Search for Invisible Decays of a Dark Photon Produced in e+e- Collisions at BaBar

TL;DR

This study searches for invisible decays of dark photons in electron-positron collisions using BaBar data, setting upper limits on their coupling strength and excluding certain dark-sector model parameters.

Contribution

First search for invisible dark photon decays in e+e- collisions at BaBar, providing new constraints on dark photon properties and dark matter models.

Findings

No evidence for dark photon production was observed.

Set 90% confidence level upper limits on the coupling strength of dark photons.

Excluded dark photon parameters suggested by the muon g-2 anomaly.

Abstract

We search for single-photon events in 53 fb^-1 of e+e- collision data collected with the BaBar detector at the PEP-II B-factory. We look for events with a single high-energy photon and a large missing momentum and energy, consistent with production of a spin-1 particle A' through the process e+e->gamma A', A'->invisible. Such particles, referred to as "dark photons", are motivated by theories applying a U(1) gauge symmetry to dark matter. We find no evidence for such processes and set 90% confidence level upper limits on the coupling strength of A' to e+e- in the mass range m_A'<=8 GeV. In particular, our limits exclude the values of the A' coupling suggested by the dark-photon interpretation of the muon (g-2) anomaly, as well as a broad range of parameters for the dark-sector models.

Tables

Table 1. Table 1: Datasets and event selections used in this paper. The characteristic energies of each dataset are listed in rows; the event selections described in the text in columns. The table entries list the integrated luminosity and the numbers of events selected by each dataset.

Dataset	“lowM”				“highM”
Dataset	$ℒ$	Selection			$ℒ$	Selection
		${ℛ}_B$	${ℛ}_L^{{}^{\prime }}$	${ℛ}_T$		${ℛ}_B$	${ℛ}_L$
${\rm Y}\left(2S\right)$	$15.9{\text{ fb}}^{-1}$	$22,590$	$42$	$6$	$15.9{\text{ fb}}^{-1}$	$405,441$	$324$
${\rm Y}\left(3S\right)$	$31.2{\text{ fb}}^{-1}$	$68,476$	$129$	$26$	$22.3{\text{ fb}}^{-1}$	$719,623$	$696$
${\rm Y}\left(4S\right)$	$5.9{\text{ fb}}^{-1}$	$7,893$	$16$	$9$

Full text

The nature of dark matter is one of the greatest mysteries of modern physics. It is transparent to electromagnetic radiation and we have only been able to infer its existence through gravitational effects. Since terrestrial searches for dark matter interactions have so far yielded null results, it is postulated to interact very weakly with ordinary matter. Recently, models attempting to explain certain astrophysical observations ref:INTEGRAL ; ref:PAMELA ; ref:FERMI ; Berezhiani:2013dea as well as the muon $(g-2)_{\mu}$ anomaly ref:g-2 have introduced an appealing idea of a low-mass spin-1 particle, referred to as $A^{\prime}$ or $U$, that would possess a gauge coupling of electroweak strength to dark matter, but with a much smaller coupling to the Standard Model (SM) hypercharge ref:Aprimerefs ; Essig:2013lka . Such a boson may be associated with a $U(1)$ gauge symmetry in the dark sector and kinetically mix with the SM photon with a mixing strength $\varepsilon\ll 1$; hence the name “dark photon”. Values as high as $\varepsilon\sim 10^{-3}$ and masses in a GeV range have been predicted in the literature ref:Aprimerefs ; Essig:2013lka .

