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Search for the decay phi ->K0 K0bar gamma with the KLOE experiment

We have searched for the decay phi ->K0 K0bar gamma, by detecting K_s pairs plus a photon and with the K_s-mesons decaying to pi^+ pi^-, in a sample of about 1.5x 10^9 phi-decays collected by the KLOE experiment at DAFNE. The reaction proceeds through the intermediate states f_0(980) gamma, a_0(980) gamma. We find five events with 3.2 events expected from background processes. We obtain the upper limit: BR (phi ->K0 K0bar gamma)<1.9x10^-8 at 90% C.L. .


Introduction
We have searched for the decay φ → K 0 K 0 γ with the KLOE experiment at DAΦNE. This decay has never been observed. In the decay the K 0 K 0 pair is produced with quantum numbers J P C = 0 ++ , so that the two-kaon state is symmetric, and can be written in terms of K S , K L as The K 0 K 0 state can be in both singlet and triplet isospin state, so that the decay proceeds mainly via intermediate f 0 (980) (I=0) and a 0 (980) (I=1) scalar mesons, φ → (f 0 (980) + a 0 (980))γ → K 0 K 0 γ.
Thus, a measurement of the φ → K 0 K 0 γ branching ratio (BR) can give information on the structure of light scalar mesons. The evaluation of the branching ratio depends on the way the scalar field dynamics is introduced and on the size of the couplings of the scalar mesons to the kaons. Moreover, interference between the f 0 and a 0 amplitudes may also contribute to the φ → K 0 K 0 γ decay amplitude. Predictions found in literature are mainly based on the decay scheme (2), and give values ranging over a large interval, from few ×10 −9 to 10 −7 [1,2,3,4,5,6,7,8,9,10]. In this respect, a similar decay into charged kaons, φ → K + K − γ, gives less information since the scalar dynamics is masked by the final state radiation.
The signature of the radiative decay of the φ meson into the state (1) is the presence of either two K S or two K L (and a low energy photon). KK invariant mass is limited by the φ mass (1020 MeV) and by twice the kaon mass (995 MeV). The photon energy is a function of the invariant di-kaon mass M KK and is given by We search for final states with a K S K S pair, with both K S decaying to π + π − . This corresponds to a reduction of the observable rate of where the factor 1/2 accounts for the choice of the K S K S final state among the two possibilities for the K 0 K 0 state. We search for two decay vertices very close to the e + e − interaction region, both having two tracks with opposite charge and invariant mass of the charged secondaries equal to the kaon mass. The invariant mass of the kaon pair must be smaller than the φ mass. A low energy photon must be detected with a momentum compatible with the kinematics of the event.
The expected photon energy spectrum (E γ ) is shown in fig. 1, corresponding to a K S K S invariant mass (M KK ) spectrum generated assuming only phasespace and radiative decay dynamics: The highest rate is expected for events with photon energy close to the maximum value (see eq. 3). The selection criteria have been optimized in order to maximize the sensitivity to the searched signal [11].  dataset) towards the collider centre. The KLOE detector consists of a largevolume cylindrical drift chamber [12] (3.3 m length and 2 m radius), operated with a 90% helium -10% isobutane gas mixture, surrounded by a sampling calorimeter [13] made of lead and scintillating fibers providing a solid angle coverage of 98%. The tracking chamber and the calorimeter are surrounded by a superconducting coil that provides an (approximately) axial magnetic field B = 0.52 T, the axis being the bisector of the external angle of the e + and e − beams. The drift chamber has a momentum resolution σ(p ⊥ )/p ⊥ ∼ 0.4%. Photon energies and arrival times are measured in the calorimeter with resolutions σ E /E = 5.7%/ √ E(GeV) and σ t = 57 ps/ √ E(GeV) 100 ps. The trigger [14] is based on the detection of at least two energy deposits in the calorimeter above a threshold that ranges between 50 and 150 MeV.
For this search the full data sample acquired at the φ-peak energy by the KLOE experiment between years 2001 and 2005 has been used. After quality selection, a data sample corresponding to an integrated luminosity of 2.18 fb −1 is available for the present analysis. The luminosity is measured with an error of less than 1% by counting large-angle Bhabha scattering events [15].
The KLOE Monte Carlo simulation (MC) package, GEANFI [16], has been used to provide high-statistics samples. The total number of events in each sample is generated with an integrated luminosity scale factor (LF) defined as LF = integrated luminosity (MC generation)/integrated luminosity (data). This scale factor is different for different φ decay modes and different data taking periods. All φ decays have been simulated with LF=1 or 2, CP-violating rare decays, such as K S K L → π + π − π + π − , have been simulated with LF=10 and 20. DAΦNE operating conditions during data taking, machine parameters and background are adjusted in the MC on a run-by-run basis.
Simulations of all φ decays and CP-violating rare decays have been used to evaluate sources of background mimicking φ → K 0 K 0 γ decays. The initialstate radiation (ISR) process e + e − → γK 0 K 0 is taken into account in all the simulations. A further possible background source is the continuum production of charged pions through the process e + e − → π + π − π + π − (γ). A pure phase- space generation with LF=10 has been used to simulate this kind of events.
The measured cross section of this process in the φ region [17] has been used to normalize MC to data.
To simulate the signal we generated a MC sample of 10 4 φ → K S K S γ → π + π − π + π − γ events, developing a modified version of the PHOKHARA5 generator [18]. Phokhara is a Monte Carlo event generator which simulates the electron-positron annihilation into hadrons plus an energetic photon from initial state radiation (ISR) process, at the next-to-leading order (NLO) accuracy. This simulation relies on general assumptions for the branching ratio dependence on the photon energy and on phase space, according to eq. 5.

