Study of the Dalitz decay φ → η e + e − with the KLOE detector

We have studied the vector to pseudoscalar conversion decay φ → η e + e − , with η → π 0 π 0 π 0 , with the KLOE detector at DA Φ NE. The data set of 1 . 7 fb − 1 of e + e − collisions at √ s ∼ M φ contains a clear conversion decay signal of ∼ 31 , 000 events from which we measured a value of BR (φ → η e + e − ) = ( 1 . 075 ± 0 . 007 ± 0 . 038 ) × 10 − 4 . The same sample is used to determine the transition form factor by a ﬁt


Introduction
We report the study of the vector to pseudoscalar conversion decay φ → ηe + e − with η → π 0 π 0 π 0 . In conversion decays, A → Bγ * → B e + e − , the radiated photon is virtual and the squared dilepton invariant mass, M 2 ee , corresponds to the photon 4-momentum transferred, q 2 . The probability of having a lepton pair of given invariant mass is determined by the electromagnetic dynamical structure of the transition A → Bγ * . The differential decay rate, normalized to the radiative width, is [1]: where M is the mass of the electron and M φ , M η are the masses of the φ and η mesons, respectively. F φη (q 2 ) is the transition form factor, TFF, that describes the coupling of the mesons to virtual photons and provides information on its nature and underlying structure. The slope of the transition form factor, b φη , is defined as: . (2) In the Vector Meson Dominance model, VMD, the transition form factor is parametrized as: The VMD successfully describes some transitions, such as η → γ μ + μ − , while is failing for others, as in the case of ω → π 0 μ + μ − [2]. Recently, new models have been developed to overcome such a kind of discrepancies [3,4]  ηe + e − ) = 1.1 × 10 −4 [7]. The SND experiment has also measured the slope of the transition form factor from the M ee invariant mass distribution, on the basis of 213 events: b φη = (3.8 ± 1.8) GeV −2 [5]. The VMD expectation is b φη = 1 GeV −2 [7].
Due to the large data sample, we have performed three different measurements: (1) the determination of the branching fraction of the φ → ηe + e − decay; (2) the direct measurement of the transition form factor slope b φη with a fit to the dilepton invariant mass spectrum; (3) the extraction of the |F φη | 2 as a function of the dilepton invariant mass.

The KLOE detector
DAΦNE, the Frascati φ-factory, is an e + e − collider running at center of mass energy of ∼ 1020 MeV. Positron and electron beams collide at an angle of π -25 mrad, producing φ mesons nearly at rest. The KLOE experiment operated at this collider from 2000 to 2006, collecting 2.5 fb −1 . The KLOE apparatus consists of a large cylindrical Drift Chamber surrounded by a lead-scintillating fiber electromagnetic calorimeter both inserted inside a superconducting coil, providing a 0.52 T axial field. The beam pipe at the interaction region is a sphere with 10 cm radius, made of a 0.5 mm thick Beryllium-Aluminum alloy. The drift chamber [8], 4 m in diameter and 3.3 m long, has 12,582 all-stereo tungsten sense wires and 37,746 aluminum field wires, with a shell made of carbon fiber-epoxy composite with an internal wall of ∼ 1 mm thickness.
The gas used is a 90% helium, 10% isobutane mixture. The momentum resolution is σ (p ⊥ )/p ⊥ ≈ 0.4%. Vertices are reconstructed with a spatial resolution of ∼ 3 mm. The calorimeter [9], with a readout granularity of ∼ Machine parameters are measured online by means of large angle Bhabha scattering events. The average value of the center of mass energy is evaluated with a precision of about 30 keV each 200 nb −1 of integrated luminosity. Collected data are processed by an event classification algorithm [11], which streams various categories of events in different output files.

