Decay of rho and a1 mesons on the lattice using distillation

Abstract: We extract the P-wave pi-pi phase shift for five values of pion relative momenta, which gives information on the rho resonance. The Breit-Wigner formula describes the pi-pi phase shift dependence nicely and we extract m(rho)=792(7)(8) MeV and the coupling g_{\rho\pi\pi}=5.13(20) at our mpi=266 MeV. We extract the P-wave scattering length a_{l=1}^{\pi\pi}=0.082(10)(3) fm^3 from the state with the lowest pion relative momenta. We also determine the S-wave rho-pi phase shift for two values of relative momenta, which provides parameters of the lowest axial resonance a1(1260). Using the Breit-Wigner fit we extract m(a1)=1.44(4) GeV and the coupling g_{a_1\rho\pi}=1.1(3) GeV. From the lowest state we also extract the rho-pi scattering length a_{l=0}^{\rho\pi}=0.23(12) fm for our mpi. The simulation is performed using one Nf=2 ensemble of gauge configurations with clover-improved Wilson quarks. The phase shifts are determined from the lowest two energy-levels, which are obtained by the variational analysis with a number of quark-antiquark and meson-meson interpolators. The correlation functions are calculated using the distillation method with the Laplacian Heaviside (LapH) smearing of quarks.