Measurement of the branching ratio and search for a CP violating asymmetry in the eta ->pi+pi-e+e-(gamma) decay at KLOE

We have studied the eta->pi+pi-e+e-(gamma) decay using about 1.7 fb^-1 collected by the KLOE experiment at the DAFNE phi-factory. This corresponds to about 72 millions eta mesons produced in phi radiative decays. We have measured the branching ratio, inclusive of radiative effects, with 4% accuracy: BR(eta->pi+pi-e+e-(gamma)) = (26.8 +/- 0.9_Stat. +/- 0.7_Syst.) x 10^-5. We have obtained the first measurement of the CP-odd pipi-ee decay planes angular asymmetry, A_phi = (-0.6 +/- 2.5_Stat. +/- 1.8_Syst.) x 10^-2.


Introduction
The decay of light pseudoscalar mesons, π 0 , η and η ′ , proceeds via electromagnetic interaction and the radiative decays of η and η ′ to pions allow to probe their electromagnetic structure [1].Conversion decays offer the possibility to measure precisely the virtual photon 4-momentum via the invariant mass of the e + e − pair.The branching ratio for internal conversion decay of the η meson, η → π + π − e + e − , has been computed with different approaches, but until recently both the theoretical and the experimental results were affected by large uncertainties.The first calculation, based on pure QED, is 40 years old: BR ∼ 3 × 10 −4 [2].The addition of ππ interaction treated with the Vector Dominance Model gives BR = 3.6 × 10 −4 with an error of about 10% [3], while an approach based on chiral perturbation theory that includes vector mesons gives (3.2 ± 0.3) × 10 −4 [4].Recently, an approach based on the chiral effective Lagrangian including ππ interactions has obtained a more precise result: BR = (2.99 +0.06  −0.09 )× 10 −4 [5].The η → π + π − e + e − decay has been first observed by the CMD-2 experiment [6], giving BR = (3.7 +2. 5  −1.8 ± 3.0) × 10 −4 , and has afterwards been confirmed by the CELSIUS-WASA experiment [7,8]: BR = (4.3+2.0 −1.6 ± 0.4) × 10 −4 .The precision of these results does not allow to test different models.Recently, a possible CP violating mechanism (CPV), not directly related to the most widely studied flavor changing neutral processes, has been proposed.This mechanism could induce interference between electric and magnetic decay amplitudes.Such CPV effect could be tested in the decays of the pseudoscalar mesons by measuring the polarization of the virtual photon and would result in an asymmetry in the angle φ between the planes containing the e + e − and the π + π − pairs in the meson rest frame, defined as: ).This kind of asymmetry has been already studied [9][10][11][12][13] and observed [14,15] in the decay of the K L meson.In the η decay this asymmetry is constrained, by experimental [16] and Standard Model [17] upper limits on the CP-violating decay η → π + π − , to be, at most of O(10 −4 ) and O(10 −15 ), respectively.However, as pointed out in [18,19], it is possible in case of sources of CPV beyond the Standard Model which do not contribute directly either to ǫ K or to the neutron electric dipole moment, d n .In this case, A φ is predicted to be up to O(10 −2 ), a value reachable with the present statistics of η mesons.

The KLOE detector
The KLOE experiment operates at DAΦNE , the Frascati φ-factory.DAΦNE is an e + e − collider running at a center of mass energy of ∼ 1020 MeV, the mass of the φ meson.Equal energy positron and electron beams collide at an angle of π-25 mrad, producing φ mesons nearly at rest.The detector consists of a large cylindrical Drift Chamber, surrounded by a lead-scintillating fiber ElectroMagnetic Calorimeter (EMC).A superconducting coil around the EMC provides a 0.52 T field.The drift chamber [20], 4 m in diameter and 3.3 m long, has 12,582 all-stereo tungsten sense wires and 37,746 aluminum field wires.The chamber shell is made of carbon fiber-epoxy composite and the gas used is a 90% helium, 10% isobutane mixture.The position resolutions are σ xy ∼ 150 µm and σ z ∼ 2 mm.The momentum resolution is σ(p ⊥ )/p ⊥ ≈ 0.4%.Vertices are reconstructed with a spatial resolution of ∼ 3 mm.The calorimeter [21] is divided into a barrel and two endcaps, for a total of 88 modules, and covers 98% of the solid angle.The modules are read out at both ends by photo-multipliers, both in amplitude and time.The readout granularity is ∼ (4.4 × 4.4) cm 2 , for a total of 2440 cells arranged in five layers.The energy deposits are obtained from the signal amplitude while the arrival times and the particles positions are obtained from the time differences.Cells close in time and space are grouped into calorimeter clusters.The cluster energy E is the sum of the cell energies.The cluster time T and position R are energy-weighed averages.Energy and time resolutions are σ E /E = 5.7%/ E (GeV) and σ t = 57 ps/ E (GeV) ⊕ 100 ps, respectively.The trigger [22] uses both calorimeter and chamber information.In this analysis the events are selected by the calorimeter trigger, requiring two energy deposits with E > 50 MeV for the barrel and E > 150 MeV for the endcaps.A cosmic veto rejects events with at least two energy deposits above 30 MeV in the outermost calorimeter layer.Data are then analyzed by an event classification filter [23], which streams various categories of events in different output files.

