BABAR-PUB-20/003SLAC-PUB-17526arXiv:2005.01885 [hep-ex]

Search for a Dark Leptophilic Scalar in e+e− Collisions

J. P. Lees,1 V. Poireau,1 V. Tisserand,1 E. Grauges,2 A. Palano,3 G. Eigen,4 D. N. Brown,5 Yu. G. Kolomensky,5

M. Fritsch,6 H. Koch,6 T. Schroeder,6 R. Cheaibb,7 C. Heartyab,7 T. S. Mattisonb,7 J. A. McKennab,7 R. Y. Sob,7

V. E. Blinovabc,8 A. R. Buzykaeva,8 V. P. Druzhininab,8 V. B. Golubevab,8 E. A. Kozyrevab,8 E. A. Kravchenkoab,8

A. P. Onuchinabc,8 S. I. Serednyakovab,8 Yu. I. Skovpenab,8 E. P. Solodovab,8 K. Yu. Todyshevab,8 A. J. Lankford,9

B. Dey,10 J. W. Gary,10 O. Long,10 A. M. Eisner,11 W. S. Lockman,11 W. Panduro Vazquez,11 D. S. Chao,12

C. H. Cheng,12 B. Echenard,12 K. T. Flood,12 D. G. Hitlin,12 J. Kim,12 Y. Li,12 D. X. Lin,12 T. S. Miyashita,12

P. Ongmongkolkul,12 J. Oyang,12 F. C. Porter,12 M. Rohrken,12 Z. Huard,13 B. T. Meadows,13 B. G. Pushpawela,13

M. D. Sokoloff,13 L. Sun,13, ∗ J. G. Smith,14 S. R. Wagner,14 D. Bernard,15 M. Verderi,15 D. Bettonia,16 C. Bozzia,16

R. Calabreseab,16 G. Cibinettoab,16 E. Fioravantiab,16 I. Garziaab,16 E. Luppiab,16 V. Santoroa,16 A. Calcaterra,17

R. de Sangro,17 G. Finocchiaro,17 S. Martellotti,17 P. Patteri,17 I. M. Peruzzi,17 M. Piccolo,17 M. Rotondo,17

A. Zallo,17 S. Passaggio,18 C. Patrignani,18, † B. J. Shuve,19 H. M. Lacker,20 B. Bhuyan,21 U. Mallik,22 C. Chen,23

J. Cochran,23 S. Prell,23 A. V. Gritsan,24 N. Arnaud,25 M. Davier,25 F. Le Diberder,25 A. M. Lutz,25

G. Wormser,25 D. J. Lange,26 D. M. Wright,26 J. P. Coleman,27 E. Gabathuler,27, ‡ D. E. Hutchcroft,27

D. J. Payne,27 C. Touramanis,27 A. J. Bevan,28 F. Di Lodovico,28, § R. Sacco,28 G. Cowan,29 Sw. Banerjee,30

D. N. Brown,30 C. L. Davis,30 A. G. Denig,31 W. Gradl,31 K. Griessinger,31 A. Hafner,31 K. R. Schubert,31

R. J. Barlow,32, ¶ G. D. Lafferty,32 R. Cenci,33 A. Jawahery,33 D. A. Roberts,33 R. Cowan,34 S. H. Robertsonab,35

R. M. Seddonb,35 N. Neria,36 F. Palomboab,36 L. Cremaldi,37 R. Godang,37, ∗∗ D. J. Summers,37 P. Taras,38 G. De

Nardo,39 C. Sciacca,39 G. Raven,40 C. P. Jessop,41 J. M. LoSecco,41 K. Honscheid,42 R. Kass,42 A. Gaza,43

