PhD thesis
**Abstract**

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.

**Postscript version (gzipped) **