Search for dark Higgsstrahlung in e+e µ+µ − − → and missing energy events with the KLOE experiment 5 The KLOE-2 Collaboration 1 0 2 D. Babuscif, G. Bencivennif, C. Bloisef, F. Bossif, n P. Branchinip, A. Budanoo,p, L. Caldeira Balkest˚ahlr, a J F. Ceradinio,p, P. Ciambronef, F. Curciarellog,b, 7 2 E. Czerwin´skie, E. Dan`ef, V. De Leop, E. De Luciaf, ] A. De Santisf, P. De Simonef, A. Di Ciccoo,p, x e A. Di Domenicok,ℓ, R. Di Salvon, D. Domenicif, A. Fantinim,n, - p G. Felicif, S. Fioreq,ℓ, A. Gajose, P. Gauzzik,ℓ, G. Giardinag,b, e h S. Giovannellaf, E. Grazianip, F. Happacherf, [ L. Heijkenskjo¨ldr, W. Ikegami Anderssonr, T. Johanssonr, 1 v D. Kamin´skae, W. Krzemiens, A. Kupscr, S. Loffredoo,p, 5 9 G. Mandagliog,b, M. Martinif,j, M. Mascolof, R. Messim,n, 7 S. Miscettif, G. Morellof, D. Moriccianin, P. Moskale, 6 0 F. Nguyenp,t, A. Palladinof, A. Passerip, V. Paterai,f, . 1 A. Ranieria, P. Santangelof, I. Sarraf, M. Schioppac,d, 0 5 M. Silarskif, L. Tortorap, G. Venanzonif, W. Wi´slickis, 1 v: M. Wolker i X aINFN Sezione di Bari, Bari, Italy. r a bINFN Sezione di Catania, Catania, Italy. cDipartimento di Fisica dell’Universit`a della Calabria, Cosenza, Italy. dINFN Gruppo collegato di Cosenza, Cosenza, Italy. eInstitute of Physics, Jagiellonian University, Cracow, Poland. fLaboratori Nazionali di Frascati dell’INFN, Frascati, Italy. gDipartimento di Fisica e Scienze della Terra dell’Universit`a di Messina, Messina, Italy. hInstitute for Theoretical and Experimental Physics (ITEP), Moscow, Russia. iDipartimento di Scienze di Base ed Applicate per l’Ingegneria dell’Universita` “Sapienza”, Roma, Italy. jDipartimento di Scienze e Tecnologie applicate, Universit`a “Guglielmo Marconi”, Preprint submitted to Physics Letters B 28 January 2015 Roma, Italy. kDipartimento di Fisica dell’Universit`a “Sapienza”, Roma, Italy. ℓINFN Sezione di Roma, Roma, Italy. mDipartimento di Fisica dell’Universit`a “Tor Vergata”, Roma, Italy. nINFN Sezione di Roma Tor Vergata, Roma, Italy. oDipartimento di Matematica e Fisica dell’Universit`a “Roma Tre”, Roma, Italy. pINFN Sezione di Roma Tre, Roma, Italy. qENEA UTTMAT-IRR, Casaccia R.C., Roma, Italy rDepartment of Physics and Astronomy, Uppsala University, Uppsala, Sweden. sNational Centre for Nuclear Research, Warsaw, Poland. tPresent Address: Laborato´rio de Instrumenta¸ca˜o e F´ısica Experimental de Part´ıculas, Lisbon, Portugal. Abstract We searched for evidence of a Higgsstrahlung process in a secluded sector, leading ′ to a final state with a dark photon U and a dark Higgs boson h, with the KLOE ′ detector at DAΦNE. We investigated the case of h lighter than U, with U decaying ′ intoamuonpairandh producingamissingenergysignature.Wefoundnoevidence of the process and set upper limits to its parameters in the range 2m < m < µ U 1000 MeV, mh′ < mU. Key words: dark matter, dark forces, U boson, upper limit, higgsstrahlung Email addresses: [email protected](E. Graziani), [email protected](F. Nguyen). 2 1 Introduction Astrophysical data reveal in a more and more convincing way that our knowl- edge of the Universe is limited to about 4-5% of the total matter-energy con- tent: thisisgenerallyinterpretedasanevidence oftheexistence ofdarkmatter and dark energy components. In recent years, several astrophysical observa- tions have failed to find a common interpretation in terms of standard as- trophysical or particle physics sources [1–10]. Although there are alternative explanations for some of these results, they could all be explained with the ex- istence of a dark matter weakly interacting massive particle, WIMP, belonging to a secluded gauge sector under which the Standard Model (SM) particles are uncharged [11–20]. In a minimal model, a new abelian U(1) gauge field is in- S troduced, the U boson or dark photon, with mass near the GeV scale, coupled to the SM only through its kinetic mixing with the SM hypercharge field. The kinetic mixing parameter ǫ is expected to be of the order 10−4 10−2 [12–21], so that observable effects can be detected at e+e− colliders [21–−25] or at fixed target experiments working in the GeV region [26–29]. The existence of the U boson, through its mixing with the ordinary photon, can also accomodate the observed discrepancy in the measured muon