiments and 4 sigma results from the combined experiments in the next couple of months of data analysis, the answer is bust - whatever is out there isn't a SM Higgs boson. As of mid-September of 2011, with about half as much data (and hence about a three-quarks as high expected sigmas) there were two sigma signals at both 119 GeV and about 140 Gev. The expected significance at that point for the SM Higgs was about 2.1 sigma at 119 Gev and about 4.5 sigma at 140 GeV. So, basically, at this point, the search for the SM Higgs boson boils down to 119 GeV +/- about 4 GeV, or bust, because the strength of the signal seen at 140 GeV is too weak to have been a SM Higgs given the amount of data available in mid-September.

Now, two sigma results happen all the time and subsequently disappear in physics. This is a 95% significance level that shows up one in twenty times as a fluke, and HEP experimenters do gobs and gobs of experiments so they see gobs and gobs of flukes. In other words, as of a month ago, experiments were not powerful enough to provide any meaningful evidence one way or the other in the 119 GeV SM Higgs boson mass vicinity.

But, now is the moment of truth. If a 3 sigma SM Higgs boson signal appears at 119 GeV based on the new data collected through today from individual teams and a stronger signal in the combined data, we probably have a winner. If we have nothing more than a 2 sigma signal lingering within the Brazil bands based on the new data (or a less significant signal than we had a month ago for a SM Higgs boson at that mass), the Standard Model Higgs probably doesn't exist and we have major beyond the Standard Model physics in play. How soon we get a verdict pretty much just depends on how long it takes to analyze the data that is already out there. The rumors should be flowing in weeks, but it might take a month or twoo to get an official announcement out, and if the signal at 119 GeV does strengthen to 3 sigma with the data through today, it will still take more months before the signal is so strong that it can be deemed a certain scientific discovery.

FWIW, a mass of 123 GeV (exactly one half of the Higgs vacuum expectation value), or 122 GeV (exactly one and a third of the W boson mass), seem numerologically more favored than 119 GeV and the statistical significance of these possibilities isn't that much different from 119 GeV.

Of course, I'm still at the point where I think that a SM Higgs still has a 33%-49% chance of not existing, so I am in rather more suspense than the true believers.

If we find a Higgs in that mass range, the various Higgsless models are sunk, although SUSY remains potentially viable and has a much narrower parameter space than it would have had pre-Higgs, making it (and a fortiori, string theory) much more falsifiable, because it will become much easier to make meaningful predictions about superpartner masses at that point.