Abstract
We propose a formalism to extract the γπ → ππ chiral anomaly F3π from calculations in lattice QCD performed at larger-than-physical pion masses. To this end, we start from a dispersive representation of the γ(*)π → ππ amplitude, whose main quark-mass dependence arises from the ππ scattering phase shift and can be derived from chiral perturbation theory via the inverse-amplitude method. With parameters constrained by lattice calculations of the P-wave phase shift, we use this combination of dispersion relations and effective field theory to extrapolate two recent γ(*)π → ππ calculations in lattice QCD to the physical point. Our formalism allows us to extract the radiative coupling of the ρ(770) meson and, for the first time, the chiral anomaly F3π = 38(16)(11) GeV−3. The result is consistent with the chiral prediction albeit within large uncertainties, which will improve in accordance with progress in future lattice-QCD computations.
Highlights
We propose a formalism to extract the γπ → ππ chiral anomaly F3π from calculations in lattice QCD performed at larger-than-physical pion masses
We start from a dispersive representation of the γ(∗)π → ππ amplitude, whose main quarkmass dependence arises from the ππ scattering phase shift and can be derived from chiral perturbation theory via the inverse-amplitude method
With parameters constrained by lattice calculations of the P -wave phase shift, we use this combination of dispersion relations and effective field theory to extrapolate two recent γ(∗)π → ππ calculations in lattice QCD to the physical point
Summary
The lattice-QCD computations of γ(∗)π → ππ are based on the formalism presented in ref. [130], which describes a two-step approach. The absolute value of the partial wave, with slkat = (Eklat), sIkAM = (EkIAM), and qa lat the virtuality of the corresponding lattice data point. To take into account the errors of the energies and virtualities, we follow the standard approach and introduce an auxiliary fit parameter for each kinematic variable, see, e.g., ref. The ππ energy levels Eklat carry an error due to the statistical nature of the lattice computation, this error is taken into account by jackknife resampling. In one place at the χ2-level the lattice spacing enters, namely via the decay constant F , whose literature value is required for the evaluation of the IAM amplitudes and needs to be translated into lattice units. The error of the IAM phase impacts the γπ fit via the covariance matrix Cγπ, and via the KT equations.
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