DIRECT DETECTION OF NUCLEAR DARK MATTER USING TONNE-SCALE EXPERIMENTS • What is Nuclear Dark Matter? • Signal and sensitivity in DEAP-3600 and XENON1T • Can it be distinguished from a vanilla WIMP signal? arXiv:1610.01840 ALISTAIR BUTCHER - ROYAL HOLLOWAY, UNIVERSITY OF LONDON 1
What is Nuclear Dark Matter? Many dark matter models which mirror the SM sector, e.g., asymmetric models (di ff erence between DM and anti-DM), composite particles (WIMPonium, dark atoms etc.) Nuclear Dark Matter (NDM) - dark matter which consists of bound states of strongly-interacting dark nucleon constituents with short-range interactions In this model: heavy scalar mediator with SM assumed (SI), no analogue of long range EM interactions between protons - this means dark nucleon number, k, can be large > 10 8 . arXiv:1411.3739 J. D. March-Russell et al. 2009, W. Shepherd et al. 2009, D. E. Kaplan et al 2010 2
What is Nuclear Dark Matter? The composite nature of these particles e ff ects how they scatter o ff SM nuclei in direct detection experiments Composite DM particles made up of k nucleons will have an elastic cross-section which is coherently enhanced by k 2 . However, the number density will decrease leaving an overall rate that scales with k. Due to its spatially extended nature a form factor for the NDM particle appears. If the radii of the NDM states are larger than the SM nuclei, direct detection experiments will probe the dark form factor at lower values of the momentum transfer compared to the SM form factor. 3
NDM Recoil Spectrum With NDM being a composite rather than point particle the differential rate is modified. d 3 v f ( v ) dR Z ρ χ χ n mA 2 σ 0 F N ( q ) 2 = 2 µ 2 dE R v v>v min Coherent enhancement d 3 v f ( v ) dR Z ρ k A 2 k 2 σ 0 F N ( q ) 2 F k ( q ) 2 = 2 µ 2 dE R v kn km 1 v>v min Dark nucleon number NDM form factor Mass of single dark nucleon The second form factor allows the characteristic zeros to appear inside a detector’s energy window. 4
Dark Form Factor Spherical top hat function assumed for the density, leading to a spherical Bessel function form factor: F k ( q ) = 3 j 1 ( qR k ) Approximate radius of a R k = k 1 / 3 R 1 single DN, taken to be 1 fm qR k 1 ) R (E 2 Ar-40 F 1 − 10 3 k = 10 4 k = 10 5 k = 10 − 2 10 3 − 10 4 − 10 5 − 10 0 20 40 60 80 100 120 140 E (keV) R Form factors for various k-DN states plotted with the Helm parameterisation for Argon-40 5
NDM Signal The finite resolution of the detectors smooth the shape into peaks and troughs. 10 - 6 WIMP DEAP - 3600 = 10 3 10 - 7 = 10 4 10 - 8 10 - 9 10 - 10 10 - 11 10 - 12 20 40 60 80 100 120 140 Values of k with m1 = 1 GeV are plotted with a WIMP spectrum of 100 GeV. 6
NDM Signal WIMP XENON1T = 10 3 10 - 5 = 10 4 10 - 6 10 - 7 10 - 8 10 - 9 10 - 10 0 10 20 30 40 50 60 XENON1T efficiency and resolution taken from: E. Aprile et al., Physics reach of the XENON1T dark matter experiment, JCAP 1604 (2016) 027 7
Sensitivity 10 - 38 DEAP - 3600 10 - 40 WIMPs XENON1T LUX 10 - 42 10 - 44 σ 0 / cm 2 10 - 46 NDM 10 - 48 10 - 50 10 - 52 10 4 10 5 10 6 1 10 100 1000 m DM / GeV 90% CL sensitivity to NDM with m1 = 1 GeV and mDM=k*m1. The k 2 enhancement of the cross section results in a sensitivity orders of magnitude below the equivalent WIMP. LUX (old) limit (1.4E4 kg.day): D. S. Akerib et al. Phys. Rev. Lett. 116 (2016) 161301, DEAP limit (3000 kg.year): P. A. Amaudruz et al. ICHEP 2014, XENON limit (2000 kg.year): E. Aprile et al. JCAP 1604 (2016) 027 8