M. Margoniab,43 M. Posoccoa,43 G. Simiab,43 F. Simonettoab,43 R. Stroiliab,43 S. Akar,44 E. Ben-Haim,44

M. Bomben,44 G. R. Bonneaud,44 G. Calderini,44 J. Chauveau,44 G. Marchiori,44 J. Ocariz,44 M. Biasiniab,45

E. Manonia,45 A. Rossia,45 G. Batignaniab,46 S. Bettariniab,46 M. Carpinelliab,46, †† G. Casarosaab,46

M. Chrzaszcza,46 F. Fortiab,46 M. A. Giorgiab,46 A. Lusianiac,46 B. Oberhofab,46 E. Paoloniab,46 M. Ramaa,46

G. Rizzoab,46 J. J. Walsha,46 L. Zaniab,46 A. J. S. Smith,47 F. Anullia,48 R. Facciniab,48 F. Ferrarottoa,48

F. Ferronia,48, ‡‡ A. Pilloniab,48 G. Pireddaa,48, ‡ C. Bunger,49 S. Dittrich,49 O. Grunberg,49 M. Heß,49 T. Leddig,49

C. Voß,49 R. Waldi,49 T. Adye,50 F. F. Wilson,50 S. Emery,51 G. Vasseur,51 D. Aston,52 C. Cartaro,52

M. R. Convery,52 J. Dorfan,52 W. Dunwoodie,52 M. Ebert,52 R. C. Field,52 B. G. Fulsom,52 M. T. Graham,52

C. Hast,52 W. R. Innes,52, ‡ P. Kim,52 D. W. G. S. Leith,52, ‡ S. Luitz,52 D. B. MacFarlane,52 D. R. Muller,52

H. Neal,52 B. N. Ratcliff,52 A. Roodman,52 M. K. Sullivan,52 J. Va’vra,52 W. J. Wisniewski,52 M. V. Purohit,53

J. R. Wilson,53 A. Randle-Conde,54 S. J. Sekula,54 H. Ahmed,55 M. Bellis,56 P. R. Burchat,56 E. M. T. Puccio,56

M. S. Alam,57 J. A. Ernst,57 R. Gorodeisky,58 N. Guttman,58 D. R. Peimer,58 A. Soffer,58 S. M. Spanier,59

J. L. Ritchie,60 R. F. Schwitters,60 J. M. Izen,61 X. C. Lou,61 F. Bianchiab,62 F. De Moriab,62 A. Filippia,62

D. Gambaab,62 L. Lanceri,63 L. Vitale,63 F. Martinez-Vidal,64 A. Oyanguren,64 J. Albertb,65 A. Beaulieub,65

F. U. Bernlochnerb,65 G. J. Kingb,65 R. Kowalewskib,65 T. Lueckb,65 I. M. Nugentb,65 J. M. Roneyb,65

R. J. Sobieab,65 N. Tasneemb,65 T. J. Gershon,66 P. F. Harrison,66 T. E. Latham,66 R. Prepost,67 and S. L. Wu67

(The BABAR Collaboration)1Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP),

Universite de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France2Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain3INFN Sezione di Bari and Dipartimento di Fisica, Universita di Bari, I-70126 Bari, Italy

4University of Bergen, Institute of Physics, N-5007 Bergen, Norway5Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA

6Ruhr Universitat Bochum, Institut fur Experimentalphysik 1, D-44780 Bochum, Germany7Institute of Particle Physics a; University of British Columbiab, Vancouver, British Columbia, Canada V6T 1Z1

8Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090a,Novosibirsk State University, Novosibirsk 630090b,

Novosibirsk State Technical University, Novosibirsk 630092c, Russia9University of California at Irvine, Irvine, California 92697, USA

10University of California at Riverside, Riverside, California 92521, USA

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11University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA12California Institute of Technology, Pasadena, California 91125, USA

13University of Cincinnati, Cincinnati, Ohio 45221, USA14University of Colorado, Boulder, Colorado 80309, USA

15Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France16INFN Sezione di Ferraraa; Dipartimento di Fisica e Scienze della Terra, Universita di Ferrarab, I-44122 Ferrara, Italy

17INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy18INFN Sezione di Genova, I-16146 Genova, Italy

19Harvey Mudd College, Claremont, California 91711, USA20Humboldt-Universitat zu Berlin, Institut fur Physik, D-12489 Berlin, Germany21Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India

22University of Iowa, Iowa City, Iowa 52242, USA23Iowa State University, Ames, Iowa 50011, USA

24Johns Hopkins University, Baltimore, Maryland 21218, USA25Universite Paris-Saclay, CNRS/IN2P3, IJCLab, F-91405 Orsay, France

26Lawrence Livermore National Laboratory, Livermore, California 94550, USA27University of Liverpool, Liverpool L69 7ZE, United Kingdom

28Queen Mary, University of London, London, E1 4NS, United Kingdom29University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom

30University of Louisville, Louisville, Kentucky 40292, USA31Johannes Gutenberg-Universitat Mainz, Institut fur Kernphysik, D-55099 Mainz, Germany

32University of Manchester, Manchester M13 9PL, United Kingdom33University of Maryland, College Park, Maryland 20742, USA

34Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA35Institute of Particle Physics a; McGill Universityb, Montreal, Quebec, Canada H3A 2T8

36INFN Sezione di Milanoa; Dipartimento di Fisica, Universita di Milanob, I-20133 Milano, Italy37University of Mississippi, University, Mississippi 38677, USA

38Universite de Montreal, Physique des Particules, Montreal, Quebec, Canada H3C 3J739INFN Sezione di Napoli and Dipartimento di Scienze Fisiche,

Universita di Napoli Federico II, I-80126 Napoli, Italy40NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands

41University of Notre Dame, Notre Dame, Indiana 46556, USA42Ohio State University, Columbus, Ohio 43210, USA

43INFN Sezione di Padovaa; Dipartimento di Fisica, Universita di Padovab, I-35131 Padova, Italy44Laboratoire de Physique Nucleaire et de Hautes Energies, Sorbonne Universite,

Paris Diderot Sorbonne Paris Cite, CNRS/IN2P3, F-75252 Paris, France45INFN Sezione di Perugiaa; Dipartimento di Fisica, Universita di Perugiab, I-06123 Perugia, Italy

46INFN Sezione di Pisaa; Dipartimento di Fisica,Universita di Pisab; Scuola Normale Superiore di Pisac, I-56127 Pisa, Italy

47Princeton University, Princeton, New Jersey 08544, USA48INFN Sezione di Romaa; Dipartimento di Fisica,

Universita di Roma La Sapienzab, I-00185 Roma, Italy49Universitat Rostock, D-18051 Rostock, Germany

50Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom51IRFU, CEA, Universite Paris-Saclay, F-91191 Gif-sur-Yvette, France

52SLAC National Accelerator Laboratory, Stanford, California 94309 USA53University of South Carolina, Columbia, South Carolina 29208, USA

54Southern Methodist University, Dallas, Texas 75275, USA55St. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G 2W5

56Stanford University, Stanford, California 94305, USA57State University of New York, Albany, New York 12222, USA

58Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel59University of Tennessee, Knoxville, Tennessee 37996, USA60University of Texas at Austin, Austin, Texas 78712, USA

61University of Texas at Dallas, Richardson, Texas 75083, USA62INFN Sezione di Torinoa; Dipartimento di Fisica, Universita di Torinob, I-10125 Torino, Italy

63INFN Sezione di Trieste and Dipartimento di Fisica, Universita di Trieste, I-34127 Trieste, Italy64IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain

65Institute of Particle Physics a; University of Victoriab, Victoria, British Columbia, Canada V8W 3P666Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

67University of Wisconsin, Madison, Wisconsin 53706, USA

Many scenarios of physics beyond the Standard Model predict the existence of new gauge singlets,which might be substantially lighter than the weak scale. The experimental constraints on additional

2

scalars with masses in the MeV to GeV range could be significantly weakened if they interactpredominantly with leptons rather than quarks. At an e+e− collider, such a leptophilic scalar (φL)would be produced predominantly through radiation from a τ lepton. We report herein a search fore+e− → τ+τ−φL, φL → `+`− (` = e, µ) using data collected by the BABAR experiment at SLAC.No significant signal is observed, and we set limits on the φL coupling to leptons in the range0.04 GeV < mφL < 7.0 GeV. These bounds significantly improve upon the current constraints,excluding almost entirely the parameter space favored by the observed discrepancy in the muonanomalous magnetic moment below 4 GeV at 90% confidence level.

PACS numbers: 12.60.-i, 14.80.-j, 95.35.+d

Many theories beyond the Standard Model (SM) pre-dict the existence of additional scalars, and discoveringor constraining their existence might shed light on thephysics of electroweak symmetry breaking and the Higgssector (e.g., see Ref. [1]). Some of these particles may besubstantially lighter than the weak scale, notably in theNext-to-Minimal Supersymmetric Standard Model [2],but also in more generic singlet-extended sectors [3, 4].In the MeV− GeV range, new scalars could mediate in-teractions between the SM and dark matter, as well asaccount for the discrepancy in the observed value of themuon anomalous magnetic dipole moment [5–7].

The possible coupling of a new scalar φL to SM parti-cles is constrained by SM gauge invariance. In the sim-plest case, the mixing between the scalar and the SMHiggs boson gives rise to couplings proportional to SMfermion masses. Because the new scalar couples predom-inantly to heavy-flavor quarks, this minimal scenario isstrongly constrained by searches for rare flavor-changingneutral current decays of mesons, such as B → Kφand K → πφ [8]. However, these bounds are evadedif the coupling of the scalar to quarks is suppressed andthe scalar interacts preferentially with heavy-flavor lep-tons [3, 4, 9, 10]. We refer to such a particle as a lep-tophilic scalar, φL. Its interaction Lagrangian with lep-tons can be described by:

L = −ξ∑

`=e,µ,τ

m`

v¯φL`,

where ξ denotes the flavor-independent coupling strengthto leptons and v = 246 GeV is the SM Higgs vacuum ex-pectation value [11]. Model independent constraints re-lying exclusively on the coupling to leptons are derivedfrom a BABAR search for a muonic dark force [12] andbeam dump experiments [13, 14]. A large fraction ofthe parameter space, including the region favored by themeasurement of the muon anomalous magnetic moment,is still unexplored [3, 9, 10]. Examples of model depen-dent bounds from B and h decays for a specific UV-completion of the theory can be found in Ref. [3].

The large sample of τ+τ− pairs collected by BABAR of-fers a clean environment to study model independent φLproduction via final-state radiation in e+e− → τ+τ−φL.The mass-proportionality of the coupling, in particularthe feeble interaction with electrons, dictates the ex-perimental signature. For 2me < mφL

< 2mµ, the

scalar decays predominantly into electrons, leading todisplaced vertices for sufficiently small values of the cou-pling. Prompt decays into a pair of muons (taus) domi-nate when 2mµ ≤ mφL

< 2mτ (2mτ < mφL).

We report herein the first search for a leptophilic scalarin the reaction e+e− → τ+τ−φL, φL → `+`− (` = e, µ)for 0.04 GeV < mφL

< 7.0 GeV. The cross section formφL

< 2mµ is measured separately for φL lifetimes cor-responding to cτφL

values of 0, 1, 10 and 100 mm. Abovethe dimuon threshold, we determine the cross section forprompt φL → µ+µ− decays. In all cases, the φL width ismuch smaller than the detector resolution, and the sig-nal can be identified as a narrow peak in the dileptoninvariant mass.

