A comprehensive analysis of the dark matter direct detection experiments in the mirror dark matter framework
aa r X i v : . [ h e p - ph ] A ug August 2010
A comprehensive analysis of the dark matter directdetection experiments in the mirror dark matter framework
R. Foot School of Physics,University of Melbourne,Victoria 3010 Australia
Mirror dark matter offers a framework to explain the existing dark matter directdetection experiments. Here we confront this theory with the most recent exper-imental data, paying attention to the various known systematic uncertainties, inquenching factor, detector resolution, galactic rotational velocity and velocity dis-persion. We perform a detailed analysis of the DAMA and CoGeNT experimentsassuming a negligible channeling fraction and find that the data can be fully ex-plained within the mirror dark matter framework. We also show that the mirrordark matter candidate can explain recent data from the CDMS/Ge, EdelweissII andCRESSTII experiments and we point out ways in which the theory can be furthertested in the near future. E-mail address: [email protected]
Introduction
The field of dark matter direct detection has blossomed in recent times, with ex-citing positive signals from DAMA[1, 2, 3], CoGeNT[4], as well as interesting hintsfrom CDMS/Ge[5] and CDMS electron scattering[6]. Very recently, more excitingevidence for the direct detection of dark matter has arisen from the CRESSTII[7]and EdelweissII[8] experiments.Mirror dark matter has emerged as a simple predictive framework which canexplain all of the direct detection experiments[9, 10, 11, 12, 13]. The purpose of thisarticle is to provide a comprehensive update of the experimental status of the mirrordark matter candidate, paying particular attention to the various known systematicuncertainties,in quenching factor, detector resolution, galactic rotational velocityand velocity dispersion.Recall, mirror dark matter posits that the inferred dark matter in the Uni-verse arises from a hidden sector which is an exact copy of the standard modelsector[14] (for a review see ref.[15]). That is, a spectrum of dark matter particles ofknown masses are predicted: e ′ , H ′ , He ′ , O ′ , F e ′ , ... (with m e ′ = m e , m H ′ = m H , etc).The galactic halo is then presumed to be composed predominately of a sphericallydistributed self interacting mirror particle plasma comprising these particles[16].In addition to gravity, ordinary and mirror particles interact with each other via(renormalizable) photon-mirror photon kinetic mixing[14, 17]: L mix = ǫ F µν F ′ µν , (1)where F µν ( F ′ µν ) is the ordinary (mirror) U (1) gauge boson field strength tensor.This interaction enables mirror charged particles to couple to ordinary photonswith electric charge q = ǫe and thus allows mirror particles to elastically scatteroff ordinary particles. This means that mirror dark matter can be probed in darkmatter direct detection experiments. It turns out that this simple predictive theorycan explain the DAMA annual modulation signal, the CoGeNT low energy excessas well as hints from CDMS, Edelweiss and CRESSTII consistently with the nullresults of other experiments.The outline of this paper is as follows. In section 2 we provide a brief reviewof the mirror dark matter theory. In section 3 we provide some necessary technicaldetails: cross section and halo distribution which are characteristic of mirror darkmatter. In section 4 (5), we examine the implications of the most recent DAMA(CoGeNT) data for the mirror dark matter theory. These experiments are sensitiveto dark matter particles heavier than around 10 GeV which makes them excellentprobes of the dominant mirror metal component of the galactic halo, A ′ . We showthat these experiments can be simultaneously explained and lead to a measurementof the parameters: ǫ √ ξ A ′ and m A ′ both of which are consistent with the theoreticalexpectations of ǫ ∼ − (from galactic halo energy balance) and A ′ ∼ O ′ ⇒ m A ′ ∼ m p (from analogy with the ordinary matter sector). In section 5 we also showthat the DAMA and CoGeNT signals are consistent with the results of the other1xperiments including the null results of XENON100 and CDMS/Si. In section 6 weexamine the constraints on e ′ scattering from the DAMA absolute rate. We showthat these constraints when combined with the DAMA and CoGeNT data suggest ahalo mirror metal proportion ξ A ′ > ∼ − . In section 7 we examine recent data fromthe CDMS/Ge, EdelweissII and CRESSTII experiments. CDMS/Ge and Edelweissare excellent probes of the anticipated F e ′ component, and the data are