Extended Parameterisations for MSTW PDFs and their effect on Lepton Charge Asymmetry from W Decays

TL;DR

This paper extends the MSTW parton distribution function parameterisation using Chebyshev polynomials, leading to improved fit stability and more accurate predictions for W boson decay lepton charge asymmetry at the LHC.

Contribution

It introduces a Chebyshev polynomial extension to MSTW PDFs, enhancing fit precision and stability, especially for valence quarks, and improves predictions for LHC lepton charge asymmetry measurements.

Findings

Four polynomial powers suffice for high-precision PDFs.

Extended parameterisation improves fit stability and alters valence quark distributions.

Predictions for LHC lepton charge asymmetry are significantly improved.

Abstract

We investigate the effect of extending the standard MSTW parameterisation of input parton distribution functions (PDFs) using Chebyshev polynomials. We find evidence that four powers in the polynomial are sufficient for extremely high precision. Applying this to valence and sea quarks 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. 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, $d_V$. For the extended set of MSTW PDFs, their uncertainties can be obtained using 23, rather than the usual 20, orthogonal `uncertainty' eigenvectors. 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 $W^\pm$ 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.