The search is based on 514 fb−1 of data collected at theΥ (2S), Υ (3S), Υ (4S) resonances and their vicinities [15]by the BABAR experiment at the SLAC PEP-II e+e− col-lider. The BABAR detector is described in detail else-where [16, 17]. A sample corresponding to about 5% ofthe data, called the optimization sample, is used to opti-mize the search strategy and is subsequently discarded.The remaining data are examined only once the analysisprocedure has been finalized.

Signal Monte Carlo (MC) samples with prompt de-cays are simulated for 36 different φL mass hypotheses bythe MadGraph event generator [18] and showered usingPythia 8 [19], including final-state radiation. FormφL

<0.3 GeV, events with cτφL

values up to 300 mm are alsogenerated. We simulate the following reactions to studythe background: e+e− → e+e−(γ) (BHWIDE [20]),e+e− → µ+µ−(γ) and e+e− → τ+τ−(γ) (KK with theTAUOLA library [21, 22]), e+e− → qq with q = u, d, s, c(JETSET [23]), and e+e− → BB and generic e+e− →Υ (2S, 3S) decays (EvtGen [24]). The resonance produc-tion e+e− → γψ(2S), ψ(2S) → π+π−J/ψ , J/ψ → µ+µ−

is simulated with EvtGen using a structure functiontechnique [25, 26]. The detector acceptance and re-construction efficiencies are estimated with a simulationbased on GEANT4 [27].

We select events containing exactly four charged trackswith zero net charge, focusing on τ lepton decays to sin-gle tracks and any number of neutral particles. TheφL → `+`− candidates are formed by combining twoopposite-sign tracks identified as an electron or muon pairby particle identification (PID) algorithms [12, 16]. We

3

do not attempt to select a single φL candidate per event,but simply consider all possible combinations. RadiativeBhabha and dimuon events in which the photon convertsto an e+e− pair are suppressed by rejecting events witha total visible mass greater than 9 GeV. We further vetoe+e− → e+e−e+e− events by requiring the cosine of theangle between the momentum of the φL candidate andthat of the nearest track to be less than 0.98, the miss-ing momentum against all tracks and neutral particles tobe greater than 300 MeV, and that there be three or lesstracks identified as electrons. We perform a kinematic fitto the selected φL candidates, constraining the two tracksto originate from the same point in space. The dimuonproduction vertex is required to be compatible with thebeam interaction region, while we only constrain the mo-mentum vector of the e+e− pair to point back to thebeam interaction region since the dielectron vertex canbe substantially displaced. We select dielectron (dimuon)combinations with a value of the χ2 per degree of freedomof the fit, χ2/n.d.f., less than 3 (12).

A multivariate selection based on boosted decisiontrees (BDT) further improves the signal purity [28]. TheBDTs include variables capturing the typical τ and φLdecay characteristics: a well-reconstructed `+`− vertex,either prompt or displaced; missing energy and momen-tum due to neutrino emission; relatively large track mo-menta; low neutral particle multiplicity; and two or moretracks identified as electrons or muons. A few vari-ables are also targeted at specific backgrounds, such asψ(2S) → π+π−J/ψ , J/ψ → µ+µ− production in initial-state radiation (ISR) events. The φL mass is specificallyexcluded to limit potential bias in the classifier. A fulldescription of these variables can be found in the Sup-plemental Material [29]. We train a separate BDT foreach of the different final states and cτφL

values withsignal events modeled using a flat mφL

distribution andbackground events modeled using the optimization sam-ple data.

The final selection of φL candidates for each lifetimeselection and decay channel is made by applying a mass-dependent criterion on the corresponding BDT score thatmaximizes signal sensitivity. The distributions of the re-sulting dielectron and dimuon masses for prompt decaysare shown in Fig. 1, and spectra for other lifetimes forφL → e+e− decays are shown in Fig. 2, together with thedominant background components among the set of sim-ulated MC samples. The differences between the dataand summed-MC distributions are mainly due to pro-cesses that are not simulated, dominated by ISR pro-duction of high-multiplicity QED and hadronic eventsas well as two-photon processes. Peaking contributionsfrom J/ψ → µ+µ− and ψ(2S) → µ+µ− decays are alsoseen, and the corresponding regions are excluded fromthe signal search. In addition, the dielectron spectrumfor cτφL

= 1 mm features a broad enhancement fromπ0 → γγ decays in which one or both photons convert to

(GeV)eem0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24

En

trie

s / 0

.004

(G

eV)

1

10

210

310Data qq→-e+ e

BB→-e+ e -τ+τ→-e+ e

(GeV)µµm0 1 2 3 4 5 6 7 8

En

trie

s / 0

.1 (

GeV

)

10

210

310

410 Data

qq→-e+ e

BB→-e+ e-τ+τ→-e+ e

ψJ/

(2S)ψ

FIG. 1: The distribution of (top) the dielectron invariantmass and (bottom) the dimuon invariant mass for promptdecays, together with simulated predictions for the indicatedprocesses normalized to the integrated luminosity of the data(stacked histograms).

e+e− pairs. Since this feature is much broader than thesignal, we do not exclude this mass region but insteadtreat it as an additional background component. No sta-tistically significant π0 component is observed for othervalues of cτφL

.

