Eur. Phys. J. C (2013) 73: 2318
https://doi.org/10.1140/epjc/s10052-013-2318-9

Regular Article - Theoretical Physics

Extended parameterisations for MSTW PDFs and their effect on lepton charge asymmetry from W decays

¹ Institute for Particle Physics Phenomenology, University of Durham, Durham, DH1 3LE, UK
² Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, UK
³ Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK
⁴ Department of Physics and Astronomy, University College London, London, WC1E 6BT, UK
⁵ Institut für Theoretische Physik, Universität Zürich, 8057, Zürich, Switzerland

^* e-mail: thorne@hep.ucl.ac.uk

Received: 13 November 2012
Revised: 31 January 2013
Published online: 28 February 2013

Abstract

We investigate the effect of extending the standard MSTW parameterisation of input parton distribution functions (PDFs) using Chebyshev polynomials, rather than the usual expressions which involve a factor of the form (1+ϵx ^0.5+γx). We find evidence that four powers in the polynomial are generally sufficient for high precision. Applying this to valence and sea quarks, the gluon already being sufficiently flexible and needing only two powers, we find an improvement in the global fit, but a significant change only in the small-x valence up-quark PDF, u _V . We investigate the effect of also extending, and making more flexible, the ‘nuclear’ correction to deuteron structure functions. We show that the extended ‘Chebyshev’ parameterisation results in an improved stability in the deuteron corrections that are required for the best fit to the ‘global’ data. The resulting PDFs have a significantly, but not dramatically, altered valence down-quark distribution, d _V . It is shown that, for the extended set of MSTW PDFs, their uncertainties can be obtained using 23, rather than the usual 20, orthogonal ‘uncertainty’ eigenvectors. This is true both without and with extended deuteron corrections. Since the dominant effect is on the valence quarks, we present a detailed study of the dependence of the valence–sea separation on the predictions for the decay lepton charge asymmetry which results from W ^± production at the LHC, illustrating the PDFs and the x range probed for different experimental scenarios. We show that the modified MSTW PDFs make significantly improved predictions for these data at the LHC, particularly for high values of the p _T cut of the decay lepton. However, this is a special case, since the asymmetry is extremely sensitive to valence–sea details, and in particular to the combination u _V −d _V of valence PDFs for at low lepton rapidities. We show that the predictions for a wide variety of total cross sections are very similar to those obtained using the MSTW2008 PDFs, with changes being much smaller than the PDF uncertainties.