## Abstract

We review the Euclidean path-integral formulation of the nucleon hadronic tensor and classify the gauge invariant and topologically distinct insertions in terms of connected and disconnected insertions and also in terms of leading and higher-twist contributions in the DIS region. Converting the Euclidean hadronic tensor back to the Minkowski space requires solving an inverse problem of the Laplace transform. We have investigated several inverse algorithms and studied the pros and cons of each. We show a result with a relatively large momentum transfer (Q^{2} ∼ 4GeV^{2}) to suppress the elastic scattering and reveal the contributions from the resonance and inelastic region of the neutrino-nucleon scattering. For elastic scattering, the hadronic tensor is the the product of the elastic form factors for the two corresponding currents. We checked numerically for the case of two charge vector currents (V_{4}) with the electric form factor calculated from the three-point function and found they agree within errors.

Original language | English |
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Article number | 046 |

Journal | Proceedings of Science |

Volume | 363 |

State | Published - 2019 |

Event | 37th International Symposium on Lattice Field Theory, LATTICE 2019 - Wuhan, China Duration: Jun 16 2019 → Jun 22 2019 |

### Bibliographical note

Funding Information:This work is partially support by the U.S. DOE grant DE-SC0013065 and DOE Grant No. DE-AC05-06OR23177 which is within the framework of the TMD Topical Collaboration. 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 (XSEDE), which is supported by National Science Foundation Grant No. ACI-1053575. We also thank the National Energy Research Scientific Computing Center (NERSC) for providing HPC resources that have contributed to the research results reported within this paper.

Publisher Copyright:

© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0).

## ASJC Scopus subject areas

- General