A measurement of $K^{\pm} \to \pi^{\pm} \gamma \gamma$ decay with the NA48 Detector

The goal of this thesis was an experimental test of an eective theory of strong interactions at low energy, called Chiral Perturbation Theory (ChPT). Weak decays of kaon mesons provide such a test. In particular, K ! decays are interesting because there is no tree-level O(p2) contribution in ChPT, and the leading contributions start at O(p4). At this order, these decays include one undetermined coupling constant, ^c. Both the branching ratio and the spectrum shape of K ! decays are sensitive to this parameter. O(p6) contributions to K ! ChPT predict a 30-40% increase in the branching ratio. From the measurement of the branching ratio and spectrum shape of K ! decays, it is possible to determine a model dependent value of ^c and also to examine whether the O(p6) corrections are necessary and enough to explain the rate. About 40% of the data collected in the year 2003 by the NA48/2 experiment have been analyzed and 908 K ! candidates with about 8% background contamination have been selected in the region with z = m2 =m2 K 0:2. Using 5,750,121 selected K ! 0 decays as normalization channel, a model independent dierential branching ratio of K ! has been measured to be: BR(K ! ; z 0:2) = (1:018 0:038stat 0:039syst 0:004ext) 10􀀀6: From the t to the O(p6) ChPT prediction of the measured branching ratio and the shape of the z-spectrum, a value of ^c = 1:54 0:15stat 0:18syst has been extracted. Using the measured ^c value and the O(p6) ChPT prediction, the branching ratio for z = m2 =m2 K < 0:2 was computed and added to the measured result. The value obtained for the total branching ratio is: BR(K ! ) = (1:055 0:038stat 0:039syst 0:004ext +0:003^c 􀀀0:002^c) 10􀀀6; where the last error re ects the uncertainty on ^c. The branching ratio result presented here agrees with previous experimental results, improving the precision of the measurement by at least a factor of ve. The precision on the ^c measurement has been improved by approximately a factor of three. A slight disagreement with the O(p6) ChPT branching ratio prediction as a function of ^c has been observed. This might be due to the possible existence of non-negligible terms not yet included in the theory. Within the scope of this thesis, 􀀀 0 mixing eects in O(p4) ChPT have also been measured.