Observation of the rare eta->e+e-e+e- decay with the KLOE experiment
KLOE Collaboration, F.Ambrosino, A.Antonelli, M.Antonelli, F.Archilli, I.Balwierz, G.Bencivenni, C.Bini, C.Bloise, S.Bocchetta, F.Bossi, P.Branchini, G.Capon, T.Capussela, F.Ceradini, P.Ciambrone, E.Czerwinski, E.DeLucia, A.DeSantis, P.DeSimone, G.DeZorzi, A.Denig, A.DiDomenico, C.DiDonato, B.DiMicco, M.Dreucci, G.Felici, S.Fiore, P.Franzini, C.Gatti, P.Gauzzi, S.Giovannella, E.Graziani, M.Jacewicz, J.Lee-Franzini, M.Martemianov, M.Martini, P.Massarotti, S.Meola, S.Miscetti, G.Morello, M.Moulson, S.Muller, M.Napolitano, F.Nguyen, M.Palutan, A.Passeri, V.Patera, I.PradoLonghi, P.Santangelo, B.Sciascia, M.Silarski, T.Spadaro, C.Taccini, L.Tortora, G.Venanzoni, R.Versaci, G.Xu, J.Zdebik, as members of the KLOE-2 collaboration, D.Babusci, D.Badoni, V.Bocci, A.Budano, S.A.Bulychjev, P.Campana, E.Dane, G.DeRobertis, D.Domenici, O.Erriquez, G.Fanizzi, F.Gonnella, F.Happacher, B.Hoistad, E.Iarocci, T.Johansson, V.Kulikov, A.Kupsc, F.Loddo, M.Matsyuk, R.Messi, D.Moricciani, P.Moskal, A.Ranieri, I.Sarra, M.Schioppa, A.Sciubba, W.Wislicki, M.Wolke
aa r X i v : . [ h e p - e x ] O c t Observation of the rare η → e + e − e + e − decaywith the KLOE experiment The KLOE CollaborationF. Ambrosino d , e , A. Antonelli a , M. Antonelli a , F. Archilli i , j ,I. Balwierz b , G. Bencivenni a , C. Bini g , h , C. Bloise a ,S. Bocchetta k ,ℓ , F. Bossi a , P. Branchini ℓ , G. Capon a ,T. Capussela a , F. Ceradini k ,ℓ , P. Ciambrone a , E. Czerwi´nski a ,E. De Lucia a , A. De Santis g , h , P. De Simone a , G. De Zorzi g , h ,A. Denig c , A. Di Domenico g , h , C. Di Donato e , B. Di Micco k ,ℓ ,M. Dreucci a , G. Felici a , S. Fiore g , h , P. Franzini g , h , C. Gatti a ,P. Gauzzi g , h , S. Giovannella a , ∗ , E. Graziani ℓ , M. Jacewicz a ,J. Lee-Franzini a , m , M. Martemianov o , M. Martini a , f , p ,P. Massarotti d , e , S. Meola d , e , S. Miscetti a , G. Morello a ,M. Moulson a , S. M¨uller c , M. Napolitano d , e , F. Nguyen k ,ℓ ,M. Palutan a , A. Passeri ℓ , V. Patera a , f , I. Prado Longhi k ,ℓ ,P. Santangelo a , B. Sciascia a , M. Silarski b , T. Spadaro a ,C. Taccini k ,ℓ , L. Tortora ℓ , G. Venanzoni a , R. Versaci a , f , q , ∗ ,G. Xu a , n , J. Zdebik b and, as members of the KLOE-2 collaboration:D. Babusci a , D. Badoni i , j , V. Bocci h , A. Budano k ,ℓ ,S. A. Bulychjev o , P. Campana a , E. Dan´e a , G. De Robertis s ,D. Domenici a , O. Erriquez r , s , G. Fanizzi r , s , F. Gonnella i , j ,F. Happacher a , B. H¨oistad v , E. Iarocci f , a , T. Johansson v ,V. Kulikov o , A. Kupsc v , F. Loddo s , M. Matsyuk o , R. Messi i , j ,D. Moricciani j , P. Moskal b , A. Ranieri s , I. Sarra a ,M. Schioppa t , u , A. Sciubba f , a , W. Wi´slicki w , M. Wolke v a Laboratori Nazionali di Frascati dell’INFN, Frascati, Italy. b Institute of Physics, Jagiellonian University, Krakow, Poland. c Institut f¨ur Kernphysik, Johannes Gutenberg - Universit¨at Mainz, Germany. d Dipartimento di Scienze Fisiche dell’Universit`a “Federico II”, Napoli, Italy
Preprint submitted to Elsevier 22 November 2018
INFN Sezione di Napoli, Napoli, Italy f Dipartimento di Scienze di Base ed Applicate per l’Ingegneria dell’Universit`a“Sapienza”, Roma, Italy. g Dipartimento di Fisica dell’Universit`a “Sapienza”, Roma, Italy. h INFN Sezione di Roma, Roma, Italy. i Dipartimento di Fisica dell’Universit`a “Tor Vergata”, Roma, Italy. j INFN Sezione di Roma Tor Vergata, Roma, Italy. k Dipartimento di Fisica dell’Universit`a “Roma Tre”, Roma, Italy. ℓ INFN Sezione di Roma Tre, Roma, Italy. m Physics Department, State University of New York at Stony Brook, USA. n Institute of High Energy Physics of Academica Sinica, Beijing, China. o Institute for Theoretical and Experimental Physics, Moscow, Russia. p Present Address: Dipartimento di Scienze e Tecnologie Applicate, Universit`aGuglielmo Marconi, Roma, Italy. q Present Address: CERN, CH-1211 Geneva 23, Switzerland. and r Dipartimento di Fisica dell’Universit`a di Bari, Bari, Italy. s INFN Sezione di Bari, Bari, Italy. t Dipartimento di Fisica dell’Universit`a della Calabria, Cosenza, Italy. u INFN Gruppo collegato di Cosenza, Cosenza, Italy. v Department of Nuclear and Particle Physics, Uppsala Univeristy,Uppsala,Sweden. w A. Soltan Institute for Nuclear Studies, Warsaw, Poland.
