Towards the nucleon hadronic tensor from lattice QCD

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36 Scopus citations


We present the first calculation of the hadronic tensor on the lattice for the nucleon. The hadronic tensor can be used to extract structure functions in deep inelastic scatterings and to provide information for neutrino-nucleon scattering which is crucial to neutrino-nucleus scattering experiments at low energies. The most challenging part in the calculation is to solve an inverse problem. We have implemented and tested three algorithms using mock data, showing that the Bayesian reconstruction method has the best resolution in extracting peak structures while the Backus-Gilbert and maximum entropy methods are somewhat more stable for smooth functions. Numerical results are presented for both the elastic case (clover fermions on domain wall configurations with mπ∼370 MeV and a∼0.06 fm) and a case (anisotropic clover lattice with mπ∼380 MeV and at∼0.035 fm) with large momentum transfer. For the former case, the reconstructed Minkowski hadronic tensor gives precisely the vector charge which proves the feasibility of the approach. For the latter case, the resonance and possibly shallow inelastic scattering contributions around energy transfer ν=1 GeV are clearly observed but no information is obtained for higher excited states with ν>2 GeV. A check of the effective masses of the ρ meson with different lattice setups indicates that, in order to reach higher energy transfers, using lattices with smaller lattice spacings is essential.

Original languageEnglish
Article number114503
JournalPhysical Review D
Issue number11
StatePublished - Jun 1 2020

Bibliographical note

Publisher Copyright:
© 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "" Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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