(In)Direct Detection of Boosted Dark Matter
((In)Direct Detection of Boosted Dark Matter
Kaustubh Agashe † , Yanou Cui † (cid:91) , Lina Necib ‡ , Jesse Thaler ‡ † Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742,USA (cid:91)
Perimeter Institute, 31 Caroline Street North Waterloo, Ontario N2L 2Y5, Canada ‡ Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA02139, USAE-mail: [email protected], [email protected], [email protected],[email protected]
Abstract.
We present a new multi-component dark matter model with a novel experimentalsignature that mimics neutral current interactions at neutrino detectors. In our model, the darkmatter is composed of two particles, a heavier dominant component that annihilates to producea boosted lighter component that we refer to as boosted dark matter. The lighter component isrelativistic and scatters off electrons in neutrino experiments to produce Cherenkov light. Thismodel combines the indirect detection of the dominant component with the direct detectionof the boosted dark matter. Directionality can be used to distinguish the dark matter signalfrom the atmospheric neutrino background. We discuss the viable region of parameter space incurrent and future experiments.
1. Introduction
Despite overwhelming gravitational evidence for the existence of dark matter (DM), this non-baryonic matter has so far evaded all other means of observation. It is therefore essential toinvestigate less conventional models for DM with non-traditional experimental signatures. Inthese proceedings, we discuss a new DM model with novel signals at neutrino experiments. OurDM model involves two components, a dominant secluded GeV scale species ψ A , that annihilatesinto a lighter species ψ B at regions of high DM density, and in particular the galactic center (GC).The ψ B particles are produced with a large boost, and we therefore term them boosted DM.Detection of ψ B occurs through the scattering ψ B e − → ψ B e − at neutrino experiments. Thebackground to this process consists of electrons produced from charged current atmosphericneutrino reactions. Due to the kinematics of the signal, the scattered electron is emitted in theforward direction and a search cone can be used to optimize for signal significance and resultsin a detectable signal in current and future neutrino experiments. A more detailed discussion ispresented in Ref. [1].
2. Two-component Dark Matter
We begin by outlining the particle content of our model. We assume that DM is comprisedof two Dirac fermions: ψ A and ψ B . We take ψ A to be the dominant DM component, which Speaker at TAUP conference, Turin, Italy Sept 7-11, 2015 a r X i v : . [ h e p - ph ] D ec nnihilates to ψ B via the dimension six operator L int = 1Λ ψ A ψ B ψ B ψ A . (1)The scale of the process Λ ∼ O (100 GeV) is set by the requirement that the abundance of ψ A matches the observed DM abundance. The abundance of ψ A is controlled by the annihilationrate ψ A ψ A → ψ B ψ B which requires m A > m B to be kinematically allowed.The particle ψ B is charged under a dark force, mediated by a dark photon γ (cid:48) , thatkinematically mixes with the photon through the interaction L ⊃ − (cid:15) F (cid:48) µν F µν , (2)where F µν is the photon field and F (cid:48) µν is the dark photon field. The coupling (cid:15) ∼ O (10 − )sets the scale of the mixing. The gauge coupling of this dark force is taken to be large yetperturbative g (cid:48) ∼ O (0 . ψ B are the annihilationof ψ A : ψ A ψ A → ψ B ψ B and the ψ B annihilation to dark photons: ψ B ψ B → γ (cid:48) γ (cid:48) , where we haveassumed m B > m γ (cid:48) . The coupling of ψ B to the dark photon is taken such that the abundanceof thermal ψ B is subdominant to that of ψ A .Throughout this paper, we use the benchmark m A = 20 GeV , m B = 200 MeV , m γ (cid:48) = 20 MeV , g (cid:48) = 0 . , (cid:15) = 10 − , (3)to quantify scattering cross sections. In Sec. 5, we explore the full range of parameter space,carefully taking into account experimental constraints, and discuss prospects for future discovery.
3. Dark Matter Production Mechanism
In our model, while ψ A provides the dominant DM density, ψ B particles produced throughthe ψ A ψ A → ψ B ψ B process today provide a candidate for detection. Production of ψ B occurspredominantly in region of high DM ( ψ A ) density, in particular the GC. The flux of ψ B at theGC is d Φ GC d Ω dE B = 14 r Sun π (cid:18) ρ local m A (cid:19) J (cid:104) σ AA → BB v (cid:105) v → dN B dE B , (4)where r Sun = 8 .
