Search for Light Gauge Bosons of the Dark Sector at the Mainz Microtron
H. Merkel, P. Achenbach, C. Ayerbe Gayoso, J. C. Bernauer, R. Böhm, D. Bosnar, L. Debenjak, A. Denig, M. O. Distler, A. Esser, H. Fonvieille, I. Friščić, D. G. Middleton, U. Müller, L. Nungesser, J. Pochodzalla, M. Rohrbeck, S. Sánchez Majos, B. S. Schlimme, M. Schoth, S. Širca, M. Weinriefer
aa r X i v : . [ nu c l - e x ] J un Search for light gauge bosons of the dark sector at MAMI
H. Merkel, ∗ P. Achenbach, C. Ayerbe Gayoso, J. C. Bernauer, † R. B¨ohm, D. Bosnar, L. Debenjak, A. Denig, M. O. Distler, A. Esser, H. Fonvieille, I. Friˇsˇci´c, D. G. Middleton, U. M¨uller, L. Nungesser, J. Pochodzalla, M. Rohrbeck, S. S´anchez Majos, B. S. Schlimme, M. Schoth, S. ˇSirca,
3, 5 and M. Weinriefer (A1 Collaboration) Institut f¨ur Kernphysik, Johannes Gutenberg-Universit¨at Mainz, D-55099 Mainz, Germany ‡ Department of Physics, University of Zagreb, HR-10002 Zagreb, Croatia Joˇzef Stefan Institute, SI-1000 Ljubljana, Slovenia Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, LPC, BP 10448, F-63000 Clermont-Ferrand, France Department of Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia (Dated: January 21, 2011)A new exclusion limit for the electromagnetic production of a light U (1) gauge boson γ ′ decaying to e + e − was determined by the A1 Collaboration at the Mainz Microtron. Such light gauge bosons appear in severalextensions of the standard model and are also discussed as candidates for the interaction of dark matter withstandard model matter. In electron scattering from a heavy nucleus, the existing limits for a narrow state couplingto e + e − were reduced by nearly an order of magnitude in the range of the lepton pair mass of
210 MeV /c 300 MeV /c . This experiment demonstrates the potential of high current and high resolution fixedtarget experiments for the search for physics beyond the standard model. PACS numbers: 14.70.Pw, 25.30.Rw, 95.35.+d Introduction.— An additional U (1) interaction appears tobe natural in nearly all theoretical extensions of the standardmodel. Large gauge symmetries have to be broken and U (1) bosons provide the lowest-rank local symmetries. For exam-ple, in standard embedding of most variants of string theoriesa U (1) boson is generated by symmetry breaking. Such ad-ditional U (1) bosons may be hidden; e.g., no standard modelparticles are charged under the corresponding symmetry, buttheir mass is allowed in the range of the standard modelmasses.Recently, several experimental anomalies were discussedas possible signatures for a hidden force. A light U (1 ) bo-son in the mass range below /c might explain e.g. theobserved anomaly of the muon magnetic moment [1, 2]. Cos-mology and astrophysics provide an abundant amount of ev-idence for the existence of dark matter (for a summary, see,e.g., Ref. [3]). Several experimental hints point to a U (1) bo-son coupling to leptons as the mediator of the interaction ofdark matter with standard model matter (see, e.g. , Ref. [4] fora detailed discussion). For example the lively debated annualmodulation signal of the DAMA-LIBRA experiment [5] couldbe brought into accordance with the null result of bolometricexperiments if one assumes an interaction via a light U (1) bo-son [6]. Observations of cosmic rays show a positron excess[7]. While this excess may be due to astrophysical processlike quasars, this could also be a hint for the annihilation ofdark matter into leptons. If the experimental evidence is inter-preted as annihilation of dark matter, the excess of positronsand no excess of antiprotons in cosmic rays hints again to amass of the U (1) boson below /c .The interaction strength of such a U (1) boson (in the fol-lowing denoted as γ ′ , in the literature also denoted as A ′ , U ,or φ ) with standard model particles is governed by the mech-anism of kinetic mixing [8]. The coupling can be subsumed by an effective coupling constant ǫ and a vertex structure of amassive photon.Bjorken et al. [9] discussed several possible experimentalschemes for the search of a γ ′ in the most likely mass rangeof a few MeV /c up to a few GeV /c . Since the couplingis small, the cross section for coherent electro magnetic pro-duction of the γ ′ boson can be enhanced by a factor Z bychoosing a heavy nucleus as the target (see Fig. 1). The sub-sequent decay of the γ ′ boson to a lepton pair is the signatureof the reaction.The cross section of signal and background were estimatedin Ref. [9] in the Weizs¨acker-Williams approximation. In thisapproximation, the cross section shows a sharp peak, in bothsignal and background, where nearly all the energy of the in-cident electron is transferred to the lepton pair ( E e + + E e − ) = E . Correspondingly, the pair is produced dominantly in thedirection of the incident electron.The