Coupled channel analysis of the rho meson decay in lattice QCD

Abstract: We employ a variational basis with a number of $\bar{q}q$ and $\pi\pi$ lattice interpolating fields with quantum numbers of the $\rho$ resonance to extract the discrete energy spectrum in a finite volume. In the elastic region, this spectrum is related to the phase shift of the continuum scattering amplitude by L\"uscher's formula and the relation allows the extraction of resonance parameters from the spectrum calculation. The simulations are performed at three different total momenta of the coupled $\bar q q-\pi\pi$ system, which allows us to extract the p-wave scattering phase at five values of pion relative momenta near the resonance region. The effective range formula describes the phase-shift dependence nicely and we extract the resonance mass $m_\rho=792(7)(8)$ MeV and the coupling $g_{\rho\pi\pi}=5.13(20)$ at our $m_\pi\simeq 266 $MeV. The coupling $g_{\rho\pi\pi}$ is directly related to the width of the $\rho$ meson and our value is close to the value derived from the experimental width. The simulations are performed using dynamical gauge configurations with two mass-degenerate flavors of tree-level improved clover-Wilson fermions. Correlation functions are calculated using the recently proposed distillation method with Laplacian Heaviside (LapH) smearing of quarks, which enables flexible calculations, in many cases with unprecedented accuracy.