BFKL predictions at small x from k_T and collinear factorization viewpoints

Hard scattering processes involving hadrons at small $x$ are described by a $k_T$-factorization formula driven by a BFKL gluon. We explore the equivalence of this description to a collinear-factorization approach in which the anomalous dimensions $\gamma_{gg}$ and $\gamma_{qg}/\alpha_S$ are expressed as power series in $\alpha_S \log (1/x)$, or to be precise $\alpha_S/\omega$ where $\omega$ is the moment index. In particular we confront the collinear-factorization expansion with that extracted from the BFKL approach with running coupling included.Comment: 11 LaTeX pages, 1 figure (uuencoded

Asymptotic properties of DVCS

We compute the deeply virtual Compton scattering (DVCS) amplitude for forward and backward scattering in the asymptotic limit. We make use of the Regge calculus to resum important logarithmic contributions that are beyond those included by the DGLAP evolution. We find a power-like behavior for the forward DVCS amplitude.Comment: 3 pages, LaTeX, 3 figures. To be published in the proceedings of 7th International Workshop on Deep Inelastic Scattering and QCD (DIS 99), Zeuthen, Germany, 19-23 Apr 199

Inclusive production of J/ψJ/\psi meson in proton-proton collisions at BNL RHIC

Inclusive cross sections for $J/\psi$ production in proton-proton collisions were calculated in the $k_t$-factorization approach for the RHIC energy. Several mechanisms were considered, including direct color-singlet mechanism, radiative decays of $\chi_c$ mesons, decays of $\psi'$, open-charm associated production of $J/\psi$ as well as weak decays of B mesons. Different unintegrated gluon distributions from the literature were used. We find that radiative $\chi_c$ decays and direct color-singlet contributions constitute the dominant mechanism of $J/\psi$ production. These process cannot be consistently treated within collinear-factorization approach. The results are compared with recent RHIC data. The new precise data at small transverse momenta impose stringent constraints on UGDFs. Some UGDFs are inconsistent with the new data. The Kwieci\'nski UGDFs give the best description of the data. In order to verify the mechanism suggested here we propose $J/\psi$ -- jet correlation measurement and an independent measurement of $\chi_c$ meson production in $\pi^+ \pi^-$ and/or $K^+ K^-$ decay channels. Finally, we address the issue of \J spin alignment.Comment: 26 pages, 20 figures, the text was slightly modified, the title was modified, more discussion was added, one figure was removed, one was adde

QCD running coupling effects for the non-singlet structure function at small x

A generalization of the leading-order DGLAP evolution at small x is performed for the non-singlet structure function by resumming the leading-order DGLAP anomalous dimension to all orders in the QCD coupling. Explicit expressions are obtained for the non-singlet structure function of the deep inelastic scattering, taking into account both the double-logarithmic and the single-logarithmic contributions, including the running alpha_s effects. It is shown that when these contributions are included, the asymptotic small-x behaviour is power-like, with an exponent of about 0.4.Comment: Latex, 20 pages, 7 figure

Dijet Production at HERA as a Probe of BFKL Dynamics

We calculate the rate for the deep-inelastic electroproduction of dijets at HERA. We study the weakening of the azimuthal (back-to-back) correlation between the jets, as $x$ decreases, to see whether it can be used to identify BFKL dynamics from conventional fixed-order QCD effects. We show how this may give information on the transverse momentum ($k_T)$ dependence of the gluon distribution of the proton.Comment: 7 pages (LaTeX) + 4 pages of figures appended in the end of the file as a uuencoded postscript file, Durham DTP/94/56, CERN-TH.7357/9

Central exclusive production of scalar \chi_c meson at the Tevatron, RHIC and LHC energies

We calculate several differential distributions for exclusive double diffractive $\chi_c(0^{++})$ production in proton-antiproton collisions at the Tevatron and in proton-proton collisions at RHIC and LHC in terms of unintegrated gluon distributions (UGDFs) within the $k_t$-factorisation approach. The uncertainties of the Khoze-Martin-Ryskin approach are discussed in detail. The $g^* g^* \to \chi_c(0^{++})$ transition vertex is calculated as a function of gluon virtualities applying the standard pNRQCD technique. The off-shell effects are discussed and quantified. They lead to a reduction of the cross section by a factor 2--5, depending on the position in the phase space and UGDFs. Different models of UGDFs are used and the results are shown and discussed. The cross section for diffractive component depends strongly on UGDFs. We calculate also the differential distributions for the $\gamma^* \gamma^* \to \chi_c(0^{++})$ fusion mechanism. The integrated cross section for photon-photon fusion is much smaller than that of diffractive origin. The two components have very different dependence on momentum transfers $t_1, t_2$ in the nucleon lines as well as azimuthal-angle correlations between both outgoing nucleons.Comment: 34 pages, 23 figures, 2 table

Physics at Low x

The QCD expectations concerning the deep inelastic lepton - hadron scattering at low $x$ and their phenomenological implications for HERA are summarised. Theoretical predictions for the structure function $F_2(x,Q^2)$ based on the leading log$1/x$ resummation are presented and compared with the results obtained from the Altarelli-Parisi equations. Theoretical predictions are confronted with the recent data from HERA. The role of studying the final states in deep inelastic scattering for revealing the dynamics at low $x$ is emphasised and some dedicated measurements like deep inelastic plus jet events, transverse energy flow and dijet production in deep inelastic scattering are discussed.Comment: 16 pages, 8 figures, review talk presented at the Workshop "QCD94", 7-13 July 1994, Montpellier, France (to appear in the Proceedings of the Workshop), Krak\'ow INP report N0 1681/PH, hard copies of the figures available on request from the author at [email protected]

Intercepts of the non-singlet structure functions

Infrared evolution equations for small-$x$ behaviour of the non-singlet structure functions $f_1^{NS}$ and $g_1^{NS}$ are obtained and solved in the next-to-leading approximation, to all orders in $\alpha_s$, and including running $\alpha_s$ effects. The intercepts of these structure functions, i.e. the exponents of the power-like small-$x$ behaviour, are calculated. A detailed comparison with the leading logarithmic approximation (LLA) and DGLAP is made. We explain why the LLA predictions for the small-$x$ dependence of the structure functions may be more reliable than the prediction for the $Q^2$ dependence in the range of $Q^2$ explored at HERA.Comment: 26 pages, LaTeX, 5 Postscript figure

THE GLUON DISTRIBUTION AT SMALL x OBTAINED FROM A UNIFIED EVOLUTION EQUATION.

We solve a unified integral equation to obtain the $x, Q_T$ and $Q$ dependence of the gluon distribution of a proton in the small $x$ regime; where $x$ and $Q_T$ are the longitudinal momentum fraction and the transverse momentum of the gluon probed at a scale $Q$. The equation generates a gluon with a steep $x^{- \lambda}$ behaviour, with $\lambda \sim 0.5$, and a $Q_T$ distribution which broadens as $x$ decreases. We compare our solutions with, on the one hand, those that we obtain using the double-leading-logarithm approximation to Altarelli-Parisi evolution and, on the other hand, to those that we determine from the BFKL equation.Comment: LaTeX file with 10 postscript figures (uuencoded

Associated Jet Production at HERA

We compare the BFKL prediction for the associated production of forward jets at HERA with fixed-order matrix element calculations taking into account the kinematical cuts imposed by experimental conditions. Comparison with H1 data of the 1993 run favours the BFKL prediction. As a further signal of BFKL dynamics, we propose to look for the azimuthal dependence of the forward jets.Comment: 11 pages, latex & Figures appended as uuencoded fil