## Archive for February 24, 2010

### Update of the Higgs Boson Mass p.d.f.

Jens Erler recently updated his calculations for a *probability density function* for the Higgs boson mass (M_{H}), based on measurements and searches. The article is arXiv:1002.1320.

The whole discussion is couched in the standard model, so the conclusions pertain only to the standard model Higgs boson, the properties of which are well known as a function of its unknown mass. If you want to think about theories beyond the standard model, then the results may not apply.

In this context, the interesting question is: *What is the mass of the Higgs boson?*. One could also add: *Is the standard model consistent with a Higgs boson that has not already been ruled out by searches at colliders?*

As many bloggers have explained, some electroweak observables depend on M_{H} through radiative corrections. A good theorist such as Jens can confront the calculations of these radiative corrections with precision measurements of the observables, and find the value of M_{H} which gives the best match, or “fit.” Nearby values of M_{H} give a slightly poorer match, while others are simply incompatible. This qualitative behavior can be quantified in terms of a chi-squared or other figure of merit. Using Bayes’ Theorem, one can even interpret the variation of that chi-squared as a probability density function, telling you where to place your bet.

Experts in Statistics will take issue with this, but I find the results interesting nonetheless. One can see that some values really don’t fit the present picture, for example, M_{H} = 200 GeV, where the famous H→ZZ→4 *leptons* would be most fruitful. Even more cruelly, Nature points a finger at 117 GeV, where the Tevatron a priori is unable to establish a signal, and the LHC would require a very large data sample. (On the other hand, the Tevatron might be expected to place a 95% CL bound in this mass range, if the Higgs does not exist with that mass, and there are no untoward statistical fluctuations. See the nice discussion by Tommaso Dorigo, especially the last few paragraphs.) Don’t bet a lot on the basis of this distribution, however, since it assumes the standard model which is known to be inadequate, and one can argue about the statistical basis for these calculations.

For the record, Jens reports the 90% preferred range (95% CL lower and upper limits) to be: 115 GeV≤M_{H}≤148 GeV. This represents a huge improvement over the past decade, thanks to precision measurements of the top quark and W boson masses at the Tevatron. For illustration, here is Jens’ result published in 2001 (hep-ph/0102143):

So, what will this look like in a year or two? How much will 1 fb^{-1} of LHC data at 7 TeV change this picture, if at all?