First observation of the KS->pi0 gamma gamma decay

Using the NA48 detector at the CERN SPS, 31 KS->pi0 gamma gamma candidates with an estimated background of 13.7 +- 3.2 events have been observed. This first observation leads to a branching ratio of BR(KS->pi0 gamma gamma) = (4.9 +- 1.6(stat) +- 0.9(syst)) x 10^-8 in agreement with Chiral Perturbation theory predictions.

Radiative non-leptonic rare kaon decays have proved to be useful tests for low energy hadron dynamics studied in the framework of the Standard Model by the Chiral Perturbation theory (χP T ). This paper describes the first observation of the K S → π 0 γγ decay obtained from data taken by the NA48 experiment in the year 2000.
In the decay K S → π 0 γγ, the photon pair production is described by an amplitude dominated by a pseudo-scalar meson pole. In χP T this pole is dominated by π 0 contribution, and the lowest order amplitude is non-vanishing, in contrast to the similar K L → γγ decay. The theoretical prediction for the branching ratio is 3.8 × 10 −8 with higher order corrections expected to be small [1] and is quoted in the kinematic region z = m 2 γγ /m 2 K > 0.2 which is free from the overwhelming K S → π 0 π 0 background. A measurement of the branching ratio can provide information about the presence of extra non-pole contributions studied e.g. in [2]. In addition, the momentum dependence of the weak vertex which is predicted by χP T can be tested by the measured shape of the z spectrum. The lowest previously published limit on the branching ratio is BR(K S → π 0 γγ) z>0.2 < 3.3 × 10 −7 at 90% confidence level [3].

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Experimental set-up and data taking The NA48 detector was designed to measure direct CP violation in the decays of K L and K S into ππ, described by the parameter Re(ε ′ /ε), using simultaneous far-and near-target beams [4]. The analysis presented in this paper is based on data recorded during a special 40-day run performed in the year 2000 with near-target beam only and with an intensity of about ∼ 10 10 400 GeV protons hitting the target during the 3.2 s long SPS spill. The exit of the collimator, 6 m downstream of the target, is followed by a wide vacuum tube approximately 113 m long containing the decay region and terminated by an aluminium window close to the detector 1) .
The detector elements used in the analysis are the following: -A liquid krypton calorimeter (LKr) [5], placed less than 2 m behind the aluminium window, is used to measure the energy, position and time of electro-magnetic showers. The energy resolution is where E is in GeV. The position and time resolutions for a single photon with energy larger than 20 GeV are better than 1.3 mm and 300 ps, respectively. -A sampling hadron calorimeter composed of 48 steel plates, interleaved with scintillator planes, with a readout in horizontal and vertical projections. -Seven ring shaped scintillator counters equipped with iron converters (AKL), used to detect photons escaping the outer limits of the calorimeter acceptance. The trigger decision, common to π 0 γγ and π 0 π 0 decays, is based on quantities which are derived from the projections of the energy deposited in the electro-magnetic liquid krypton calorimeter [6]. The trigger required that the total deposited energy E tot is larger than 50 GeV, the radial distance of the centre of energy from the beam axis is smaller than 15 cm and the proper life time of the kaon is less than 9 K S lifetimes downstream of the collimator. The inefficiency of the trigger was measured to be at the level of 0.1%.
More about the detector and the experimental configuration during data taking in the year 2000 can be found in [7].

