@Article{Hansen_etal2020,
author="Hansen, M. T.
and Romero-Lopez, F.
and Sharpe, S. R.",
title="Generalizing the relativistic quantization condition to include all three-pion isospin channels",
journal="Journal of High Energy Physics",
year="2020",
publisher="Springer",
volume="07",
number="7",
pages="047--49pp",
optkeywords="Lattice QCD; Scattering Amplitudes",
abstract="We present a generalization of the relativistic, finite-volume, three-particle quantization condition for non-identical pions in isosymmetric QCD. The resulting formalism allows one to use discrete finite-volume energies, determined using lattice QCD, to constrain scattering amplitudes for all possible values of two- and three-pion isospin. As for the case of identical pions considered previously, the result splits into two steps: the first defines a non-perturbative function with roots equal to the allowed energies, E-n(L), in a given cubic volume with side-length L. This function depends on an intermediate three-body quantity, denoted K-df;3, which can thus be constrained from lattice QCD input. The second step is a set of integral equations relating K-df,K-3 to the physical scattering amplitude, M-3. Both of the key relations, E-n(L) <-> K-df,K-3 and K-df,K-3 <-> M-3, are shown to be block-diagonal in the basis of definite three-pion isospin, I-pi pi pi, so that one in fact recovers four independent relations, corresponding to I-pi pi pi = 0; 1; 2; 3. We also provide the generalized threshold expansion of K-df,K-3 for all channels, as well as parameterizations for all three-pion resonances present for I-pi pi pi = 0 and I-pi pi pi = 1. As an example of the utility of the generalized formalism, we present a toy implementation of the quantization condition for I-pi pi pi = 0, focusing on the quantum numbers of the omega and h(1) resonances.",
optnote="WOS:000551981200002",
optnote="exported from refbase (https://references.ific.uv.es/refbase/show.php?record=4474), last updated on Fri, 07 Aug 2020 10:51:21 +0000",
issn="1029-8479",
doi="10.1007/JHEP07(2020)047",
opturl="https://arxiv.org/abs/2003.10974",
opturl="https://doi.org/10.1007/JHEP07(2020)047",
language="English"
}