Abstract
We report the first observation of the rare η → e + e − e + e − decay based on 1.7 fb − collected by the KLOE experiment at the DAΦNE φ -factory. The selection of the e + e − e + e − final state is fully inclusive of radiation. We have identified 362 ± . ± . stat + bckg ± . syst ) × − . Key words: e + e − collisions, rare η decays PACS: ∗ Corresponding author.
Email addresses: [email protected] (S. Giovannella), [email protected] (R. Versaci). Introduction
The η → e + e − e + e − decay proceeds through two virtual photons intermediatestate with internal photon conversion to e + e − pairs. Conversion decays offerthe possibility to precisely measure the virtual photon 4-momentum via theinvariant mass of the e + e − pair. The lack of hadrons among the decay prod-ucts makes the matrix element directly sensitive to the η meson transitionform factor [1]. The knowledge of the η meson coupling to virtual photonsis important for the calculation of the anomalous magnetic moment of themuon, being pseudoscalar exchange the major contribution to the hadroniclight-by-light scattering.The first theoretical evaluation, Γ( η → e + e − e + e − ) / Γ( η → γγ ) = 6 . × − ,dates from 1967 [2]. The width ratio translates into a branching ratio (BR) BR ( η → e + e − e + e − ) = 2 . × − when the world average of the BR ( η → γγ )measurements [3] is taken as normalization factor. Other predictions exist inliterature [4,5,6,7], with differences at the level of 10%.Double lepton-antilepton η decays have been searched by the CMD-2 andthe WASA experiments, obtaining the upper limits at 90% C.L., BR ( η → e + e − e + e − ) < . × − [8] and BR ( η → e + e − e + e − ) < . × − [9], respec-tively. The KLOE experiment operates at DAΦNE , the Frascati φ -factory. DAΦNEis an e + e − collider running at a center of mass energy of ∼ φ meson. Equal energy positron and electron beams collide at anangle of π -25 mrad, producing nearly at rest φ mesons.The detector consists of a large cylindrical Drift Chamber (DC), surrounded bya lead-scintillating fiber electromagnetic calorimeter. A superconducting coilaround the EMC provides a 0.52 T field. The beam pipe at the interactionregion is spherical in shape with 10 cm radius, it is made of a Beryllium-Aluminum alloy of 0.5 mm thickness. Low beta quadrupoles are located atabout ±
50 cm distance from the interaction region. The drift chamber [10],4 m in diameter and 3.3 m long, has 12,582 all-stereo tungsten sense wires and37,746 aluminum field wires. The chamber shell is made of carbon fiber-epoxycomposite with an internal wall of 1.1 mm thickness, the gas used is a 90%helium, 10% isobutane mixture. The spatial resolutions are σ xy ∼ µ m and σ z ∼ σ ( p ⊥ ) /p ⊥ ≈ . ∼ ∼ (4.4 × , for a to-3al of 2440 cells arranged in five layers. The energy deposits are obtained fromthe signal amplitude while the arrival times and the particles positions are ob-tained from the time differences. Cells close in time and space are grouped intocalorimeter clusters. The cluster energy E is the sum of the cell energies. Thecluster time T and position ~R are energy-weighted averages. Energy and timeresolutions are σ E /E = 5 . / q E (GeV) and σ t = 57 ps / q E (GeV) ⊕
100 ps,respectively. The trigger [12] uses both calorimeter and chamber information.In this analysis the events are selected by the calorimeter trigger, requiringtwo energy deposits with
E >
50 MeV for the barrel and
E >
150 MeV forthe endcaps. A cosmic veto rejects events with at least two energy depositsabove 30 MeV in the outermost calorimeter layer. Data are then analyzed byan event classification filter [13], which selects and streams various categoriesof events in different output files.