Distinguishing NDM from WIMPs To determine whether a NDM signal can be distinguished from a WIMP signal we look at the most indistinguishable case. For each value of k to be tested we find the WIMP signal which takes the greatest number of events to be ruled out. Define a likelihood ratio test statistic: " , k, m 1 ) } Q N obs # Poisson { N obs , N NDM ( σ NDM i =1 f NDM ( E i | k, m 1 ) exp 0 λ = − 2 ln , m ) } Q N obs ( σ WIMP Poisson { N obs , N WIMP i =1 f WIMP ( E i | m ) exp 0 The most indistinguishable case occurs when the expected number of events for both hypotheses is the same. Since each cross section can be varied independently the problem becomes simple shape analysis: "Q N obs # i =1 f NDM ( E i | k, m 1 ) λ = − 2 ln Q N obs i =1 f WIMP ( E i | m ) Z ∞ p = g ( λ | N obs ) d λ Probability of mis-identifying NDM as WIMPs: 0 C = 1 − p Probability of correctly identifying NDM under the NDM hypothesis: 9
The Most Indistinguishable Case Tables of NDM and WIMP spectra were built and a grid search was performed to find the most indistinguishable WIMP for each NDM. In each case p was determined via Monte-Carlo and the WIMP which required the maximum number of events to be distinguished at a given confidence level was found. 10 - 7 10 - 7 k = 1412 k = 5012 m WIMP = 29.9 GeV m WIMP = 23.4 GeV 10 - 8 10 - 8 1234 Events Required 23 Events Required 10 - 9 10 - 9 10 - 10 10 - 10 - NDM - NDM 10 - 11 10 - 11 - WIMP (3 sigma) - WIMP (3 sigma) 10 - 12 10 - 12 20 40 60 80 100 120 20 40 60 80 100 120 WIMP tracks the majority of the First trough appears close to the NDM signal. beginning of the window. As the WIMP spectrum is exponentially falling the position of the first trough (and consequently rising edge) is the most important feature. 10
NDM and WIMP Spectra 10 - 7 10 - 7 k = 17785 k = 28187 m WIMP = 34.1 GeV m WIMP = 25.4 GeV 71 Events Required 43 Events Required 10 - 8 10 - 8 10 - 9 10 - 9 10 - 10 10 - 10 - NDM - NDM - WIMP (3 sigma) - WIMP (3 sigma) 10 - 11 10 - 11 20 40 60 80 100 120 20 40 60 80 100 120 10 - 7 10 - 7 k = 10 7 k = 501245 m WIMP = 42.3 GeV m WIMP = 44.1 GeV 134 Events Required 384 Events Required 10 - 8 10 - 8 10 - 9 10 - 9 10 - 10 10 - 10 - NDM - NDM - WIMP (3 sigma) - WIMP (3 sigma) 10 - 11 10 - 11 20 40 60 80 100 120 20 40 60 80 100 120 11
Number of events required to identify NDM against the most indistinguishable case. Peaks and troughs correspond to where the first NDM trough appears in the energy window for each experiment. Flat region appears when the NDM shape is no longer resolvable. This occurs at lower k for XENON1T as it has a lower energy resolution than DEAP-3600. 12
Discovery Potential The maximum number of events it’s possible to see for each detector assuming the cross-section is at the value of the old LUX limit (Phys. Rev. Lett. 116 (2016) 161301). 200 200 WIMPs WIMPs XENON1T DEAP - 3600 NDM NDM 3 σ CL 3 σ CL 150 150 2 σ CL 2 σ CL Max. No of Events Max. No of Events 1 σ CL 1 σ CL 100 100 50 50 0 0 10 4 10 5 10 6 10 7 10 4 10 5 10 6 10 7 10 100 1000 10 100 1000 m DM / GeV m DM / GeV In either detector it only possible to distinguish NDM at the 2 sigma level for limited regions of the parameter space. 13
Combined Probability of positively identifying a WIMP in at least one detector: C combined = 1 − p D p X Probability of misidentifying NDM in DEAP XENON1T Regions of the k parameter space become available at the 3 sigma confidence level. 14
Conclusions We have set a constraint on NDM using the 1.4E4 kg.day LUX limit, and calculated the sensitivity of the current running experiments DEAP-3600 and XENON1T The sensitivity on the zero momentum transfer cross-section of NDM is orders of magnitude lower than the equivalent WIMP sensitivity - 2 enhancement of the scattering cross-section. this is due to the k The ability to distinguish between WIMPs and NDM depends on both the energy threshold (position of first trough) and energy resolution (shape of oscillations). It is possible to see “hints” of NDM at 2 and 3 sigma in DEAP-3600 and XENON1T. Future experiments should be able to distinguish NDM from WIMPs at 3 sigma over the entire k range. 15
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