The Standard model prediction for K(e2)/K_(mu2) and pi(e2)/pi(mu2)

TL;DR

This paper calculates the ratio of leptonic decay rates for pions and kaons within the Standard Model using Chiral Perturbation Theory, providing precise theoretical predictions that are crucial for testing new physics in ongoing experiments.

Contribution

The paper provides the first high-precision Standard Model predictions for the ratios R_{e/μ}^{(π)} and R_{e/μ}^{(K)} up to order e^2p^4, including detailed theoretical uncertainties.

Findings

Predicted R_{e/μ}^{(π)} = (1.2352 ± 0.0001) × 10^{-4}

Predicted R_{e/μ}^{(K)} = (2.477 ± 0.001) × 10^{-5}

Results are consistent with current experimental data and serve as benchmarks for new physics searches.

Abstract

We have calculated the ratios $R_{e/\mu}^{(P)} \equiv \Gamma(P \to e \bar{\nu}_e [\gamma])/ \Gamma(P \to \mu \bar{\nu}_\mu [\gamma])$ ($P=\pi,K$) in Chiral Perturbation Theory up to $\mathcal{O}(e^2p^4)$, finding $R_{e/\mu}^{(\pi)} = (1.2352 \pm 0.0001) \times 10^{-4}$ and $R_{e/\mu}^{(K)} = (2.477 \pm 0.001) \times 10^{-5}$. This observable is helicity suppressed in the Standard Model, so that it is a sensitive probe of all Standard Model extensions that induce pseudoscalar currents and nonuniversal corrections to the lepton couplings. Ongoing experimental searches plan to reach uncertainties that are comparable to these results. At the moment $R_{e/\mu}^{(K)}$ is in agreement with the final result by the KLOE Collaboration at DAFNE and it is at $1.4 \sigma$ of the preliminary result by the NA62 Experiment at CERN. New measurements of $R_{e/\mu}^{(\pi)}$ are under way by the PEN Collaboration at PSI and by the PIENU Collaboration at TRIUMF.