Critical tests of unintegrated gluon distributions

Abstract

The purpose of the present investigation is to study the longitudinal structure function (SF) FL(x,Q ) as well as the charm and beauty contributions to the proton SF F2(x,Q ) using the kT−factorization approach of QCD [1]. The SF FL(x,Q ) is directly connected to the gluon density in the proton. Only in the naive quark-parton-model FL(x,Q ) = 0, and becomes non-zero in pQCD. However the pQCD leads to controversal results still. It was shown recently [2], that the FL experimental data from HERA seem to be inconsistent with some of the NLO predictions (in particular the MRST one) at small x. BFKL effects significantly improve the description of the low x data when compared to a standard NLO MS-scheme global fit. The NNLO global fit becomes better when taking into account higher order terms involving powers of ln(1/x). It means, that we need a resummation procedure. On the other hand it is known, that the BFKL effects are taken into account from the very beginning in the kT−factorization approach [1], which is based on the BFKL [3] or CCFM [4] evolution equations summing up the large logarithmic terms proportional to ln(1/x) or ln(1/(1 − x)) in the LLA. Some applications of the kT−factorization approach were shown in Refs. [5]. In the framework of kT -factorization the study of the longitudinal SF FL began already ten years ago [6], where the small x asymptotics of FL has been evaluated, using the BFKL results. Since we want to analyze the SF data in a broader range at small x we use a more phenomenological approach in our analyses of F2 and FL data [7, 8]. Using the kT -factorization approach for the description of different SF at small x we hope to obtain additional information (or restrictions), in particular, about one of the main ingradient of kT -factorization approach the unintegrated gluon distribution (UGD) In the kT -factorization the SF F2,L(x,Q ) are driven at small x primarily by gluons and are related in the following way to the UGD xA(x,k2T , μ )