Gluons functions

Integrating out the fast modes, modes far from the Fermi surface and hard gluons, the QCD partition function (1) becomes... 

Fig. 3.1 Graphs which contribute to the (3 function in the one loop approximation (a) fermion loop, (b) gluon loop...

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]...

In gluon splitting events the heavy quark occurs in QQ events in the initial- or final-state shower. The resulting heavy flavored final state can carry a large combined transverse momentum and thus be concentrated within a small cone of angular separation. The contribution of the different processes to the total Z -quark production cross section predicted by PYTHIA (see Sect. 3.6) is shown in Fig. 3.8 as a function of the center of mass energy. 

Fig. 3.8 Total b cross-section as a function of the center-of-mass energy in proton-proton collisions. The contributions from pair production, flavor excitation and gluon splitting are shown [25]...

One expects from lowest-order QCD that the short range part of the potential (which arises mainly from one-gluon exchange) is vector in character. On the other hand, lattice QCD calculations and some flux-tube models indicate that the confining potential is a scalar. The experimental evidence is not conclusive, but is consistent with this picture. If these ideas are correct, then there should not be any appreciable spin-spin splitting in quarkonium states with L > 0 because in such states the wave function is small at short distances because of the centrifugal barrier. Measurements of the spin-spin splitting in L > 0 states therefore provide important tests of QCD-motivated potentials. 

Note that we do not consider any fundamental component of c, b or t quarks in the nucleon. Their presence, in the form of qq pairs, is better thought of as a dynamic effect arising from pair production from gluons (see Fig. 16.10), i.e. a QCD effect, and will be treated in Section 23.8. This means that the formulae for the scaling functions to be presented in this section require additional contributions to be added to them when the kinematics is such as to allow charm or bottom production. Given present estimates of the top mass the production of top is not a relevant consideration. 

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