The analysis has been performed using 1,733 pb − from the 2004-2005 dataset at √ s ≃ .
02 GeV. 242 pb − of data taken off-peak at √ s = 1 . e + e − continuum. Monte Carlo (MC) events are usedto simulate the signal and the background. The signal is generated accord-ing to the matrix element in [5], assuming BR = 2 . × − , in a sample of167,531 pb − . Other MC samples are: 3,447 pb − simulating the main φ de-cays ( φ → K ¯ K and φ → ρπ ) and 17,517 pb − simulating others more rare φ decays. All MC productions account for run by run variations of the maindata-taking parameters such as background conditions, detector response andbeam configuration. Data-MC corrections for calorimeter cluster energies andtracking efficiency, evaluated with radiative Bhabha events and φ → ρπ sam-ples respectively, have been applied. Effects of Final State Radiation (FSR)have been taken into account using the PHOTOS MC package [14,15]. Thispackage simulates the emission of FSR photons by any of the decay productstaking also into account the interference between different diagrams. PHO-TOS is used in the Monte Carlo at the event generation level, so that oursimulation fully accounts for radiative effects.At KLOE, η mesons are produced together with a monochromatic recoil pho-ton ( E γ = 363 MeV) through the radiative decay φ → ηγ . In the considereddata sample about 72 × η ’s are produced. As first step of the analysis, a pre-selection is performed requiring at least four (two positive and two negative)tracks extrapolated inside a fiducial volume defined by a cylinder centered inthe interaction point and having radius R = 4 cm and length ∆ z = 20 cm.For each charge, the two tracks with the highest momenta are selected. Oneand only one neutral cluster, having energy E cl ≥
250 MeV and polar angle inthe range (23 ◦ − ◦ ), is required. A cluster is defined neutral if it does not4ave any associated track and has a time of flight compatible with the photonhypothesis. To improve the energy and momentum resolution, a kinematic fitis performed imposing the four-momentum conservation and the photon timeof flight. A very loose cut on the χ of the kinematic fit ( χ < Two sources of background are present:(1) φ background:this is mainly due to φ → π + π − π events (with π Dalitz decay) andto φ → ηγ events either with η → π + π − π (with π Dalitz decay) or η → π + π − e + e − or with η → e + e − γ (with photon conversion on the BeamPipe, BP, or the DC inner Wall, DCW). This last background has thesame signature of the signal. Background from φ → K ¯ K is also presentat the preselection level.(2) e + e − continuum background:this is mainly due to e + e − → e + e − ( γ ) events with photon conversions,split tracks or interactions in the DAΦNE low beta quadrupoles. Thisbackground has been studied using off-peak data taken at √ s = 1 GeV,where φ decays are negligible.A first background rejection is performed cutting on the sum of the absolutevalue of the momenta of the four selected tracks requiring (600 < P | ~p i | < e + e − continuum background from interactions in the low betaquadrupoles, the quantities h cos θ f i and h cos θ b i have been defined as the av-erage polar angle of forward and backward selected particles. Events having h cos θ f i > .
85 and h cos θ b i < − .