We extract the signal yield for the different lifetimesand final states separately by scanning the correspondingmass spectrum in steps of the signal mass resolution, σ.The latter is estimated by performing fits of a double-sided Crystal Ball function [30] to each signal MC sam-ple and interpolating the results to the full mass range.The resolution ranges from 1 MeV near mφL

= 40 MeVfor cτφL

= 100 mm to 50 MeV near mφL= 7.0 GeV

for prompt decays. The signal MC predictions are val-idated with samples of K0

S → π+π− and ψ(2S) →π+π−J/ψ , J/ψ → µ+µ− decays; agreement with the datais observed. For each mass hypothesis, we perform anunbinned likelihood fit over an interval varying between20 − 50σ (fixed to 60σ) for the dielectron (dimuon) fi-nal state. To facilitate the background description, the

4

(GeV)eem0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24

En

trie

s / 0

.004

(G

eV)

10

210

310

410 Data qq→-e+ e

BB→-e+ e -τ+τ→-e+ e = 1 mm

Lφτc

(GeV)eem0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24

En

trie

s / 0

.004

(G

eV)

1

10

210

310 Data qq→-e+ e

BB→-e+ e -τ+τ→-e+ e = 10 mm

Lφτc

(GeV)eem0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24

En

trie

s / 0

.004

(G

eV)

10

210

310

Data qq→-e+ e

BB→-e+ e -τ+τ→-e+ e = 100 mm

Lφτc

FIG. 2: The distribution of the dielectron invariant mass forthe (top) cτφL = 1 mm, (middle) cτφL = 10 mm, and (bot-tom) cτφL = 100 mm samples, together with simulated predic-tions for the indicated processes normalized to the integratedluminosity of the data (stacked histograms).

reduced dimuon mass, mR = (m2µµ − 4m2

µ)1/2, is usedfor 2mµ < mφL

< 260 MeV. In that region, fits are per-formed over a fixed interval mR < 0.2 GeV.

The likelihood function includes contributions fromsignal, continuum background, and, where needed, peak-ing components describing the π0, J/ψ → µ+µ−, andψ(2S) → µ+µ− resonances. The signal probability den-sity function (pdf) is described by a non-parametric ker-nel density function modeled directly from the signal MC

mass distribution. An algorithm based on the cumula-tive density function [31] is used to interpolate the pdfbetween simulated mass points. The uncertainty associ-ated with this procedure is on average 4% (3%) of thecorresponding statistical uncertainty for the dielectron(dimuon) analysis.

The dielectron continuum background is modeled by asecond-order polynomial for the cτφL

= 100 mm sampleand by a second-order polynomial plus an exponentialfunction for the other lifetimes. The peaking π0 shapefor the cτφL

= 1 mm sample is determined from sidebanddata obtained by applying all selection criteria, but re-quiring the χ2/n.d.f. of the kinematic fit to be greaterthan 3. The peaking π0 yield and all the continuumbackground parameters are determined in the fit. Toassess systematic uncertainties, we repeat the fits witha third-order polynomial for the continuum background,vary the width of the π0 shape within its uncertainty, orinclude a π0 component for all lifetime samples. The re-sulting systematic uncertainties are typically at the levelof the statistical uncertainty, but dominate the total un-certainty for several mass hypotheses in the vicinity ofthe π0 peak.

The reduced mass distribution of the dimuon contin-uum background is modeled by a third-order polyno-mial constrained to intersect the origin, and the dimuoncontinuum is described by a second-order polynomial athigher masses. The shape of the J/ψ and ψ(2S) reso-nances are fixed to the predictions of the correspondingMC samples, but their yields cannot be accurately esti-mated from MC simulations and are therefore left to floatfreely in the fit. A range of ±50 MeV around the nom-inal J/ψ and ψ(2S) masses is therefore excluded fromthe search. The systematic uncertainty associated withthe choice of the background model, assessed by repeat-ing the fits with alternative descriptions, is typically atthe level of a few events, but can be as large as half thestatistical uncertainty for a few points in the high massregion, where statistical precision is limited.

The fitted signal yields and statistical significances arepresented in the Supplemental Material [29], togetherwith a few examples of fits. The bias in the fitted valuesis determined from pseudo-experiments to be negligiblecompared to the statistical uncertainties. Since the sys-tematic uncertainty associated with the choice of back-ground model can be large in the dielectron channel, wedefine the signal significance as the smallest of the signif-icance values determined from each background model.Including trial factors, the largest significance is 1.4σ ob-served near mφL

= 2.14 GeV, consistent with the nullhypothesis.

The signal efficiency varies between 0.2% for mφL=

40 MeV and cτφL= 100 mm, to 26% around mφL

=5 GeV for prompt decays. The effect of ISR, not includedin the samples generated by MadGraph, is assessed bysimulating events with Pythia 8 using the matrix ele-

5

ments calculated by MadGraph, and reweighting thissample to match the pT distribution of the φL predictedby MadGraph. The resulting change in efficiency isfound to be about 4% over the full mass range coveredby the dielectron channel, and varies from 7% near thedimuon threshold to less than 1% at mφL

∼ 7 GeV. Halfthe value of each of these differences is propagated as asystematic uncertainty in the signal yield. A correctionfactor of 0.98 (0.93) on the signal efficiency is includedfor the dielectron (dimuon) final state to account for dif-ferences between data and simulation in track and neu-tral reconstruction efficiencies, charged particle identifi-cation, and trigger efficiencies. The correction for the di-electron channel is derived from a sample of K0

S → π+π−

produced in τ decays, while that for the dimuon channelis assessed from the BDT score distribution for eventsin which the missing transverse momentum is greaterthan 2 GeV, a region where the contribution of unsim-ulated background components can be neglected. Anuncertainty of 3.8% (4.0%) in the dielectron (dimuon)efficiency correction is propagated as a systematic uncer-tainty.

