Hadron structure functions are ubiquitous in the description of leptonic interactions with hadrons, encoding: elastic form factors, inclusive electro- (and photo-) production of resonances, diffractive processes and Regge phenomena, and partonic structure in deep inelastic scattering. Lattice QCD, however, has really only been able to probe some limited kinematic corners of the all-encompassing structure functions primarily being limited to elastic form factors and low(est) moments of leading-twist parton distributions. The particular interest in partonic structure has motivated a number of strategies to overcome limitations in the lattice formulation, including: the Euclidean hadron tensor, lattice OPE, heavy-quark Compton amplitude, symmetry-improved operator construction, factorisable matrix elements, and quasi-PDFs and related quantities. We have embarked on a complementary program to extract the forward Compton amplitude in the unphysical region . Computationally, we are able to take advantage of the efficiency of the Feynman-Hellmann approach to hadron structure and avoid the need to compute 4-point functions. Here we highlight [2,3] some recent progress towards revealing scaling and higher twist-phenomena in the low-order moments of the Compton amplitude from lattice QCD.
-  A. Chambers et al., Phys. Rev. Lett. 118 (2017) 242001.
-  A. Hannaford-Gunn et al., PoS (LATTICE2019) 278.
-  R. Horsley et al., ibid 137.