Abstract
We briefly summarize experimental and theoretical results on the rare decay π 0 → e + e − . The notorious 3.3σ discrepancy between the Standard Model prediction and the experimental value provided by KTeV collaboration is discussed in the view of a complete set of next-to-leading-order QED radiative corrections. We also present the Two-Hadron Saturation (THS) scenario for the PVV correlator and apply it to the decay under discussion. The discrepancy under discussion then reduces down to 1.8σ. Finally, we turn our attention the the Dalitz decay π 0 → e + e − γ . We have recalculated the Mikaelian and Smith radiative corrections beyond the soft-photon approximation, i.e. over the whole range of the Dalitz plot and with no restrictions on the radiative photon. In contrast to the previous calculations, we also included the one-photon irreducible contribution at one-loop level. Our results can be also used for a further treatment of the processes with heavier particles in the final state.
Highlights
Discovering and quantifying beyond-Standard Model phenomena at the precision frontier is a very complicated task, since it goes along with having first our present knowledge under control
Besides the well-known discrepancy between the measurement of the anomalous magnetic moment of the muon and the theoretical prediction based on the Standard Model (SM), one of the other examples of such disagreement is the rare decay of a neutral pion, i.e. the process π0 → e+e−
Taking into account the complete set of the next-to-leading-order (NLO) radiative corrections presented in Section 3 and the Two-Hadron Saturation (THS) model presented in the previous section, we get for the theoretical prediction of the quantity measured by KTeV experiment BTHS = (5.8 ± 0.2) × 10−8
Summary
Discovering and quantifying beyond-Standard Model phenomena at the precision frontier is a very complicated task, since it goes along with having first our present knowledge under control. Besides the well-known discrepancy between the measurement of the anomalous magnetic moment of the muon and the theoretical prediction based on the Standard Model (SM), one of the other examples of such disagreement is the rare decay of a neutral pion, i.e. the process π0 → e+e−. Soon after it has been shown that the prediction based on the Standard Model is in the 3.3 σ disagreement with this measurement [2], which immediately drew attention of the theorists for the following years. In what follows we will investigate in detail the radiative corrections and suggest a new model for the electromagnetic transition form factor of a neutral pion
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