The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractWe describe how to calculate the parton distributions f a (x, k 2 t , µ 2 ), unintegrated over the parton transverse momentum k t , from auxiliary functions h a (x, k 2 t ), which satisfy single-scale evolution equations. The formalism embodies both DGLAP and BFKL contributions, and accounts for the angular ordering which comes from coherence effects in gluon emission. We check that the unintegrated distributions give the measured values of the deep inelastic structure function F 2 (x, Q 2 ).

We introduce a general expression which enables the parton distribution, unintegrated over the parton transverse momentum, to be obtained from the conventional parton densities. We use the formalism to study the effects of the transverse momentum q t of the incoming partonic system on the calculation of the transverse momentum spectra of prompt photons produced in high energy pp and pp collisions. For the purposes of illustration, we use the double logarithm approximation. For large q t we calculate the effect directly from the perturbative formalism, whereas for small q t we bound the effect using two extreme hypotheses. In both q t domains we find that the shapes of the prompt photon spectra are not significantly modified, although the cross sections are enhanced.

We introduce a general expression which enables the parton distribution, unintegrated over the parton transverse momentum, to be obtained from the conventional parton densities. We use the formalism to study the effects of the transverse momentum q t of the incoming partonic system on the calculation of the transverse momentum spectra of prompt photons produced in high energy pp and pp collisions. For the purposes of illustration, we use the double logarithm approximation. For large q t we calculate the effect directly from the perturbative formalism, whereas for small q t we bound the effect using two extreme hypotheses. In both q t domains we find that the shapes of the prompt photon spectra are not significantly modified, although the cross sections are enhanced.

The gluon distribution f (x,k t 2 , 2 ), unintegrated over the transverse momentum k t of the gluon, satisfies the angular-ordered CCFM equation which interlocks the dependence on the scale k t with the scale of the probe. We show how, to leading logarithmic accuracy, the equation can be simplified to a single-scale problem. In particular we demonstrate how to determine the two-scale unintegrated distribution f (x,k t 2 , 2 ) from knowledge of the integrated gluon obtained from a unified scheme embodying both BFKL ͓log(1/x)͔ and DGLAP (log 2 ) evolution.PACS number͑s͒: 12.38.Bx, 13.60.Hb 1 Called the kinematic constraint in ͓12͔.

Starting from an unintegrated gluon distribution which satisfies a `unified' equation which embodies both BFKL and DGLAP behaviour, we compute the shadowing corrections to the integrated gluon in the small x domain that will be accessible at the LHC. The corrections are calculated via the Korchegov equation, which incorporates the leading ln(1/x) triple-Pomeron vertex, and are approximately resummed using a simple Pade technique. We find that the shadowing corrections to xg(x,Q^2) are rather small in the HERA domain, but lead to a factor of 2 suppression in the region x \sim 10^-6, Q^2 \sim 4 GeV^2 accessible to experiments at the LHC.Comment: LaTeX, 8 pages including 1 figure, second version with extra comments and references, accepted by Physics Letters