Detailed study of the $\mathrm{K^{\pm}} \rightarrow \pi^{0} \pi^{0} \mathrm{e^{\pm}} \nu$ ($\mathrm{K}_{\mathrm{e}4}^{00}$) decay properties

TL;DR

This paper reports a detailed experimental study of the rare $K^{ ightarrow} ightarrow ightarrow$ decay, measuring form factors, observing a cusp structure, and providing a highly precise branching ratio, advancing understanding of kaon decay dynamics.

Contribution

It presents the first measurement of hadronic form factor variation in this decay mode and improves the branching ratio precision by an order of magnitude.

Findings

First measurement of form factor variation in the decay plane.

Evidence for a cusp-like structure in the $ ightarrow$ invariant mass distribution.

Branching ratio measured with 1.4% relative precision.

Abstract

A sample of 65210 $\mathrm{K^{\pm}} \rightarrow \pi^{0} \pi^{0} \mathrm{e^{\pm}} \nu$ ($\mathrm{K}_{\mathrm{e}4}^{00}$) decay candidates with $1\%$ background contamination has been collected in 2003$-$2004 by the NA48/2 collaboration at the CERN SPS. A study of the differential rate provides the first measurement of the hadronic form factor variation in the plane $(M_{\pi\pi}^2,M_{e\nu}^2)$ and brings evidence for a cusp-like structure in the distribution of the squared $\pi^{0} \pi^{0}$ invariant mass around $4m_{\pi^+}^2$. Exploiting a model independent description of this form factor, the branching ratio, inclusive of radiative decays, is obtained using the $\mathrm{K^{\pm}} \rightarrow \pi^{0} \pi^{0} \pi^{\pm}$ decay mode as normalization. It is measured to be BR($\mathrm{K}_{\mathrm{e}4}^{00}$) = $(2.552 \pm 0.010_{stat} \pm 0.010_{syst} \pm 0.032_{ext} ) \times 10^{-5}$, which improves the current world average precision by an order of magnitude while the $1.4\%$ relative precision is dominated by the external uncertainty from the normalization mode. A comparison with the properties of the corresponding mode involving a $\pi^{+} \pi^{-}$ pair ($\mathrm{K}_{\mathrm{e}4}^{+-}$) is also presented.