## The present situation in the theory of the Deep-Inelastic Scattering

By: Boris Ermolaev

From: Ioffe Physico-Technical Institute, St. Petersburg, Russia

At: Complexo Interdisciplinar, Anfiteatro

[2008-11-12]

The most popular theoretical instrument for describing the Deep-Inelastic Scattering (DIS) is Standard Approach (SA). It is applied to description of all DIS structure function. SA combines the DGLAP evolution equations and standard fits for the initial parton densities. In spite of the fact that DGLAP was originally suggested for describing DIS at large *x* and large *Q*^{2}, it is rather successfully applied to experiment beyond this region at small *x*, though without theoretical grounds. The small-x alternative to SA for the unpolarized DIS involves the BFKL equation. The presently available experimental data cannot discriminate between those approaches. We present an alternative approach to the Polarized DIS. It accounts for the total resummation of the leading logs of *x* and *Q*^{2}. Contrary to DGLAP, the value of *Q*^{2} in our approach should not be kept large. We re-examine the well-known DGLAP parametrization of alpha_s and find it to be true at large *x* and large starting point of the *Q*^{2} -evolution only, otherwise it should be changed. We show that efficiency of SA at small *x* is entirely based on using special fits for the initial parton densities which mimic the total resummation of ln(*x*). When the resummation is taken into account, the fits can be seriously simplified. We demonstrate that using SA beyond the proper DGLAP applicability region (large *x* and large *Q*^{2}) leads to various misconceptions and discuss them.