Study of the rare decay K ± − →

The NA62 and NA48/2 experiments at CERN collected a large sample of charged kaon decays with a low intensity beam and minimum bias trigger conditions in 2004 (NA48/2) and 2007 (NA62). This allowed measurements of a number of rare decays that are difficult to address in conventional high intensity experiments with highly selective trigger conditions. In particular, large samples of K± → ± decays have been collected, allowing precision tests of the Chiral Perturbation Theory.


Introduction
The CERN kaon facility is located in the North Area (NA) extraction line of the SPS accelerator: charged kaon beams are produced, for NA48/2 in 2004 and NA62 (R K phase, more details can be found in [1]) in 2007, by 400 GeV/c protons impinging on a beryllium target.The NA48/2 experiment used two simultaneous K ± beams with (60 ± 3) GeV/c momentum range, while the NA62 experiment used a modified beam line which provided K + or K − with momenta of (74.0 ± 1.4) GeV/c.For both the experiments the main subdetectors used for the analyses are: a magnetic spectrometer, composed by 4 drift chambers ( p /p = 1.02% ⊕ 0.044% × p for NA48/2 and p /p = 0.48% ⊕ 0.009% × p for NA62 with p in GeV/c); an hodoscope which can provide a fast trigger, t = 150 ps; a Liquid a e-mail: cassese@fi.infn.it,For the NA48/2 and NA62 Collaborations: F. Ambrosino, A. Antonelli, G. Anzivino, R. Arcidiacono, W. Baldini, S. Balev, J.R. Batley, M. Behler, S.   Krypton electromagnetic calorimeter with high granularity and quasi-homogeneous medium 5 mm@10 GeV)).A detailed description of the detectors can be found in [2].

K ± → ±
The double differential rate for unpolarized photon, predicted by the Chiral Perturbation Theory (CHPT) [3], is: where (a, b, c) = a2 + b 2 + c 2 − 2(ab + bc + ca), r = m m K .A, B, C and D are invariant amplitudes functions of the two kinematic variables z and y, defined as: This decay is particularly interesting because it vanishes at tree level 1 and is expected to show a "cusplike" effect for m = 2m ± (z ∼ 0.32); at O(p 4 ) the B and D amplitude are still zero (they arise only at O(p 6 )) and the rate and the spectrum are predicted to depend on A and C. While C depends only on known quantities, A depends on a single O(1) unknown parameter: ĉ.The z spectrum dependence on ĉ at O(p 4 ) is shown in Fig. 1a, where the predicted cusp threshold is visible.An O(p 6 ) complete evaluation has not been performed yet, but the main contributions have been estimated: unitary corrections [4] increase the branching ratio (BR) at low ĉ values and result in a non-zero rate at m → 0, as shown in Fig. 1b.In this theoretical context the aim of NA48/2 and NA62 is to determine the ĉ value by fitting the z spectrum: knowing ĉ it is possible to determine a model dependent BR.Concretely two separate analyses have been performed on the NA48/2 data sample, collected in 2004, and on the data sample collected in 2007 by NA62.In 2004 data have been collected for 3 days with a minimum bias trigger, while in 2007 the minimum bias trigger was downscaled (D ≈ 20): in 3 months of data taking a comparable statistics with 2004 run data was collected.Final results have been obtained combining the two analyses and taking into account the correlated systematics.The invariant mass distribution, M( ± ), for both 2004 and 2007 data is shown in Fig. 2, where a cut on m > 220 MeV/c 2 is applied; the simulations for the    signal and the backgrounds2 are also shown.On the other hand Fig. 3 shows the z distribution for both 2004 and 2007 data; the simulations based on O(p 6 ) calculations for signal and backgrounds are also shown.There is a visible signal region above the K + → + 0 peak, i.e. z > 0.2, and also indications of cusp-like behavior at 2m .which is compatible with the PDG [5] value: BR = (1.10 ± 0.32) × 10 −6 but with a factor ∼ 5 of uncertainty improvement.
It is also possible to evaluate a model independent Branching Ratio in the signal region, z > 0.2, by computing partial branching fractions in 8 sufficiently small z bins, such that the acceptance is almost independent of kinematical distribution.The value obtained is BR MI (z > 0.2) = (0.877 ± 0.087 stat ± 0.017 syst ) × 10 −6 where the main systematic effect are caused by the background estimate (LKr cluster merging).

Conclusions
Combined results for K ± → ± decays, in 2004 and 2007 data, allow the measurement of ĉ in both O(p 4 ) and O(p 6 ) frame.The model dependent BR obtained is compatible with the PDG value, but with a much smaller error (∼ 5 times).Moreover the model independent Branching Ratio has been presented.

Table 1 .
Signal candidates and main backgrounds contributions for both NA48/2 and NA62 data.