experimental challenge is the suppression of the back-ground which is dominated by radiative pair production(Fig. 2). Radiation by the final or initial electron [Figs. 2(a)and 2(b)] has the same cross-section structure as the desiredsignal and is an irreducible background to this experiment. γ'Ze − e − Z Ze − e − Z (a) (b) γ' FIG. 1. Electromagnetic production of the γ ′ boson. The couplingof the γ ′ boson is parametrized as i ǫ e γ µ . TABLE I. Kinematic settings. The incident beam energy was E = 855 MeV , and the settings areroughly centered around E e + + E e − = E and m γ ′ = 250 MeV /c .Spec. A ( e + ) Spec. B ( e − ) p (MeV) θ d Ω (msr) p (MeV) θ d Ω (msr) EventsSet-up 1 346.3 . ◦ 21 507.9 . ◦ × Set-up 2 338.0 . ◦ 21 469.9 . ◦ × ll + Ze − − e − Z ll + Ze − − e − Zll + Ze − − e − Z ll − Ze − + e − Z (a) (b) (c) (d) FIG. 2. Dominant background processes. While graphs (a) and (b)have the same structure as the signal and present an irreducible back-ground, the contributions of graphs (c) and (d) can be suppressed bythe choice of kinematic setting. Radiation with an internal lepton line [Figs. 2(c) and 2(d)]has a maximum if the internal electron line is nearly on themass shell, i.e., if one of the leptons carries nearly all the en-ergy of the pair. This background can be reduced by choosinga kinematic setting in which the electron and positron are de-tected at equal angles and momenta. Experiment.— The experiment took place at the spectrom-eter setup of the A1 Collaboration at the Mainz Microtron(MAMI) (see Ref. [10] for a detailed description). An unpo-larized electron beam with a beam energy of E = 855 MeV and a beam current of µ A was incident on a tantalum foil(99.9% Ta, Z = 73 ) with an area density of . / cm ,leading to a luminosity of L Z = 8 . · s − cm − . Thebeam was rastered across the target to reduce the local thermalload on the target foil.For the detection of the electron-positron pair, two high-resolution spectrometers were used. The particles were de-tected by vertical drift chambers for tracking and scintilla-tor detectors for trigger and timing purpose. In addition, athreshold-gas- ˇCerenkov detector was used in each arm to dis-criminate between electrons or positrons and pions.Table summarizes the kinematic setups used. Setup 1 waschosen to be close to E e + + E e − = E where the cross sectionhas a sharp peak to ensure high count rates. In addition, setup2 was selected at E e + + E e − = 0 . E during the experiment −30 −20 −10 0 10 20 30 40 0 5 10 15 20 E v en t s / . n s T A ∧ B [ns] FIG. 3. Coincidence time distribution after particle identification byˇCerenkov detectors (set-up 1). The events of the light shaded areawere used as true coincidences, while the dark shaded area was usedas an estimate of the accidental coincidences. 200 250 300 050010001500200025003000 E v en t s / . M e V m e+e− [MeV/c ] FIG. 4. Mass distribution of the reconstructed e + - e − pair (setup1). The dark shaded area denotes the background due to accidentalcoincidences (scaled to a time window of 2 ns). to optimize the total count rates. The angles of the spectrome-ters were set to be nearly symmetric to reduce the backgroundby the Bethe-Heitler process [Figs. 2(c) and 2(d)]. In total,data of four days of beam time were used for the analysis. Theelectrons and the positrons were detected by the coincidenceof the raw scintillator signals. The ˇCerenkov signals were notincluded in the trigger logic but recorded for off-line analysis. 200 250 300−200−100 0 100 200 300 E v en t s / . M e V m e+e− [MeV/c ] CL = 90% (Average of 10 Bins)CL = 90% FIG. 5. Upper exclusion limits with 90% confidence level determined by the Feldman-Cousins algorithm (all data). The averaged limit isincluded for subjective judgement only ( ≈ of the data points should be above this line at 90% C.L.). Data analysis.— Only events with a positive signal in theˇCerenkov detectors were selected with an efficiency of 98%for spectrometer A and 95% for spectrometer B [10]. Fig-ure 3 shows the coincidence time between the correspondingspectrometers after correction for the flight path of ≈ 12 m within the spectrometers for these events. A timing resolu-tion of better than 1 ns FWHM was achieved, and a cut of − < t A ∧ B < was used to mark the true electron-positron pairs. Below the peak, a background due to acci-dental coincidences is present. To estimate this background,events in the coincidence side band < t A ∧ B < 25 ns were selected and weighted by the ratio of the timing win-dows.For the real electron-positron pairs the invariant masssquared of the pair was determined by the four-momentumsum m e + e − = ( p e + + p e − ) . Figure 4 shows the resultingmass spectrum. The contribution of the accidental backgroundis indicated by the dark shaded area.In this figure, a possible candidate for