A Kinematically Complete Measurement of the Proton Structure Function F2 in the Resonance Region and Evaluation of Its Moments

TL;DR

This study presents a kinematically complete measurement of the proton structure function F2 in the resonance region using the CLAS detector, enabling direct extraction of Mn^N(Q^2) up to n=8 by combining CLAS data with world data. It analyzes the Q^2 evolution of these Nachtmann moments with a twist expansion that includes soft-gluon resummation for the leading twist and phenomenological higher-twist terms, extracting parameters up to tau=6. The results show that the leading twist remains dominant down to Q^2 ~1–2 GeV^2, while higher-twist effects are non-negligible for Q^2 <5 GeV^2 but tend to cancel among terms, supporting a duality picture in the resonance region. The work highlights the precision enabled by CLAS for testing nonperturbative QCD and emphasizes the need for improved theoretical understanding of higher-twist operators, including lattice-based approaches.

Abstract

We measured the inclusive electron-proton cross section in the nucleon resonance region (W < 2.5 GeV) at momentum transfers Q**2 below 4.5 (GeV/c)**2 with the CLAS detector. The large acceptance of CLAS allowed for the first time the measurement of the cross section in a large, contiguous two-dimensional range of Q**2 and x, making it possible to perform an integration of the data at fixed Q**2 over the whole significant x-interval. From these data we extracted the structure function F2 and, by including other world data, we studied the Q**2 evolution of its moments, Mn(Q**2), in order to estimate higher twist contributions. The small statistical and systematic uncertainties of the CLAS data allow a precise extraction of the higher twists and demand significant improvements in theoretical predictions for a meaningful comparison with new experimental results.

Figures (12)

• Figure 1: Experimental data on the structure function $F_2(x,Q^2)$ used for the moment evaluation in the CLAS kinematic region: points - world data; shaded area - CLAS data.
• Figure 2: Twist diagrams:(a) the leading twist contribution evaluated at leading order of pQCD; (b) the contribution of higher twists, where current quark and nucleon remnant can exchange by a system of particles consisting of gluons and $q\bar{q}$-pairs whose complexity is increasing with twist order.
• Figure 3: Photoelectron distribution in the Cherenkov detector versus the energy deposited in the EC detector divided by the momentum of the particle as determined by the drift chamber. The black vertical line represents the cut to reduce the pion contamination.
• Figure 4: The fitted photoelectron distribution for two different sets of kinematics after removing some of the pion contamination via the $EC_{tot}/P$ cut: solid triangles show the distribution obtained with $4$ GeV beam, scattered electron angle $\theta=31^{\circ}$ and momentum $P=1$ GeV; empty diamonds represent data taken with $2.5$ GeV beam, scattered electron angle $\theta=41^{\circ}$ and momentum $P=1$ GeV.
• Figure 5: Typical ratio of the measured elastic scattering cross section to the parametrization from Refs. Bostedhall-a (points) with radiative corrections, in comparison to that obtained from the simulations (continuous line); errors are statistical only.