Lattice QCD Calculation of π^{0}→e^{+}e^{-} Decay

Norman Christ; Xu Feng; Luchang Jin; Cheng Tu; Yidi Zhao

doi:10.1103/PhysRevLett.130.191901

Lattice QCD Calculation of π^{0}→e^{+}e^{-} Decay

Phys Rev Lett. 2023 May 12;130(19):191901. doi: 10.1103/PhysRevLett.130.191901.

Authors

Norman Christ¹, Xu Feng², Luchang Jin³, Cheng Tu³, Yidi Zhao¹

Affiliations

¹ Physics Department, Columbia University, New York, New York 10027, USA.
² School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China; and Center for High Energy Physics, Peking University, Beijing 100871, China.
³ Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046, USA.

PMID: 37243653
DOI: 10.1103/PhysRevLett.130.191901

Abstract

We extend the application of lattice QCD to the two-photon-mediated, order α^{2} rare decay π^{0}→e^{+}e^{-}. By combining Minkowski- and Euclidean-space methods we are able to calculate the complex amplitude describing this decay directly from the underlying theories (QCD and QED) which predict this decay. The leading connected and disconnected diagrams are considered; a continuum limit is evaluated and the systematic errors are estimated. We find ReA=18.60(1.19)(1.05) eV, ImA=32.59(1.50)(1.65) eV, a more accurate value for the ratio (ReA/ImA)=0.571(10)(4), and a result for the partial width Γ(π^{0}→γγ)=6.60(0.61)(0.67) eV. Here the first errors are statistical and the second systematic. This calculation is the first step in determining the more challenging, two-photon-mediated decay amplitude that contributes to the rare decay K→μ^{+}μ^{-}.