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@ARTICLE{Bulava:473389,
      author       = {Bulava, John and Hansen, Maxwell T. and Hansen, Michael W.
                      and Patella, Agostino and Tantalo, Nazario},
      title        = {{I}nclusive rates from smeared spectral densities in the
                      two-dimensional {O}(3) non-linear $\sigma$-model},
      reportid     = {PUBDB-2022-00012, arXiv:2111.12774. DESY-21-201.
                      HU-EP-21/49},
      year         = {2021},
      note         = {26 pages, 11 figures},
      abstract     = {This work employs the spectral reconstruction approach of
                      Ref. [1] to determine an inclusive rate in the $1+1$
                      dimensional O(3) non-linear $\sigma$-model, analogous to the
                      QCD part of ${e}^+{e}^- \rightarrow \rm {hadrons}$. The
                      Euclidean two-point correlation function of the conserved
                      current $j$ is computed using Monte Carlo lattice field
                      theory simulations for a variety of spacetime volumes and
                      lattice spacings. The spectral density of this correlator is
                      related to the inclusive rate for $j \rightarrow {\rm X}$ in
                      which all final states produced by the external current are
                      summed. The ill-posed inverse problem of determining the
                      spectral density from the correlation function is made
                      tractable through the determination of smeared spectral
                      densities in which the desired density is convolved with a
                      set of known smearing kernels of finite width $\epsilon$.
                      The smooth energy dependence of the underlying spectral
                      density enables a controlled $\epsilon \to 0$ extrapolation
                      in the inelastic region, yielding the real-time inclusive
                      rate without reference to individual finite-volume energies
                      or matrix elements. Systematic uncertainties due cutoff
                      effects and residual finite-volume effects are estimated and
                      taken into account in the final error budget. After taking
                      the continuum limit, the results are consistent with the
                      known analytic rate to within the combined statistical and
                      systematic errors. Above energies where 20-particle states
                      contribute, the overall precision is sufficient to discern
                      the four-particle contribution to the spectral density.},
      keywords     = {density: spectral (INSPIRE) / width: finite (INSPIRE) /
                      finite size: effect (INSPIRE) / density: correlation
                      function (INSPIRE) / dimension: 2 (INSPIRE) / current:
                      conservation law (INSPIRE) / O(3) (INSPIRE) / sigma model:
                      nonlinear (INSPIRE) / quantum chromodynamics (INSPIRE) /
                      Euclidean (INSPIRE) / lattice (INSPIRE) / lattice field
                      theory (INSPIRE) / statistical (INSPIRE) / continuum limit
                      (INSPIRE) / energy dependence (INSPIRE) / hadron (INSPIRE) /
                      Monte Carlo (INSPIRE)},
      cin          = {$Z_ZPPT$},
      cid          = {$I:(DE-H253)Z_ZPPT-20210408$},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611)},
      pid          = {G:(DE-HGF)POF4-611},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2111.12774},
      howpublished = {arXiv:2111.12774},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2111.12774;\%\%$},
      doi          = {10.3204/PUBDB-2022-00012},
      url          = {https://bib-pubdb1.desy.de/record/473389},
}