The e+e− → τ+τ−φL cross section at the Υ (4S) en-ergy is derived for each lifetime and final state by takinginto account the variation of the cross section and signalefficiencies with the beam energy and the φL → `+`−

branching fraction:

σ4S =Nsig∑

i=2S,3S,4S

(σth,i

σth,4SεiLi) BF (φL → `+`−)

,

where Nsig denotes the number of signal events, andσth,nS , εnS and LnS (n = 2, 3, 4) are the theoreticale+e− → τ+τ−φL cross section, signal efficiency, and dataluminosity at the Υ (nS) center-of-mass energy, respec-tively. In the absence of a significant signal, Bayesianupper limits at 90% confidence level (CL) on the crosssections are derived by assuming a uniform prior in thecross section. Systematic effects are taken into accountby convolving the likelihood with a Gaussian having awidth equal to the systematic uncertainty. The uncer-tainties due to the luminosity (0.6%) [15] and the limitedstatistical precision of the signal MC sample (1–4%) areincorporated. The resulting limits are shown in Fig. 3.The sharp increase just above the ditau threshold is areflection of the φL → µ+µ− branching fraction decreas-ing quickly in favor of the τ+τ− final state. The limiton the production cross section of a scalar S without anyassumptions on other decay modes is presented in theSupplemental Material [29].

The limits on the scalar coupling ξ, presented in Fig. 4,are derived with an iterative procedure that accounts fora potentially long φL lifetime. An estimate of ξ is firstchosen, and the corresponding lifetime and cross sectionare calculated [3]. These values are compared to the crosssection limit interpolated at that lifetime, and the esti-

(GeV)L

φm0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

) (f

b)

Lφ- τ+ τ →- e+

(eσ

-110

1

10

210

310

= 0τc = 1 mmτc = 10 mmτc = 100 mmτc

-e+ e→ L

φ 90% CL limit

(GeV)L

φm0 1 2 3 4 5 6 7

) (f

b)

Lφ- τ+ τ →- e+

(eσ

-110

1

10

90% CL limit

-µ+µ →L

φ

FIG. 3: The 90% CL upper limits on the σ(e+e− → τ+τ−φL)cross section at the Υ (4S) resonance derived from (top) thedielectron and (bottom) dimuon final states. The gray bandsindicate the regions excluded from the search around the nom-inal J/ψ and ψ(2S) masses.

mate of the coupling is updated. The procedure is iter-ated until convergence is obtained. Bounds at the level of0.5−1 are set on the dielectron final state, correspondingto cτφL

values of the order of 1 cm, and limits down to 0.2are derived for dimuon decays. These results are approx-imately an order of magnitude smaller than the couplingsfavored by the muon anomalous magnetic moment belowthe ditau threshold [3] and rule out a substantial fractionof previously unexplored parameter space at 90% CL.

In summary, we report the first model-independentsearch for the direct production of a new dark leptophilicscalar. The limits significantly improve upon the pre-vious constraints over a large range of masses, almostentirely ruling out the remaining region of parameterspace below the dimuon threshold. More significantly,this search excludes the possibility of the dark leptophilicscalar accounting for the observed discrepancy in themuon magnetic moment for almost all φL masses below4 GeV. Since these results rely only on φL productionin association with tau leptons and its subsequent lep-

6

tonic decay, they can also be reinterpreted to providepowerful constraints on other leptonically decaying newbosons interacting with tau leptons. The Belle II exper-iment should be able to further probe these possibilities,and cover the remaining parameter space above the beamdump constraints.

(GeV) L

φm-210 -110 1 10

ξ

-310

-210

-110

1

10

210

σ 2±µ(g-2)

excl.µ(g-2)

E137

Orsay

Z'BABAR

90% CLL

φ BABAR

FIG. 4: The 90% CL limits on the coupling ξ as a functionof the φL mass (green shaded area), together with existingconstraints [9, 10, 12–14] (gray shaded areas) and the param-eter space preferred by the muon anomalous magnetic mo-ment [3, 10] (red band).