Event selection
This analysis has been performed using 1,733 pb −1 from the 2004-2005 dataset, 242 pb −1 from the 2006 off-peak ( √ s = 1000 MeV ) data, 3,447 pb −1 of Monte Carlo (MC) simulating all φ decays, 50,506 pb −1 of signal Monte Carlo.Signal MC has been generated according to the matrix element in [19], with BR = 4 × 10 −4 and having A φ = 0.All MC productions account for run by run variation of the main data-taking parameters such as background conditions, detector response and beams configuration.Data-MC corrections for calorimeter clusters and tracking efficiency, evaluated with radiative Bhabha events and φ → ρπ samples respectively, have been applied.Effects of Final State Radiation (FSR) have been taken into account using the PHOTOS MC package [24,25].This package simulates the emission of FSR photons by any of the decay products taking also into account possible interference between different diagrams.We have inserted PHOTOS in our Monte Carlo at the event generation level, simulating FSR for the electrons, therefore our simulation fully accounts for radiative decays.At KLOE, η mesons are produced together with a monochromatic recoil photon through the radiative decay φ → ηγ (E γ = 363 MeV ).In the considered data sample about 72 × 10 6 η's are present.As first step of the analysis, a preselection is performed requiring at least four tracks (two positive and two negative) coming from the Interaction Point.The Fiducial Volume is defined by a cylinder having radius R = 4 cm and height h = 20 cm.For each charge, the two tracks with the highest momenta are selected.After track selection, one and only one neutral cluster, having energy E cl ≥ 250 MeV and polar angle in the range (23 does not have any associated track and has a time compatible with the photon time of flight.After preselection, the signal is about 1.4% of the sample.Mass assignment for each track is performed by either identifying a pion decay from a kink in the track, or using the Time Of Flight (TOF) of the particles.For each track associated to a calorimeter cluster, the quantity ∆t = t track − t cluster in both electron (∆t e ) and pion (∆t π ) hypothesis is evaluated; t track is defined as the length of the track divided by β(m)c.The mass hypothesis minimizing ∆t is then chosen.If two tracks of the same charge satisfy the same mass hypothesis, the minimum ∆t e identifies the electron.When only one of the same charge tracks is identified as pion (electron), the other one is assumed to be electron (pion).For the remaining events the tracks with higher momentum are assumed to be pion.
To improve the energy and momentum resolution, a kinematic fit is performed imposing the four-momentum conservation and the TOF of the photon.A very loose cut on the χ 2 of the kinematic fit is applied in order to discard poorly reconstructed events.

