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arXiv · 1707.05817

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

Colin Morningstar·John Bulava·Bijit Singha·Ruairí Brett·Jacob Fallica·Andrew Hanlon·Ben Hörz
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Abstract

An implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the L\"uscher 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 $\rho$-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.

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Colin Morningstar, John Bulava, Bijit Singha, Ruairí Brett, Jacob Fallica, Andrew Hanlon, Ben Hörz. 2017-07-18. Estimating the two-particle $K$-matrix for multiple partial waves and decay channels from finite-volume energies. https://doi.org/10.1016/j.nuclphysb.2017.09.014

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