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The Compton Amplitude, lattice QCD and the Feynman-Hellmann approach

by K.U. Can, A. Hannaford-Gunn, R. Horsley, Y. Nakamura, H. Perlt, P.E.L. Rakow, E. Sankey, G. Schierholz, H. Stuben, R.D. Young and J.M. Zanotti

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Submission summary

Authors (as registered SciPost users): Roger Horsley
Submission information
Preprint Link: scipost_202201_00026v1  (pdf)
Date accepted: 2022-04-11
Date submitted: 2022-01-21 11:46
Submitted by: Horsley, Roger
Submitted to: SciPost Physics Proceedings
Proceedings issue: XXXIII International Workshop on High Energy Physics (IWHEP2021)
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory


A major objective of lattice QCD is the computation of hadronic matrix elements. The standard method is to use three-point and four-point correlation functions. An alternative approach, requiring only the computation of two-point correlation functions is to use the Feynman-Hellmann theorem. In this talk we develop this method up to second order in perturbation theory, in a context appropriate for lattice QCD. This encompasses the Compton Amplitude (which forms the basis for deep inelastic scattering) and hadron scattering. Some numerical results are presented showing results indicating what this approach might achieve.

Published as SciPost Phys. Proc. 6, 003 (2022)

Reports on this Submission

Anonymous Report 1 on 2022-3-28 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202201_00026v1, delivered 2022-03-28, doi: 10.21468/SciPost.Report.4790


New powerful method of computations in the lattice QCD is presented


The problem of computations in lattice QCD is discussed. The LQCD is a source of first-principle results for hadronic matrix elements. It is important to compute the Compton amplitude needed for computation of the structure functions. The Compton amplitude is a 4-point correlation function and hence it is difficult to compute using standard approaches of the Lattice QCD. To circumvent this problem the authors apply a Feynman–Hellmann approach which they developed in their previous publications. This approach has many advantages: it avoids operator mixing, renormalisation is simple, it allows investigation of power corrections to the leading behaviour of the OPE.
The approach is described in details with numerical result for the valence PDF as example of its application. The authors additionally discuss other possible applications of the approach developed, in particular, spin dependent structure functions and electromagnetic corrections to the proton – neutron mass splitting.
I definitely recommend the manuscript for publication.

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