Calculating the Two-photon Contribution to $\pi^0 \rightarrow e^+ e^-$ Decay Amplitude

TL;DR

This paper introduces a novel lattice QCD method to calculate the two-photon contribution to the rare decay of neutral pions into electron-positron pairs, providing first-principles results for both real and imaginary parts of the amplitude.

Contribution

It presents a new approach for handling two-photon intermediate states in lattice QCD, enabling precise calculation of the $ ext{π}^0 ightarrow e^+ e^-$ decay amplitude from first principles.

Findings

Calculated the decay amplitude's real part as 19.68(52)(1.10) eV.

Successfully compared the imaginary part with optical theorem predictions.

Demonstrated the effectiveness of the new method in lattice QCD calculations.

Abstract

We develop a new method that allows us to deal with two-photon intermediate states in a lattice QCD calculation. We apply this method to perform a first-principles calculation of the $\pi^0 \rightarrow e^+ e^-$ decay amplitude. Both the real and imaginary parts of amplitude are calculated. The imaginary part is compared with the prediction of optical theorem to demonstrate the effectiveness of this method. Our result for the real part of decay amplitude is $19.68(52)(1.10) \ \text{eV}$, where the first error is statistical and the second is systematic.