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.
|Journal||Physical Review D|
|State||Published - Jun 1 2020|
Bibliographical noteFunding Information:
K.-F. L. thanks X. Feng, A. Kronfeld, J. C. Peng, J. Qiu, and Y. Hatta for illuminating and useful discussions. We also thank the RBC and UKQCD Collaborations for providing their DWF gauge configurations. This work is supported in part by the U.S. DOE Grants No. DE-SC0013065 and No. DE-AC05-06OR23177 which is within the framework of the TMD Topical Collaboration. Y.-B. Y. is supported by Strategic Priority Research Program of Chinese Academy of Sciences, Grant No. XDC01040100. A. R. acknowledges support by the Research Council of Norway under the FRIPRO Young Research Talent Grants No. 286883 and No. 295310. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. This work used Stampede time under the Extreme Science and Engineering Discovery Environment, which is supported by National Science Foundation Grant No. ACI-1053575. We also thank the National Energy Research Scientific Computing Center for providing high performance computing resources that have contributed to the research results reported within this paper. We acknowledge the facilities of the USQCD Collaboration used for this research in part, which are funded by the Office of Science of the U.S. Department of Energy.
© 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/" 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