consistentwith a F e ′ component with mass fraction: ξ F e ′ /ξ A ′ ∼ − . We also point out thatthe CRESSTII experiment is potentially sensitive to both A ′ and F e ′ componentsand their recently announced low energy excess can be explained by A ′ and F e ′ interactions. In section 8 we draw our conclusions. Mirror dark matter conjectures that the inferred dark matter in the Universe arisesfrom a hidden sector which is an exact copy of the standard model sector. That is,the standard model of particle physics is extended: L = L SM ( e, u, d, γ, ... ) + L SM ( e ′ , u ′ , d ′ , γ ′ , ... ) . (2)Such a theory can be theoretically well motivated from symmetry considerations ifleft and right handed chiral fields are interchanged in the extra sector. In this wayspace-time parity symmetry and in fact the full Poincar´ e group can be realized asan unbroken symmetry of nature, and for this reason we refer to the particles in theextra sector as mirror particles. The standard model extended with a mirror sectorwas first studied in ref.[14] and shown to be a phenomenologically consistent renor-malizable extension of the standard model. The concept, though, has a long historydating back prior to the advent of the standard model of particle interactions[18].For a review and more complete list of references see ref.[15].If we include all interaction terms consistent with renormalizability and the sym-metries of the theory then we must add to the Lagrangian a U (1) kinetic mixinginteraction[17, 14] and Higgs - mirror Higgs quartic coupling[14]: L mix = ǫ F µν F ′ µν + λφ † φφ ′† φ ′ , (3)where F µν ( F ′ µν ) is the ordinary (mirror) U (1) gauge boson field strength tensorand φ ( φ ′ ) is the electroweak Higgs (mirror Higgs) field. The most general Higgspotential, including the quartic Higgs mixing term (above) was studied in ref.[14]and shown to have the vacuum h φ i = h φ ′ i for a large range of parameters. Withthis vacuum, the mirror symmetry is unbroken and consequently the masses of themirror particles are all identical to their ordinary matter counterparts.In this framework, dark matter is comprised of a spectrum of stable massivemirror particles: e ′ , H ′ , He ′ , O ′ ... etc, with masses m e ′ = m e , m H ′ = m H , m He ′ = m He etc. To explain the rotation curves in spiral galaxies, the dark matter needsto be roughly spherically distributed in galactic halos. Given the upper limit on2ompact star sized objects (MACHOs) in the halo from microlensing observations,roughly f macho < ∼ . − . .Observations of colliding clusters, such as the bullet cluster[20] indicate that darkmatter does not have self interactions on galaxy cluster scales. This suggests thatthe gaseous mirror dark matter component is confined to galactic halos (c.f. [21]).Gravity and the mirror particle self interactions may well be sufficient to achievethis.A dissipative dark matter candidate like mirror matter can only survive in anextended spherical distribution in galaxies without collapsing if there is a substantialheating mechanism to replace the energy lost due to radiative cooling. In fact,ordinary supernova can plausibly supply the required heating if the photon andmirror photon are kinetically mixed with ǫ ∼ − [16] . For kinetic mixing of thismagnitude about half of the total energy emitted in ordinary Type II Supernovaexplosions ( ∼ × erg) will be in the form of light mirror particles ( ν ′ e,µ,τ , e ′± , γ ′ )originating from kinetic mixing induced plasmon decay into e ′ + e ′− in the supernovacore[23]. Given the observed rate of Supernova’s in our galaxy of about 1 per century,this implies a heating of the halo (principally due to the e ′± component), of around: L SNheat − in ∼ × × erg years ∼ erg / s , for the Milky Way . (4)It turns out that this matches (to within uncertainties) the energy lost from the halodue to radiative cooling[16]: L haloenergy − out = Λ Z n e ′ πr dr ∼ erg / s , for the Milky Way . (5)In other words, a gaseous mirror particle halo can potentially survive without col-lapsing because the energy lost due to dissipative interactions can be replaced by theenergy from ordinary supernova explosions. Presumably there are feedback mecha-nisms which maintain this balance. For example if L haloenergy − out > L SNheat − in then thehalo would contract which in turns increases the gravitational pull on the ordinarymatter component. This compression of the ordinary matter component should in-crease ordinary star formation rates, thereby increasing L SNheat − in until the energy isbalanced. In this way the ordinary supernova rate might be dynamically adjusted