We are grateful for the extraordinary contributions ofour PEP-II colleagues in achieving the excellent luminos-ity and machine conditions that have made this work pos-sible. The success of this project also relies critically onthe expertise and dedication of the computing organiza-tions that support BABAR. The collaborating institutionswish to thank SLAC for its support and the kind hospi-tality extended to them. This work is supported by theUS Department of Energy and National Science Foun-dation, the Natural Sciences and Engineering ResearchCouncil (Canada), the Commissariat a l’Energie Atom-ique and Institut National de Physique Nucleaire et dePhysique des Particules (France), the Bundesministeriumfur Bildung und Forschung and Deutsche Forschungsge-meinschaft (Germany), the Istituto Nazionale di FisicaNucleare (Italy), the Foundation for Fundamental Re-search on Matter (The Netherlands), the Research Coun-cil of Norway, the Ministry of Education and Science ofthe Russian Federation, Ministerio de Economıa y Com-petitividad (Spain), the Science and Technology Facili-ties Council (United Kingdom), and the Binational Sci-ence Foundation (U.S.-Israel). Individuals have receivedsupport from the Marie-Curie IEF program (EuropeanUnion) and the A. P. Sloan Foundation (USA).

∗ Now at: Wuhan University, Wuhan 430072, China

† Now at: Universita di Bologna and INFN Sezione diBologna, I-47921 Rimini, Italy

‡ Deceased§ Now at: King’s College, London, WC2R 2LS, UK¶ Now at: University of Huddersfield, Huddersfield HD1

3DH, UK∗∗ Now at: University of South Alabama, Mobile, Alabama

36688, USA†† Also at: Universita di Sassari, I-07100 Sassari, Italy‡‡ Also at: Gran Sasso Science Institute, I-67100 L’Aquila,

Italy[1] G. C. Branco, P. M. Ferreira, L. Lavoura, M. N. Rebelo,

M. Sher and J. P. Silva, Phys. Rept. 516, 1 (2012).[2] B. A. Dobrescu and K. T. Matchev, J. High Energy Phys.

09, 031 (2000).[3] B. Batell, N. Lange, D. McKeen, M. Pospelov and

A. Ritz, Phys. Rev. D 95, 075003 (2017).[4] C. Y. Chen, H. Davoudiasl, W. J. Marciano and

C. Zhang, Phys. Rev. D 93, 035006 (2016).[5] J. P. Leveille, Nucl. Phys. B 137, 63 (1978).[6] G. W. Bennett et al. [Muon g-2 Collaboration], Phys.

Rev. D 73, 072003 (2006).[7] M. Tanabashi et al. [Particle Data Group], Phys. Rev. D

98, 030001 (2018).[8] J. Beacham et al., J. Phys. G 47, 010501 (2020).[9] Y. S. Liu, D. McKeen and G. A. Miller, Phys. Rev. Lett.

117, no.10, 101801 (2016).[10] J. Liu, N. McGinnis, C. E. M. Wagner and X. P. Wang,

JHEP 04, 197 (2020).[11] Natural units (h = c = 1) are used throughout this paper.[12] J. P. Lees et al. [BABAR Collaboration], Phys. Rev. D 94,

011102 (2016).[13] J. D. Bjorken et al., Phys. Rev. D 38, 3375 (1988).[14] M. Davier and H. Nguyen Ngoc, Phys. Lett. B 229, 150

(1989).[15] J. P. Lees et al. [BABAR Collaboration], Nucl. Instrum.

Meth. A 726, 203 (2013).[16] B. Aubert et al. [BABAR Collaboration], Nucl. Instrum.

Meth. A 479, 1 (2002).[17] B. Aubert et al. [BABAR Collaboration], Nucl. Instrum.

Meth. A 729, 615 (2013).[18] J. Alwall et al., JHEP 1407, 079 (2014).[19] T. Sjostrand et al., Comput. Phys. Commun. 191, 159

(2015).[20] S. Jadach, W. Placzek and B. F. L. Ward, Phys. Lett. B

390, 298 (1997).[21] S. Jadach, B. F. L. Ward and Z. Was, Phys. Rev. D 63,

113009 (2001).[22] S. Jadach, Z. Was, R. Decker and J. H. Kuhn, Comput.

Phys. Commun. 76 (1993) 361.[23] T. Sjostrand, Comput. Phys. Commun. 82, 74 (1994).[24] D. J. Lange, Nucl. Instrum. Meth. A 462, 152 (2001).[25] A. B. Arbuzov et al., J. High Energy Phys. 9710, 001

(1997).[26] M. Caffo, H. Czyz, and E. Remiddi, Nuovo Cim. A 110,

515 (1997); Phys. Lett. B 327, 369 (1994).[27] S. Agostinelli et al. [GEANT4 Collaboration], Nucl. In-

strum. Meth. A 506, 250 (2003).[28] Y. Freund and R. E. Schapire, J. Comput. Syst. Sci. 55,

119 (1997).[29] See Supplemental Material at http://link.aps.org/

supplemental/10.1103/PhysRevLett.125.181801 for ad-ditional plots and a complete description of the variablesused for the Boosted Decision Trees.

7

[30] T. Skwarnicki, Ph.D Thesis, DESY F31-86-02, AppendixE, (1986).

[31] A. L. Read, Nucl. Instrum. Meth. A 425, 357 (1999).

8

Supplemental Material for BABAR-PUB-20/003

Search for a Dark Leptophilic Scalar in e+e− Collisions

Additional details and figures for the dark leptophilic scalar search are presented in this Supplemental Material.

TABLE I: List of variables used as input to the dimuon boosted decision trees.