Background rejection
Two sources of background have to be distinguished: (1) φ background: this is mainly due to φ → π + π − π 0 events (with π 0 Dalitz decay) and to φ → ηγ events either with η → π + π − π 0 (with π 0 Dalitz decay) or with η → π + π − γ (with photon conversion on the beam pipe).Note that this last background has the same signature as the signal.Background from φ → K K is also present at the preselection level.
(2) Continuum background: this is due to e + e − → e + e − (γ) events with photon conversions, split tracks or interactions with some material in the region of DAΦNE quadrupoles inside KLOE.Because of poor MC statistics, this background has been studied using off-peak data taken at √ s = 1 GeV , where φ decays are negligible.This sample has been properly normalized for luminosity and √ s behaviour.
A first background rejection is performed cutting on the sum of the absolute value of the momenta of the two particles having the highest momenta and opposite charge, s2p )|, and cutting on the sum of the absolute value of the momenta of the four selected tracks, s4p = 4  1 | p i |.It is required that: (270 < s2p < 460) MeV and (450 < s4p < 600) MeV .To reject the events due to photon conversion on the beam pipe, we extrapolate backward the e + e − candidate tracks, down to the intersection with the BP, and compute there the invariant mass (M ee ) and their distance (D ee ).A clear signal of photon conversion is visible in the D ee (BP )-M ee (BP ) plane (figure 1).We reject events having M ee (BP ) < 15 MeV and D ee (BP ) < 2.5 cm.The expected M ππee spectrum before and after this cut is shown in figure 2. The φ background events peaked at the η invariant mass are significantly reduced by this cut.Finally, to remove continuum background from interactions with quadrupoles, we have defined the quantities cos θ f and cos θ b as the average polar angle of forward and backward particles identified as signal.Events having cos θ f > 0.85 and cos θ b < −0.85 are rejected.This cut affects neither the signal nor background from φ decay events.
5 Fit to the π + π − e + e − invariant mass spectrum and event counting In order to evaluate the background contribution, we perform a fit to the data distribution of the π + π − e + e − invariant mass after the cuts on the momenta.The fit is done on sidebands in order not to introduce correlations between  Upper and lower limits (450 and 650 MeV ) have been chosen in order not to include in the fit tails from background distributions.The central range (520 and 570 MeV ) is wide enough to well contain the tails of the signal distribution.Then the fit is performed using the background shapes only.
The most precise background evaluation has been obtained fixing the offpeak data scale factor with luminosity at 7.14 ± 0.03 and fitting the MC background from φ meson decay.The output of the fit is χ 2 /dof = 32.5/30(P (χ 2 ) = 0.35), with a scale factor of 0.528±0.009,which is in good agreement with expectation from luminosity.The other possible approaches (fixing both the background scale factors with luminosity, leaving both free in the fit or fixing the φ decay and leaving free the continuum background shape) have been used for the evaluation of systematic uncertainties.The result of the fit is shown in figure 3 both in a wide M ππee window and around the signal region.For the signal estimate we limit ourselves to the region [535, 555] MeV and perform the event counting after background subtraction: we find 1555 (368) signal (background) events, see table 1. Data-MC comparisons show a very good agreement for all considered variables.The most relevant distributions are reported in figure 4.
6 Measurement of the BR(η → π + π − e + e − (γ)) The branching ratio has been evaluated according to the formula:  where N η→π + π − e + e − (γ) is the number of signal events and ǫ η→π + π − e + e − (γ) is the efficiency taken from MC.The number of φ → ηγ events, N ηγ , has been obtained using the formula N ηγ = L • σ φ→ηγ , where L is the integrated luminosity and the cross section σ φ→ηγ takes into account the φ meson line shape.σ φ→ηγ has been evaluated with η → π 0 π 0 π 0 events collected in the range 1017 MeV < √ s < 1022 MeV [26].Inserting all the numbers summarized in table 2, we obtain the value: where the error accounts for the event counting and the background subtraction.
The systematic uncertainties have been evaluated in the following way: • fixing with the luminosity or leaving free in the fit the background scale factors; • varying the sideband upper and lower limits in the ranges [400,535] MeV and [555, 700] MeV respectively; • varying the binning of the histogram used for the fit from 1 MeV/bin to 5 MeV/bin; • repeating the whole analysis chain after moving selection criteria on s2p, s4p, D ee (BP ), M ee (BP ), cos θ f , cos θ b and M ππee by ±1σ, ±2σ's, ±3σ's around the reference value.The BR is then recomputed for all of these variations.The systematic uncertainty has been evaluated as the quadratic sum of RMS's obtained for each case.
The uncertainty on N ηγ has been also added to the systematics in the normalization term.The results of the systematics evaluation are summarized in table 3. The largest contributions are due to the normalization and to the cut on M ee (BP ).Taking the total systematic error into account, the measurement of the branching ratio is: γ)) = (26.8± 0.9 Stat.± 0.7 Syst. ) × 10 −5 . (3)

