Lattice Calculation of Light Meson Radiative Leptonic Decays

TL;DR

This paper presents a lattice QCD calculation of radiative leptonic decay form factors for pions and kaons, employing the IVR method to control finite volume effects, and compares results with experimental data.

Contribution

First lattice QCD study using the IVR method to compute radiative leptonic decay form factors at physical pion mass, including radiative corrections.

Findings

Results for π→eν_eγ agree with PIBETA measurements.

Results for K→eν_eγ are consistent with KLOE data but show tension with E36.

Results for K→μν_μγ confirm discrepancies at large photon energies.

Abstract

In this work, we perform a lattice QCD calculation of the branching ratios and the form factors of radiative leptonic decays $P \to \ell \nu_\ell \gamma$ ($P = \pi, K$) using $N_f=2+1$ domain wall fermion ensembles generated by the RBC and UKQCD collaborations at the physical pion mass. We adopt the infinite volume reconstruction (IVR) method, which extends lattice data to infinite volume and effectively controls the finite volume effects. This study represents a first step toward a complete calculation of radiative corrections to leptonic decays using the IVR method, including both real photon emissions and virtual photon loops. For decays involving a final state electron, collinear radiative corrections, enhanced by the large logarithmic factors such as $\ln(m_\pi^2/m_e^2)$ and $\ln(m_K^2/m_e^2)$, can reach the level of $O(10\%)$ and are essential at the current level of theoretical and experimental precision. After including these corrections, our result for $\pi \to e\nu_e\gamma$ agrees with the PIBETA measurement; for \(K \to e\nu_e\gamma\), our results are consistent with the KLOE data and exhibit a $1.7\sigma$ tension with E36; and for $K \to \mu\nu_\mu\gamma$, where radiative corrections are negligible, our results confirm the previously observed discrepancies between lattice results and the ISTRA/OKA measurements at large photon energies, and with the E787 results at large muon photon angles.