Event selection
The energies and positions of electro-magnetic showers initiated by photons, measured in the liquid krypton calorimeter, are used to calculate the kaon energy and decay vertex. To select K S → π 0 γγ and K S → π 0 π 0 candidates, all events with ≥ 4 energy clusters are considered. All combinations of four clusters which are within 5 ns from the average time and with no other cluster with energy > 1.5 GeV closer in time than 7 ns with respect to the event time are selected. The event time is computed from the times of the most energetic cells of the selected clusters. In addition, the clusters must pass the following cuts: -The energy of each cluster must be greater than 3 GeV and less than 100 GeV.
-The transverse distance between two clusters is required to be greater than 10 cm.
-The total energy of the selected cluster combination is required to be less than 170 GeV and greater than 70 GeV. 1) In the usual NA48 experimental configuration the vacuum tube is terminated at 89 m by a thin Kevlar window followed by a helium filled tank which contains drift chambers and a spectrometer magnet. For these data however, the Kevlar window and the drift chambers were removed, the helium tank was evacuated and the magnet was switched off.
-The distance of the centre of energy from the beam axis, is required to be less than 5 cm, where E i , x i , y i are the i-th cluster energy, x and y coordinates at LKr, respectively. -The energy deposited in the hadron calorimeter must not exceed 3 GeV in a time window of ±15 ns around the event time. -The AKL counter should not register any hit in a time window of ±7 ns around the event time The decay vertex position z vertex of a kaon is calculated using the kaon mass constraint, m K , where z Lkr is the longitudinal coordinate of the LKr calorimeter with respect to the end of the collimator and d ij is the transverse distance between i-th and j-th cluster at the calorimeter. The invariant mass of photon pairs is calculated using z vertex .
The K S → π 0 γγ candidates must have a photon pair with an invariant mass within 2 MeV/c 2 of the π 0 mass, m π 0 , and the other pair must satisfy the condition m 2 γγ /m 2 K > 0.2. In the K S → π 0 π 0 sample a χ 2 cut of 27 (∼ 5σ) is applied to the invariant masses of photon pairs, defined as where σ ± are the resolutions on (m 1 ± m 2 )/2 measured from the data and parametrised as a function of the lowest photon energy. The typical value of σ + is 0.4 MeV/c 2 and σ − is 0.8 MeV/c 2 [8]. For K S → π 0 γγ candidates the χ 2 is required to be larger than 5400. In order to suppress the large background from K S → π 0 π 0 D decays with one particle escaping the acceptance the decay region was restricted to be between -1 m and 8 m with respect to the exit of the collimator. Most of the K S → π 0 π 0 D background events have an apparent z vertex downstream of this region because of the missing energy. This condition is even more effective against background from K L → π 0 π 0 π 0 . The K S → π 0 π 0 D background is further suppressed by imposing the π 0 mass hypothesis on the remaining four pairings 2) of photon showers and calculating the vertex positions z π 0 for each of these γ pairs. Denoting as z * π 0 the closest z π 0 to the exit of the collimator, events with are accepted (Fig. 1). This cut is very effective in suppressing K S → π 0 π 0 D background because, as shown by Monte Carlo studies, this background is completely dominated by events with one of the π 0 D → eeγ decay products escaping detection. In addition, this cut removes events from inelastic scattering of beam particles in the collimator with multiple π 0 production. The downstream end of this cut is intentionally extended in order to reduce background from pile-up of a π 0 from K S → π 0 π 0 with γ's from another decay.
A small amount of K S → π 0 π 0 D background survives the above cuts if a γ from one π 0 and a γ or an e from the other π 0 overlap. In this case the reconstructed z vertex does not move downstream because the entire kaon energy is collected in the LKr calorimeter and there is no pair of showers which would give a correct z π 0 under a π 0 hypothesis. Still, by assuming this type of overlap the correct vertex position can be reconstructed by where index 1 refers to the γ from the π 0 , indexes 2 and 3 to γ or e's from π 0 D and index 4 to the overlapping shower. For π 0 γγ events z overlap = z vertex and hence a cut |z overlap − z vertex | > 1.5 m on all 12 possible combinations reduces this type of background to a sufficiently low level, without significant loss of signal.
2) If indexes 1 and 2 refer to γ's assigned to the π 0 then these four pairings are 1-3, 1-4, 2-3 and 2-4. z* π 0 (m) z vertex (m) Figure 1: Illustration of z vertex and z * π 0 cuts on the data. All other cuts were applied. Rejected areas are shaded. Both variables are defined with respect to the exit of the collimator. The accumulation of events around small z * π 0 values is due to K S → π 0 π 0 D background at high z vertex and due mainly to pile-up events at low or negative z vertex .
In order to remove events with hadrons or overlapping showers from the π 0 γγ sample, the shower width is required to be less than 3σ above the average value for photon showers of a given energy. This cut, which is calibrated using showers in K S → π 0 π 0 decays, removes < 1% of good K S → π 0 γγ events.
In addition, residual background from Ξ 0 → Λπ 0 with subsequent Λ → nπ 0 decay, where one γ escapes and the neutron produces a photon-like shower in the LKr calorimeter, is suppressed by exploiting the large momentum asymmetries in both Ξ 0 and Λ decays and accepting only events with: where indexes 1 and 2 refer to the shower pair identified as photons from the π 0 and 3, 4 to other two showers.
The background from accidental pile-up events is reduced by strengthening the requirements on shower times. Two configurations of a pile-up are considered: 3+1 showers and 2+2 showers. The 3+1 configuration is best described by a variable where the difference between any shower time and the average of the other three is maximised. Similarly for the 2+2 configuration one can use a variable in which only two of three remaining shower times are averaged. For the 3+1 pile-up topology t 2max and t 3max are always equal within the time resolution, however in the 2+2 case the two variables have different values in principle. This allows one to analyse this type of background in more detail. For the selection of the signal sample a single cut on t 2max of <1 ns is chosen, because t 2max describes both configurations in the same way. After all selection cuts 31 events remain in the sample. For the normalisation a sample scaled-down by factor 1000 of about 285 × 10 3 K S → π 0 π 0 events has been used.

