Fyzikální ústav Akademie věd ČR

The experimental activities of the Department are currently concentrated on the ATLAS experiment at the LHC collider at CERN. LHC started to provide sizable amounts of experimental data at highest energies ever only during the present year 2010. The collider is still under development, its parameters being tuned. The amount of collected data will increase with the optimization of the LHC performance. Discoveries reached by LHC experiments can thus be expected only in the next few years. Significant results reached by the Department members are thus connected with the previous era of CERN experiments – the DELPHI experiment at the electron-positron collider LEP.

Determination of the number of light neutrino generations

One of the most significant results of the experiments at LEP, to which also the research team of the DELPHI experiment with physicists from the Institute of Physics in Prague contributed, is the determination of the number of families (or generations) of fundamental particles based on the precise measurement of the total decay width of the neutral intermediate vector boson of weak interactions Z0.

This quantity depends on the number of decay channels, i.e. the number of particle species to which Z0 can decay. The measured value of the decay width agrees with the Standard Model calculations for the 3 generations of particles. All particles–members of these generations are known - they have been observed in experiments (u and d quarks, electron and its neutrino; c and s quarks, muon and its neutrino; t (top) and b quark, tau lepton and its neutrino). Neutrinos have an important property of having very low (almost zero) mass. If other generations similar to those known to us (i.e. again with very light neutrinos) existed , the Z0 particle could decay to pairs of these new neutrinos. Thus, new decay channels would open and different (higher) value of the decay width would have been observed. As nothing like this is observed, there can be no more generations of particles with light neutrinos than those 3 we already know.

The total cross section of the e+e- collisions as a function of the center-of-mass energy in the neighborhood of the Z0 rest mass. The total decay width of Z0 is determined from the shape of the curve describing the cross section. Colored lines correspond to theoretical calculations of the Standard Model of electroweak interactions with different numbers of particle generations. Dark circles label the measured values. (© DELPHI, CERN)

The first DELPHI publication which dealt with this problem is ref. [1] which was published shortly after the LEP startup in November 1989. It presents the analysis of about 1000 Z0 decays, the very first ones detected by DELPHI. It gives the values of the Z0 mass

M_Z = 91,06 ± 0,09 (stat.) ± 0,05 (syst.) GeV/c²

and the Z0 decay width

Γ_Z = 2,42 ± 0,21 GeV .

From this, it follows that the number of light neutrinos (and, thus, of generations) is

N = 2,4 ± 0,4 (stat.) ± 0,5 (syst.)

This value is compatible with the number of generations equal to 3. Rather big errors are due to statistics – the number of analyzed events was low. Nevertheless, the results were long awaited and had been considered valuable. The paper collected over 290 citations.

With increasing number of collected and analyzed data the precision of these quantities was growing. The above values can be compared e.g. with the results of the final analysis of Z0 decays performed after the LEP experiments had been finished. They were obtained combining the results of all four LEP experiments and included the biggest available amount of data, i.e. maximal statistics. Among the authors from the DELPHI collaboration are again physicists from the Institute of Physics.

Analysis of 17 million of Z0 boson decays collected during almost 12 years of the LEP activity gave the results

M_Z = 91,1875 ± 0,0021 GeV/c²

Γ_Z= 2,4952 ± 0,0023 GeV

and, from the last quantity, the number of light neutrinos

N = 2,9840 ± 0,0082

It is evident that the precision of measurement fundamentally increased. The value of the number N is indeed very near to 3.

Higgs boson searches and setting lower limit on its mass

Higgs boson is about the only important missing link in the extremely successful Standard Model of elementary particle interactions. It is a particle whose discovery would reassure physicists that they properly understand the mechanism which gives fundamental particles their rest mass. It can be considered a real Holy Grail of the present experimental particle physics.

The Higgs searches have not been successful up to now, but even negative results enable physicists to set lower limit on its mass m_H. The value of this limit depends on the energy of collisions in the experiment under consideration. For a long time, the most stringent lower limits on the Higgs mass came from the LEP experiments.

As the number of available data increased, quite a number of publications have been devoted to searches for the Standard Model Higgs and setting lower limits on its mass – e.g. DELPHI papers [1] ,[2] or the ‘LEP Working Group’ paper [3] based on the results of all four LEP experiments and highest possible statistics. Also particles corresponding to more complicated realizations of the Higgs sector have been searched for.

SM Higgs boson: confidence levels as a function of m_H.
Top: 1-CL_b for the background hypothesis. The full curve is the observation, the dashed curve is the median expected for background only, and the dash-dotted curve is the median expected at a particular m_H value when tested for that m_H value. A signal would appear as a downward deviation.
Bottom: CL_s, the pseudo-confidence level for the signal hypothesis. Curves are the observed (full) and expected median (dashed) confidences from experiments with only background channels while the bands correspond to the 68.3% and 95.0% confidence intervals for the hypothesis of only background processes. The intersections of the curves with the horizontal line at 5% define the expected and observed 95% CL lower limits on m_H
(From ref. [2]).

All analyses came to the conclusion that no signal for the existence of the Standard Model Higgs boson had been observed in the kinematical region under study.

The lower limit on m_H according to DELPHI [2] is

m_H > 114,1 GeV/c²

at 95% confidence level.

The combined analysis [3] gives the result

m_H > 114,4 GeV/c²

at 95% confidence level.

It is evident that this sort of quantity, lower bound on the mass following from non-observation of a particle, is not particularly sensitive to statistics.