Searching for Light Dark Matter with the SLAC Millicharge Experiment

Searching for Light Dark Matter with the SLAC Millicharge Experiment

M. Diamond Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada    P. Schuster Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada
July 30, 2019

New sub-GeV gauge forces (“dark photons”) that kinetically mix with the photon provide a promising scenario for dark matter, and are the subject of a program of searches at fixed-target and collider facilities around the world. In such models, dark photons produced in collisions may decay invisibly into dark matter states, thereby evading current searches. We re-examine results of the SLAC mQ electron beam dump experiment designed to search for millicharged particles, and find that it was strongly sensitive to any secondary beam of dark matter produced by electron-nucleus collisions in the target. The constraints are competitive for dark photon masses in the range, covering part of the parameter space that can reconcile the apparent anomaly. Simple adjustments to the original SLAC search for millicharges may extend sensitivity to cover a sizeable portion of the remaining anomaly-motivated region. The mQ sensitivity is therefore complementary to on-going searches for visible decays of dark photons. Compared to existing direct detection searches, mQ sensitivity to electron-dark matter scattering cross sections is more than an order of magnitude better for a significant range of masses and couplings in simple models.

thanks: miriam.diamond@alumni.carleton.cathanks:

Identifying dark matter is one of the most pressing open problems in fundamental physics. Although a rich experimental program continues to probe dark matter (DM) interactions for masses in the - range, sensitivity to DM at lower masses remains remarkably poor. There are well motivated scenarios of sub- DM, especially those that include new gauge forces (“dark forces”) that kinetically mix with the photon – these models can account for the observed relic density consistently with all available data, and have been the focus of intense discussion in the literature Holdom (1986).

In this note, we show that the electron beam dump millicharge search at SLAC (mQ) was sensitive to sub-GeV DM interacting through dark photons. In a simple model, we compute the total detection yield for -scale DM components that would have been produced in the mQ target. We use these yields and the original mQ analysis to establish constraints on such DM. The new constraints cover part of the parameter space that can reconcile the apparent anomaly, and future adjustments to the original analysis may significantly extend sensitivity. We also provide estimates for the level of sensitivity that might be attained with a re-designed version of this experiment at modern high-intensity electron beam facilities. These results highlight the potential for using electron beam dump experiments to powerfully probe any DM components (or other long-lived particles) that couple to leptons and quarks (see Izaguirre et al. (2013)), and they complement the on-going effort to search for dark photons in visible decay channels Abrahamyan et al. (2011).

As a simple example, we consider a benchmark model consisting of a long-lived fermion coupled to a dark sector gauge boson that kinetically mixes with the photon. The Lagrangian is

where is the field strength tensor for Standard Model (SM) hypercharge , for the new , and is the interaction current of the with any dark-sector fields, in this case a fermion . We define where is the SM weak mixing angle, and . A field redefinition removes the kinetic mixing term and generates a coupling between the and SM electrically-charged particles. This effectively gives charged particles a small dark force charge, without giving dark sector particles electric charge. Kinetic mixing with can be generated by loops of heavy fields charged under both and U(1), and is a natural range to consider Bjorken et al. (2009).

Previous literature has considered numerous constraints on sub-GeV DM derived from the CMB, supernovae, B-factory searches, rare Kaon decay measurements, and precision and measurements Hewett et al. (2012). For comparison to the mQ sensitivity, we include the constraints relevant for the low range. A companion paper Izaguirre et al. (2013) discusses the viability of using the simple benchmark Lagrangian above to model fixed-target physics, where can be all of or a sub-dominant part of the DM consistent with all available data.

In the mQ experiment, 1.35 Coulombs () of electrons were deposited on a tungsten production target. Approximately 90 m of sandstone separated the target from the detector (Bicron-408 plastic scintillator), which was sensitive to signals as small as a single scintillation photon and subtended a solid angle of mrad. SM particles essentially ranged out in the sandstone, while any penetrating particles like mQ’s were able to reach the detector and trigger a small scintillation signal Prinz et al. (1998). Collected data consisted entirely of timing and height of PMT pulses. No significant signal was found over a rather large (K) but well-measured instrumental background Prinz (2001).

