The Linked Dipole Chain Monte Carlo

We present an implementation of the Linked Dipole Chain model for deeply inelastic ep scattering into the framework of the Ariadne event generator. Using this implementation we obtain results both for the inclusive structure function as well as for exclusive properties of the hadronic final state. (The original publication was based on results from an implementation containing an error. In this revised version this error has been corrected, some of the beyond leading-log assumptions have been revised and so have some of the results.)Comment: 26 page

Investigations into the BFKL Mechanism with a Running QCD Coupling

We present approximations of varying degree of sophistication to the integral equations for the (gluon) structure functions of a hadron (``the partonic flux factor'') in a model valid in the Leading Log Approximation with a running coupling constant. The results are all of the BFKL-type, i.e. a power in the Bjorken variable x_B^{-\lambda} with the parameter \lambda determined from the size \alpha_0 of the ``effective'' running coupling \bar{\alpha}\equiv 3\alpha_s/\pi= \alpha_0/\log(k_{\perp}^2) and varying depending upon the treatment of the transverse momentum pole. We also consider the implications for the transverse momentum (k_{\perp}) fluctuations along the emission chains and we obtain an exponential falloff in the relevant \kappa\equiv \log(k_{\perp}^2)-variable, i.e. an inverse power (k_{\perp}^2)^{-(2+\lambda)} with the same parameter \lambda. This is different from the BFKL-result for a fixed coupling, where the distributions are Gaussian in the \kappa-variable with a width as in a Brownian motion determined by ``the length'' of the emission chains, i.e. \log(1/x_B). The results are verified by a realistic Monte Carlo simulation and we provide a simple physics motivation for the change.Comment: 24 pages, 10 supplementary files, submitted to Physical Review

Gluon Distribution Functions in the kT-factorization Approach

At small x, the effects of finite transverse momenta of partons inside a hadron become increasingly important, especially in analyses of jets and heavy-quark production. These effects can be systematically accounted for in a formalism based on kT-factorization and unintegrated distribution functions. We present results for the unintegrated distribution function, together with the corresponding integrated one, obtained within the framework of the Linked Dipole Chain model. Comparisons are made to results obtained within other approaches

Uncertainties on Central Exclusive Scalar Luminosities from the unintegrated gluon distributions

In a previous report we used the Linked Dipole Chain model unintegrated gluon densities to investigate the uncertainties in the predictions for central exclusive production of scalars at hadron colliders. Here we expand this investigation by also looking at other parameterizations of the unintegrated gluon density, and look in more detail on the behavior of these at small k_T. We confirm our conclusions that the luminosity function for central exclusive production is very sensitive to this behavior. However, we also conclude that the available densities based on the CCFM and LDC evolutions are not constrained enough to give reliable predictions even for inclusive Higgs production at the LHC

Small-x Dipole Evolution Beyond the Large-N_c Limit

We present a method to include colour-suppressed effects in the Mueller dipole picture. The model consistently includes saturation effects both in the evolution of dipoles and in the interactions of dipoles with a target in a frame-independent way. When implemented in a Monte Carlo simulation together with our previous model of energy--momentum conservation and a simple dipole description of initial state protons and virtual photons, the model is able to reproduce to a satisfactory degree both the gamma*-p cross sections as measured at HERA as well as the total p-p cross section all the way from ISR energies to the Tevatron and beyond

Energy Conservation and Saturation in Small-x Evolution

Important corrections to BFKL evolution are obtained from non-leading contributions and from non-linear effects due to unitarisation or saturation. It has been difficult to estimate the relative importance of these effects, as NLO effects are most easily accounted for in momentum space while unitarisation and saturation are easier in transverse coordinate space. An essential component of the NLO contributions is due to energy conservation effects, and in this paper we present a model for implementing such effects together with saturation in Mueller's dipole evolution formalism. We find that energy conservation severely dampens the small-x rise of the gluon density and, as a consequence, the onset of saturation is delayed. Using a simple model for the proton we obtain a reasonable qualitative description of the x-dependence of F2 at low Q^2 as measured at HERA even without saturation effects. We also give qualitative descriptions of the energy dependence of the cross section for gamma*-gamma* and gamma*-nucleus scattering

The general behavior of NLONLO unintegrated parton distributions based on the single-scale evolution and the angular ordering constraint

To overcome the complexity of generalized two hard scale ($k_t$,$\mu$) evolution equation, well known as the $Ciafaloni$, $Catani$, $Fiorani$ and $Marchsini$ ($CCFM$) evolution equations, and calculate the unintegrated parton distribution functions ($UPDF$), $Kimber$, $Martin$ and $Ryskin$ ($KMR$) proposed a procedure based on ($i$) the inclusion of single-scale ($\mu$) only at the last step of evolution and ($ii$) the angular ordering constraint ($AOC$) on the $DGLAP$ terms (the $DGLAP$ collinear approximation), to bring the second scale, $k_t$ into the $UPDF$ evolution equations. In this work we intend to use the $MSTW 2008$ (Martin et al) parton distribution functions (PDF) and try to calculate $UPDF$ for various values of $x$ (the longitudinal fraction of parton momentum), $\mu$ (the probe scale) and $k_t$ (the parton transverse momentum) to see the general behavior of three dimensional $UPDF$ at the $NLO$ level up to the $LHC$ working energy scales ($\mu^2)$. It is shown that there exits some pronounced peaks for the three dimensional $UPDF$ $(f_a(x,k_t))$ with respect to the two variables $x$ and $k_t$ at various energies ($\mu$). These peaks get larger and move to larger values of $k_t$, as the energy ($\mu$) is increased. We hope these peaks could be detected in the $LHC$ experiments at $CERN$ and other laboratories in the less exclusive processes

Central Exclusive Scalar Luminosities from the Linked Dipole Chain Model gluon densities

We investigate the implication of uncertainties in the unintegrated gluon distribution for the predictions for central exclusive production of scalars at hadron colliders. We use parameterizations of the kT-unintegrated gluon density obtained from the Linked Dipole Chain model, applying different options for the treatment of non-leading terms. We find that the luminosity function for central exclusive production is very sensitive to details of the transverse momentum distribution of the gluon which, contrary to the kT-integrated distribution, is not very well constrained experimentally

Study of the Linked Dipole Chain Model in heavy quark production at the Tevatron

We present calculations of charm and beauty production at Tevatron within the framework of kT-factorization, using the unintegrated gluon distributions as obtained from the Linked Dipole Chain model. The analysis covers transverse momentum and rapidity distributions and the azimuthal correlations between b and bbar quarks (or rather muons from their decay) which are powerful tests for the different unintegrated gluon distributions. We compare the theoretical results with recent experimental data taken by D0 and CDF collaborations at the Tevatron Run I and II.Comment: 16 page

kt - factorization and CCFM - the solution for describing the hadronic final states - everywhere ?

The basic ideas of kt-factorization and CCFM parton evolution is discussed. The unintegrated gluon densities, obtained from CCFM fits to the proton structure function data at HERA are used to predict hadronic final state cross sections like jet production at HERA, but also comparisons with recent measurements of heavy quark production at the Tevatron are presented. Finally, the kt-factorization approach is applied to Higgs production at high energy hadron hadron colliders and the transverse momentum spectrum of Higgs production at the LHC is calculated.Comment: to be published in MPLA, replaced with new reference