In a few days we will get the next big update from CERN on the Higgs boson and it is likely that the main question they are investigating will switch from “Is there a Higgs Boson?” to “Is it the standard model Higgs Boson?” Already the 2011 data shown during the winter carried signs that the cross-sections for some decay signatures are quite different from the standard model predictions. In particular the digamma rate is high and the WW is very low. Significance levels were not strong but if this is reinforced by the 2012 data people are going to suspect that new beyond-standard-model physics is at play. Many theory papers will be written as I predicted a year ago, but how well can the numbers be relied on? The ATLAS and CMS discuss many of the details behind closed doors and do not publish every detail. If theorists want to be sure that the results are good they will have to ask some probing questions at the talks. They need to go along to the conference prepared.
So let’s look at the data so far. Using the unofficial combinations for CDF, D0, CMS and ATLAS the μ signal at 126 GeV for the accessible decay channels looks like this
In this diagram the green line represents the prediction for a standard model Higgs while the red line is the background level with no Higgs. The first observation is that the Higgs is clearly favoured across the channels. After that, much has been said about the digamma excess because it is a high-resolution channel and an enhancement of this branching ratio could indicate new physics such as a new heavy charged boson. But what about the WW channel? It is now quite a bit below the standard model and is more consistent with no branching to WW. Even taking into account that these combinations are unofficial and approximate there is clearly something odd here.
From a theoretical point of view this is very perplexing because the digamma decay is (in theory) dominated by loops involving the W boson. If the direct decay to WW is lower than predicted then the diphoton decay should be too. This really cannot be made sense of and if it is correct then the Higgs nature of the observed resonance would have to be questioned, but let’s not be too hasty.
There are several sources of error that can affect these results so let’s take a step back and think about those first. They can be broken down along these lines
- Statistical errors from the limited amount of experimental data
- Theoretical errors in the approximate calculations of the standard model production rates and branching ratios
- Errors from the measured standard model parameters such as the masses of the W,Z, top etc.
- Statistical and other errors from the monte carlo simulations used to predict the background and signal
- Measurement errors from the detectors
All these things should have been taken into account and included in the error bars but before we draw too many conclusions and new theories we should ask questions, especially since the results do not make good theoretical sense. I think it is instructive to look at how the WW channel plot has evolved in ATLAS and CMS from the early days when they had 1/fb to the full 5/fb from last year. I’m not going to copy all the plots here but you can look at them on the Higgs combination plot. When there was only 1/fb of data we got excited because of an excess in the WW channel. It was most significant at about 144 GeV with over 3-sigmas but it was a broad excess which at the time suggested a Higgs in the range 135 ± 10 GeV, so with hindsight it was consistent with the present signal at 125 GeV. Sadly this signal faded as more data came in even though it was present in both CMS and ATLAS and is now nearly completely gone. What happened? Let’s walk through some of te possibilities.
1. Statistical fluctuations – On the face of it this seems like the most likely explanation. The original excess after just 1/fb faded slowly in both CMS and ATLAS. This then was a remarkable fluke but given enoigh things to look at we will always find remarkable flukes somewhere, so perhaps this is it. The present low signal for the Higgs in WW at 125 GeV where digamma is strong could equally well be part of that fluke. The 2012 data will tell us whether it is or not but the WW analysis is harder and we may not get full results until after ICHEP
2. and 3. Theoretical errors – The calculation of production rates is thought to be good to about 15%, but some theorists sat less and some more. The branching ratios are known to about 5%. Background estimates are another source of theoretical errors. Putting it altogether we may expect errors as high as 25% and it is not clear that this much error has been included in the analysis. This could eat into some of the significance of the observed deviations from the standard model.
4. Errors from the monte carlo – We have to assume that the monte carlo simulations have been run long enough so that statistical errors are sufficiently small to be negligible, but what about other errors. As far as I understand it, ATLAS and CMS have detailed simulators of their detectors that include everything from pile-up to the efficiency of the parts in the detector. One thing that could be very relevant is the effect of the pile-up. WW at low Higgs masses decays to leptons and neutrinos so there is missing energy to be accounted for. Pile-up has been said to make this difficult because particles from one event contaminate another. The simulations must include not just the pile-up but also the triggers and the algorithms used to reconstruct the individual events. How well has this been done? The first inverse femtobarn of data had low pile-up numbers so if they have not understood the effects of pile-up correctly it could account for the fact that the signal faded as high pile-up data was added. I dont know if this is a plausible explanation but it is something the collaborations should be talking about and if they don’t say anything about it theorists should be asking them questions.
5. measurement errors – From the 2011 data it was noticed that the CMS signal peak was at a lower mass than the ATLAS peak in the digamma channel. The difference was only about 1 or 2 GeV, well within the expected errors from the detectors, but this can still be significant. The WW channel has much lower mass resolution so how good is the estimate for the reconstructed Higgs mass? The reason that this is so important id that the WW branching ratio increases rapidly at around 125 GeV. If there are systematic errors that result in a mass offset they could be comparing experimental measurements with theoretical branching ratios and backgrounds at a slightly offset mass and this could result in big errors. For the digamma channel the problem is less acute because the branching ratio is a maximum at 125 GeV so it varies slowly in this region. the background also varies quite slowly.
Another part of the measurement process that could affect the result is the resolution of the detectors. How well is this resolution understood for different parts of the detector? This effects how much the signal is spread out over different energy bins. If the resolution is better than expected there would be more events in the central bin than expected and the signal would be bigger than expected. The opposite happens if the resolution is worse than expected. How well have they taken this into account?
The moral of this story is that if CMS and ATLAS do report significant deviations from the standard model next week, we as theorists should keep an element of skepticism in our interpretations. It ios easy to get excited by results that appear to agree with what we want to see, i.e. new physics rather than plain old standard model Higgs Boson. It will be impossible to resist speculating about what new physics can explain it and it will be a healthy excercise to do so, but don’t be surprised if more careful analysis sees some of the results fade away.
We have become addicted to the beguiling green and yellow brazil-band plots that have been produced in hundreds to show where the Higgs does and does not show up, but as we move into the next stage of exploration at the electro-weak scale these need to be put to one side. What will count next is estimates for the mass of the Higgs and the actual cross sections for the different decay channels with error bars. The cross-sections need to be independent of the mass estimate so that we don’t get messed around by the ways these errors combine when branching ratios are varying rapidly, It may take a little longer before we can really be sure whether or not we are seeing the SM Higgs or a BSM Higgs. Reults from the LHC may improve as we head into the long-shutdown next year and we may need a linear collider to get really good measurements of the Higgs Boson properties. But meanwhile theorists imaginations may run wild.