sothat the halo is stabilized. Extending these ideas to galaxies beyond the Milky Way,the hypothesized connection between Supernova rates and dark matter distribution Naturally a MACHO subcomponent consisting of mirror white dwarfs, mirror neutron starsetc are also expected and can be probed by microlensing observations. Since most of the stellarmass is ejected as gas in the explosions producing these stellar remnants, it is plausible that theMACHO mass fraction can satisfy the observational limit of f macho < ∼ . − . A mirror sector with such kinetic mixing is consistent with all known laboratory, astrophysicaland cosmological constraints[22]. T ′ ≪ T in the early Universe (required to achieve successful big bangnucleosynthesis and large scale structure formation) and ǫ ∼ − the primordialmirror He ′ abundance is expected to be relatively high, Y He ′ ≈ . ∼ O ′ component if ǫ ∼ − .This provides important experimental evidence in favour of the mirror dark mattercandidate, which we now examine in detail. The interaction rate in an experiment depends on the cross-section, dσ/dE R , andhalo velocity distribution, f ( v ). The photon-mirror photon kinetic mixing enables amirror nucleus [with mass and atomic numbers A ′ , Z ′ and velocity v ] to elasticallyscatter with an ordinary nucleus [presumed at rest with mass and atomic numbers A, Z ]. In fact the cross-section is just of the standard Rutherford form correspondingto a particle of electric charge Ze scattering off a particle of electric charge ǫZ ′ e . Thecross-section can be expressed in terms of the recoil energy of the ordinary nucleus, E R [9]: dσdE R = λE R v , (6) See ref.[26] for further discussions about early Universe cosmology with mirror dark matter. λ ≡ πǫ Z Z ′ α m A F A ( qr A ) F A ′ ( qr A ′ ) , (7)and F X ( qr X ) ( X = A, A ′ ) are the form factors which take into account the finite sizeof the nuclei and mirror nuclei. [The quantity q = (2 m A E R ) / is the momentumtransfer and r X is the effective nuclear radius] . A simple analytic expression for theform factor, which we adopt in our numerical work, is the one given by Helm[27, 28]: F X ( qr X ) = 3 j ( qr X ) qr X e − ( qs ) / , (8)with r X = 1 . X / fm, s = 0 . j is the spherical Bessel function of index1. The halo mirror particles are presumed to form a self interacting plasma at anisothermal temperature T . This means that the halo distribution function is givenby a Maxwellian distribution: f i ( v ) = e − m i v /T = e − v /v [ i ] , (9)where the index i labels the particle type [ i = e ′ , H ′ , He ′ , O ′ , F e ′ , ... ] and v [ i ] ≡ T /m i . The dynamics of such a mirror particle plasma has been investigatedpreviously[16, 9], where it was found that the condition of hydrostatic equilibriumimplied that the temperature of the plasma satisfied: T ≃
12 ¯ mv rot , (10)where ¯ m = P n i m i / P n i is the mean mass of the particles in the plasma, and v rot ≈ ±
16 km/s is the galactic rotational velocity of the Milky Way[29]. Thevelocity dispersion of the particles in the mirror particle halo evidently depends onthe particular particle species and satisfies: v [ i ] = v rot mm i . (11)Note that if m i ≫ m , then v [ i ] ≪ v rot . Consequently heavy mirror nuclei havetheir velocities (and hence energies) relative to the Earth boosted by the Earth’s(mean) rotational velocity around the galactic center, ≈ v rot . This allows a mirrornuclei in the ‘oxygen’ mass range ∼ m ≈
15 GeV to provide a significant annualmodulation signal in the energy region probed by DAMA ( E R > Unless otherwise specified, we use natural units, ¯ h = c = 1 throughout. v [ i ], we need to estimate the mean mass of the mirror particles in theplasma. The plasma is expected to be completely ionized since it turns out thatthe temperature of the plasma is T ≈ keV. We start by making the simplifyingassumption that the mirror metal component of the plasma is dominated by a singleelement, A ′ . Under this assumption, the plasma consists of e ′ , H ′ , He ′ and A ′ . It isstraightforward to estimate ¯ m :¯ mm p ≃ − ξ He ′ + ξ A ′ ( A ′ − ) , (12)where ξ i ≡ n i m i n H ′ m p + n He ′ m He + n A ′ m A ′ is the halo mass fraction of species i , m p is theproton mass and A ′ is the mass number. Thus, combining Eq.(11) and Eq.(12) wehave v [ A ′ ] = v rot A ′ [2 − ξ He ′ + ξ A ′ ( A ′ − )] . (13)If we vary ξ A ′ between 0 and 1, then we obtain a lower and upper limit for v [ A ′ ]:1 A ′ (2 − ξ He ′ ) < v [ A ′ ] v rot <
11 + A ′ . (14)Mirror BBN studies[24] indicate that the primordial Helium mass fraction, Y He ′ , isrelatively high, with Y He ′ ≃ .
