Quark distributions

In the previous chapter we expressed all the measurable scaling functions in terms of the quark distributions or number densities. Notice that there are many more experimental scaling functions than quark nmnber densities u, d, s, u,d,s = s, so that the predictive power is in principle very great. 

In this paper we study the distribution of the magnehc held of a neutron star with superconducting CFL quark matter core in the framework of the Ginzburg-Landau theory. We solve the Ginzburg-Landau equations with proper boundary conditions. 

Bergstrom, L., Bergstrom, U., 1999. Species diversity and distribution of aquatic macrophytes in the Northern Quark, Baltic Sea. Nordic Journal of Botany, 19, 375-383. 

A measurement of the beauty quark production cross-section based on the semi-leptonic decay of b quarks into muons is performed in this thesis. Because of the large mass of the b quark, muons from semileptonic -decays have larger transverse momenta with respect to the quark direction than muons from the decay of lighter quarks. In the experiment, the quark direction is approximated by the axis of the fragmentation jet and the transverse momentum of the muon relative to that axis (p ) is measured. The contribution of -events to the measured distribution is determined by performing a fit based on simulated template distributions for signal and background events. 

In this chapter the theoretical concepts relevant to describe the physics of heavy quarks at the LHC are introduced. The main ideas of Quantum Chromodynamics are reviewed, before their appUcation to high-energy hadron-hadron collisions is discussed. This includes the factorization ansatz, the evolution of the parton distribution functions, the partonic processes important for beauty quark production and the phenomenological treatment of heavy quark fragmentation. A further section is dedicated to the description of the decay of -hadrons via the weak interaction. The Monte Carlo event generators which are used in this analysis to generate full hadronic events within the QCD framework are presented in the last section. 

Fig. 3.5 The proton par-ton distribution functions measured at HERA at 2 = lOGeV, for valence quarks and xd, sea quarks xS, and gluons xg. The gluon and sea distributions are scaled down by a factor 20 [23]...

At a center-of-mass energy of s/s = 7 TeV, an inclusive fe-quark production cross-section of trj = 322 yttb is predicted by PYTHIA. The simulated transverse momentum and pseudorapidity distributions of the b quark are shown in Fig. 4.2. In about 20% of the cases a muon is found among the decay products of the b quark. In Fig. 4.3 the transverse momentum and the pseudorapidity of the muon generated either in the semileptonic decay of the b quark or the subsequent c quark is displayed. The visible kinematic range for muons in the measurement presented here is pr > 5GeV and —2.1 < p < 2.1, which corresponds to an acceptance of 2%. 

Fig. 4.2 Transverse momentum (left) and pseudorapidity (right) distribution of h quarks originating from proton-proton collisions at a center-of-mass energy of = 1 TeV. The inclusive distribution is shown in blue, the gmen distribution corresponds to b quarks that decay semileptonically into muons and the md one describes quarks whose decay produce muons within the visible kinematic range (pj > 5GeV and —2.1 < 77 < 2.1)...

Fig. 4.13 - distribution of the inclusive sample separated by the quark content and normalized... 

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. 5.4 the number of tracks reconstructed within a TrackJet and the transverse momentum of the highest transverse momentum track are compared to the MC simulation and a good agreement is found. These results are relevant in view of the measurement of the -quark production cross-section as the analysis presented here is based on a precise determination of the muon momentum with respect to the TrackJet direction. A good understanding of the TrackJet reconstruction and a reliable simulation of the TrackJet distributions are thus of utmost importance. 

According to the PYTHIA simulation, the fc-quark production cross section is ai, = 28 /xb at = 900 GeV and ai, = 96/ttb at = 2.36 TeV. Thus, the number of events containing b-quarks is very low in the 2009 collision data and a measurement of the cross section using the method will not be possible. Nonetheless it is instructive to study the distribution in this data in order to better understand the background. 

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. 

The p f distribution of re-weighted tracks in minimum bias events is compared to the one of simulated muons in light quark events in Fig. 6.5. The udsg template determined from data is harder than in simulation. In order to evaluate the systematic uncertainty of the cross-section measurement due to an imperfect background description, the distribution obtained from data as well as from simulation is used in the fitting procedure. 

Fig. 6.5 distribution in light quark background events obtained by re-weighting the hadronic track spectrum in data by the simulated muon fake probability (circles). 

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. 

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