the dark photonwould appear as a peak on top of the background. The widthof such a peak can only be estimated by simulation. For this,the experimental resolution of the four-vector determinationof a single spectrometer was determined by the width of thelowest lines of the nuclear excitation spectrum in elastic elec-tron scattering. This single spectrometer resolution was usedas input for the simulation of the experiment. A mass resolu-tion of better than . /c was determined, correspond-ing to the chosen bin width in Fig. 4.No significant peak in the mass spectrum was observed.The corresponding upper limit was determined by theFeldman-Cousins algorithm [11]. As input for this algorithmthe raw mass spectrum was used, and as a background esti-mate for each bin the mean of the three neighboring bins oneither side was used. This choice of the background estimateintroduces systematic errors, which have to be investigated inthe case of a positive signal but only enhance statistical fluc- E v en t s (E e+ +E e− )/E Model: e+ Ta → e’+ Ta+2eWeizsäcker−Williams • Data| FIG. 6. Comparison of simulation with data (setup 1). As a modelthe coherent electro-production from a heavy nucleus was used. tuations in the case of an upper limit. Figure 5 shows theresulting exclusion limits. Results and Interpretation.— In order to interpret the re-sult in terms of the effective coupling ǫ of a possible darkphoton candidate, a model for the production process hasto be used. Unfortunately, it turns out that the Weizs¨acker-Williams-approximation used in Ref. [9] fails in this energyrange by orders of magnitude, mainly since the recoil of thenucleus cannot be neglected. Taking into account the nuclearrecoil, the peak at ( E e + + E e − ) = E in Ref. [9] is regularizedand the cross section at this point becomes zero. In addition,the assumption of a real initial photon exactly in the directionof the electron beam introduces a peak in the angular distribu-tion, which is not present in electro production due to helicityconservation of the scattered electron.Instead, we used as a model for the γ ′ production the coher-ent electro production from the tantalum nucleus, calculated 100 200 300 400 50010 −7 −6 −5 −4 α ’ / α m γ ’ [MeV/c ] a µ MAMI/A1 BaBare + e − → γ µ + µ − FIG. 7. Exclusion limits with 90% confidence level in terms of rel-ative coupling α ′ /α = ǫ . Also shown are the previous results by BABAR [12] and for a µ of the muon [2]. as the coherent sum of the graphs of Fig. 1. The charge dis-tribution of tantalum was approximated as a solid sphere. Forthe QED background we used the coherent sum of the graphsof Fig. 2. The corresponding cross sections were includedon an event by event basis in the simulation. The simulationincluding this model shows excellent agreement with data,as demonstrated in Fig. 6, where the background-subtractedyields as an estimate for the QED background graphs are com-pared to the simulation of this process.The remaining model dependence of this interpretationmainly affects the nuclear vertex, since, e.g., the possiblebreakup of the recoil nucleus is neglected. Since this vertexis common to both the signal and the QED background chan-nels, to further reduce the model dependence we use only theratio of the signal to QED background of the simulation inaddition to the accidental background. The ratio can be trans-lated to the effective coupling for a given mass resolution δ m by using Eq. (19) of Ref. [9]: dσ ( X → γ ′ Y → e + e − Y ) dσ ( X → γ ∗ Y → e + e − Y ) = 3 π N f ǫ α m γ ′ δ m and the measured event rate as an estimate for the background channel. The number of final states N f includes the ratio ofphase space for the corresponding decays above the µ + µ − threshold.Figure 7 shows the result of this experiment in terms of theratio of the effective coupling to the fine structure constant α ′ /α = ǫ . For clarity of the figure, the exclusion limit wasaveraged. Also shown are the existing limits published byBaBar [12] and the standard model prediction [2] of the muonanomalous magnetic moment a µ = g µ / − (calculation ofexclusion limits in ǫ by [13]). The existing exclusion limithas been extended by an order of magnitude.In this experiment, the discovery potential of the existinghigh luminosity electron accelerators has been demonstrated.The background conditions are well under control due to ex-cellent timing and missing mass resolution. An extensive pro-gram to cover further mass regions with similar experimentsis planned at MAMI, Jefferson Lab[13], and other laboratories(for a review see Ref. [14]).The authors thank the MAMI accelerator group for provid-ing the excellent beam quality and intensity necessary for thisexperiment and T. Beranek for fruitful discussions on the QEDcalculations. 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