anomalous magnetic moment a µ with respect to the SM prediction [30]. Several searches of the U boson have been performed in recent years with negative results, setting upper limits to ǫ: A1 [31, 32], APEX [33], WASA [34], HADES [35], KLOE [36, 37], BaBar [38]. Since the U boson needs to be massive, one can implement, in close analogy with the SM, a spontaneous breaking mechanism of the U(1) symmetry, thus S ′ introducing a Higgs-like particle, h or dark Higgs, whose mass hierarchy with the dark photon is not constrained by the theory [22]. TheUbosoncanbeproducedate+e− colliders viadifferent processes: e+e− Uγ , e+e− Uh′ (dark Higgsstrahlung) and in decays of vector particles→to pseudoscala→rs. In this work the Higgsstrahlung process e+e− Uh′ is studied, using data collected by the KLOE experiment at the e+e−→collider DAΦNE at the Frascati laboratory, both at a center of mass energy of 1019 MeV, ∼ the mass of the φ meson (on-peak sample), and at a center of mass energy of 1000 MeV (off-peak sample). The process e+e− Uh′, with U decaying i∼nto lepton or hadron pairs, is an interesting reaction→to be studied at an e+e− collider, being less suppressed, in terms of the mixing parameter, than the otherfinalstateslistedabove.Therearetwoverydifferent scenariosdepending onthemasses ofthedarkphotonmU andofthedarkHiggsbosonmh′. Formh′ larger than 2m , the dark Higgs boson would decay dominantly and promptly U to a U boson pair, thus giving rise to a six charged particle final state (the scenario with mh′ larger than mU but smaller than 2mU is similar, with one dark photon off shell): this case was recently investigated by the BaBar [39] 3 and Belle [40] experiments. On the other side, Higgs bosons lighter than the dark photon would have, in most of the parameter space region, such a large lifetime to escape detection, showing up as a missing energy signature. We confined the search only to the latter case, mh′ < mU, the so called “invisible” dark Higgs scenario. The lifetime of the dark Higgs boson depends on the kinetic mixing parameter ǫ, the boson masses mh′ and mU and the dark coupling constant αD [22]. For boson masses of the order of 100 MeV and α = α , the dark Higgs boson D em lifetime would be 5µs for ǫ 10−3, corresponding, for the energy range ∼ ∼ explored in this analysis, to a decay length of 100 m. The dark Higgs boson would be thus invisible up to ǫ 10−2 10−1∼, depending on the h′ mass. ∼ ÷ In this work the search is limited to the decay of the U boson in a muon pair: the final state signature is then a pair of opposite charge muons plus missing energy. The measurement is thus performed in the range 2m < m < 1000 µ U MeV with the constraint mh′ < mU. The production cross section of the dark Higgsstrahlung process is propor- tional to the product α ǫ2 and depends on the boson masses [22]. Values as D × high as hundreds of fb are reachable in this model. Compared to the B-factory case [39, 40], KLOE benefits of the 1/s factor and of the resonance-like be- haviour expected for the production cross section [22]. The branching ratio of the U boson into muon pairs is predicted to be just below the 50% level for masses slightly above the kinematical threshold m = 2m , then to decrease U µ uptoaminimumaround5%,formasses correspondingtotheρresonance(due to the concurrent decay into hadrons), and then to increase to 30 40% up ∼ ÷ to m 1 GeV [22]. U ≃ 2 The KLOE Detector DAΦNE, the Frascati φ-factory, is an e+e− collider working at the center of mass energy, √s m = 1.0195 GeV [41]. Positron and electron beams col- φ ∼ lide at an angle of π 25 mrad, producing φ mesons nearly at rest. The KLOE − detector is made up of a large cylindrical drift chamber (DC) [42], surrounded by a lead scintillating fiber electromagnetic calorimeter (EMC) [43]. A super- conducting coil around the EMC provides a 0.52 T magnetic field along the axis of the colliding beams. The EMC consists of barrel and end-cap modules covering 98% of the solid angle. The calorimeter modules are segmented into five layers in depth and read out at both ends by 4880 photomultipliers. Energy and time resolutions are σ /E = 0.057/ E(GeV) and σ = 57ps / E(GeV) 100ps, respec- E q t q ⊕ 4 tively. The drift chamber, with only stereo sense wires, 4 m in diameter and 3.3 m long, has a mechanical structure in carbon-fiber and operates with a low-mass gas mixture (90% helium, 10% isobutane). The spatial resolutions are σ 150µm and σ 2 mm. The momentum resolution for large angle xy z ∼ ∼ tracks isσp⊥/p⊥ ≈ 0.4%. The trigger[44] uses bothEMC andDCinformation. Data are then analysed by an event classification filter [45] , which selects and streams various categories of events in different output files. 