Understanding the internal structure of hadrons from first principles remains one of the foremost tasks in particle and nuclear physics. It is an active field of research with important phenomenological implications in high-energy, nuclear and astroparticle physics. The static properties of hadrons, from the hybrid structure of quark and meson degrees of freedom at low energies down to the partonic structure at short distances, are encoded in structure functions. The forward Compton amplitude describes the process of virtual photon scattering from a hadron (here a nucleon) and via the optical theorem provides an essential ingredient in the determination of the structure functions.
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. In a breakthrough paper published in Physical Review Letters , we demonstrated how it is possible to extract the forward Compton amplitude from lattice QCD. This is achieved by taking advantage of the efficiency of the Feynman-Hellmann approach and avoids the need to compute 4-point functions. This advance opens a new avenue to study a range of features of hadronic states, including non-trivial correlations in their partonic structure that can provide novel insights into parton dynamics.
In a recent paper , we extended this investigation and demonstrated for the first time that the Q2-dependence of the moments of structure functions can be probed directly within a lattice simulation (seen in the left figure below). This breakthrough calculation clearly shows that power-corrections (curvature at small- Q2) can be significant and will have important consequences for attempts to extract the leading-twist parton distributions from experimental data at low- Q2. One possible source of power-corrections is due higher-twist effects which go beyond the simple parton picture. Such contributions are suppressed by extra powers of Q2, however their size in the small-Q2 domain has until now been poorly known. The right figure shows a first attempt  at isolating one such higher-twist term for three values of Q2 which clearly shows an enhancement at small Q2.
 A. Chambers et al., Phys. Rev. Lett. 118 (2017) 242001.
 K. U. Can et al., Phys. Rev. D 102 (2020) 114505.
 A. Hannaford-Gunn et al., PoS LATTICE2019 (2020), 278; R. Horsley et al., PoS LATTICE2019 (2020), 137.