The decay modes of the dark photon depend on its mass and couplings, as well as on the particle spectrum of the dark sector. If the lowest-mass dark matter state $\chi$ is sufficiently light: $m_{\chi}<m_{A^{\prime}}/2$, then the dominant decay mode of the $A^{\prime}$ is invisible: $A^{\prime}\rightarrow\chi{\overline{\chi}}$. The cleanest collider signature of such particles is the production of monochromatic single photons in $e^{+}e^{-}\rightarrow\gamma A^{\prime}$, accompanied by significant missing energy and momentum. The photon energy $E_{\gamma}^{*}$ in the $e^{+}e^{-}$ center-of-mass (CM) is related to the missing mass $M_{X}$ through $M_{X}^{2}=s-2E_{\gamma}^{*}\sqrt{s}$, where $s$ is the square of the CM energy, and the asterisk hereafter denotes a CM quantity. We seek a signal of the dark photon $A^{\prime}$ as a narrow peak in the distribution of $M_{X}^{2}$ in events with a single high-energy photon. As expected for the dark matter coupling $\alpha_{D}<1$ Essig:2013lka , we assume that the decay width of the $A^{\prime}$ is negligible compared to the experimental resolution, and that the $A^{\prime}$ decays predominantly to dark matter (i.e. the invisible branching fraction is $\approx 100\%$). Furthermore, we assume that a single $A^{\prime}$ state exists in the range $0<m_{A^{\prime}}\leq 8$ GeV; or if two or more states are present, they do not interfere.

The current best limits on the mixing strength $\varepsilon$ of the dark photon are from searches for narrow peaks in the $e^{+}e^{-}$ or $\mu^{+}\mu^{-}$ invariant mass spectra BaBarDM ; KLOE ; NA48 ; WASA ; HADES ; A1 ; APEX and from beam-dump and neutrino experiments Blumlein:2013cua ; Andreas:2012mt . These limits assume that the dominant decays of the $A^{\prime}$ are to the visible SM particles, but are not valid if there are low-mass invisible degrees of freedom. There are constraints on invisible decays of the $A^{\prime}$ from kaon decays Pospelov ; E787 ; E949 and from the recent search for missing energy events in electron-nucleus scattering NA64 .

We search for the process $e^{+}e^{-}\rightarrow\gamma A^{\prime}$, followed by invisible decays of the $A^{\prime}$ in a $53$ fb*-1* dataset Lumi collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}e^{-}$ collider at the SLAC National Accelerator Laboratory. The data were collected in 2007–2008 with CM energies near the $\mathchar 28935\relax(2S)$, $\mathchar 28935\relax(3S)$, and $\mathchar 28935\relax(4S)$ resonances with a special “single photon” trigger described below. The $e^{+}e^{-}$ CM frame was boosted relative to the detector approximately along the detector’s magnetic field axis by $\beta_{z}\approx 0.5$. Since the production of the $A^{\prime}$ is not expected to be enhanced by the presence of the $\mathchar 28935\relax$ resonances, we combine the datasets collected in the vicinity of each $\mathchar 28935\relax$ resonance. In order to properly account for acceptance effects and changes in the cross section as a function of $\sqrt{s}$, we measure the signal event yields separately for the $\mathchar 28935\relax{(2S)}$, $\mathchar 28935\relax{(3S)}$, and $\mathchar 28935\relax{(4S)}$ datasets.

Since the BABAR detector is described in detail elsewhere detector , only the components of the detector crucial to this analysis are summarized below. Charged particle tracking is provided by a five-layer double-sided silicon vertex tracker (SVT) and a 40-layer drift chamber (DCH). Photons and neutral pions are identified and measured using the electromagnetic calorimeter (EMC), which comprises 6580 thallium-doped CsI crystals. These systems are mounted inside a 1.5 T solenoidal superconducting magnet. The Instrumented Flux Return (IFR) forms the return yoke of the superconducting coil, instrumented in the central barrel region with limited streamer tubes for the identification of muons and the detection of clusters produced by neutral hadrons. We use the Geant4 geant software to simulate interactions of particles traversing the BABAR detector, taking into account the varying detector conditions and beam backgrounds.

