Compton Amplitude and Nucleon Structure Functions via the Feynman-Hellmann theorem

Compton Amplitude and Nucleon Structure Functions via the Feynman-Hellmann theorem

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

structure of hadrons relevant for deep-inelastic scattering are completely characterized by the

Compton amplitude (see LH figure). A direct calculation of the Compton amplitude within

the framework of lattice QCD [1] provides an opportunity to investigate the non-perturbative

effects at low scales which are less well-understood and might have significant implications

for global QCD analyses. In the RH figure [2] we show the lowest moment of the F2

structure function for the proton versus Q2. There is clearly an effect from higher twist terms

(terms proportional to1/Q2), following the experimental results.

Left panel: Deep inelastic scattering where a proton is broken up by a highly energetic electron

emitting a photon which strikes a quark or parton in the hadron. The measured cross section is the

square of this and is described by the Compton amplitude shown in the figure.

Right panel: The computed lowest moment of the F2 structure for the proton. The experimental

Cornwall-Norton results are shown as black stars. The fit is based on the twist expansion.

Several phenomenologically relevant quantities, e.g. low- and high-x regions of parton

distribution functions, power corrections, subtraction function, and generalised parton

distributions in the zero-skewness region to name a few, are accessible. Our long term

objective is improving particle and nuclear physics community’s overall understanding of

non-perturbative effects in hadron structure from first principles.

The simulations and analysis were performed on the DiRAC-3 Extreme Scaling service

(Edinburgh) and Data Intensive service (Cambridge).

[1] K. U. Can et al. [QCDSF/UKQCD/CSSM], Phys. Rev. D 102 (2020), 114505.

[2] M. Batelaan et al. [QCDSF/UKQCD/CSSM], Phys. Rev. D 107 (2023), 054503.