As illustrated in Figure 1, this setup would have produced significant numbers of s in the target via a bremsstrahlung-like process. We examine the case of prompt invisible decay ; the ’s would have traversed the sandstone given their large mean free path. The secondary beam of ’s could have deposited energy in the mQ detector via -enhanced elastic scattering off carbon nuclei (and sub-dominantly though quasi-elastic -nucleon scattering, which we neglect).

Figure 1: Layout of the SLAC mQ experiment Prinz et al. (1998). We investigate the possibility of production in the target, followed by prompt decay to long-lived dark sector particles , which could traverse the sandstone and undergo elastic scattering off carbon nuclei in the detector.

Our analysis assumes (on-shell ), but we expect this approach to have sensitivity even for where ’s are produced via an off-shell (see Bjorken et al. (2009)). We used the procedure in Bjorken et al. (2009), based on a variation on the Weizsacker-Williams method, for computing production. We also simulated all reactions using MadGraph and MadEvent 4 Alwall et al. (2007). We assigned to the vertex the coupling , and to the vertex (for target nucleus of atomic number , with the square root of the form-factor in Bjorken et al. (2009).)

The typical emission angle for the relative to the beam is parametrically smaller than the opening angle of decay products, and is collinear to a good approximation. Neglecting ,


where is the atomic number of the target nucleus, with the lab-frame energy of the beam electron, and is an factor dependent upon kinematics, atomic screening, and nuclear size effects Bjorken et al. (2009).

Since the angular size of the mQ detector was mrad, angular acceptance limits overall sensitivity. Produced s typically carry most of the beam energy, with Bjorken et al. (2009). In the decay, the angle of the ’s relative to the beamline scales as . The angular distribution of is shown in Figure 2 for reference.

Figure 2: Sample angular distributions, generated using MG/ME (MeV). Normalized to 1. Angular acceptance of mQ detector is 0.002 rad.  GeV (steep curve): 90% accepted.  GeV (shallow): 6% accepted.

For the coherent scattering illustrated in Figure 1, we assigned the vertex the coupling (for detector nucleus carbon.) With the lab-frame kinetic energy of the recoiling nucleus of mass , the coherent scattering cross-section (neglecting ) is approximately


The recoil distributions in full simulation for representative are shown in Figure 3. The nuclear recoil energy is typically  MeV. Based on neutron scattering experiments with plastic scintillator, a proton recoiling with kinetic energy 1 MeV should produce PEs, and 0.1 MeV PEs. The quenching factor for a C nucleus is about half that for a proton Ahlen et al. (1985). Therefore a 1 MeV recoiling C should produce PEs, and 0.1 MeV PE. Figure 3 shows that with a  MeV threshold for producing a PE, about 20% of the -C events would produce at least a single PE at GeV, and 90% at GeV.

Figure 3: Sample nuclear recoil distributions, generated using MG/ME (MeV), at the approximate median lab-frame energy (12 GeV for  GeV, 27 GeV for  GeV.) Normalized to 1.

In finding the total number of produced in the target, we can neglect production in lower energy showers initiated by the beam electron because the angular acceptance of mQ is small. To account for the more important effect of the energy loss of the beam as it traverses the target, we use an “effective” radiation length of . This can be justified as follows. For the small angular size of mQ, the angular acceptance scales as (for low masses), where is the beam electron energy. Thus, the -weighted average of the beam energy distribution integrated over the thickness of the target (6 radiation lengths) and energy yields an effective thickness (in units of radiation length). Using the beam energy distribution in Bjorken et al. (2009), we obtain . To a good approximation, the differential production yield for fixed energy is


where is the total number of beam incident on target, is Avogadro’s number, is the unit radiation length of target material, and is the target atomic mass. The differential production cross section at fixed energy, , was computed with full simulation. To find the number of expected scattering events in the mQ detector, , we include angular acceptance cuts with full simulation, which reduces to . The final yield is then


where is the detector thickness, and is the number density of C nuclei in the detector.

An order-of-magnitude estimate can be obtained by , where the probability per beam to produce a pair is

the probability of -C coherent nuclear scattering is

and is the fraction of ’s that pass angular acceptance cuts. Table 1 gives the simulated cross-sections and production totals, along with the corresponding analytical estimates, for one example set of parameter values – the agreement is quite good.