Detection of low-multiplicity single photon events requires dedicated trigger lines. Event processing and selection proceeds in three steps. First, the hardware-based Level-1 (L1) trigger accepts single-photon events if they contain at least one EMC cluster with energy above $800$ MeV (in the laboratory frame). Second, L1-accepted events are forwarded to a software-based Level-3 (L3) trigger, which forms DCH tracks and EMC clusters and makes decisions for a variety of physics signatures. Two single-photon L3 trigger lines were active during the data-taking period. The high-energy photon line (low $M_{X}$, “LowM” hereafter) requires an isolated EMC cluster with energy $E^{*}_{\gamma}>2$ GeV, and no tracks originating from the $e^{+}e^{-}$ interaction region (IR). The “LowM” dataset amounts to $5.9$ fb*-1* collected at the $\mathchar 28935\relax{(4S)}$ resonance ($\sqrt{s}=10.58$ GeV), $28.5$ fb*-1* collected at the $\mathchar 28935\relax{(3S)}$ resonance ($\sqrt{s}=10.36$ GeV), $2.7$ fb*-1* collected 30 MeV below the $\mathchar 28935\relax{(3S)}$, $14.4$ fb*-1* collected at the $\mathchar 28935\relax{(2S)}$ resonance ($\sqrt{s}=10.02$ GeV), and $1.5$ fb*-1* collected 30 MeV below the $\mathchar 28935\relax{(2S)}$ resonance. The total data sample collected with the “LowM” triggers is $53$ fb*-1*.

A low-energy (high $M_{X}$, “HighM”) L3 single-photon trigger, which requires an EMC cluster with energy $E^{*}_{\gamma}>1$ GeV and no tracks originating from the $e^{+}e^{-}$ interaction region, was active for a subset of the data: $20$ fb*-1* collected at the $\mathchar 28935\relax{(3S)}$ resonance as well as all of the data collected below $\mathchar 28935\relax{(3S)}$ and at the $\mathchar 28935\relax{(2S)}$ resonance. The total data sample collected with the “HighM” triggers is $35.9$ fb*-1*.

Additional offline software filters are applied to the stored data. We accept single-photon events if they satisfy one of the two following criteria. The “LowM” selection requires one EMC cluster in the event with $E^{*}_{\gamma}>3$ GeV and no DCH tracks with momentum $p^{*}>1$ GeV. The “HighM” selection requires one EMC cluster with the transverse profile consistent with an electromagnetic shower and $E^{*}_{\gamma}>1.5$ GeV, and no DCH tracks with momentum $p^{*}>0.1$ GeV. The two selection criteria are not mutually exclusive.

The trigger and reconstruction selections naturally split the dataset into two broad $M_{X}$ ranges. The “LowM” selections are used for the low $M_{X}$ region $-4<M_{X}^{2}<36~{}\mathrm{GeV}^{2}$. The backgrounds in this region are dominated by the QED process $e^{+}e^{-}\rightarrow\gamma\gamma$, especially near $M_{X}\approx 0$ ($E^{*}_{\gamma}\approx\sqrt{s}/2$). Due to the orientation of the EMC crystals, which point towards the IR, one of the photons may escape detection even if it is within the nominal EMC acceptance. The event selection is optimized to reduce this peaking background as much as possible. The “HighM” trigger selection defines the high $M_{X}$ range $24<M_{X}^{2}<69\ (63.5)~{}\mathrm{GeV}^{2}$ for the $\mathchar 28935\relax{(3S)}$ ($\mathchar 28935\relax{(2S)}$) dataset. This region is dominated by the low-angle radiative Bhabha events $e^{+}e^{-}\rightarrow e^{+}e^{-}\gamma$, in which both the electron and the positron escape the detector.

We suppress the SM backgrounds, which involve one or more particles that escape detection, by requiring that a candidate event be consistent with a single isolated photon shower in the EMC. We accept photons in the polar angle range $|\cos\theta^{*}_{\gamma}|<0.6$, rejecting radiative Bhabha events that strongly peak in the forward and backward directions, and we require that the event contain no charged particle tracks.

