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

  • Regular Article - Theoretical Physics
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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 \(x \sim M_{W}/\sqrt{s}\) 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.

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Notes

  1. The HERAPDF fit [5] uses fewer free parameters in their study. However, in that analysis the effect of adding extra parameters is included as part of the additional “parameterisation” uncertainty.

  2. It was, however, shown how an arbitrary number of Monte Carlo sets of PDFs could be generated starting with the eigenvector definition.

  3. At NNLO it is necessary to make some approximations in modelling unknown coefficient functions for some processes.

  4. We may compare our correction with that obtained in a study [36] which appeared after the submission of our paper. Our result lies between the smaller (CJ12min) and middle (CJ12mid) estimates of the corrections in [36]; the larger corrections (CJ12max) are disfavoured by the fit quality. Hence, there is complete compatibility.

  5. We note that an NNPDF study on DIS data only noticed a small change of PDFs relative to uncertainties when nuclear corrections were added to the default fit, in which they are omitted [31].

  6. There is also in principle some sensitivity to the numerical value below which the improvement in χ 2 with successive iterations must fall for the fit to stop. This is normally taken as 0.1, but further reductions generally lead to changes very much smaller than the PDF uncertainty, as has been checked in this study.

  7. For massless leptons, the pseudorapidity η ℓ is equal to the rapidity y ℓ .

  8. We note that the particularly good description by CT10 is probably due to the larger strange distribution in their PDF set than in the others. A study by ATLAS has shown that their data prefer a large strange distribution, in fact seemingly one which is the same size as the \(\bar{u}\) and \(\bar{d}\) distributions even at low Q 2 [47]. We do indeed see some small improvement in fit quality associated with the eigenvector most associated with the strange PDF normalisation, but rather less than for the three eigenvectors 9, 14, 18 mentioned below. This means that only a marginal improvement can be obtained by changing the strange distribution by one standard deviation. We have confirmed this by making a more thorough study. Moreover, a study by the NNPDF group has reached a similar conclusion [6].

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Acknowledgements

We would like to thank Stefano Forte and Jon Pumplin for discussion on some of the issues in this article. The work of R.S.T. is supported partly by the London Centre for Terauniverse Studies (LCTS), using funding from the European Research Council via the Advanced Investigator Grant 267352.

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Authors and Affiliations

  1. Institute for Particle Physics Phenomenology, University of Durham, Durham, DH1 3LE, UK

    A. D. Martin

  2. Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, UK

    A. J. Th. M. Mathijssen

  3. Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK

    W. J. Stirling

  4. Department of Physics and Astronomy, University College London, London, WC1E 6BT, UK

    R. S. Thorne & B. J. A. Watt

  5. Institut für Theoretische Physik, Universität Zürich, 8057, Zürich, Switzerland

    G. Watt

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  1. A. D. Martin
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Correspondence to R. S. Thorne.

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Work of A.J.Th.M. Mathijssen mainly done while at University College London.

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Martin, A.D., Mathijssen, A.J.T.M., Stirling, W.J. et al. Extended parameterisations for MSTW PDFs and their effect on lepton charge asymmetry from W decays. Eur. Phys. J. C 73, 2318 (2013). https://doi.org/10.1140/epjc/s10052-013-2318-9

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