9, which is quite unlike the case of ordinary matter.However, like the ordinary matter sector, the primordial value for ξ A ′ is expected[24]to be small ξ A ′ ≪
1. That is, heavy mirror elements are anticipated to be synthesisedin mirror stars. If the net A ′ production from mirror stars remains subdominant,i.e. ξ A ′ ≪
1, then we expect that v [ A ′ ] to be given by the lower limit in Eq.(14)with ξ He ′ = Y He ′ ≃ .
9. The situation where ξ A ′ ≈ v [ A ′ ]. It turns out, though, that our resultsare relatively insensitive to the possible variation of v [ A ′ ] given by Eq.(14) simplybecause v [ A ′ ] /v rot << The DAMA experiments[1, 2, 3] employ large mass scintillation sodium iodide de-tectors operating in the Gran Sasso National Laboratory. These experiments wereinitially operating with a target mass of around 100 kg and since 2003 with a targetof ∼
250 kg. These experiments have been running for more than 13 years and nowhave a cumulative exposure of 1 .
17 ton × year. Importantly, the DAMA experimentshave consistently observed a positive dark matter signal, with statistical significanceof around 8.9 σ C.L.[3]. 6he DAMA experiments utilize the annual modulation signature, which providesa “smoking gun” signal for dark matter. The idea[30] is very simple. The interactionrate must vary periodically since it depends on the Earth’s velocity, v E , whichmodulates due to the Earth’s motion around the Sun. That is, R ( v E ) = R ( v ⊙ ) + ∂R∂v E ! v ⊙ ∆ v E cos ω ( t − t ) (15)where v ⊙ = v rot + 12 km/s is the sun’s velocity with respect to the galactic halo and∆ v E ≃
15 km/s, ω ≡ π/T ( T = 1 year) with t = 152 . This gives a strong systematic check on their results. Such an annual modulationhas been found in the 2-6 keVee recoil energy region at the 8 . σ confidence level,with T, t measured to be[3]: T = 0 . ± .
002 year t = 146 ± . (16)Clearly, both the period and phase are consistent with the theoretical expectationsof halo dark matter. There are no known systematic effects which could produce themodulation of the signal seen and thus it is reasonable to believe that the DAMAexperiments have detected dark matter.Mirror dark matter explains the DAMA annual modulation signal via kineticmixing induced elastic (Rutherford) scattering of the dominant mirror metal com-ponent, A ′ , off target nuclei. [The H ′ and He ′ components are too light to give asignal above the DAMA energy threshold]. We leave it up to the experimental datato determine m A ′ , although our best ‘theoretical’ guess would be A ′ ∼ O ′ given that O is the dominant metal in the ordinary matter sector. The differential interactionrate is given by: dRdE R = N T n A ′ Z dσdE R f A ′ ( v , v E ) k | v | d v = N T n A ′ λE R Z ∞| v | >v min ( E R ) f A ′ ( v , v E ) k | v | d v (17)where N T is the number of target atoms per kg of detector (we must sum over N a and I interactions separately), k = ( πv [ A ′ ]) / is the Maxwellian distributionnormalization factor and n A ′ = ρ dm ξ A ′ /m A ′ is the number density of the mirrornuclei A ′ at the Earth’s location (we take ρ dm = 0 . GeV /cm ). Here v is thevelocity of the halo particles relative to the Earth and v E is the velocity of theEarth relative to the galactic halo. Note that the lower velocity limit, v min ( E R ), is Deviations from t = 152 . t = 152 . v min = vuut ( m A + m A ′ ) E R m A m A ′ . (18)The velocity integral in Eq.(17), I ≡ Z ∞| v | >v min ( E R ) f A ′ ( v ) k | v | d v (19)can easily be evaluated in terms of error functions assuming a Maxwellian distribu-tion: f A ′ ( v , v E ) /k = ( πv [ A ′ ]) − / exp ( − ( v + v E ) /v [ A ′ ]). In fact, I = 12 yv [ A ′ ] [ erf ( x + y ) − erf ( x − y )] , (20)where x ≡ v min ( E R ) v [ A ′ ] , y ≡ v E v [ A ′ ] . (21)The differential interaction rate, Eq.