## New bounds for the Higgs: 115-135 GeV!August 1, 2008

Posted by dorigo in news, physics, science.
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From yesterday’s talk by Johannes Haller at ICHEP 2008, I post here today two plots showing the latest result of global fits to standard model observables, evidencing the Higgs mass constraints. The first only includes indirect information, the second also includes direct search resuls.

The above plot is tidy, yet the amount of information that the Gfitter digested to produce it is gigantic. Decades of studies at electron-positron colliders, precision electroweak measurements, W and top mass determinations. Probably of the order of fifty thousand man-years of work, distilled and summarized in a single, useless graph.

Jokes aside, the plot does tell us a lot. Let me try to discuss it. The graph shows the variation from its minimum value of the fit chisquared -the standard quantity describing how well the data agree with the model- as a function of the Higgs boson mass, interpreted as a free parameter. The fit prefers a 80 GeV mass for the Higgs boson, but the range of allowed values is still broad: at 1-sigma, the preferred range is within 57-110 GeV. At 2-sigma, the range is of course even wider, from 39 and 156 GeV. If we keep the two-sigma variation as a reference, we note that the $H \to WW$ decay is not likely to be the way by which the Higgs will be discovered.

Also note that the LEP II experiment limits have not been inserted in the fit: in fact, the 114 GeV lower limit is hatched but has no impact in the curve, which is smooth because unaffected by direct Higgs searches.

Take a look instead at the plot below, which attempts at summarizing the whole picture, by including the direct search results at LEP II and at the Tevatron (without the latest results however) in the fit.

This is striking new information! I will only comment the yellow band, which -like the one in the former plot- describes the deviation of the log-likelihood ratio in data and the signal plus background hypothesis. If you do not know what that means, fear not. Let’s disregard how the band was obtained and concentrate instead on what it means. It is just a measure of how likely it is that the Higgs mass sits at a particular value of mass, given all the information from electroweak fits AND the direct search results, which have in various degrees “excluded” (at 95% confidence level) or made less probable (at 80%, 90% CL or below) specific Higgs mass values.

In the plot you can read off that the Higgs mass has a preferred range of masses which is now quite narrow! $M_H = 120_{-5}^{+15} GeV$. That is correct: the lower 1-sigma error is very small because the LEP II limit is very strong. Instead, the upper limit is much less constrained. Still, the above 1-sigma band is very bad news for the LHC: it implies that the Higgs is very unlikely to be discovered soon. That is because at low invariant mass ATLAS and CMS need to rely on very tough discovery channels, relying on the very rare $H \to \gamma \gamma$ decay (one in a thousand Higgses decay that way) or the even more problematic $H \to \tau \tau$ decay. Not to mention the $H \to b \bar b$ final state, which can be extracted only when the Higgs is produced in association with other bodies, and still with huge difficulties, given the prohibitive amount of backgrounds from QCD processes mimicking the same signature.

The 2-sigma range is wider but not much prettier: 114.4 – 144 GeV. I think this really starts to be a strong indication after all: the Higgs boson, if it exists, is light! And probably close to the reach of LEP II. Too bad for the LEP II experiments – which I dubbed “a fiasco” in a former post to inflame my readers for once. In truth, LEP II appear likely to one day turn out to have been very, very unlucky!