PhD thesis


The results I have obtained can be summarised in two main categories. First of all, I have studied implications of Regge theory in DIS. I have shown [1] that all hadronic amplitudes must have the same complex-j-plane singularities and are related by t-channel unitarity (tCU) rules. For example, one may use the tCU rules to obtain the photon-photon amplitude from the proton-proton and photon-proton ones. We have also shown that, using a generalised double- or a triple-pole pomeron model, which corresponds to an amplitude growing like a logarithm or a squared logarithm of the energy, one can describe all amplitudes involving protons and protons, at all values of Q2, using tCU rules. On the other hand, it is well known that the proton structure function F2 can be described using the DGLAP evolution equation. In the second part of my Ph.D. thesis, I have developed new methods to combine this kind of description with the Regge approach. Basically, the motivation is that in the existing DGLAP global fits, the j-plane singularities in the quark distribution are not the same as those in the gluon distribution and, moreover, these singularities are not present in the total cross-sections. Therefore, since one must have the same singularities in hadronic amplitudes, one may ask if it is possible to extend this argument to the case of parton distributions and thus to have the same singularity structure in DGLAP initial distributions. I have shown [2] that all initial parton distribution may be described using a generalised double- or a triple-pole pomeron in the small-x region. In this case, F2 is described by Regge theory at small Q2 and by DGLAP evolution at large Q2. In addition, this method splits the pomeron into quark components and predicts a gluon distribution. If we introduce powers of (1-x) in initial distributions and include the deuteron structure function, the neutron structure function and the neutrino data in addition to the proton structure function, one can extend these results to the large-x domain. Therefore, one obtains [3] a new global QCD fit compatible with Regge theory. With this result at hand, one may ask if it is possible to use the DGLAP evolution equation to extract the Q2 dependence of the pomeron residues. Actually, in the usual Regge approach, one assume some analytical Q2 dependence for these residues and fit the experimental data to fix the free parameters. However, if we assume that Regge theory applies at all valuers of Q2, one may expect that the Regge residues are compatible with DGLAP evolution at high Q2. We have shown [4] that using both forward and backward DGLAP evolution one can obtain the residues of the triple-pole pomeron in the Regge domain. This method also gives the parton content of the pomeron and predicts large uncertainties on the gluon distribution at moderately small Q2 and small x, which is of prime importance for the LHC. Finally, The description of F_2 obtained at large Q2 from DGLAP evolution can be extended to Q2=0 using analytical Q2 form factors.


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