Soft-gluon resummation effects on parton distributions

TL;DR

This paper investigates how soft-gluon threshold resummation influences parton distribution functions, focusing on large-x quark distributions, by performing a toy DIS fit with both NLO and NLL-resummed coefficient functions applied to NuTeV, NMC, and BCDMS data. Neural parametrizations of structure functions enable a moment-based extraction of up-quark moments, revealing that resummation suppresses large-x quark moments by several percent up to about 20% depending on x and Q^2, with momentum-sum constraints inducing smaller-x compensations. The results, though not a global fit, demonstrate a non-negligible impact of resummation on PDFs and suggest that including such effects could reduce theoretical uncertainties and allow more data at large x to constrain PDFs. The study argues for integrating resummation into global PDF analyses and calls for a fully consistent treatment that combines resummed PDFs with resummed hard-scattering cross sections to refine LHC phenomenology. Overall, the work provides a first quantitative assessment that motivates future, more comprehensive fits incorporating soft-gluon resummation.

Abstract

We gauge the impact of soft-gluon resummation on quark distributions by performing a simple fit of Deep Inelastic Scattering structure function data using next-to-leading order (NLO) and next-to-leading-logarithmic (NLL)-resummed coefficient functions. We make use of NuTeV charged-current data, as well as New Muon Collaboration (NMC) and Bologna-CERN-Dubna-Munich-Saclay (BCDMS) neutral-current results, which probe large values of x. Our results suggest that the inclusion of resummation effects in global fits of parton distributions is both feasible and desirable, in order to achieve at large x the accuracy goals of the LHC physics program.

Figures (10)

• Figure 1: A sampling of the neural parametrization of NMC and BCDMS data for $F_2^{\rm ns} (x, Q^2)$ at $Q^2 = 12.59 ~{\rm GeV}^2$ (a) and at $Q^2 = 31.62~{\rm GeV}^2$ (b), from the NNPDF Collaboration Forte:2002fg.
• Figure 2: NuTeV data on the structure function $x F_3$, at $Q^2 = 12.59 ~{\rm GeV}^2$ (a) and at $Q^2 = 31.62 ~{\rm GeV}^2$ (b), along with the best fit curve parametrized by Eq. (\ref{['fitF3']}).
• Figure 3: NuTeV data on the quark-initiated contribution $F_2^q$ to the structure function $F_2$, for $Q^2 = 12.59 ~{\rm GeV}^2$ (a), and $Q^2 = 31.62 ~{\rm GeV}^2$ (b). The solid lines are the best fit predictions according to Eq. (\ref{['fitF2']}).
• Figure 4: Moments of the resummed and NLO up quark distribution with statistical errors, in the range $2 \leq N \leq 15$, at $Q^2=12.59$ GeV$^2$.
• Figure 5: As in Fig. \ref{['figun1']}, but at $Q^2=31.62$ GeV$^2$.