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Background subtraction The following processes have been considered as potential sources of residual background: -irreducible K L → π 0 γγ background from the K L component of the beam -K S → π 0 π 0 with mis-reconstructed energy -K S → π 0 π 0 D with a γ or an e escaping detection or with a shower overlap -Hadron background, mainly Ξ 0 → Λπ 0 with subsequent Λ → nπ 0 , with three photon showers and one narrow neutron shower in the LKr calorimeter -Pile-up of two decays where the two decaying particles originate at the target either from two protons (accidental pile-up) or from a single proton (in-time pile-up). The amount of K L → π 0 γγ admixture in the signal sample is estimated using the K L flux measured from the K S → π 0 π 0 rate assuming equal production of K S and K L at the target. The acceptance was calculated using a Monte Carlo simulation. This background amounts to 3.8 ± 0.2 events.
K S → π 0 π 0 events can pass the cuts on invariant masses, and especially χ 2 > 5400, only if far non-Gaussian tails are present in the energy reconstruction from the LKr calorimeter. In order to study cases where one of the four shower energies may be mis-reconstructed, making use of the over-constraint of K S → π 0 π 0 events, the invariant mass of the event is reconstructed by using only three out of four shower energies and all four positions. None of the signal events has been found to have an invariant mass close to the kaon mass in any of the shower combinations. In addition, a toy Monte Carlo was employed to generate K S → π 0 π 0 events using realistic resolutions and non-Gaussian tails in energy, enhanced by an order of magnitude with respect to those known from E/p studies of electrons from the Re(ε ′ /ε) analysis. In a sample equivalent to twice the flux of the 2000 near-target run no event passes the χ 2 , m γγ and z vertex cuts at the same time.
The residual K S → π 0 π 0 D background has been studied using Monte Carlo simulations. Generating 1.7 times the collected flux, 4 events have been found to pass all cuts. Three of them have overlapping showers and reside in the tail of the z overlap − z vertex distribution. The fourth event decays in the collimator, and one of the photons undergoes a conversion in the collimator walls, while the e + e − pair from the π 0 passes trough the central hole of the detector. Scaling these events to the observed kaon flux, a background estimate of 2.4 ± 1.2 events is obtained with an uncertainty dominated by the statistics. The systematic error of this estimate has been checked by relaxing z * π 0 and z overlap cuts. The number of events and their z vertex distribution agree with data within few percent.
The amount of hadron background surviving cuts on energy deposited in the hadron calorimeter, the shower width and the energy asymmetry (7) was estimated by extrapolating the shower width distribution from large widths to the signal region. The shower width distribution of neutrons was extracted from fully reconstructed Ξ 0 → Λπ 0 → nπ 0 π 0 events. An estimate of 0.1 ± 0.1 events has been obtained.
The accidental pile-up background has been studied using time variables t 2max (9) and t 3max (8) in a time window of 6 ns which is six times larger than the signal time window. In this time window the event distribution is not affected by any selection cut. It turns out that about 50% of the background is in a 3+1 configuration while 50% is 2+2. Since both of these configurations are described equivalently by t 2max this variable is used to extrapolate from the control region 2 < |t 2max | < 6 ns to the signal region |t 2max | < 1 ns assuming a flat distribution. This extrapolation gives an estimate of 7.0 ± 1.3 events for the accidental pile-up background. The order of magnitude of this estimate was confirmed by overlaying 3-photon events from a K S → π 0 π 0 toy Monte Carlo with random showers detected close in time (20-30 ns) to fully reconstructed K S → π 0 π 0 events and by taking into account the kaon flux. The in-time pile-up background in general has a topology similar to the accidental pile-up, but, since it is generated by the same proton in the target, its rate cannot be measured by extrapolating from the out-of-time sample. The relative rate of in-time and accidental pile-up has been studied using fully reconstructed K S → π 0 π 0 with additional showers in the LKr calorimeter. It has been found that a 20% enhancement of pile-up background due to an in-time component cannot be excluded. In order to estimate the amount of total pile-up background without using time variables, the distribution of R C has been employed. The background is extrapolated from a control region 7 < R C < 10 cm to the signal region R C < 5 cm by using the R C shape obtained from the out-of-time sample in the t 2max control region. This extrapolation leads to an estimate of 6.8 ± 2.9 events for both in-time and accidental pile-up backgrounds. The uncertainty takes into account the statistical error of the data in the control region as well as the uncertainty of the extrapolation. This measurement is in good agreement with previous considerations and, since it contains the least number of assumptions, it is used for the branching ratio calculation. As can be seen from Fig. 2, the K S → π 0 π 0 D background is not double-counted in this subtraction because it populates the R C < 7 cm region.
Recently, the K S → π 0 e + e − decay has been observed for the first time. Using the measured branching ratio [9] and taking into account the cutoff on the invariant mass of the e + e − pair m 2 ee /m 2 K > 0.2 this background has been estimated to contribute 0.6 ± 0.3 events.

