The γπ → ππ anomaly from lattice QCD and dispersion relations
Abstract
We propose a formalism to extract the γπ → ππ chiral anomaly F_{3π} from calculations in lattice QCD performed at largerthanphysical pion masses. To this end, 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 inverseamplitude method. With parameters constrained by lattice calculations of the Pwave 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 F_{3π} = 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 latticeQCD computations.
 Publication:

Journal of High Energy Physics
 Pub Date:
 December 2021
 DOI:
 10.1007/JHEP12(2021)038
 arXiv:
 arXiv:2110.11372
 Bibcode:
 2021JHEP...12..038N
 Keywords:

 Chiral Lagrangians;
 Effective Field Theories;
 Lattice QCD;
 Nonperturbative Effects;
 High Energy Physics  Phenomenology;
 High Energy Physics  Experiment;
 High Energy Physics  Lattice;
 Nuclear Theory
 EPrint:
 29 pages, 5 figures