85 are rejected. This cut has no effect onsignal selection efficiency.To reject events due to photon conversion, each track is extrapolated backwardto the intersection with the BP and with the DCW. For each track pair, theinvariant mass ( M ee ) and the relative distance ( D ee ) are computed. A clearsignal of photon conversion is visible in the D ee - M ee
2D plot for BP and DCW(figure 1). Events having at least one combination satisfying M ee ( BP ) < D ee ( BP ) < M ee ( DCW ) <
30 MeV and D ee ( DCW ) < t = t track − t cluster in both electron and pion hypothesis is evaluated; t track is definedas the length of the track divided by β ( m ) c . Track with ∆ t e / ∆ t π < > able 1Number of events in data, MC signal efficiency, background rejection factor at dif-ferent steps of the analysis.Cut N(data) ε ana (sig) R η → e + e − γ R φ → K ¯ K/ρπ R others Preselection 451924 0 . . × . × . × χ . . × . × . × Σ | ~p i | . . × . × . × cos θ b , cos θ f . . × . × . × γ conversion 12198 0 . . × . × . × PID 4239 0 . . × . × . × are identified as electron (pion). Events having more than two pions or noelectrons are discarded.The effects of background rejection cuts on the various data components arevisible in figure 2, where the four electrons invariant mass, M e + e − e + e − , isshown at different steps of the analysis. In table 1, number of events in data,N(data), MC signal efficiencies, ε ana (sig), and background rejection factor R ,defined as the ratio of analysis efficiency between signal and background, arealso reported. The R value has been evaluated for three different cathegories: φ → ηγ with η → e + e − γ ( R η → e + e − γ ), φ → K ¯ K and φ → ρπ ( R φ → K ¯ K/ρπ )and all other φ decays products ( R others ). After all cuts, background fromkaons and φ → π + π − π events is negligible. The same holds for all other φ decays but η → e + e − γ which, as will be shown in the next section, resultsin ∼
15% contamination level. Systematics on the Monte Carlo description ofphoton conversion have been studied using events with similar characteristics.A clean control sample is provided by the φ → η e + e − , η → π + π − π decaychain, where simple analysis cuts provide a good data-MC agreement, withnegligible background contamination. As for the η → e + e − e + e − channel, be-fore dedicated analysis cuts the control sample is significantly contaminatedby background from photon conversion ( φ → ηγ with photon converting onbeam pipe or drift chamber walls). This background is completely removedrejecting events with D ee ( DCW ) <
10 cm and M ee ( DCW ) <
80 MeV. Forthe η → e + e − e + e − channel this cut has not been applied because, havingtwo electrons and two positrons in the final state, the search for a conversionhas to be performed over all the four e + e − combinations, thus spreading thesignal contribution in the M ee ( DCW )– D ee ( DCW ) plane and lowering signif-icantly the analysis efficiency. Removing the cuts on M ee – D ee planes in thecontrol sample, a clear background contamination from photon conversionis visible. Data-MC comparison shows that, increasing in the simulation theprobability of conversion by 10%, an excellent agreement is found. A 10%systematic error is then assigned to photon conversion and added to the un-certainties coming from MC statistics and BR( η → e + e − γ ) measurement [3]:6 ee [ MeV ] D ee [ c m ] ee [ MeV ] D ee [ c m ] Fig. 1. D ee vs M ee evaluated at the drift chamber wall for MC φ → ηγ background (top panel) and MC signal (bottom panel). Events in the box M ee ( DCW ) <
30 MeV ∩ D ee ( DCW ) < N ( η → e + e − γ ) = 80 ± MC ± BR ± syst . η → e + e − e + e − ( γ )) As discussed in the previous section, the only significant background con-tamination surviving all the analysis cuts is due to η → e + e − γ events withphoton conversion, that have a signature similar to the signal. The overallestimated background from φ decays has been subtracted bin-by-bin to the M e + e − e + e − spectrum obtained in data (figure 3 top), taking into account alsosystematic errors. The event counting is done fitting the resulting spectrumwith the two residual contributions: signal and e + e − continuum backgroundevents. The M e + e − e + e − shape for the signal is obtained by fitting MC eventswith two Gaussian functions plus a third order polynomial function. The fitrange is 500 < M e + e − e + e − <
600 MeV. The M e + e − e + e − distribution for e + e − continuum events has been studied on the data taken at √ s = 1 GeV, wherecontributions from φ decays are suppressed. Even though the small statis-tics of the sample does not allow to precisely extract the shape, a first orderpolynomial well reproduces the data in the signal region. The free parametersare an overall scale factor for signal and the two parameters describing the e + e − continuum background. Fit results are shown in figure 3 bottom. Theresulting χ / ndf is 43.9/34, corresponding to P( χ ) = 0 .
