Treatment of the infrared contribution: NLO QED evolution as a pedagogic example

We show that the conventional prescription used for DGLAP parton evolution at NLO has an inconsistent treatment of the contribution from the infrared (IR) region. We illustrate the problem by studying the simple example of QED evolution, treating the electron and photon as partons. The deficiency is not present in a physical approach which removes the IR divergency and allows calculation in the normal 4-dimensional space.Comment: 15 pages, 2 figures, erratum at the end of the articl

Improving the Drell-Yan probe of small x partons at the LHC via a k_t cut

We show that the observation of the Drell-Yan production of low-mass lepton-pairs (M 3) at the LHC can make a direct measurement of parton distribution functions (PDFs) in the low x region, x < 10^{-4}. We describe a procedure that greatly reduces the sensitivity of the predictions to the choice of the factorization scale and, in particular, show how, by imposing a cutoff on the transverse momentum of the lepton-pair, the data are able to probe PDFs in the important low scale, low x domain. We include the effects of the Sudakov suppression factor.Comment: 14 pages, 5 figures, version to be published in EPJC, with expanded explanatio

Physical factorisation scheme for PDFs for non-inclusive applications

We introduce the physical factorisation scheme, which is necessary to describe observables which are `not completely inclusive'. We derive the formulae for NLO DGLAP evolution in this scheme, and also for the `rotation' of the conventional MSbar PDFs into the physical representation. Unlike, the MSbar prescription, where, for example, the gluon PDF at NLO obtains an admixture of the quark-singlet PDF, and vice-versa, the physical approach does not mix parton PDFs of different types. That is, the physical approach retains the precise quantum numbers of each PDF. The NLO corrections to DGLAP evolution in the physical scheme are less than those in the MSbar case, indicating a better convergence of the perturbative series

The LHC can probe small x PDFs; the treatment of the infrared region

First, we show how to reduce the sensitivity of the NLO predictions of the Drell-Yan production of low-mass, lepton-pairs, at high rapidity, to the choice of factorization scale. In this way, observations of this process at the LHC can make direct measurements of parton distribution functions in the low x domain; x < 10^{-4}. Second, we find an inconsistency in the conventional NLO treatment of the infrared region. We illustrate the problem using the NLO coefficient function of Drell-Yan production.Comment: 5 pages, 1 figure, contribution to the Proceedings of "Diffraction2012", Puerto del Carmen, Lanzarote, Spain, Sept. 10-15th, 201

Treatment of heavy quarks in QCD

We show that to correctly describe the effects of the heavy-quark mass, m_h, in DGLAP evolution, it is necessary to work in the so-called `physical' scheme. In this way, we automatically obtain a smooth transition through the heavy-quark thresholds. Moreover, we show that to obtain NLO accuracy, it is sufficient to account for the heavy-quark mass, m_h, just in the LO (one-loop) splitting function. The use of the MS-bar factorisation scheme is not appropriate, since at NLO we deal with a mixture of quarks and gluon (that is, the mass of the heavy parton is not well-defined). The formulae for the explicit m_h dependence of the splitting functions, and for alpha_s, are presented.Comment: 14 pages, 3 figures, references updated, version to be published in EPJ

Unintegrated parton distributions in nuclei

We study how unintegrated parton distributions in nuclei can be calculated from the corresponding integrated partons using the EPS09 parametrization. The role of nuclear effects is presented in terms of the ratio $R^A=\text{uPDF}^A/A\cdot \text{PDF}^N$ for both large and small $x$ domains.Comment: 9 pages, 4 figure

Are the Tails of Percolation Thresholds Gaussians ?

The probability distribution of percolation thresholds in finite lattices were first believed to follow a normal Gaussian behaviour. With increasing computer power and more efficient simulational techniques, this belief turned to a stretched exponential behaviour, instead. Here, based on a further improvement of Monte Carlo data, we show evidences that this question is not yet answered at all.Comment: 7 pages including 3 figure