P -wave π π scattering and the ρ resonance from lattice QCD

Abstract

We calculate the parameters describing elastic I = 1, P-wave pp scattering using lattice QCD with 2 + 1 flavors of clover fermions. Our calculation is performed with a pion mass of m(pi) approximate to 320 MeV and a lattice size of L approximate to 3.6 fm. We construct the two-point correlation matrices with both quark-antiquark and two-hadron interpolating fields using a combination of smeared forward, sequential and stochastic propagators. The spectra in all relevant irreducible representations for total momenta vertical bar(P) over right arrow vertical bar <= root 32 pi/L are extracted with two alternative methods: a variational analysis as well as multiexponential matrix fits. We perform an analysis using Luscher's formalism for the energies below the inelastic thresholds, and investigate several phase shift models, including possible nonresonant contributions. We find that our data are well described by the minimal Breit-Wigner form, with no statistically significant nonresonant component. In determining the rho resonance mass and coupling we compare two different approaches: fitting the individually extracted phase shifts versus fitting the t-matrix model directly to the energy spectrum. We find that both methods give consistent results, and at a pion mass of am(pi) = 0.18295(36)(stat) obtain g(rho pi pi) = 5.69(13)(stat)(16)(sys), am(rho) = 0.4609(16)(stat)(14)(sys), and am(rho)/am(N) = 0.7476(38)(stat)(23)(sys), where the first uncertainty is statistical and the second is the systematic uncertainty due to the choice of fit ranges.