Decay plane asymmetry evaluation
The decay plane asymmetry is calculated starting from the momenta of the four particles and is expressed as function of φ, the angle between the pion  and the electron planes in the η rest frame (figure 5): The quantity sin φ cos φ is given by (n ee × nππ )ẑ(n ee • nππ ), where the n's are the unit normals to the electron and pion planes and ẑ is the unit vector along the axis defined by the intersection of the two planes.The distribution of the sin φ cos φ variable in the signal region is shown in figure 6.We remind that the signal MC has been produced with A φ = 0.While the analysis efficiency is completely flat in the sin φ cos φ distribution, some distortion is introduced by the reconstruction, because of events with wrong mass assignment.The correction to this distortion has been evaluated by MC, fitting with a linear function the ratio between the generated and reconstructed sin φ cos φ distributions.The resulting slope is -0.032 ± 0.016.The use of higher polynomials does not improve the fit.The origin of this slope has been investigated by MC and it is completely due to the 14% of signal events with wrong particle identification.This because the particle identification algorithm forces the mass assignment in case of ambiguities without discarding events.The aim is to preserve the statistics, which completely dominates the asymmetry measurement.The asymmetry has been evaluated for the events in the 535 MeV < M ππee < 555 MeV mass region after background subtraction.After applying the correction, we obtain: which is the first measurement of this asymmetry.
As for the branching ratio, the systematic error has been evaluated repeating the whole analysis chain after varying selection criteria by ±1σ, ±2σ's and ±3σ's around the reference value and taking as uncertainty the quadratic sum of the resulting RMS's.The uncertainty due to the correction has been evaluated varying its slope by ±1σ.The contribution is due to the cut on M ππee while the contribution of the slope correction is 0.5 × 10 −2 .In order to check the distortion correction applied to A φ , we have defined a control sample having only events without ambiguities in particle identification.In this case the probability of wrong particle identification is almost zero and no distortions are observed in the MC sin φ cos φ distribution.The fraction of this control sample in data and MC events is in good agreement (0.62 ± 0.02 and 0.64 ± 0.02 respectively), showing that our simulation reproduces the real data well.The asymmetry evaluated with the control sample is in good agreement with our measurement but has a larger statistical error: A φ = (−1.2± 3.1 Stat. ) × 10 −2 .
Radiative events slightly modify momentum distribution of the charged particles and have been carefully considered in the efficiency evaluation.As a result, the measured branching ratio is fully radiation inclusive.
The final sample of 1555 signal events allows us to perform the first measurement of the CP-violating asymmetry A φ , which is consistent with zero at the 3% percent precision level: A φ = (−0.6 ± 2.5 Stat.± 1.8 Syst. ) × 10 −2 .(7)

Fig. 1 .Fig. 2 .
Fig. 1.D ee vs M ee evaluated at the beam pipe for φ background (top panel) and MC signal (bottom panel).Events in the box M ee (BP ) < 15 M eV ∩ D ee (BP ) < 2.5 cm are rejected.

Fig. 3 .
Fig. 3. π + π − e + e − invariant mass spectrum on a wide range (left panel) and zoomed around the η mass (right panel).The background scale factors have been obtained as described in section 5. Dots: data.The black histogram is the expected distribution, i.e. signal MC (dark grey), φ background (light grey) and continuum background (white).

Fig. 4 .
Fig.4.Spectra of opening angle (top) and invariant mass (bottom) for the e + e − (left) and π + π − (right) pairs for events in the signal region.The background scale factors have been obtained as described in section 5. Dots: data.The black histogram is the expected distribution, i.e. signal MC (dark grey), φ background (light grey) and continuum background (white).

Fig. 5 .
Fig. 5. Definition of the angle φ between the pion and electron decay planes.

Fig. 6 .
Fig.6.Distribution of the sin φ cos φ variable in the signal region.The background scale factors have been obtained as described in section 5. Dots: data.The black histogram is the expected distribution, i.e. signal MC (dark grey), φ background (light grey) and continuum background (white).

Table 1
Event counting in the signal region.

Table 2
Summary of the numbers used in the master formula (1) for the branching ratio evaluation.

Table 3
Summary of the systematic uncertainties on the branching ratio.