(17), can then be expanded in a Taylor seriesyielding a time independent part (which we subsequently denote as the ‘absolute’rate) and time dependent modulated component: dRdE R ≃ dR dE R + dR dE R cos ω ( t − t ) , (22)with dR dE R = N T n A ′ λI ( E R , y ) E R dR dE R = N T n A ′ λ ∆ yE R ∂I∂y ! y = y . (23)Here y = v ⊙ /v [ A ′ ] , ∆ y = ∆ v E /v [ A ′ ] and ∂I∂y ! y = y = − I ( E R , y ) y + 1 √ πy v [ A ′ ] h e − ( x − y ) + e − ( x + y ) i . (24)To compare with the measured rates we must take into account the quenchingfactor and detector resolution. We include detector resolution effects by convolvingthe rates with a Gaussian: dR , dE mR = 1 √ πσ res Z dR , dE R e − ( E R − E mR ) / σ res dE R , (25)8here E mR is the measured energy. The resolution is given by[31] σ res E R = α q E R ( keV ee ) + β (26)where α = 0 . ± . , β = (9 . ± . × − . The unit of energy is the electronequivalent energy, keVee. For nuclear recoils, in the absence of any channeling,keVee = keV/ q A , where q A is the quenching factor. For DAMA, q Na ≈ . q I ≈ .
09. Channeled events where target atoms travel down crystal axis and planeshave q A ≃ < S mi ± σ i , are binned into ∆ E = 0 . dR i dE mR = 1∆ E Z E i +∆ EE i dR dE mR dE mR . (27)It is convenient to define a χ quantity: χ ( ǫ q ξ A ′ , m A ′ ) = X dR i dE mR − S mi /σ i . (28)We consider the energy range 2-8 keVee, separated into 12 bins of width 0 . m A ′ , ǫ √ ξ A ′ around the best fit, we can obtain the DAMA allowed region . There area number of systematic uncertainties which can be included in the analysis and wehave examined the following: a) considering v [ A ′ ] within its expected limits givenby Eq.(14), b) varying the quenching factors for Iodine and sodium by ± q Na = 0 . ± .
06 and q I = 0 . ± .
02, c) varying the detector resolution over The DAMA data are efficiency corrected so there is no need to include the detection efficiencyin Eq.(27). For the purposes of the fit, we analytically continue the mass number, A ′ , to non-integer values,with Z ′ = A ′ /
2. Since the realistic case will involve a spectrum of elements, the effective mass canbe non-integer σ uncertainty and d) varying v rot = 254 ±
32 km/s, that is around ± σ from itsestimated value. The variation of quenching factor and resolution were taken intoaccount by minimizing χ ( q I , q Na , σ res , m A ′ , ǫ √ ξ A ′ ) over 20% variation of q I and q Na ,and over the 2 σ uncertainty in σ res . This defines − χ ( m A ′ , ǫ √ ξ A ′ ). The best fit forDAMA has − χ min ≃ . -0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04 1 2 3 4 5 6 7 8 S m c oun t s / ( k g k e V ee da y ) Energy [keVee] v rot = 254 km/s D A M A T HR ES H O L D -0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04 1 2 3 4 5 6 7 8 S m c oun t s / ( k g k e V ee da y ) Energy [keVee] v rot = 254 km/s D A M A T HR ES H O L D -0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04 1 2 3 4 5 6 7 8 S m c oun t s / ( k g k e V ee da y ) Energy [keVee] v rot = 254 km/s D A M A T HR ES H O L D -0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04 1 2 3 4 5 6 7 8 S m c oun t s / ( k g k e V ee da y ) Energy [keVee] v rot = 254 km/s D A M A T HR ES H O L D Figure 1: DAMA annual modulation amplitude versus measured recoil Energy forthe parameters: m A ′ /m p = 20 , ǫ √ ξ A ′ = 7 . × − and v rot = 254 km/s. Thesolid (dashed) line corresponds to the lower (upper) v [ A ′ ] limit given in Eq.(14).Negligible channeling has been assumed.Favoured regions in the m A ′ , ǫ √ ξ A ′ plane can be obtained by evaluating thecontours with − χ = − χ min +9 (roughly 99% C.L.). In figure 2 we plot the allowedregions for DAMA assuming v rot = 222 km/s [fig 2a], v rot = 254 km/s [fig 2b] and v rot = 286 km/s [fig 2c] . Also shown in the figures are the DAMA allowed region as-suming that channeling occurs with fractions as originally estimated by the DAMAcollaboration[33]. It has been emphasised recently[34] that the systematic uncer-tainty in q Na might be as large as q Na = 0 . ± .