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Result Of the selected 31 events, 13.7 ± 3.2 are estimated to be background ( Table 1). The probability to observe 31 or more events in absence of a signal with a background of 13.7 ± 3.2 events is 1.5 × 10 −3 . Subtraction of the background from the selected sample leads to a signal of 17.3 ± 6.4 events. In the control region, defined as 3 < |m 12 − m π 0 | < 5 MeV, the observed data agree well with the background estimate (Fig. 3).  Table 1: Summary of background composition in both signal and control regions, the latter being defined as 3 < |m 12 − m π 0 | < 5 MeV, compared to data. The detector acceptances of the K S → π 0 γγ decay and of the normalisation decay channel K S → π 0 π 0 were calculated using a full Monte Carlo simulation of the detector based on GEANT [10] 3) . The K S → π 0 π 0 acceptance was determined to be 18.6%. The K S → π 0 γγ generator used the decay matrix element calculated by [1] using χP T . The acceptance of the K S → π 0 γγ for z > 0.2 is 7.2 ± 0.3%, where the uncertainty is extracted from the comparison with a simulation using a pure phase-space decay generator. The K S → π 0 γγ acceptance is smaller than that of K S → π 0 π 0 mainly due to cuts on z * π 0 and energy asymmetry defined in (5) and (7).

Events in signal region
Normalising the signal to the collected K S → π 0 π 0 sample and taking into account the acceptances results in a ratio of decay widths Γ(K S → π 0 γγ) z>0.2 Γ(K S → π 0 π 0 ) = (1.57 ± 0.51 stat ± 0.29 syst ) × 10 −7 (10) where the systematic uncertainty takes into account the background subtraction and acceptance calculation uncertainties. This result is stable against variations of most relevant cuts. In particular, the result does not change significantly by releasing the cut on the AKL anti-counter which increases the pile-up background by a factor 5, and when requiring no associated hit in a scintillator hodoscope placed upstream of the LKr calorimeter, which reduces the K S → π 0 π 0 D background by a factor 3. Using BR(K S → π 0 π 0 ) from [11], one obtains BR(K S → π 0 γγ) z>0.2 = (4.9 ± 1.6 stat ± 0.9 syst ) × 10 −8 (11) = (4.9 ± 1.8) × 10 −8 which agrees with the predictions of [1]. In order to test the momentum dependence of the weak vertex predicted by the χP T the z distribution of the sample after background subtraction has been compared to z distributions of simulated K S → π 0 γγ events using two decay generators, one with the χP T matrix element and one with pure phase space. Fig. 4 shows that both calculations agree within errors with the data and more statistics would be needed to prove the chiral structure of the weak vertex.  Figure 4: The z distribution of data after background subtraction compared to a Monte Carlo K S → π 0 γγ simulation using phase space (dashed line) and χP T matrix element [1] (continuous line) in the decay generator.