The only thing I think I can discuss with you here now is the predictions on the Higgs boson significance level produced by CMS in October 2010 - a couple of geological eras ago, that is. Those predictions can be trusted because 2011 data showed to be perfectly in line with them, both for the 95% CL limits and for the significance -of course the former are valid in the full mass range and provide more verification power than the single significance number, which is only valid if the Higgs boson exists and has a particular mass.

So the 2010 predictions were produced with 10 inverse femtobarns in mind and 7 TeV running. Now let me remind you that 10/fb is exactly what CMS has available to analyze for Summer 2012 conferences, and that in 2012 we have actually ran at 8 TeV, where the Higgs production rate is higher and signal to noise ratios are slightly better. So a sensitivity plot made with 10/fb at 7 TeV is a slightly pessimistic view. Still, let us see what is the prediction for a 125 GeV Higgs boson, below.

You should be looking at the black curve, at the point where the horizontal axis corresponds to 125 GeV: that is between the second and third vertical line after the 100 GeV one (this is a logarithmic x-axis plot, so it is not completely straightforward to read it). If you look carefully, you will get the following predictions:

- a >3-sigma excess in the gamma-gamma mode

- a 2.5 sigma excess in the ZZ -> 4 leptons mode

- smaller excesses in the WW decay mode and other channels

- a combined significance just short of 5 sigma.

Now, the above are median values of wide distributions. To explain what that means, imagine the histogram of heights of sixth graders in a school. The distribution will be wide, with a peak at about five feet. That is the mode of the distribution. The median, instead, is the value above which there are half of the kids (and below which there's the other half). In the plot above, each curve was computed by looking, for each mass hypothesis m, at a distribution of possible experimental outcomes (given the presence of a Higgs boson at that mass value); the median is computed, and plot, for each mass and for each curve. So while the black curve could be telling you "CMS will have a 4.7 sigma significance with 10/fb at 7 TeV", what you should read is "the median significance will be 4.7 sigma". You will not be able to know, from the figure, how wide is the distribution -not any more than you will be able to tell how many kids are 5'6" or taller in the sixth graders example. The distributions of possible significances is wide, and if the experiment is unlucky the significance may be much lower than the median; or if it is lucky, it may well exceed five sigma.

I hope this helps you putting in the right context the information that is circulating in the web these days, together with the predictions above.

## Comments

Ravi, it would translate into a taller sixth grader.

Could that sixth grader be taller because he is a mutant alien from outer space? Sure, but it is not enough to rule out pure random chance. The difference between a 3.5

[…so, apparently wordpress barfs when I type a greek character…as I was saying…]

Ravi, it would translate into a taller sixth grader.

Could that sixth grader be taller because he is a mutant alien from outer space? Sure, but it is not enough to rule out pure random chance. The difference between a 3.5 sigma prediction and 4 sigma result for gamma gamma alone is certainly too small, don't you think?

Thanks Peter. Yeah I guess we shd just subtract the two right ? I was also more asking for general info purposes -- for example if it is 4 sigma observed and 3 sigma expected then the difference is 1 sigma for 1 detector with both 2011 and 2012 data. It could be a 1.4 sigma excess for new physics if both detectors show similar excesses at same mass in same channel -- and these are combined in quadrature.This is the way to look at it?

Ha! There's the tri-modal probability distribution in view at last. Now we face an interminable argument about particle metaphysics and dimensionality. The hypothesis operationalizes as a tree, and the branches distribute tri-modally. Arguably that is evidence for a variable dynamic at loop level, a vortex of sorts, which rather undermines the original hypothesis.....

Hi Tomaso,

ZZ-->4l prediction has a centroid at different mass than gamma-gamma?

This is the only line, which is different?!

What could be the reason for that?

Best regards,

Nick

The plot above shows projected sensitivities as a function of Higgs mass.

Each point on the horizontal axis should be understood to be a different,

alternative hypothesis - namely, that the Higgs has a mass corresponding

to that point. The "shape" of those sensitivity curves depends on several

things, but it is meaningless to compare those for different channels.

The only thing you should compare is the significance level (the vertical

height of the curves) at a given mass point (i.e. along a vertical axis).

If that is understood, the reason for the different sensitivities at different

masses is the varying probability that the Higgs decays to each different

final state. The h->γγ decay, for instance, dies out for M>130 GeV; the

H->ZZ branching fraction has a funny shape with two local maxima at 140

and 200 GeV. Acceptances and backgrounds also influence these curves

non trivially.

Cheers,

T.

The combined projected significance peaks at around 160 GeV, at a value of 9.5 sigma. What could be causing this large event count, other than the Higgs? What again is the reason why this value for the Higgs mass is being ruled out? I'm sorry if these questions have been asked before.

The combined projected significance is not an actual observation. It is what CMS would see if the Higgs boson had a particular mass value. For MH=160 GeV, indeed CMS would see a very large event count, which nothing else could produce. But... Nothing like that was observed, because in fact the Higgs does not have that mass.

The plot, in other words, is only saying what would be seen IF there were a Higgs boson; and it is a combination of many different mutually exclusive hypotheses - if the Higgs has a mass of 150 GeV, of course it does not have a mass of 160; and so on.

Cheers,

T.

Tommaso,

just for curiosity: could the 125 GeV signal be due to a Regge trajectory state of a neutral meson? (at least on some channels?)

If we assume a standard model Higgs at 125 GeV and make the plots we should expect no deviation from that in case standard model with 125 GeV is good. This way we can also find if there is any deviation for the gamma-gamma and other modes that may point to new physics beyond the standard model. For example in Peter's blog a 4 sigma excess is rumored in gamma gamma mode (assuming no Higgs at 125 GeV). This would translate to some deviation from the standard model assuming a Higgs at 125 GeV? What would be the sigma of that? Can we infer it also from the kind of plots you put or because they refer to the medians this information is lost?