Pion scattering in the isospin I=2 channel from elongated lattices

C Culver,F X Lee,M Mai,M Döring,A Alexandru

doi:10.1103/physrevd.100.034509

Abstract

Pion-pion elastic scattering in the isospin I=2 channel is investigated in two-flavor dynamical lattice QCD. Six ensembles are used with lattices elongated in one of the spatial dimensions at two quark masses corresponding to a pion mass of 315 MeV and 226 MeV. The energy of the low-lying states below the inelastic threshold are extracted in each case using the standard variational method.The extracted finite-volume spectrum is fitted by the inverse amplitude method simultaneously for both quark masses and extrapolated thereafter to the physical point. The resulting phase-shifts and scattering length are compared with those from experiment, leading-order chiral perturbation theory and other lattice studies. Our calculations match the experimental results.

Highlights

The prediction of scattering phase-shifts of strongly interacting systems directly from quark-gluon dynamics has become possible through rapid advances in lattice QCD calculations
These higher phase-shifts are expected to be small in the kinematic region we explore and can be safely neglected
We have performed a calculation of the pion-pion elastic scattering in the isopsin I 1⁄4 2 channel in twoflavor dynamical lattice QCD

Summary

INTRODUCTION

The prediction of scattering phase-shifts of strongly interacting systems directly from quark-gluon dynamics has become possible through rapid advances in lattice QCD calculations. The data and obtain predictions for the phase-shifts at the physical quark mass This model is unitary and matches the chiral pion-pion amplitude [59,60] up to the next-to-leading order. In comparison to previous studies in which this method was applied [61,62,63,64] we allow here the pion mass and decay constant to vary and include their full correlations with the energy eigenvalues in the fit. In an upcoming paper [65] we will use the I 1⁄4 2 energy eigenvalues determined here, together with the corresponding results of the isovector and isoscalar channels [12,23], to perform a global analysis of pion-pion-scattering with IAM.

LATTICE SETUP

EXTRACTING FINITE-VOLUME SPECTRUM

EXTRACTING PHYSICAL QUANTITIES

Effective range expansion

Inverse amplitude method

CONCLUSION