The signal events are further selected by a multivariate Boosted Decision Tree (BDT) discriminant TMVA , based on the following 12 discriminating variables. First, after a relatively coarse selection, we include the EMC variables that describe the shape of the electromagnetic shower: the difference between the number of crystals in the EMC cluster and the expectation for a single photon of given energy, and two transverse shower moments ref:LAT . Second, we include both the total excess EMC energy in the laboratory frame not associated with the highest-energy photon, and the CM energy and polar angle of the second most energetic EMC cluster. We also compute the azimuthal angle difference $\Delta\phi_{12}$ between the highest and second-highest energy EMC clusters; the $e^{+}e^{-}\rightarrow\gamma\gamma$ events with partial energy deposit in the EMC tend to peak at $\Delta\phi_{12}\sim\pi$. Third, a number of variables improve containment of the background events. We extrapolate the missing momentum vector to the EMC face, and compute the distance (in $(\theta,\phi)$ polar lab-frame coordinates) to the nearest crystal edge. This allows us to suppress $e^{+}e^{-}\rightarrow\gamma\gamma$ events where one of the photons penetrates the EMC between crystals leaving little detectable energy. Furthermore, we look for energy deposited in the IFR, and compute the correlation angle $\Delta\phi_{NH}$ between the primary photon and the IFR cluster closest to the missing momentum direction; $e^{+}e^{-}\rightarrow\gamma\gamma$ events produce a peak at $\cos\Delta\phi_{NH}\sim-1$. We also apply a fiducial selection to the azimuthal angle $\phi_{\mathrm{miss}}$ of the missing momentum by including $\cos(6\phi_{\mathrm{miss}})$ into the BDT. This accounts for uninstrumented regions between six IFR sectors detector . Finally, $\cos\theta^{*}_{\gamma}$ is included in the BDT to take advantage of the different angular distributions for signal and background events.

The BDT discriminants are trained separately in “LowM” and “HighM” regions. Each BDT is trained using $2.5\times 10^{4}$ simulated signal events with uniformly distributed $A^{\prime}$ masses, and $2.5\times 10^{4}$ background events from the $\mathchar 28935\relax{(3S)}$ on-peak sample that corresponds to approximately 3 $\mbox{\,fb}^{-1}$. We test the BDT, define the final selection, and measure the signal efficiency using sets of $2.5\times 10^{4}$ signal and background events statistically independent from the BDT training samples. The BDT score is designed so that the signal peaks near 1 while the background events are generally distributed between $-1<\mathrm{BDT}<0$.

The event selection is optimized to minimize the expected upper limit on the $e^{+}e^{-}\rightarrow\gamma A^{\prime}$ cross section $\sigma_{A^{\prime}}$. Since the number of peaking $e^{+}e^{-}\rightarrow\gamma\gamma$ events cannot be reliably estimated and has to be determined from the fit to the data, this background limits the sensitivity to $e^{+}e^{-}\rightarrow\gamma A^{\prime}$ at the low $A^{\prime}$ masses where the photon energies for the two types of events are indistinguishable. In this regime, we define a “tight” selection region $\mathcal{R}_{T}$ which maximizes the ratio $\varepsilon_{S}/N_{B}$ for large $N_{B}$, and $\varepsilon_{S}/2.3$ in the limit $N_{B}\rightarrow 0$, where $\varepsilon_{S}$ is the selection efficiency for the signal and $N_{B}$ is the number of background events expected in the full data sample. We also require $-0.4<\cos\theta^{*}_{\gamma}<0.6$ in order to suppress $e^{+}e^{-}\rightarrow\gamma\gamma$ events in which one of the photons would have missed the central region of the EMC.

A “loose” selection region $\mathcal{R}_{L}$ maximizes $\varepsilon_{S}/\sqrt{N_{B}}$. This selection is appropriate at higher $M_{X}$ where the background is well described by a featureless continuum distribution, and maximal $\varepsilon_{S}/\sqrt{N_{B}}$ corresponds to the lowest upper limit on the $e^{+}e^{-}\rightarrow\gamma A^{\prime}$ cross section.

Finally, a background region $\mathcal{R}_{B}$ is defined by $-0.5<\mathrm{BDT}<0$ and is used to determine the $M_{X}^{2}$ distribution of the background events. The selection criteria used in this analysis and the numbers of events selected in different datasets are summarized in Table 1.

