%0 Journal Article
%T Generalizing the relativistic quantization condition to include all three-pion isospin channels
%A Hansen, M. T.
%A Romero-Lopez, F.
%A Sharpe, S. R.
%J Journal of High Energy Physics
%D 2020
%V 07
%N 7
%I Springer
%@ 1029-8479
%G English
%F Hansen_etal2020
%O WOS:000551981200002
%O exported from refbase (https://references.ific.uv.es/refbase/show.php?record=4474), last updated on Fri, 07 Aug 2020 10:51:21 +0000
%X 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.
%K Lattice QCD
%K Scattering Amplitudes
%R 10.1007/JHEP07(2020)047
%U https://arxiv.org/abs/2003.10974
%U https://doi.org/10.1007/JHEP07(2020)047
%P 047-49pp