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

Area of Science:

• Theoretical particle physics
• Quantum chromodynamics (QCD)
• Quantum electrodynamics (QED)

Background:

• Rare decays of neutral pseudoscalar mesons provide sensitive probes of fundamental physics.
• Previous calculations of the π⁰→e⁺e⁻ decay amplitude were limited in precision.

Purpose of the Study:

• To calculate the complex decay amplitude of the two-photon-mediated π⁰→e⁺e⁻ decay.
• To provide accurate theoretical predictions for the decay width and amplitude ratio.

Main Methods:

• Application of lattice QCD combined with Minkowski- and Euclidean-space methods.
• Inclusion of leading connected and disconnected diagrams.
• Evaluation of the continuum limit and estimation of systematic errors.

Main Results:

• Precise values for the real and imaginary parts of the decay amplitude: ReA=18.60(1.19)(1.05) eV, ImA=32.59(1.50)(1.65) eV.
• Accurate ratio of the amplitude components: ReA/ImA=0.571(10)(4).
• Precise prediction for the partial decay width: Γ(π⁰→γγ)=6.60(0.61)(0.67) eV.

Conclusions:

• This work represents the first direct calculation of the π⁰→e⁺e⁻ decay amplitude from QCD and QED.
• The results are a significant step towards calculating the two-photon-mediated decay amplitude for K→μ⁺μ⁻.
• The methodology provides a framework for studying other rare meson decays.