33 kpc is the distance from the galactic center to the Sun, ρ local = 0 . is the local density of DM, and (cid:104) σ AA → BB v (cid:105) v → is the thermal cross section for the productionof ψ B , which we assume is dominated by the s − wave process. The spectrum of ψ B is given by dN B dE B = 2 δ ( E B − m A ) , (5)since every annihilation of ψ A produces two ψ B particles with energies E B = m A . Due to themass hierarchy m A ≈ O (10) GeV (cid:29) m B ≈ O (100) MeV, the ψ B particles are produced with alarge boost, and we therefore refer to ψ B as boosted DM. Subsequently, ψ B can be detected atneutrino experiments.The DM density is incorporated in Eq. (4) through the J -factor of the GC which is definedby J = (cid:90) l . o . s dsr Sun (cid:18) ρ ( r ( s, θ )) ρ local (cid:19) , (6) More accurately, the dark U (1) mixes with hypercharge. Since the publication of this work, this combination for ( m γ (cid:48) , (cid:15) ) has been excluded by the preliminary work ofthe NA48/2 collaboration [2]. A new benchmark can be found in the parameter space around this point. here the integral is along the line of sight, with s the distance from an earth-located observerto a point in the DM halo. The coordinate r is the distance from the center of the halo and isrelated to s as r ( s, θ ) = ( r + s − r Sun s cos θ ) / . (7)The angle θ is the angle between a point in the halo and the center of the galaxy from thepoint of view of an observer on earth. For simplicity, we assume an NFW profile for the DMdensity distribution ρ ( r ( s, θ )), and use the numerical code of Ref. [3] to compute the J -factoras a function of the angle θ . Having found the boosted DM ψ B flux, we use the differential crosssection of the process ψ B e − → ψ B e − to infer the expected number of signal events.
4. Kinematics of Boosted DM Detection
Proceeding from the production mechanism of the boosted DM component ψ B to its detection,we set up a framework to optimize for the observation of ψ B through electron scattering inneutrino detectors. Due to the kinematics of ψ B e − → ψ B e − scattering, the electron is emitted inthe forward direction and thus correlates with the direction of the incoming ψ B , as schematicallyshown in Fig. 1. Since the GC is the densest region of DM, we search for events where theemitted electron, and by extension the incoming ψ B , is within an angle θ C of the GC. Theangle θ C can be optimized for maximal discrimination between the boosted DM signal and thebackground by studying the analytical form of the scattering cross section. This involves thekinematics of the ψ B -electron scattering, and the convolution of the electron angular distributionwith the initial DM distribution in the GC. We discuss each in turn.The differential cross section for the ψ B e − → ψ B e − process is dσ Be − → Be − dt = 18 π ( (cid:15)eg (cid:48) ) ( t − m γ (cid:48) ) E B m e + t ( t + 2 s ) λ ( s, m e , m B ) , (8)where λ ( x, y, z ) = x + y + z − xy − xz − yz , s = m B + m e + 2 E B m e , t = q = 2 m e ( m e − E e ).The energy of ψ B is m A , since ψ B is produced from the annihilation of ψ A at rest. To obtainthe full cross section, Eq. (8) must be integrated over the valid range of electron energies. Thelower bound of integration is given by E min e = E thresh e , as the energy of the outgoing electronhas to be above the experimental threshold. The maximum scattered electron energy allowedby kinematics is E max e = m e ( E B + m e ) + E B − m B ( E B + m e ) − E B + m B . (9)For the benchmark values of Eq. (3) and a minimum allowed energy of the electron E min e = 100 MeV, we find σ Be − → Be − = 1 . × − cm (cid:18) (cid:15) − (cid:19) (cid:18) g (cid:48) . (cid:19) (cid:32)
20 MeV m γ (cid:48) (cid:33) . (10)Convolving the NFW distribution of ψ B with the angular distribution of the scatteredelectrons, we find the number of expected signal events in which the emitted electron is withinan angle θ C of the GC N θ C signal = ∆ T N target (Φ GC ⊗ σ Be − → Be − )) (cid:12)(cid:12)(cid:12) θ C = 12 ∆ T ρ Water / Ice V exp m H O r Sun π (cid:18) ρ local m A (cid:19) (cid:104) σ AA → BB v (cid:105) v → (11) × (cid:90) π dφ (cid:48) e π (cid:90) θ (cid:48) max θ (cid:48) min dθ (cid:48) e sin θ (cid:48) e dσ Be − → Be − d cos θ (cid:48) e (cid:90) π/ dθ B sin θ B πJ ( θ B )Θ( θ C − θ e ) . GC ) θ B z θ C z ′ ( Lab ) Be − φ ′ e θ ′ e Figure 1.