Quantity Simulated Value Analytic Estimate
[pb] 37722 38000
No. produced
0.52 0.60
[pb] 3950 4200
No. scattering evts 189 239
Table 1: For the benchmark point  GeV,  GeV with , : production cross-section, total no. produced, fraction of that pass the angular acceptance cut, -C coherent scattering cross-section for relativistic , and total no. of -C coherent scattering events in the mQ detector.

Using five “benchmark” points with GeV, in the range, we evaluated the limits in the parameter space by comparing total yields to single PE mQ background measurements. The mQ data analysis estimated of the 146061 background events involved only a single PE Prinz (2001). For , scattering events should produce much more than one PE, so it should be possible to use a PMT pulse-height cut to help separate signal from background. It is reasonable to expect such a cut to improve S/B by at least an order of magnitude in the higher range because the vast majority of the background is single PE noise. Figure 4 shows the constraints that would be obtained for MeV with no background reduction, and with the reported S/B. Note, Figure 4 assumes every scattering event in the detector produces at least one photo-electron and is observed. Losses from failure to produce any PEs could reduce sensitivity by a factor of in the lowest part of the range.

Given significant background reduction, mQ would be able to cover a sizeable swath of unexplored parameter space, including part of the anomaly-motivated region for  GeV. It should be noted that there is currently a MiniBooNE proposal for further running specifically to cover this range Dharmapalan et al. (2012). Likewise, LSND could likely impose constraints at the level of for (), though no analysis is yet publicly available.

Our analysis results can be interpreted as constraints on electron- scattering cross sections , which can also be probed by direct detection. Recent results from XENON10 established limits on as a function of DM mass in the 1–1000 MeV range Essig et al. (2012). Using “benchmark” points shown in Figure 5, we employed mQ constraints on to establish constraints on via . If accounts for all the DM, mQ sets limits more stringent than XENON10 for  MeV. could instead be a sub-dominant DM component, in which case XENON10 constraints are weakened.

Figure 4: For each benchmark with GeV, the that would correspond to a result in SLAC mQ. Note the dependence on , and the improvement that would come from achieving the reported mQ S/B. These results change fairly little with . Overlaid on existing constraints; is a power constrained limit Izaguirre et al. (2013). Yellow band: anomaly-favoured Giudice et al. (2012). Note, LSND would be expected to provide additional constraints, at the level of for  GeV.
Figure 5: For benchmark with GeV and GeV (), the constraints on scattering cross-section of DM off corresponding to a result in mQ, assuming the reported mQ signal-to-background. Overlaid on the XENON10 direct detection results Essig et al. (2012); direct comparison valid only assuming accounts for all the DM in the universe.

It is convenient to consider mQ because the data already exists – but this experiment was not optimized for light DM searches. Characteristics that would make future beam-dumps even more effective for this purpose include optimal sensitivity to quasi-elastic -nucleon processes, broader angular acceptance, greater luminosity, and an effective background-rejection scheme Izaguirre et al. (2013). The main backgrounds are typically intrinsic detector noise, cosmic rays, ’s from ambient radioactivity, and fast neutrons (produced from the target). Neutral-current interactions are negligible Prinz (2001). As an exercise, each benchmark point in Figure 4 was re-calculated for a luminosity of electrons, with no angular acceptance cuts. This luminosity could be reasonably achieved at a facility such as Jefferson Laboratory or a future Linear Collider. Sensitivity to 500 signal events for example (realistic for PE yield signals), would cover an impressive swath of parameter space (dotted line in Figure 4).

In conclusion, we find the SLAC mQ search is indeed relevant for exploring the parameter of models where a dark photon of mass decays to lighter, long-lived ’s. This includes a parameter region in which dark photon models can alleviate the current discrepancy, and adjustments to the original SLAC analysis are expected to strengthen the constraints – or make a discovery – in this region. In a broader context, our analysis provides a proof-of-concept for the use of beam-dumps to search for DM particles with masses of tens to hundreds of MeV, a regime that poses great difficulty for direct detection and collider experiments. In simple models, we find that mQ constrains the DM-electron scattering cross-section  cm for – up to an order of magnitude stronger than the leading direct-detection limits where applicable.

Acknowledgments We thank Natalia Toro, Gordan Krnjaic, and Eder Izaguirre for helpful feedback and discussion. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.


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