Ratio of second to zeroth Fox-Wolfram moment of all tracks and neutrals.Invariant mass of the four track system, assuming the pion (muon) mass for the tracks originating from the tau (φL) decays.Invariant mass and transverse momentum of all tracks and neutrals.Invariant mass squared of the system recoiling against all tracks and neutrals.Transverse momentum of the system recoiling against all tracks and neutrals.Number of neutral candidates with an energy greater than 50 MeV.Invariant masses of the three track systems formed by the φL and the remaining positively or negatively charged tracks.Momentum of each track from φL decays.Angle between the two tracks produced by the tau decay.Variable indicating if a track has been identified as a muon or an electron by PID algorithm for each track.

TABLE II: List of variables used as input to the dielectron boosted decision trees.

Transverse momentum of the system recoiling against all tracks and neutrals.Energy of the system recoiling against all tracks and neutrals.Number of tracks identified as electron candidates by a PID algorithm applied to each track.Angle between φL candidate momentum and closest track produced in tau decay.Angle between φL candidate momentum and farthest track produced in tau decay.Angle of φL candidate relative to the beam in the center-of-mass frame.Angle between the two tracks produced by the tau decay.Angle between φL candidate and nearest neutral candidate with E > 50 MeV.Energy of nearest neutral candidate (with E > 50 MeV) to φL candidate.Total energy in neutral candidates, each of which has an energy greater than 50 MeV.Distance between beamspot and φL candidate vertex.Uncertainty in the distance between beamspot and φL candidate decay vertex.φL candidate vertex significance, defined by the beamspot-vertex distance divided by its uncertainty.Angle between the φL candidate momentum, and line from beamspot to φL decay vertex.Distance of closest approach to beamspot of e− in φL candidate.Distance of closest approach to beamspot of e+ in φL candidate.Transverse distance between φL decay vertex and best-fit common origin of τ candidates and φL candidate.χ2 of the kinematic fit to the φL and τ candidates constraining their origin to the same production point.χ2 of the kinematic fit of the φL candidate with the constraint that the e+e− pair is produced from a photonconversion in detector material.Dielectron mass for φL candidate when re-fit with the photon conversion constraint.

9

(GeV)L

φm0 1 2 3 4 5 6 7

S

N

-100

-50

0

50

100

(GeV)L

φm0 1 2 3 4 5 6 7

S

S

-5

0

5 (GeV)

Lφm

0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

S

N

-100

0

100 = 1 mmL

φτc

(GeV)L

φm0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

S

S

-5

0

5

(GeV)L

φm0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

S

N

-100

0

100 = 10 mmL

φτc

(GeV)L

φm0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

S

S

-5

0

5 (GeV)

Lφm

0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

S

N

-100

0

100 = 100 mmL

φτc

(GeV)L

φm0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

S

S

-5

0

5

FIG. 5: The distribution of signal events (Ns) and local signal significance (Ss) from the fits as a function of the φL mass for(top left) prompt decays; (top right) cτφL = 1 mm; (bottom left) cτφL = 10 mm; (bottom right) cτφL = 100 mm. The promptdecays include contributions from both the dielectron and dimuon final states.

(GeV)Sm0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

)) (

fb)

- e+ e→

S(

- τ+ τ →- e+

(eσ

-110

1

10

210

310

= 0L

φτc = 1 mm

Lφτc

= 10 mmL

φτc = 100 mm

Lφτc

-e+ e→S 90% CL limit

(GeV)Sm0 1 2 3 4 5 6 7

)) (

fb)

- µ+ µ→

S(

- τ+ τ →- e+

(eσ -110

1

90% CL limit

-µ+µ →S

FIG. 6: The 90% CL limits on (left) the σ(e+e− → τ+τ−S(S → e+e−)) and (right) the σ(e+e− → τ+τ−S(S → µ+µ−)) crosssections for the production of a generic scalar S at the Υ (4S) resonance. The gray bands indicate the regions excluded fromthe search around the nominal J/ψ and ψ(2S) masses.

10

(GeV)eem0.03 0.04 0.05 0.06 0.07 0.08 0.09

Eve

nts

/ (

0.00

12 G

eV )

20

40

60

80

100

120

140

160

180

200

(GeV)eem0.12 0.14 0.16 0.18 0.2 0.22

Eve

nts

/ (

0.00

24 G

eV )

0

10

20

30

40

50

60

70

(GeV)eem0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14

Eve

nts

/ (

0.00

15 G

eV )

0

5

10

15

20

25

30

(GeV)eem0.14 0.16 0.18 0.2 0.22 0.24 0.26

Eve

nts

/ (

0.00

3 G

eV )

0

2

4

6

8

10

12

14

16

18

20

(GeV)µµm1.9 2 2.1 2.2 2.3 2.4

Eve

nts

/ (

0.01

2 G

eV )

90

100

110

120

130

140

150

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170

(GeV)µµm4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6

Eve

nts

/ (

0.03

6 G

eV )

0

20

40

60

80

100

120

140

FIG. 7: Example of fits to (top) the dielectron mass with cτ = 1 mm; (middle left) cτ = 10 mm; (middle right) cτ = 100 mm;(bottom) the dimuon mass. The full fit is shown as a solid blue line, and the background as a dashed green line.

11