3 Event selection The analysis of the process e+e− Uh′ , U µ+µ−, h′ invisible (e+e− Uh′in the following), has been per→formed on a→data sample of 1.65 fb−1 co→l- lected at a center of mass energy of 1019 MeV, corresponding to the mass ∼ of the φ meson (on-peak sample in the following), and on a data sample of 0.206 fb−1 at a center of mass energy of 1000 MeV (off-peak sample in the ∼ following), well below the φ resonance. s t i n u y 104 r a r t i b r a 3 10 -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 cosθ Fig. 1. Distribution of the polar angle of the muon pair momentum for the signal e+e− Uh′ (black line) and for e+e− µ+µ−γ (red line). Here the two processes → → are not normalised and are shown only in order to compare the shapes of the dis- tributions. All the generated samples at various mU and mh′ are included in the signal distribution. The Monte Carlo simulation of the signal process e+e− Uh′has been pro- → duced using an ad hoc generator interfaced with the standard KLOE simula- 5 tion program [45]. Signal samples have been generated for various pairs of mh′ - m values along a grid with steps of 30 MeV to cover all the allowed kine- U ∼ matic region. The invariant mass resolution varies between 0.5 and 2 MeV for the muon pair (M ), and between 3 and 17 MeV for the event missing mass µµ (M ). The signal process signature would thus be the appearance of a sharp miss peak in the bidimensional distribution M - M . Moreover, the distribu- µµ miss tion of the polar angle direction of the muon pair momentum, θ, contrarily to most of the dominant background processes, is expected to prefer large angles. The differential cross section has two dominant terms proportional to sinθ and sin3θ [22], with relative weights smoothly dependent on the boson masses. This angular distribution allows to reject most of the background of QED processes with a simple geometrical selection and implies that the miss- ing momentum direction preferably points to a very well equipped region of the KLOE detector, where the best efficiency is achieved. Fig.1 shows the distributions of the muon pair polar angle direction for the signal e+e− Uh′ (black line) and the e+e− µ+µ−γ background (red line), where a→ll the → generated samples at various mU and mh′ masses are included in the signal sample. As a first step of the analysis, a preselection was performed by requiring: events with only two opposite charge tracks with associated EMC clusters, • with polar angles cosθ < 0.8 and momenta below 460 MeV, that form a 1,2 | | reconstructed vertex inside a cylinder of 30 cm length, 4 cm radius, centered at the interaction point (IP); the sum of the momenta of the two tracks to be greater than 450 MeV; • the polar angle of the dimuon momentum to be in the barrel acceptance: • cosθ < 0.75; | | the modulus of the missing momentum to exceed 40 MeV. • After this selection, mostly aimed at rejecting backgrounds from QED pro- cesses, the hermeticity and tightness of the electromagnetic calorimeter was used as a veto to avoid the presence of photons in the event by requiring no prompt EMC clusters unassociated to tracks. The calorimeter veto inef- ficiency as a function of the energy was studied with a sample of radiative Bhabha scattering events e+e− e+e−γ and found to range between 10% at → 20 Mev and 0.1% at about 200 MeV. The event selection then proceeded by applying a particle identification (PID) algorithm to the two tracks, based on the excellent energy and time resolution of the EMC. A set of feed-forward neural networks, organised for different values of track momentum and track polar angle, was trained on simulated Monte Carlo samples to perform muon to electron discrimination. The neural networks used five input variables (cluster time, energy to momentum ratio and three variables