Branching ratio
The analysis of the decay chain φ → ηe + e − , η → 3π 0 , has been performed on a data sample of about 1.7 fb −1 . The Monte Carlo (MC) simulation for the signal has been produced with dΓ (φ → ηe + e − )/dM ee according to VMD model. The signal production corresponds to an integrated luminosity one hundred times larger than collected data. Final state radiation has been included using PHOTOS Monte Carlo generator [12]. For the background, all φ decays and the not resonant e + e − → ωπ 0 process have been simulated with a statistics two times larger than data.
All MC productions take into account changes in DAΦNE operation and background conditions on a run-by-run basis. Data-MC corrections for cluster energies and tracking efficiencies are evaluated with radiative Bhabha and φ → ρπ samples, respectively. The main steps of the analysis are: (1) a preselection requiring two tracks of opposite sign extrapolated to a cylinder around the interaction point and 6 prompt photon candidates; (2) a loose cut on the six photon invariant mass: 400 < M 6γ < 700 MeV; The first peak on the left corresponds to the η mass. The second peak at ∼ 590 MeV is due to K S → π + π − events with a wrong mass assignment.
(3) a 3σ cut on the recoil mass against the e + e − pair, M ee (recoil), shown in Fig. 1: 536.5 < M ee (recoil) < 554.5 MeV 1 ; (4) a cut on the invariant mass and the distance between the two tracks extrapolated to the beam pipe and at the drift chamber wall surfaces, to reject photon conversion; (5) a cut based on the time of flight (TOF) of the tracks to the calorimeter to reject events with charged pions in the final state.
These cuts are described in details in Ref. [13], which reports the results for a search of a light vector boson using the same data sample. The M ee and cos ψ * 2 distributions, after the M ee (recoil) cut and at the end of the analysis chain, are shown in Fig. 2, compared to MC expectations. The residual background contamination is concentrated at high masses and is dominated by φ → K S K L → π + π − 3π 0 events with an early K L decay.
The analysis efficiency for signal events as a function of the e + e − invariant mass is shown in Fig. 3 for 5 MeV mass bins. It is about 10% at low masses and increases to ∼ 35% at 460 MeV, due to the larger acceptance for higher momentum tracks.
At the end of the analysis chain, 30,577 events are selected, with ∼ 3% background contamination. After bin to bin background subtraction, 29,625 ± 178 φ → ηe + e − , η → 3π 0 , candidates are present in the dataset. The branching ratio has been calculated using bin-by-bin efficiency correction: The luminosity measurement is obtained using very large angle Bhabha scattering events [14], giving an integrated luminosity of L = (1.68 ± 0.01) fb −1 . The effective φ production cross section takes into account the center of mass energy variations (at 1% level) [15]: σ = (3310 ± 120) nb. The value of the BR(η → 3π 0 ) = (32.57 ± 0.23)% is taken from [16]. Our result is: where the error includes the uncertainties on luminosity and φ production cross section. The systematic error has been evaluated moving by ±1σ the analysis cuts on the recoil mass and 1 We observed a shift of about 2 MeV with respect to the η mass (∼ 547.85 MeV). The shift is due to the treatment of the energy loss for the electrons in the tracking reconstruction, that assumes the energy loss for pions. 2 The cos ψ * variable is defined as the angle between the η and the e + in the e + e − rest frame. TOF, and by ±20% those related to conversion cuts (Table 1). In order to evaluate the systematic due to the variation of the analysis efficiency for low M ee values, the BR has been measured for M ee > 100 MeV, where the efficiency has a smoother behaviour.
These systematics are negligible with respect to the normalization error.

Measurement of the electromagnetic transition form factor
The fit procedure, based on the MINUIT package [17], is applied to the M ee distribution, after a bin-by-bin background subtraction. Analysis efficiency and smearing effects have been folded into the theoretical function of Eq. (1), using as free parameters Λ φη with an overall normalization factor. The M ee distribution is then fitted, in the whole range, using a bin width of 5 MeV, by minimizing a χ 2 function, defined as: where N DATA is the number of event in the reconstructed i-th M ee bin after background subtraction and N expected is the expected number of events in the same bin, evaluated by performing a convolution of the theoretical function with reconstruction effects as follows: where f theory (m j ) is the integrated VMD spectrum in the j-th bin, Systematics for the M ee (recoil), TOF and photon conversion cuts have been evaluated as for the BR measurement and summarized in Table 2. Systematics related to the fit procedure have been evaluated as the RMS of the deviation from the central value obtained by varying the mass range used for the fit. The total systematic error is the quadrature of all contributions. The result for the slope of the transition form factor is: b φη= 1.28±0.10 +0.09 −0.08 GeV −2 . (8)

Transition form factor as a function of M ee
The modulus squared of the transition form factor, |F φη (q 2 )| 2 , as a function of the e + e − invariant mass, is obtained by dividing bin by bin the M ee spectrum of Fig. 5 (top) by the one of reconstructed signal events, generated with F MC φη = 1, after all analysis cuts. MC sample is normalized in order to reproduce the number of events in the first bin of data. In Table 3, the values of |F φη (q 2 )| 2 as a function of the dilepton invariant mass, with the corresponding statistical errors are reported.   The |F φη (q 2 )| 2 distribution has been fitted as a function of the invariant mass with two free parameters, one corresponding to the normalization and the other to Λ φη , as shown in Fig. 6, together with the predictions form the VMD and from Ref. [3]. From this fit, the value of the slope b φη is: in agreement within the uncertainties with the value obtained from the fit to the invariant mass spectrum (Eq. (8)) and consistent with the reproducibility of the measurement.
The BR(φ → ηe + e − ) is in agreement with VMD predictions [7] and with the SND and CMD-2 results [5,6]. The transition form factor slope is in agreement with VMD predictions [7], with a precision that is a factor of five better than previous SND measurement.
The transition form factor has been used [18] to derive the upper limit for the production of a light dark boson U in φ → ηU → ηe + e − decay. Present measurement confirms the exclusion plot    obtained by KLOE in the mass range (5 < M U < 470) MeV, where b φη = 1 GeV −2 was assumed [13].