Power corrections in deep inelastic structure functions at large Bjorken x

TL;DR

This work investigates power corrections to DIS structure functions $F_2$ and $F_L$ at large $x$, where the conventional OPE falters due to narrow jet formation. The authors advocate ultraviolet dominance, positing that the twist-$n$ contributions are governed by the subset of operators that mix with the leading twist, and they show that twist-two and jet-function factorization extends to higher twists, enabling exponentiation of $1/W^{2n}$ corrections. A detailed renormalon analysis demonstrates that infrared renormalon ambiguities in twist-two coefficient functions cancel against ultraviolet divergences of twist-four matrix elements, providing a consistent framework at order $1/Q^2$. In the large-$x$ limit, twist-four is dominated by twist-two–like configurations with a gluon carrying vanishing longitudinal momentum, leading to a simplified, universal description through a non-perturbative jet (shape) function that sums power corrections. The results point toward a generalized large-$x$ factorization where higher twists can be resummed into a single non-perturbative function, with implications for other structure functions and for phenomenology near the end point.

Abstract

We study power corrections to the spin-averaged structure functions F_2 and F_L in the semi-inclusive region. The dramatic breakdown of the operator product expansion at large Bjorken x due to the formation of a narrow jet with invariant mass W (W^2=Q^2(1-x)/x) calls for an alternative approach. Our main conjecture is that the dominant contribution at each twist is the one which mixes under renormalization with the leading twist (ultraviolet dominance). At twist two the dominant perturbative corrections at large x due to soft and collinear radiation can be factorized into a jet function. From the ultraviolet dominance conjecture it follows that the twist two parton distribution as well as the jet function actually factorize to any order in the twist expansion. This factorization suggests that non-perturbative corrections ~1/W^{2n} exponentiate together with the leading twist. We verify explicitly, at the level of a single dressed gluon, the cancellation between ambiguities due to infrared renormalons in the twist-two coefficient functions and those due to the ultraviolet divergence of twist-four matrix elements. Independently of the renormalon analysis, we show that the dominant contribution to twist four at large x is associated with a twist-two like configuration: the final states are identical to those of twist two, whereas the initial states differ just by additional partons carrying small momentum fractions. This picture is consistent with the ultraviolet dominance conjecture.

Figures (5)

• Figure 1: Diagrams that contribute to the twist-two coefficient function at leading order.
• Figure 2: Forward matrix elements of the non-local light-cone operators ${\cal O}_{3,7}(v;y)$.
• Figure 3: Contributions to the quadratic ultraviolet divergence of twist-four matrix elements. Insertion of fermion loops into the gluon lines is assumed. The contribution (b), corresponding to non-local operators with a quark-antiquark pair and two gluons, vanishes.
• Figure 4: (a) The non-local four-quarks operators ${\cal O}_{1,2}$; (b) a diagram contributing to the quadratic divergence of the matrix element of ${\cal O}_{1,2}(s_1,s_2;s_3,s_4)$ in the large-$N_f$ limit.
• Figure 5: (a) Local Feynman diagram from which four-quark operators emerge by taking the operator product expansion; (b) The origin of figure \ref{['non_local']} (b).