Geometry of a search cone for incoming ψ B particles originating at the GC andscattering off electrons at neutrino experiments.Here ∆ T is the exposure time, N target is the number of target electrons, and Φ GC is the ψ B flux.In order to find the number of targets per experiment, we use the density of the material (in thiscase water or ice) ρ Water / Ice , the volume of the experiment V exp , and the mass of a water molecule m H O . We parameterize the direction of the emitted electron by an azimuthal angle φ (cid:48) e and apolar angle θ (cid:48) e . As shown in Fig. 1, the detection geometry respects a cylindrical symmetry,while the angle θ (cid:48) e is constrained by the minimum allowed energy of the electron (experimentalresolution) and a maximum energy determined by both the kinematics of the scattering and theexperimental setup that might divide events into Sub-GeV and Multi-GeV events, according theelectron energy.For the benchmark values given in Eq. (3), the expected number of signal events within anangle θ C = 10 ◦ of the GC is N ◦ signal ∆ T = 25 . − . (12)
5. Detection Prospects for Current and Future Experiments
In this section, we discuss the detection limits of boosted DM in Super-K [4] and its upgradeHyper-K [5], as well as the IceCube extensions PINGU [6] and MICA [7]. Despite its largevolume, IceCube’s energy threshold is too high for the considered DM scale [8]. At the energyscale of ψ B , the largest background to ψ B e − → ψ B e − is atmospheric neutrinos. They interactthrough the charged current processes ν e n → e − p and ν e p → ne + , producing electrons of similarenergies as signal events. A few features can help discriminate between signal and background: • Directionality: The atmospheric neutrinos have an isotropic flux while boosted DM isfocused at the direction of largest J -factor, which in this case is the GC. • No muon events: While atmospheric neutrinos come in different flavors, and thus produceboth electron and muon events, signal events produce solely electrons. • Gadolinium: Experiments such as Super-K are currently investigating using Gadolinium toimprove detection efficiency [9]. Gadolinium has the highest neutron capture cross sectionand can thus discriminate with high efficiency against the ν e p → ne + background events.Extrapolating from the atmospheric neutrino data of Super-K [10], we derive the expectednumber of background events at other experiments. Since the signal is analyzed within an angle θ C of the GC, we only look at the fraction of background events that fall into the same solidangle N θ C bkgd = 1 − cos θ C N allskybkgd . (13)We define the signal significance as Signal / √ Bkg , and use it as a measure to optimize for theopening angle of the search cone. We find that θ C = max(10 ◦ , θ rese ), where θ res e is the experimental Γ ' (cid:61)
20 MeV, g' (cid:61)
Ε(cid:61) (cid:45) (cid:248) Super (cid:45)
K Limit Super (cid:45)
KPINGUHyper (cid:45)
KMICA (cid:45) (cid:45) (cid:45) m B (cid:72) GeV (cid:76) m A (cid:72) G e V (cid:76) Super (cid:45)
K Limit and Future Prospects
Figure 2.
Signal significance at Super-K, Hyper-K, PINGU and MICA as a function of theparameter space m A − m B , for fixed m γ (cid:48) , g (cid:48) and (cid:15) with the benchmark values of Eq. (3). Regionsshown are 2 σ reaches for 10 years of data.angular resolution. In the case of PINGU and MICA , it exceeds 10 ◦ . For θ C = 10 ◦ , as relevantfor Super-K, we have N ◦ bkgd ∆ T = 5 .
85 year − . (14)Within θ C = 10 ◦ , the number of background events is subdominant to the number of expectedsignal events given by Eq. (12). The resulting significance as a function of m A and m B is shownin Fig. 2. Already, without the use of directionality, the hatched black region of parameterspace is ruled out by Super-K. A dedicated analysis using the suggested search cone would beable to extend its detection reach to encompass our benchmark values of Eq. (3).
6. Conclusions
In these proceedings, we presented an example of a DM model that provides a new experimentalsignature. Starting from a multi-component model, we looked into the annihilation of a DMcomponent resulting in a boosted DM particle. The boosted DM component, if coupled tothe Standard Model through a dark photon, can scatter off electrons at neutrino experimentsand produce detectable Cherenkov light. The signal can be distinguished from backgroundevents using the angular information of emitted electrons, as signal events are in the forwarddirection and point to the GC. Furthermore, unlike background events, mainly produced fromatmospheric neutrinos, the signal electron events are not accompanied by muon events. BoostedDM is therefore an exciting new paradigm that opens the door to new experimental possibilitiesfor DM detection.
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