13 given the lack of measurementsof the quenching factor in the low energy region. If this is the case, then we findthat the favoured regions extend out to somewhat ( ≈ − m A ′ valuesthan that given in figure 2. 10 ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling D A M A - no c hanne li ng Figure 2a: DAMA [99% C.L.] allowed region in the m A ′ , ǫ √ ξ A ′ plane, assumingnegligible channeling fraction, for v rot = 222 km/s. Solid (dashed) line correspondsto the lower (upper) v [ A ′ ] limit given in Eq.(14). Also shown for comparison is theDAMA allowed regions if channeling occurs with fractions originally estimated bythe DAMA collaboration. ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChanneling D A M A - no c hanne li ng Figure 2b: Same as figure 2a, except with v rot = 254 km/s.11 ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchanneling D A M A - no c hanne li ng ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchanneling D A M A - no c hanne li ng Figure 2c: Same as figure 2a, except with v rot = 286 km/s.The main features of the annual modulation spectrum predicted by A ′ darkmatter can be easily understood. As discussed earlier[10], at low E R , where x ( E R ) ≪ y , dR /dE R is negative. As E R increases, dR /dE R changes sign and reaches amaximum at the value of E R where x ( E R ) ≈ y , or equivalently, the value of E R where v min ( E R ) = v rot . At high E R ( x ≫ y ), dR /dE R →
0. From Eq.(18) thismeans that the position of the peak, E peakR , is given by: E peakR ≈ m A m A ′ ( m A + m A ′ ) v rot . (29)For low m A ′ < ∼ m p the annual modulation signal arises predominantly from A ′ scattering with N a , while for m A ′ > ∼ m p scattering off both N a and I contributessignificantly to produce the signal . Note that since v [ A ′ ] ≪ v rot the velocitydistribution is so narrow that the width of the peak is dominated by the detectorresolution. This explains the relative insensitivity of the fit to the particular v [ A ′ ]value which is evident in figures 1,2.To summarize, we see that without channeling the DAMA annual modulationsignal can be explained for a relatively wide range of m A ′ values, which includesthe region around m A ′ /m p ∼
16, expected if A ′ = O ′ dominates the mirror metal In the case where channeling is assumed with the fractions originally estimated by the DAMAcollaboration[33] the annual modulation signal is dominated by interactions with I only. See ref.[10]for further discussion of this case. The CoGeNT experiment operating in the Soudan Underground Laboratory hasrecently presented new results in their search for light dark matter interactions[4].With a low energy threshold of 0 . A ′ mirror dark matter interactions. In ref.[13] we showed that theCoGeNT excess is compatible with mirror dark matter expectations and thus pro-vides a model dependent check of the DAMA signal, which we now examine in moredetail.To compare with the measured event rate, we include detector resolution effectsand overall detection efficiency: dR dE mR = ǫ f ( E mR ) 1 √ πσ Z dR dE R e − ( E R − E mR ) / σ dE R (30)where E mR is the measured energy and σ = σ n + (2 . E R ηF with σ n = 69 . η = 2 .