Data analysis
We search for K S K S γ events by requiring two pairs of tracks with opposite charge, each pair originating from a vertex contained inside a cylindrical volume centered on the interaction point and the beam line, 16 cm long in z and of 3 cm radius. We reconstruct the invariant masses m 1 and m 2 , for each pair of tracks, using the pion mass hypothesis. The distribution of signal events in the plane m 1 , m 2 is well contained inside a circle of a few MeV radius centered on the K S mass. We require the events to satisfy a 4 MeV cut on this radius.
Once the two K S mesons are identified, we build the invariant mass of the K S pair, M KK . In order to reject background from φ → K S K L → π + π − π + π − events, we retain only those events with K S K S invariant mass below 1010 MeV. Moreover, in order to reject badly reconstructed K S semileptonic decays, which could mimic a two-pion decay, we define the missing mass m γ using four-momentum conservation: where P φ , P K S1 and P K S2 are the 4-vectors of the φ and of the two reconstructed K S . This variable must be zero in case of two K S,L to π + π − decays, even with an extra photon, and is required to be zero within ±500 MeV 2 . Figure 2 shows the distribution of signal simulation, data and background simulation for M KK and M 2 γ . Ninety five events survive these cuts.
We then look for the radiative photon, by searching for a calorimeter cluster, without any associated track. The cluster must be in time with the observed event, and its position in the calorimeter must be compatible with the direction of the missing momentum. The angle Ω between the missing momentum and the photon direction, derived from the cluster position, is required to be below 0.6 rad. Figure 3 shows the Ω distributions for data and MC simulations.
We verified the correct simulation of low-energy clusters in the MC using the φ → π + π − π 0 control sample: a time resolution of 520 ps is achieved for low energy clusters in both data and MC simulation, well reproduced by MC signal simulation.
After the selection, 33 events are present in the non-rescaled MC samples for CP-violating rare decays and e + e − → π + π − π + π − (γ) decays. No event is present in the MC sample for all φ decays. The overall efficiency for the signal is (24.8±0.5)%, evaluated from signal simulation. The efficiency is shown in fig. 4 as a function of M KK .The evaluation of this efficiency can vary depending on the scalar field dynamics and the size of couplings used for the signal simulation. To study this effect the kaon-loop approach [6] has been used, varying the couplings g SKK , with S=f 0 , a 0 in ranges larger than the present spread of experimental measurements and theoretical evaluations. Signal efficiency has been recalculated throughout this range and compared with the one used in the analysis: the variation is within the statistical error.
To normalize MC distributions to data we have estimated effective scale factors, one for each MC sample, fitting the MC distributions for M KK and m 2 γ to the corresponding data distributions. The results of the fits are shown in fig. 5. For this purpose we used a control sample made of events surviving all the selection requirements, except the M KK and m 2 γ cuts. For the simulation of all φ decays, the scale factor obtained from the fit is equal to 0.47 ± 0.04, while the MC scale factor for CP-violating rare decays and e + e − → π + π − π + π − (γ) decays is 0.096 ± 0.015. These factors differ from the LF scale factors by at most 15% and are in agreement within errors. Rescaled background events are listed in tab. 1.
The expected number of background events, once scale factors obtained from fits are applied, is 3.2±0.7 ; the error is the combination of the statistical error and the systematic error due to the fit. The number of residual events in the data sample is five. These numbers will be used for the upper limit evaluation.

Result
The upper limit on BR(φ → K 0 K 0 γ) is evaluated as follows: Ldt is the integrated luminosity, 2.18 fb −1 . σ(e + e − → φ) is the cross section for φ production from e + e − annihilation, equal to 3.09 µb; this is evaluated from the fit to the visible cross section for the process φ → ηγ with the data taken around the φ peak, with a fractional error of 2.4%. BR(K S → π + π − ) is taken as 0.692 [19]. The signal efficiency ǫ is (24.8 ± 0.5)%. The upper limit on the number of events at 90% CL, S 90CL , is calculated using the so-called "unified approach" [11], using the number of residual data events, and the residual background events reduced by 1σ to take into account the systematic error on the background evaluation in a conservative way; we get S 90CL = 7.49. Our result for the upper limit is: This is the only existing experimental result for this branching ratio. In fig. 6 the upper limit is compared with theoretical predictions [1,2,3,4,5,6,7,8,9,10].
Ref. [1] is based on the scalar kaon-loop model: in fig. 6 2q and 4q indicate the prediction for a scalar qq structure or a tetraquark structure respectively; Ref. [2] describes this decay with a low-energy effective lagrangian. Ref. [3] only takes into account the f 0 contribution, without considering the a 0 , which explains the large BR value; the authors criticize the result of ref. [7]. Ref. [4] makes use of a chiral perturbation lagrangian which does not include explicitly the scalar mesons in the intermediate state. Ref. [5,8] calculates this BR through unitarized chiral perturbation theory based on resonant and nonresonant φ → (f 0 + a 0 ) coupling. In ref. [6] the couplings of the kaon-loop model are evaluated by using the SND experiment data [24]. Ref. [9] introduces a well-defined U(3) × U(3) chiral model which incorporates ab initio the pseudoscalar and scalar mesons nonets. Ref. [10] repeats the calculation of ref. [6] using the first published KLOE data [21,22], with and without the σ(600) contribution, and gives a large set of values.
Following the kaon-loop model [6] we have evaluated predictions for BR(φ → K 0 K 0 γ) based on the g f 0KK , g f 0ππ and g a0KK couplings obtained by KLOE [21,22,23] by fitting the data of φ decays into π + π − γ, π 0 π 0 γ and ηπγ. Allowing for variations of the couplings within the corresponding errors, the predicted BRs vary between 0.4×10 −8 and 6.8×10 −8 , the lower values being still compatible with the present upper limit.