Pion transition form factor from twisted-mass lattice QCD and the hadronic light-by-light <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math>-pole contribution to the muon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:math>
Constantia Alexandrou, Simone Bacchio, Georg Bergner, Sebastian Burri, J. Finkenrath, Andrew Gasbarro, Kyriakos Hadjiyiannakou, K. Jansen, Gurtej Kanwar, Bartosz Kostrzewa, Giannis Koutsou, Konstantin Ottnad, Marcus Petschlies, Ferenc Pittler, Fernanda Steffens, Carsten Urbach, Urs Wenger
Abstract
The neutral pion generates the leading pole contribution to the hadronic light-by-light tensor, which is given in terms of the nonperturbative transition form factor ${\mathcal{F}}_{{\ensuremath{\pi}}^{0}\ensuremath{\gamma}\ensuremath{\gamma}}({q}_{1}^{2},{q}_{2}^{2})$. Here we present an ab-initio lattice calculation of this quantity in the continuum and at the physical point using twisted-mass lattice QCD. We report our results for the transition form factor parametrized using a model-independent conformal expansion valid for arbitrary spacelike kinematics and compare it with experimental measurements of the single-virtual form factor, the two-photon decay width, and the slope parameter. We then use the transition form factors to compute the pion-pole contribution to the hadronic light-by-light scattering in the muon $g\ensuremath{-}2$, finding ${a}_{\ensuremath{\mu}}^{{\ensuremath{\pi}}^{0}\ensuremath{-}\mathrm{pole}}=56.7(3.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$.