96 eV and F = 0 . ǫ f ( E mR ), was given infigure 3 of ref.[4], which we approximate via ǫ f ( E mR ) ≃ .
871 + (0 . /E mR ) . (31)The energy is in keVee units (ionization energy). For nuclear recoils in the absenceof any channeling, keV ee = keV /q , where q ≃ .
21 is the relevant quenching factorin the near threshold region[34].We fit the CoGeNT data in the low recoil energy range assuming A ′ dark matterand that the background is an energy independent constant, together with twoGaussians to account for the Zn (1.1 keV) and Ge (1.29 keV) L-shell electroncapture lines. Initially fixing m A ′ /m p = 20 and v rot = 254 km/s, as an example,we find a best fit of χ min ≃ . − ǫ √ ξ A ′ =6 . × − (independently of whether we take the upper or lower limiting values of v ). This fit for CoGeNT is shown in figure 3.13 c oun t s / . k e V . k g da y Ionization energy (keVee) v rot = 254 km/s C o G e N T T h r e s ho l d c oun t s / . k e V . k g da y Ionization energy (keVee) v rot = 254 km/s C o G e N T T h r e s ho l d c oun t s / . k e V . k g da y Ionization energy (keVee) v rot = 254 km/s C o G e N T T h r e s ho l d c oun t s / . k e V . k g da y Ionization energy (keVee) v rot = 254 km/s C o G e N T T h r e s ho l d c oun t s / . k e V . k g da y Ionization energy (keVee) v rot = 254 km/s C o G e N T T h r e s ho l d c oun t s / . k e V . k g da y Ionization energy (keVee) v rot = 254 km/s C o G e N T T h r e s ho l d Figure 3: Fit of the CoGeNT spectrum for m A ′ /m p = 20 , ǫ √ ξ A ′ = 6 . × − and v rot = 254 km/s. Thick solid (dashed) line is with lower (upper) v [ A ′ ] limit givenin Eq.(14). Also shown is the dark matter contribution to the signals (thin lines).Negligible channeling has been assumed.The shape of the spectrum is nicely fit by A ′ dark matter due primarily to the E R dependent Rutherford cross section: dσ/dE R ∝ /E R . As further data is collectedthis E R dependence will be more stringently constrained, which will pose a morerigorous test of the mirror dark matter theory.As in the DAMA case, to account for some of the possible systematic uncertain-ties we vary the quenching factor by ±
20% [i.e. take q Ge = 0 . ± . χ function, χ ( q Ge , ǫ q ξ A ′ , m A ′ ) = X dR i dE mR − data i /σ i (32)where dR i dE mR is the differential rate averaged over the binned energy. We take theexperimental errors to be purely statistical, so that σ i = √ data i . We minimize χ ( q Ge , m A ′ , ǫ √ ξ A ′ ) over the 20% variation in q Ge , which defines − χ ( m A ′ , ǫ √ ξ A ′ ). Ofcourse, we also minimize χ with respect to the parameters of the background modeldescribing the amplitudes of the Zn (1.1 keV) and Ge (1.29 keV) L-shell electroncapture lines and adjusting also the constant background component. Note that no14ackground exponential is assumed (or needed) to fit the data. The CoGeNT allowedregion in the m A ′ , ǫ √ ξ A ′ plane is then defined via contours − χ = − χ min +9 (roughly99% C.L.).In figure 4 we plot the allowed regions for CoGeNT together with the DAMAallowed region for v rot = 222 km/s [fig 4a], v rot = 254 km/s [fig 4b] and v rot = 286km/s [fig 4c] . We have allowed for a 20% systematic uncertainty in both CoGeNTand DAMA quenching factors. In these figures we have assumed ξ A ′ ≪ v [ A ′ ] is given by the lower limit given in Eq.(14). The case where ξ A ′ ≃ ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling DAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling DAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling DAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling DAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling DAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling DAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling DAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling DAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/sDAMAChanneling DAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t Figure 4a: DAMA and CoGeNT [99% C.L.] allowed regions in the m A ′ /m p , ǫ √ ξ A ′ plane, assuming negligible channeling fraction, for v rot = 222 km/s. Also shown area) DAMA allowed regions if channeling occurs with fractions originally estimatedby the DAMA collaboration and b) the exclusion limits from CDMS/Si, CDMS/Geand XENON100 experiments. [The region excluded is to the right of the exclusionlimits]. 15 ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/sDAMAChannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t Figure 4b: Same as figure 4a, except with v rot = 254 km/s. ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/sDAMAchannelingDAMA - no channeling C o G e N T - no c hanne li ng X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t Figure 4c: Same as figure 4a, except with v rot = 286 km/s.16n computing the exclusion limits we have allowed for a 20% systematic uncer-tainty in energy threshold. That is, the threshold for CDMS/Si[36] was taken to be8 . keV nr rather than the quoted 7 . keV nr , the threshold for CDMS/Ge[5] was takento be 12 keV nr rather than the quoted 10 keV nr and the threshold for XENON100[37]was taken to be 10 . keV nr rather than the quoted 8 . keV nr . For the CDMS/Siexperiment, we used the quoted[36] raw exposure of 33 . E R < keV nr ,38 . < E R ( keV nr ) <
15 and 53 . E R > keV nr , andassumed a detection efficiency of 20% in the energy region near threshold. For theCDMS/Ge experiment we assumed the total raw exposure of 1010 kg-days and adetection efficiency of ǫ f = 0 .
