Isotensor $\ddot{I}€\ddot{I}€\ddot{I}€$ scattering with a $\ddot{I}$ resonant subsystem from QCD

Abstract

This work presents a lattice quantum chromodynamics (QCD) determination of $\ddot{I}€\ddot{I}€\ddot{I}€$ scattering amplitudes for the isospin-2 channel with angular momentum and parity $J^P=1^{+}$. The calculation is performed using unphysically heavy light-quark masses, corresponding to a pion mass of $m_{\ddot{I}}€\approx 400$~MeV, for which the $\ddot{I}$ meson manifests as a narrow resonance. The analysis employs a previously developed formalism that non-perturbatively relates the finite-volume spectra of two- and three-pion systems to their infinite-volume scattering amplitudes. We combine earlier lattice QCD results for $\ddot{I}€\ddot{I}€$ systems with isospins 1 and 2 with new determinations of the isospin-2 three-pion finite-volume spectrum, obtained for three cubic, periodic lattice volumes with box length ranging from $\approx 4/m_{\ddot{I}}€$ to $6/m_{\ddot{I}}€$. These combined data constrain the low-lying partial waves of the infinite-volume three-pion K matrix, from which we solve a set of coupled integral equations to extract the corresponding scattering amplitudes.

26 pages, 10 figures, v2 includes mild changes to the outlook, acknowledgments, and additional relevant references