Energy dependence of the {\rho} resonance in {\pi}{\pi} elastic scattering from lattice QCD

TL;DR

This study uses lattice QCD to analyze the energy dependence of the { ho} resonance in {} pion-pion elastic scattering, providing detailed phase shift data across multiple energies.

Contribution

It presents the first detailed lattice QCD calculation of the { ho} resonance's energy-dependent phase shift in {} pion-pion scattering.

Findings

Observed a rapidly rising phase shift consistent with a { ho} resonance.

Mapped out over thirty phase shift values in the elastic region.

Demonstrated the effectiveness of variational analysis with diverse interpolating fields.

Abstract

We determine the energy-dependent amplitude for elastic {\pi}{\pi} P-wave scattering in isospin-1 by computing part of the discrete energy spectrum of QCD in finite cubic boxes. We observe a rapidly rising phase shift that can be well described by a single {\rho} resonance. The spectrum is obtained from hadron correlators computed using lattice QCD with light quark masses corresponding to m{\pi} ~ 400 MeV. Variational analyses are performed with large bases of hadron interpolating fields including, as well as fermion bilinears that resemble q-qbar constructions, also operators that resemble pairs of pions with definite relative and total momentum. We compute the spectrum for a range of center-of-mass momenta and in various irreducible representations of the relevant symmetry group. Hence we determine more than thirty values of the isospin-1 P-wave scattering phase shift in the elastic region, mapping out its energy dependence in unprecedented detail.