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@ARTICLE{Bulava:570301,
      author       = {Bulava, John},
      title        = {{T}he spectral reconstruction of inclusive rates},
      reportid     = {PUBDB-2023-00664, arXiv:2301.04072},
      year         = {2023},
      note         = {16 pages, 10 figures, proceedings from the Lattice 2022
                      conference},
      abstract     = {A recently re-discovered variant of the Backus-Gilbert
                      algorithm for spectral reconstruction enables the controlled
                      determination of smeared spectral densities from lattice
                      field theory correlation functions. A particular advantage
                      of this approach is the $\emph{a$ priori} specification of
                      the kernel with which the underlying spectral density is
                      smeared, allowing for variation of its peak position,
                      smearing width, and functional form. If the unsmeared
                      spectral density is sufficiently smooth in the neighborhood
                      of a particular energy, it can be obtained from an
                      extrapolation to zero smearing-kernel width at fixed peak
                      position. A natural application for this approach is
                      scattering processes summed over all hadronic final states.
                      As a proof-of-principle test, an inclusive rate is computed
                      in the two-dimensional O(3) sigma model from a two-point
                      correlation function of conserved currents. The results at
                      finite and zero smearing radius are in good agreement with
                      the known analytic form up to energies at which 40-particle
                      states contribute, and are sensitive to the 4-particle
                      contribution to the inclusive rate. The straight-forward
                      adaptation to compute the $R$-ratio in lattice QCD from
                      two-point functions of the electromagnetic current is
                      briefly discussed.},
      keywords     = {density: spectral (INSPIRE) / two-point function:
                      electromagnetic (INSPIRE) / current: electromagnetic
                      (INSPIRE) / sigma model: O(3) (INSPIRE) / dimension: 2
                      (INSPIRE) / final state: hadronic (INSPIRE) / correlation
                      function (INSPIRE) / lattice field theory (INSPIRE) /
                      scattering (INSPIRE) / conservation law (INSPIRE)},
      cin          = {$Z_APR$},
      cid          = {$I:(DE-H253)Z_APR-20201126$},
      pnm          = {613 - Matter and Radiation from the Universe (POF4-613)},
      pid          = {G:(DE-HGF)POF4-613},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2301.04072},
      howpublished = {arXiv:2301.04072},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2301.04072;\%\%$},
      doi          = {10.3204/PUBDB-2023-00664},
      url          = {https://bib-pubdb1.desy.de/record/570301},
}