Quark statistics

So far we have discussed the specific behavior of fluctuations of the order parameter at fixed temperature and density. There are also fluctuations of the temperature and the local quark density. They are statistically independent quantities [19], < 5T5pq >= 0, and their mean squares are... 

The basic building blocks of the theory are Heisenberg operators (x) which create and destroy respectively, particles of type m at the space-time point x = x, (x. For the purposes of chemistry we can take the index nzs>e for electrons and a for nuclei only. Of course when energies are much larger than chemical energies, nuclei appear to be composite particles, and we must then introduce fields for their constituents (quarks, rishons). We shall not make any explicit reference to the spins carried by these fields beyond noting that odd-integral spins require fermi statistics, so that for fermi fields we have canonical anticommutation relations (CARS)... 

The fact that the number of simulated events is limited leads to a systematic uncertainty on the measured -quark production cross-section. The extent of this effect can be estimated by considering the results of the validation of the fitting procedure (Fig. 4.15). An overview of the relative error of the fitted -fraction is presented in Appendix B. The error of the fitted -fraction takes into account the limited MC statistics as well as the limited data statistics. 

Fig. 4.25 Differential i)-quark production cross-section daldpr for rf < 2.1 as a function of the muon transverse momentum. The black squares represent the cross section determined by the procedure described in this analysis. The vertical error bars show the statistical uncertainty, the systematic uncertainty is indicated by the yellow area. The horizontal error bars indicated the bin width. The bin center is corrected [28]. The distribution is compared to the prediction of the PYTHIA simulation (green circles) and the MC NLO simulettion (red triangles)...

In Fig. 4.25 the differential fc-quark production cross-section as a function of the muon transverse momentum is shown. The statistical uncertainty is of the order of 1-2%, the systematic uncertainty of the order of 17-18% depending on the muon transverse momentum. In Table 4.7 the factors for calculating the differential -quark production cross-section as a function of the transverse momentum of the muon are summarized. The results were obtained by dividing the available MC statistics into two independent subsamples using one part to extract the templates and treating the other one as data . 

A harder distribution is observed in the re-weighted data with respect to simulation. In order to validate the weighting procedure, it was applied to the simulated track spectrum. The results from simulation agree within the statistical error. For comparison, the measured distribution calculated from muons which were most likely generated in light quark or charm decays is also shown in Fig. 5.8. 

The distribution obtained in the data corresponding to = 900 GeV was determined and compared to the simulation. The MC simulation is in agreement with data although the statistics is very limited. Furthermore, the method for obtaining the light-quark background templates using a data-driven approach was validated. 

On March 30, 2010, the first proton-proton collisions at a center-of-mass energy of /s = 7 TeV happened at the LHC. The data statistics recorded by the CMS detector during the first months of data-taking allows for a first measurement of the inclusive -quark production cross-section at the LHC [1], The preliminary result has been presented at the 35th International Conference on High Energy Physics [2],... 

Fig. 6.8 Differential fj-quark production cross-section da/dpr for < 2.1 as a function of the muon transverse momentum. The black symbols show the measured cross section where the vertical error bars represent the statistical uncertainty and the horizontal error bars indicate the bin width. The yellow band shows the quadratic sum of statistical and systematic errors. The systematic error (11%) of the luminosity measurement is not included. The dashed red lines illustrate the MC NLO theoretical uncertainty as described in the text. The solid green line shows the PYTHIA result...

A study of the inclusive fe-quark production at the CMS experiment has been presented within this work. Thanks to the large -quark production cross section at the LHC, high statistics data samples are available soon after the LHC startup. The measurement of the -quark production cross section with these data is therefore a prime candidate to yield one of the first physics result obtained from proton-proton collisions at a center-of-mass energy of /s = 7TeV. 

As a result of this thesis, an analysis strategy has been developed which focusses on the reconstruction of muons originating from semileptonic decays of fe-quarks. The fraction of signal events in data is determined on a statistical basis by performing a fit to the measured distribution by means of simulated templates for signal and background events. 

We further find that it is necessary to endow eeich quark with a completely new, internal degree of freedom ceiUed colour . Eeich quark can exist in three different colour states. Severed technical problems— the statistics of quarks, the tt decay rate, and the existence of triangle anomalies— are thereby resolved. The implications of colour for the famous ratio... 

We expect PEP-II to produce high statistics samples of meson decays, thus presenting a wealth of new physics opportunities, beyond the principal objective of probing ti e origin of CP violation. These opj>ortunities in other aspects of 6-quark weak and electromagnetic decay, in charm decay, in r decay, and in two-photon physics have been discussed in detail in [1]. This section l)iiefly summarize and updates tliat discussion. 

---