related to energy depositions in calorimeter layers) and 6 produces one output. The PID performances were checked on selected data samples of e+e− e+e− , e+e− µ+µ−, e+e− π+π−: the fraction of → → → events where both tracks were identified as muons was measured to be 85% in e+e− µ+µ− events, 10−4 in e+e− e+e− events and 50% in e+e− π+π− ev→ents (showers produced by muo→ns or pions have sim∼ilar properties→at low energies). AftermissingenergyandPIDselections, alargebackgroundfromφ K+K−, ± ± → K µ ν events survived in the on-peak sample. This happens when both → kaons decay semileptonically close to the IP. Charged kaons have an average decay length of 90 cm in KLOE. The reconstructed vertex of the muon ∼ tracks is thus expected to be displaced from the IP and with a bad fit quality. Cuts on the radial and z projections of the distance between the reconstructed vertex and the IP and on the χ2 of the fit allowed to reduce by a factor 80 the φ K+K−, K± µ±ν background, lowering the signal efficiency b∼y → → ∼ 65%. Events surviving all the described selections were organized in bidimensional histograms with the muon pair mass M and the event missing mass M µµ miss on the two axes. The binning was chosen to keep most of the signal inside a single bin. For M a 5 MeV bin width was enough over all the plane; while for µµ M a variable binning of 15, 30 and 50 MeV widths was chosen. According miss to the simulation, a fraction of 90 95% of the signal was contained in one ÷ single bin. The signature of the process would thus be the appearance of an excess in a single bin in the M -M plane over the background. The signal µµ miss selection efficiency, estimated from Monte Carlo on the generated points of the mU-mh′ grid, was found to be between 15% and 25%, depending on the masses, with most frequent values of 20%. The efficiency for a generic point ∼ on the M -M plane was then evaluated by linear interpolation. µµ miss 4 Results After all the described selections, 15278 events survived in the on-peak sample (fig.2, left plot) and 783 in the off-peak sample (fig.2, right plot). In the left plot of fig.2 (on-peak sample) several sources of backgrounds can be distin- guished: φ K+K−, K± µ±ν (quadrangular region at the left of the populated • → → part of the distribution); φ π+π−π0 (quasi-horizontal band, corresponding to events in which both • → photons from the π0 decay are undetected), partly intersecting the φ K+K−, K± µ±ν region; → e+e− µ+µ→− and e+e− π+π− events in the continuum (diagonal and • → → 7 horizontal bands starting from the right-bottom part of the distribution); e+e− e+e−µ+µ− and e+e− e+e−π+π− (photon-photon interactions, • → → ± top triangular part of the distribution, for M > 350 MeV), with e in miss the final state being scattered at very small angles in the beam pipe. In the distribution in the right plot of fig.2 (off-peak sample) all the back- grounds from the φ decays are strongly suppressed and only those in the continuum remain visible. V) V) e e M M (miss400 (miss400 M M 200 200 0 0 100 200 300 400 500 600 700 800 9001000 200 400 600 800 1000 M (MeV) M (MeV) µµ µµ Fig. 2. Results for on-peak sample (left plot, 1.65 fb−1 integrated luminosity) and off-peak sample (right plot, 0.206 fb−1 integrated luminosity). Monte Carlo generators fully interfaced with the KLOE detector simulation program were available for all the background processes but for the e+e− e+e−µ+µ− and e+e− e+e−π+π−. For these two processes the Courau ge→n- → erator program [46] was used and the results smeared to keep into account the detector effects. As most of the signal is expected to populate a single bin of the mass dis- tributions, a 5 5 bin matrix in the M -M plane was built and moved µµ miss × sliding all along the distributions of fig.2 both on data and Monte Carlo. The presence of a possible signal was checked by using the central bin, while the others were used for background evaluation. This was done by computing a data-Monte Carlo scale factor k based on the sum of the contents of the 24 bins surrounding the central one in data (DT ) and Monte Carlo (MC ): 24 24 k = DT24 . The prediction for the background in the central bin is then simply MC24 defined as the product of the central bin content in Monte Carlo rescaled