The interplay between Sudakov resummation, renormalons and higher twist in deep inelastic scattering

TL;DR

This work develops a dressed-gluon exponentiation approach to deep inelastic scattering at large x, showing that Sudakov logs in the evolution kernel originate from the jet function and can be resummed to NNLL, with subleading logs modeled using large-$N_f$ information and several B[K](u) models. By fitting high-N Nachtmann moments of F2 with NNLO+NNLL (and renormalon-informed variants), the authors extract an $oldsymbol{\a_s(M_Z^2)}$ around 0.113–0.114, while highlighting substantial uncertainty from subleading logs. They find no compelling evidence for higher-twist contributions beyond resummed perturbation within current data and emphasize the need for more precise data and better theoretical control of subleading structures to sharpen constraints on power-suppressed effects. The results underscore the jet-dominated nature of Sudakov effects at large x and quantify the trade-offs between resummation, renormalons, and potential higher-twist corrections in DIS.

Abstract

We claim that factorization implies that the evolution kernel, defined by the logarithmic derivative of the N-th moment of the structure function d ln F_2^N / d ln Q^2, receives logarithmically enhanced contributions (Sudakov logs) from a single source, namely the constrained invariant mass of the jet. Available results from fixed-order calculations facilitate Sudakov resummation up to the next-to-next-to-leading logarithmic accuracy. We use additional all-order information on the physical kernel from the large-beta_0 limit to model the behaviour of further subleading logs and explore the uncertainty in extracting alpha_s and in determining the magnitude of higher-twist contributions from a comparison with data on high moments.

Figures (10)

• Figure 1: Factorization of DIS structure functions at large Bjorken $x$.
• Figure 2: Factorization of $F_2$ at large $x$. Full and dashed lines stand for a dynamical quark and a Wilson line, respectively. The vertical lines correspond to the incoming lightcone direction $p$ and the horizontal line to the outgoing jet. The three pictures correspond to the jet, the quark distribution and the soft function, respectively.
• Figure 3: Factorization of $F_2$ at large $x$. The soft function is split between the jet and the quark distribution. Different separations amount to evolution of $q(x,\mu_F^2)$. In our formulation the upper 'soft' blob is understood as part of the jet while the lower one as part of the quark distribution function.
• Figure 4: Different models for $B[{\cal K}](u)$. The points describe the calculated function in the large-$\beta_0$ limit (\ref{['large_beta_0_result']}), and the lines describe simple models for this function in QCD, inspired by the large-$\beta_0$ analytic structure, which are consistent with the first three orders ($\tilde{k}_{0,1,2}$) in the expansion of $B[{\cal K}](u)$. The full lines stand for the following models (from bottom to top in the range $0<u<1$): green -- $a$, blue -- $b$, magenta -- $c$ and red -- $d$. The dashed line describes model $e$. Arrows show the points where renormalon poles appear.
• Figure 5: Order by order calculation of the jet function $\ln J_N\left({Q^2};\mu_{F}^2\right)$ for $N=10$ and for $Q^2=2$ GeV$^2$ (right box) and $Q^2=20$ GeV$^2$ (left box). NNLL ($m=0,1,2$) are exact in all cases. Subleading logs are calculated based on each of the four models (from bottom to top): green -- $a$, blue -- $b$, magenta -- $c$ and red -- $d$. The minimal term in the series is denoted by an 'x' symbol.