ππ P-wave resonant scattering from lattice QCD

Srijit Paul,Andrew Pochinsky,Luka Leskovec,Constantia Alexandrou,John W Negele,Marcus Petschlies,Jesus Gumaro Rendon Suzuki,Stefan Meinel,Sergey Syritsyn,M Della Morte,E Gámiz Sánchez,P Fritzsch,C Pena Ruano

doi:10.1051/epjconf/201817505022

Abstract

We present a high-statistics analysis of the ρ resonance in ππ scattering, using 2 + 1 flavors of clover fermions at a pion mass of approximately 320 MeV and a lattice size of approximately 3:6 fm. The computation of the two-point functions are carried out using combinations of forward, sequential, and stochastic propagators. For the extraction of the ρ-resonance parameters, we compare different fit methods and demonstrate their consistency. For the ππ scattering phase shift, we consider different Breit-Wigner parametrizations and also investigate possible nonresonant contributions. We find that the minimal Breit-Wigner model is suffcient to describe our data, and obtain amρ = 0:4609(16)stat(14)sys and gρππ = 5:69(13)stat(16)sys. In our comparison with other lattice QCD results, we consider the dimensionless ratios amρ/amN and amπ/amN to avoid scale setting ambiguities.

Highlights

The simplest QCD-unstable hadron is the ρ resonance, which decays into two pions with a branching ratio of 99.9%
We present a high-statistics analysis of the ρ resonance in ππ scattering, using 2 + 1 flavors of clover fermions at a pion mass of approximately 320 MeV and a lattice size of approximately 3.6 fm
The ρ resonance appears as a pole in the I = 1 elastic P-wave ππ scattering amplitude

Summary

Introduction

The simplest QCD-unstable hadron is the ρ resonance, which decays into two pions with a branching ratio of 99.9%. As such, it is considered a benchmark for hadron spectroscopy on the lattice. The ρ resonance appears as a pole in the I = 1 elastic P-wave ππ scattering amplitude. Because the scattering is elastic, the energy dependence of the scattering amplitude can be expressed in terms of a single real number, the phase shift. We explore different parametrizations for the energy dependence of the scattering phase shift, and investigate whether a nonresonant background contribution is present

Lattice methods and parameters

Spectrum results

Extraction of resonant parameters using the Lüscher method

Comparison to other studies

90 NR I χ2 dof

Conclusions