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000570301 0247_ $$2arXiv$$aarXiv:2301.04072
000570301 0247_ $$2datacite_doi$$a10.3204/PUBDB-2023-00664
000570301 037__ $$aPUBDB-2023-00664
000570301 041__ $$aEnglish
000570301 088__ $$2arXiv$$aarXiv:2301.04072
000570301 1001_ $$0P:(DE-H253)PIP1010758$$aBulava, John$$b0$$eCorresponding author
000570301 245__ $$aThe spectral reconstruction of inclusive rates
000570301 260__ $$c2023
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000570301 500__ $$a16 pages, 10 figures, proceedings from the Lattice 2022 conference
000570301 520__ $$aA 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.
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000570301 650_7 $$2INSPIRE$$adensity: spectral
000570301 650_7 $$2INSPIRE$$atwo-point function: electromagnetic
000570301 650_7 $$2INSPIRE$$acurrent: electromagnetic
000570301 650_7 $$2INSPIRE$$asigma model: O(3)
000570301 650_7 $$2INSPIRE$$adimension: 2
000570301 650_7 $$2INSPIRE$$afinal state: hadronic
000570301 650_7 $$2INSPIRE$$acorrelation function
000570301 650_7 $$2INSPIRE$$alattice field theory
000570301 650_7 $$2INSPIRE$$ascattering
000570301 650_7 $$2INSPIRE$$aconservation law
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000570301 9141_ $$y2023
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