Estimating the two-particle K-matrix for multiple partial waves and decay channels from finite-volume energies

Preprint number: CP3-Origins-2017-27 DNRF90
Authors: Ruairı́ Brett (Carnegie Mellon), John Bulava (CP3-Origins & SDU), Jacob Fallica (Carnegie Mellon), Andrew Hanlon (U. of Pittsburgh), Ben Hörz (U. of Mainz), Colin Morningstar (Carnegie Mellon), and Bijit Singha (Carnegie Mellon)

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An implementation of estimating the two-to-two K-matrix from finite-volume energies
based on the Lüscher formalism and involving a Hermitian matrix known as the “box
matrix” is described. The method includes higher partial waves and multiple decay
channels. Two fitting procedures for estimating the K-matrix parameters, which properly
incorporate all statistical covariances, are discussed. Formulas and software for handling
total spins up to S = 2 and orbital angular momenta up to L = 6 are obtained for total
momenta in several directions. First tests involving ρ-meson decay to two pions include
the L = 3 and L = 5 partial waves, and the contributions from these higher waves are
found to be negligible in the elastic energy range.