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@INPROCEEDINGS{Engelhardt:1037678,
      author       = {Engelhardt, Michael and Hasan, Nesreen and Krieg, Stefan
                      and Liuti, Simonetta and Meinel, Stefan and Negele, John and
                      Pochinsky, Andrew and Rodekamp, Marcel and Syritsyn, Sergey},
      title        = {{Q}uark orbital angular momentum in the proton from a
                      twist-3 generalized parton distribution},
      publisher    = {Sissa Medialab Trieste, Italy},
      reportid     = {FZJ-2025-00841},
      series       = {Proceedings of The 40th International Symposium on Lattice
                      Field Theory — PoS(LATTICE2023) - Sissa Medialab Trieste,
                      Italy, 2024. - ISBN - doi:10.22323/1.453.0316},
      pages        = {2p.},
      year         = {2024},
      abstract     = {Quark orbital angular momentum in the proton is evaluated
                      via a Lattice QCD calculation of the second Mellin moment of
                      the twist-3 generalized parton distribution E˜2T in the
                      forward limit. The connection between this approach to quark
                      orbital angular momentum and approaches previously utilized
                      in Lattice QCD calculations, via generalized transverse
                      momentum-dependent parton distributions and via Ji's sum
                      rule, is reviewed. This connection can be given in terms of
                      Lorentz invariance and equation of motion relations. The
                      calculation of the second Mellin moment of E˜2T proceeds
                      via a finite-momentum proton matrix element of a quark
                      bilocal operator with a straight-line gauge connection and
                      separation in both the longitudinal and transverse
                      directions. The dependence on the former component serves to
                      extract the second Mellin moment, whereas the dependence on
                      the latter component provides a transverse momentum cutoff
                      for the matrix element. Furthermore, a derivative of the
                      matrix element with respect to momentum transfer in the
                      forward limit is required, which is obtained using a direct
                      derivative method. The calculation utilizes a clover fermion
                      ensemble at pion mass 317MeV. The resulting quark orbital
                      angular momentum is consistent with previous evaluations
                      through alternative approaches, albeit with greater
                      statistical uncertainty using a comparable number of
                      samples.},
      month         = {Jul},
      date          = {2023-07-31},
      organization  = {The 40th International Symposium on
                       Lattice Field Theory, Fermi National
                       Accelerator Laboratory (USA), 31 Jul
                       2023 - 4 Aug 2023},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511) / SDS005 - Towards an
                      integrated data science of complex natural systems
                      (PF-JARA-SDS005) / NRW-FAIR (NW21-024-A)},
      pid          = {G:(DE-HGF)POF4-5111 / G:(DE-Juel-1)PF-JARA-SDS005 /
                      G:(NRW)NW21-024-A},
      typ          = {PUB:(DE-HGF)8 / PUB:(DE-HGF)7},
      doi          = {10.22323/1.453.0316},
      url          = {https://juser.fz-juelich.de/record/1037678},
}