Quark-mass dependence of pion scattering amplitudes

Abstract

We analyze lattice-QCD data of the ππ → ππ P wave obtained at unphysical-high pion masses with the inverse-amplitude method at next-to-leading order and at next-to-next-to-leading order. We then extrapolate to the physical pion mass and determine the properties of the ρ resonance from its pole in the complex plane. By comparing both orders, we estimate the systematic error associated with the truncation. Subsequently, we use the inverse-amplitude method as input to Khuri-Treiman equations for γ(*)π → ππ. The resulting dispersive framework is fit to lattice-QCD data at unphysical pion masses and then again extrapolated to the physical mass, where we determine the radiative coupling of the ρ, the lineshape, and the chiral anomaly of the process. Lastly, we develop a method to assess the statistics needed in experiments to be sensitive to higher-order pion rescattering in decays of a single particle into three pions and illustrate the approach for simple cases.