Energy dependence of the ρ resonance in ππ elastic scattering from lattice QCD

Abstract

We determine the energy-dependent amplitude for elastic ππ 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 ρ resonance. The spectrum is obtained from hadron correlators computed using lattice QCD with light quark masses corresponding to mπ ~ 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.

V2: Corrected a bug in code that previously lead to incorrect normalization of certain correlation functions. Erratum prepended to existing paper shows corrected results. Qualitative features remain unchanged, determined rho resonance parameters change slightly