New determination of the branching ratio of the structure dependent radiative $K^{+} \to e^{+} \nu_{e} \gamma$ decay

TL;DR

This paper reports a new measurement of the branching ratio of the structure-dependent radiative decay of charged kaons, providing results that align with lattice QCD but challenge some Chiral Perturbation Theory predictions.

Contribution

The study presents the first combined measurement of the SD radiative decay branching ratio using data from two different detector setups, refining previous results and testing theoretical models.

Findings

Measured Br ratio: 1.20 ± 0.07

Result consistent with lattice QCD

Larger than some ChPT predictions

Abstract

The branching ratio of the structure dependent (SD) radiative $K^{+} \to e^{+} \nu_{e} \gamma$ decay relative to that of the $K^+\rightarrow e^+ \nu_{e} (\gamma)$ decay including the internal bremsstrahlung (IB) process ($K_{e2(\gamma)}$) has been measured in the J-PARC E36 experiment using plastic scintillator/lead sandwich detectors. In the analysis, the effect of IB was also taken into account in the SD radiative decay as $K_{e2\gamma(\gamma)}^{\rm SD}$. By combining the new data with the previously reported result of the E36 experiment using a CsI(Tl) calorimeter after revision for the IB correction for $K_{e2\gamma(\gamma)}^{\rm SD}$, a new value $Br(K_{e2\gamma(\gamma)}^{\rm SD})/Br(K_{e2(\gamma)})=1.20\pm0.07$ has been determined, which is consistent with a recent lattice QCD calculation, but larger than the expectation of Chiral Perturbation Theory (ChPT) at order $O(p^4)$ and the previous KLOE value. Also, using the method to relate form factor and branching ratio described in the KLOE paper, the present result is consistent with the form factor prediction based on a gauged nonlocal chiral quark model, but larger than ChPT at order $O(p^6)$.