Quark distributions distribution functions

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]...

For each type (flavour) of quark-parton or antiquark-antiparton we now allow a separate distribution function u(a ), d(x), s x) and u(a ), d x),s x) giving the nmnber densities of such objects with momentum fraction be-... 

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. 

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)...

What about the excited states in the Born-Oppenheimer approximation We consider here the optimal case m - m. This implies that it is much more economical to excite the relative motion of the heavy quarks than the motion of the light quark around them. For instance, in the harmonic oscillator model, there is a ratio exactly [2m/(2m + m)]" between the corresponding excitation energies. Then, for the first excited states, the light-quark wave function remains in the lowest adiabatic f p. A), the binding energy and the qq distribution are obtained from the low-lying excited states of eq. (7.9) or (7.6). 

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