We measure the cross section $\sigma_{A^{\prime}}$ as a function of the assumed mass $m_{A^{\prime}}$ by performing a series of unbinned extended maximum likelihood fits to the distribution of $M_{X}^{2}$. For each value of $m_{A^{\prime}}$, varied from 0 to $8.0$ GeV in 166 steps roughly equal to half of the mass resolution, we perform a set of simultaneous fits to $\mathchar 28935\relax{(2S)}$, $\mathchar 28935\relax{(3S)}$, and for the low-$M_{X}$ region, $\mathchar 28935\relax{(4S)}$ datasets. Moreover, we subdivide the data into broad event selection bins: $\mathcal{R}_{B}$ used to define the background probability density functions (PDFs), and signal regions $\mathcal{R}_{L}$ (used for $5.5<m_{A^{\prime}}\leq 8.0$ GeV), $\mathcal{R}_{T}$, and $\mathcal{R}_{L}^{{}^{\prime}}$ (used for $m_{A^{\prime}}\leq 5.5$ GeV). The region $\mathcal{R}_{L}^{{}^{\prime}}$ is defined to be the part of $\mathcal{R}_{L}$ not overlapping with $\mathcal{R}_{T}$. Thus, the simultaneous fits are performed to 9 independent samples for $m_{A^{\prime}}\leq 5.5$ GeV, and 4 independent samples for $5.5<m_{A^{\prime}}\leq 8.0$ GeV (missing mass spectra for all datasets are shown in EPAPS ).

For the fits to the $\mathcal{R}_{B}$ regions, we fix the number of signal events to zero, and determine the parameters of the background PDFs. In the fits to the $\mathcal{R}_{T}$ and $\mathcal{R}_{L}^{{}^{\prime}}$ regions, we fix the background PDF shape, and vary the number of background events $N_{B}$, the number of peaking background events $e^{+}e^{-}\rightarrow\gamma\gamma$ (for $m_{A^{\prime}}\leq 5.5$ GeV), and the $A^{\prime}$ mixing strength $\varepsilon^{2}$. The numbers of signal and background events are constrained: $\varepsilon^{2}\geq 0$ and $N_{B}>0$.

The signal PDF is described by a Crystal Ball ref:CBshape function centered around the expected value of $M_{X}^{2}=m_{A^{\prime}}^{2}$. We determine the PDF as a function of $m_{A^{\prime}}$ using high-statistics simulated samples of signal events, and we correct it for the difference between the photon energy resolution function in data and simulation using a high-statistics $e^{+}e^{-}\rightarrow\gamma\gamma$ sample in which one of the photons converts to an $e^{+}e^{-}$ pair in the detector material ref:bad2330 . The resolution for signal events decreases monotonically from $\sigma(M_{X}^{2})=1.5~{}\mathrm{GeV}^{2}$ for $m_{A^{\prime}}\approx 0$ to $\sigma(M_{X}^{2})=0.7~{}\mathrm{GeV}^{2}$ for $m_{A^{\prime}}=8$ GeV. The background PDF has two components: a peaking background from $e^{+}e^{-}\rightarrow\gamma\gamma$ events, described by a Crystal Ball function, and a smooth function of $M_{X}^{2}$ dominated by the $e^{+}e^{-}\rightarrow\gamma e^{+}e^{-}$ (second order polynomial for $m_{A^{\prime}}\leq 5.5$ and a sum of exponentiated polynomials for $5.5<m_{A^{\prime}}\leq 8.0$ GeV).

The signal selection efficiency varies slowly as a function of $m_{A^{\prime}}$ between 2.4-3.1% ($\mathcal{R}_{T}$ selection for $m_{A^{\prime}}\leq 5.5$ GeV), 3.4-3.8% ($\mathcal{R}_{L}^{{}^{\prime}}$ for $m_{A^{\prime}}\leq 5.5$ GeV), and $2.0-0.2\%$ ($\mathcal{R}_{L}$ selection for $5.5<m_{A^{\prime}}\leq 8.0$ GeV).

