About exclusion plots for Higgs

During the three days of Europhysics conference I had opportunity to see very many exclusion plots for Higgs. Phil Gibbs did wonderful work here. To understand following it is good to look at these plots.

While trying to understand the message of these plots I realized that my understanding about the procedure yielding the exclusion plots for Higgs at various mass values is very poor. Outside the competence pressures of the academic community there is a strong temptation to conclude that it is better to leave the non-poetic side of physics to experimentalists and concentrate on deep theory. Sounds good but is just an excuse telling about the light-hearted laziness of a diletant. I try to summarize how little I understand.

1. The basic question is whether the standard model without Higgs is able to mimic the Higgs within experimental resolution. Basically one must compare the theory without Higgs to that with Higgs. The convenient normalization is by the total cross section for producing final states of particular kind produced in the production and subsequence decay of a genuine Higgs. Experimentally we cannot tell whether this kind of final states are actually due to the decay of a genuine Higgs.

   Remark: What the model without Higgs means is not quite clear since Higgs is needed to explain massivation and could appear as virtual states. For sufficiently high energies its presence is necessary in order to avoid violation of unitarity.

2. One must estimate production cross section for the final states which cannot be distinguished from those produced in the decays of Higgs in the model without Higgs. For instance, the total mass of the state possibly representing decay products of Higgs cannot be too far from Higgs mass. One can do this for both the real data and for the theory without Higgs. Typically the resulting cross section normalized by the cross section for the production via genuine Higgs is above unity since there are are many final states about which one cannot say whether they are decay products of genuine Higgs or fakes.

3. In the typical exclusion plot the wiggly curve corresponds to the production cross section of a fake or genuine Higgs or something analogous to it deduced from the experimental data and the smooth curve to the cross section obtained by a simulation using the model without Higgs. If these curves are near to each other, there is no need to assume Higgs at that particular mass value if the statistics is good. Unfortunately it is not good enough yet so that the issue of Higgs remains still unsettled although the excluded region is very narrow (its identification depends on blog).

4. If the experimental curve is much above the smooth one for certain range of mass values, one can conclude that Higgs might be there with mass in this range. If the experimental curve is much below the expected, one can ask whether there is some effect causing "anti-Higgs" behavior by reducing the cross section for the production of the states mimicking decay products of Higgs: destructive interference for Feynman diagrams could lead to this kind of effect. The propagator of some unknown particle other than Higgs could cause destructive interference because the sign of its real part changes above pole. This might be perhaps used as an additional criterion for identifying the masses of M₈₉ hadrons. In fact for 325 GeV bump identified in terms of &rho: and ω of M₈₉ hadron physics the 3 sigma deficit visible in some slides at 340 GeV might be due to this effect.

5. The deviation between experimental and theoretical curves could be due to fluctuations so that one has to use a a measure for the probability of the fluctuation with given amplitude. Gaussian probability distributions for the fluctuations are typically assumed and here the familiar notion of sigma creeps in. The number of sigmas measures how probable it is that the deviation can be regarded as a fluctuation. If it is large one can conclude that one cannot explain the deviation without assuming Higgs or something else producing a similar effect.