by k. The usage of the described scaling procedure allowed to reduce the systematic uncertainties due to the background evaluation (see sec. 5). Fig.3 shows the data-Monte Carlo comparison after the scaling correction for the on-peak and off-peak samples, projected along the M and M axes, together with the µµ miss individual contributions of the different background processes. The agreement 8 s s2000 e e ntri200 ntri E E 1500 150 1000 100 500 50 0 0 100 200 300 400 500 600 700 800 9001000 0 100 200 300 400 500 M (MeV) M (MeV) µµ miss s s e e Entri 40 Data Entri MC total K+K- π+π-π0 100 30 π+π- µ+µ- eeµµ(ππ) 20 50 10 0 0 0 100 200 300 400 500 600 700 800 9001000 0 100 200 300 400 500 M (MeV) M (MeV) µµ miss Fig. 3. Data - Monte Carlo comparison for the on-peak sample (top plots) and off-peak sample (bottom plots). Projections along the M axis (left plots); projec- µµ tions along the M axis (right plots). Also shown are the various contributing miss backgrounds. is satisfactory all over the populated regions of the distributions. 5 Systematic errors Systematic uncertainties affect the signal efficiency evaluation and the back- ground estimate. Several sources of systematic uncertainties in the signal effi- ciency evaluation from Monte Carlo were taken into account. Uncertainties from the PID procedure were estimated by selecting samples of e+e− µ+µ−γ in data and Monte Carlo, applying the PID algorithms to → one of the two tracks to increase the purity of the selection and studying on the opposite track the data-Monte Carlo differences of the PID efficiency as 9 a function of the track momentum. The total effect, defined as the average product of individual effects on the single tracks, was found to vary between 2% and 3%, depending on the boson masses. A similar procedure was applied to evaluate the correction factors and systematic uncertainties of the PID algorithms for pion identification, which affect the background evaluation. The same e+e− µ+µ−γ samples selected in data and in the simulation were → used to evaluate the effect of the cut on the vertex-IP distance. A correction to the Monte Carlo signal efficiencies of the order of 15%, weakly dependent on cosθ, was derived and applied. An associated systematic error of 0.5% was estimated and added on the signal efficiency evaluation. The systematic uncertainty due to the usage of the EMC veto was evaluated by selecting samples of φ K+K−, K± µ±ν in data and Monte Carlo. → → In this case, the cut on the vertex-IP distance was slightly relaxed, in order to increase the size of the sample. A 2% data-Monte Carlo difference was observed and used both to correct the Monte Carlo efficiency and to quote a systematic uncertainty due to this source. Thesystematicuncertainty duetothekinematical preselections oftheanalysis wasestimated byvarying trackanglesandmomenta withintheir measurement errors by one standard deviation: a 1% effect was ascribed to this source. The systematic uncertainty due to the binning choice was estimated by eval- uating in the simulation the binomial statistical error on the fraction of the signal contained in one bin. This turned out to be of the order of 0.3%, on average. Finally, an average 1% uncertainty was estimated due to the linear inter- ∼ polation procedure in the signal efficiency evaluation process. The total systematic uncertainty onthe signal efficiency was then evaluated as the quadratic sum of all the above effects. It never exceeded 4%, with an av- erage value of 3.5%, very small when compared to the statistical uncertainties affecting this measurement. Most of the systematic uncertainties in the background evaluation cancel in the scale factor ratio k. All the systematic sources considered for the signal efficiency evaluation, but those related to the linear interpolation procedure, weretakenintoaccountandtheireffectonthebackgroundestimatecomputed. Additional effects were taken into account. The uncertainties on the back- ground process cross sections were varied within their theoretical and mea- surement errors; a further 1% uncertainty was added for those related to the photon-photon final states, for which no full simulation was available; the uncertainty on the integrated luminosity was estimated to be 0.3%. 10