12. The number ofsignal events is N ( η → e + e − e + e − ) = 362 ±
29. The branching ratio has been7 eeee [ MeV ] eeee [ MeV ] eeee [ MeV ] eeee [ MeV ] Fig. 2. M e + e − e + e − distribution after different analysis cuts: white: after the P | ~p i | and the h cos θ i cuts; gray: after the cut on photon conversion; black: after the PIDrequirement. Top left: data; top right: off-peak; bottom left: φ background MonteCarlo; bottom right: signal Monte Carlo. evaluated according to the formula: BR ( η → e + e − e + e − ( γ )) = N η → e + e − e + e − ( γ ) N ηγ · ǫ η → e + e − e + e − ( γ ) (1)where N η → e + e − e + e − ( γ ) is the number of signal events and ǫ η → e + e − e + e − ( γ ) is theefficiency taken from MC. The number of φ → ηγ events, N ηγ , has been ob-tained using the formula N ηγ = L · σ φ → ηγ , where L is the integrated luminosityand the cross section σ φ → ηγ has been evaluated taking into account the φ me-son line shape on a run by run basis [16]. Inserting all the numbers quoted intable 2, the value: BR ( η → e + e − e + e − ( γ )) = (2 . ± . stat + bckg ) × − (2)is obtained, where the error accounts for the uncertainty of the fit result.The systematic uncertainties due to analysis cuts have been evaluated by ap-8 eeee [ MeV ] M eeee [ MeV ] eeee [ MeV ] Fig. 3. Top panel: M e + e − e + e − data distribution at the end of the analysis chain; theexpected φ background MC shape is shown in dark gray. Bottom panel: M e + e − e + e − fit to data after φ background subtraction.Table 2Summary of the numbers used in the master formula (1) for the branching ratioevaluation. BR inputs ValuesNumber of events 362 ± ǫ η → e + e − e + e − ( γ ) . ± . ±
10) pb − e + e − → φ → ηγ cross section (41 . ± .
6) nb plying separately a variation of ± σ on all variables and re-evaluating thebranching ratio. The σ values have been obtained using MC signal events. Forthe χ variable the cut has been moved by ± ± M e + e − e + e − distribution has been evaluated considering: • the binning of the M e + e − e + e − histogram, changed from 3 MeV, used asdefault, to 2 and 4 MeV; • the M e + e − e + e − range, enlarged and reduced by 10 MeV on both sides; • the slope of the e + e − continuum background has been fixed to the value9 able 3Summary table of systematic uncertainties.Source of uncertainty Relative error χ − . / + 2 . h cos θ b i and h cos θ f i − . / + 0 . P | ~p i | +0 . γ conversion − . / + 2 . . − . / + 1 . M e + e − e + e − − . / + 0 . . ± . − . / + 4 . obtained from off-peak data fit.The relative variation of the BR for each source of systematic uncertainty isreported in table 3. The uncertainty on N ηγ has been added to the systematicsin the normalization term. The total error is taken as the quadratic sum of allcontributions. Using a sample of 1.7 fb − collected in the φ meson mass region, the firstobservation of the η → e + e − e + e − ( γ ) decay has been obtained on the basis of362 ±
29 events. The corresponding branching ratio is: BR ( η → e + e − e + e − ( γ )) = (2 . ± . stat+bckg ± . syst ) × − . (3)Radiative events slightly modify momentum distribution of the charged par-ticles and have been carefully considered in the efficiency evaluation. As aresult, the measured branching ratio is fully radiation inclusive.Our measurement is in agreement with theoretical predictions, which are inthe range (2 . − . × − [2,4,5,6,7].10 cknowledgments We would like to thank J. Bijnens for the useful discussions and for having pro-vided the signal Monte Carlo generator. We thank the DAFNE team for theirefforts in maintaining low background running conditions and their collabora-tion during all data-taking. We want to thank our technical staff: G. F. For-tugno and F. Sborzacchi for their dedication in ensuring efficient operation ofthe KLOE computing facilities; M. Anelli for his continuous attention to thegas system and detector safety; A. Balla, M. Gatta, G. Corradi and G. Pa-palino for electronics maintenance; M. Santoni, G. Paoluzzi and R. Rosellinifor general detector support; C. Piscitelli for his help during major mainte-nance periods. This work was supported in part by EURODAPHNE, contractFMRX-CT98-0169; by the German Federal Ministry of Education and Re-search (BMBF) contract 06-KA-957; by the German Research Foundation(DFG), ’Emmy Noether Programme’, contracts DE839/1-4; by the EU Inte-grated Infrastructure Initiative HadronPhysics Project under contract numberRII3-CT-2004-506078; by the European Commission under the 7th FrameworkProgramme through the ’Research Infrastructures’ action of the ’Capacities’Programme, Call: FP7-INFRASTRUCTURES-2008-1, Grant Agreement N.227431; by the Polish Ministery of Science and Higher Education through theGrant No. 0469/B/H03/2009/37.
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