Detailed study of the ${\mathrm{K}}^{\pm }\to \ddot{I}{€}^0\ddot{I}{€}^0{\mathrm{e}}^{\pm }\hat{I}½$ (${\mathrm{K}}_{\mathrm{e}4}^{00}$) decay properties

Abstract

A sample of 65210 ${\mathrm{K}}^{\pm }\to \ddot{I}{€}^0\ddot{I}{€}^0{\mathrm{e}}^{\pm }\hat{I}½$ (${\mathrm{K}}_{\mathrm{e}4}^{00}$) 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 $(M_{\ddot{I}€\ddot{I}€}^2,M_{e\hat{I}½}^2)$ and brings evidence for a cusp-like structure in the distribution of the squared $\ddot{I}{€}^0\ddot{I}{€}^0$ invariant mass around $4m_{\ddot{I}{€}^{+}}^2$. Exploiting a model independent description of this form factor, the branching ratio, inclusive of radiative decays, is obtained using the ${\mathrm{K}}^{\pm }\to \ddot{I}{€}^0\ddot{I}{€}^0\ddot{I}{€}^{\pm }$ 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 $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ pair (${\mathrm{K}}_{\mathrm{e}4}^{+-}$) is also presented.

28 pages, 12 figures, 7 tables, accepted by JHEP