The largest systematic uncertainties in the signal yield are from the shape of the signal and background PDFs, and the uncertainties in the efficiency of signal and trigger selections. We determine the uncertainty in the signal PDF by comparing the data and simulated distributions of $e^{+}e^{-}\rightarrow\gamma\gamma$ events. We correct for the small observed differences, and use half of the correction as an estimate of the systematic uncertainty. We measure the trigger selection efficiency using single-photon $e^{+}e^{-}\rightarrow\gamma\gamma$ and $e^{+}e^{-}\rightarrow e^{+}e^{-}\gamma$ events that are selected from a sample of unbiased randomly accepted triggers. We find good agreement with the simulation estimates of the trigger efficiency, within the systematic uncertainty of $0.4\%$. We compare the input BDT observables in simulation and in a sample of the single-photon data events, counting the difference as a systematic uncertainty of the signal selection efficiency. The total multiplicative error on the signal cross section is $5\%$, and is small compared to the statistical uncertainty.

Figure 1 shows the maximum-likelihood estimators of the $A^{\prime}$ mixing strength $\varepsilon^{2}$ for the 166 $m_{A^{\prime}}$ hypotheses. The values of “local” significance of observation $\mathcal{S}\equiv\sqrt{2\ln(L_{\max}/L_{0})}$, where $L_{\max}$ is the maximum value of the likelihood, and $L_{0}$ is the value of the likelihood with the signal yield fixed to zero, are shown in Fig. 2. The most significant deviation of $\epsilon^{2}$ from zero occurs at $m_{A^{\prime}}=6.21$ GeV and corresponds to $\mathcal{S}=3.1$. Parametrized simulations determine that the probability to find such a deviation in any of the 166 $m_{A^{\prime}}$ points in the absence of any signal is $\approx 1\%$, corresponding to a “global” significance of $2.6\sigma$. A representative fit for $m_{A^{\prime}}=6.21$ GeV is shown in Fig. 3.

The 90% confidence level (CL) upper limits on $\varepsilon^{2}$ as a function of $m_{A^{\prime}}$ are shown in Fig. 4. We compute both the Bayesian limits with a uniform prior for $\varepsilon^{2}>0$ and the frequentist profile-likelihood limits ref:Rolke . Figure 5 compares our results to other limits on $\varepsilon$ in channels where $A^{\prime}$ is allowed to decay invisibly, as well as to the region of parameter space consistent with the $(g-2)_{\mu}$ anomaly ref:g-2 . At each value of $m_{A^{\prime}}$ we compute a limit on $\varepsilon$ as a square root of the Bayesian limit on $\varepsilon^{2}$ from Fig. 4. Our data rules out the dark-photon coupling as the explanation for the $(g-2)_{\mu}$ anomaly. Our limits place stringent constraints on dark-sector models over a broad range of parameter space, and represent a significant improvement over previously available results.

We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and kind hospitality. This work is supported by the US Department of Energy and National Science Foundation, the Natural Sciences and Engineering Research Council (Canada), the Commissariat à l’Energie Atomique and Institut National de Physique Nucléaire et de Physique des Particules (France), the Bundesministerium für Bildung und Forschung and Deutsche Forschungsgemeinschaft (Germany), the Istituto Nazionale di Fisica Nucleare (Italy), the Foundation for Fundamental Research on Matter (The Netherlands), the Research Council of Norway, the Ministry of Education and Science of the Russian Federation, Ministerio de Economía y Competitividad (Spain), the Science and Technology Facilities Council (United Kingdom), and the Binational Science Foundation (U.S.-Israel). Individuals have received support from the Marie-Curie IEF program (European Union) and the A. P. Sloan Foundation (USA).

We wish to acknowledge Adrian Down, Zachary Judkins, and Jesse Reiss for initiating the study of the physics opportunities with the single photon triggers in BABAR, Rouven Essig for stimulating discussions and for providing data for Fig. 5, and Farinaldo Queiroz for correcting a typo in Fig. 5.

I EPAPS Material

The following includes supplementary material for the Electronic Physics Auxiliary Publication Service.