18 + 0 . E R in the low energy region of interest[5].For the XENON100 experiment we used the quoted[37] raw exposure of 447 kg-daystogether with a detection efficiency of 0 . A ′ dark matter, which is due to its light target element andrelatively low threshold. The CDMS/Si experiment constrains the allowed region to m A ′ /m p < ∼
30. Observe also that the CDMS/Si experiment seems to exclude the twoevents seen in the CDMS/Ge experiment[5] as being due to the same componentwhich can explain the DAMA and CoGeNT data. It is possible, though, to interpretthe two events seen by CDMS/Ge as a hint of a heavier ∼ F e ′ component. Thisinterpretation requires[12] ξ F e ′ /ξ A ′ ∼ − and is not excluded by CDMS/Si or anyother experiment. Such a small F e ′ component does not significantly affect the fitof the DAMA or CoGeNT experiments. We will examine the effects of the F e ′ component for the higher threshold experiments in more detail in section 7.We have also performed a global analysis of the DAMA and CoGeNT signals.Fixing v rot = 254 km/s and evaluating χ for the combined DAMA+CoGeNT data,we have found χ min = 24 . m A ′ /m p = 24 , ǫ √ ξ A ′ = 6 . × − .Excellent fits to the combined DAMA and CoGeNT data are also obtained for v rot = 222 km/s and v rot = 286 km/s. In figure 5 we plot the favoured region ofparameter space for the combined fit of the DAMA and CoGeNT data for threerepresentative values of v rot . Exclusion limits from the XENON10 experiment are only marginally better than theXENON100 exclusion limit (but not better than the CDMS/Si limit). For a recent discussionabout the calibration and other uncertainties in the XENON low energy region, see ref.[38]. ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/s D A M A + C o G e N T X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/s D A M A + C o G e N T X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/s D A M A + C o G e N T X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/s D A M A + C o G e N T X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 222 km/s D A M A + C o G e N T X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t Figure 5a: DAMA and CoGeNT [99% C.L.] global allowed region in the m A ′ /m p , ǫ √ ξ A ′ plane, assuming negligible channeling fraction, for v rot = 222 km/s. Also shown arethe exclusion limits from CDMS/Si, CDMS/Ge and XENON100 experiments. [Theregion excluded is to the right of the exclusion limits]. ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/s D A M A + C o G e N T X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/s D A M A + C o G e N T X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/s D A M A + C o G e N T X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/s D A M A + C o G e N T X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 254 km/s D A M A + C o G e N T X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t Figure 5b: Same as figure 5a except that v rot = 254 km/s.18 ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/s D A M A + C o G e N T X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/s D A M A + C o G e N T X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/s D A M A + C o G e N T X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/s D A M A + C o G e N T X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t ε ( ξ A ’ ) / m A’ /m p v rot = 286 km/s D A M A + C o G e N T X enon100 % C . L . li m i t CD M S / G e % C . L . li m i t CD M S / S i % C . L . li m i t Figure 5c: Same as figure 5a except that v rot = 286 km/s.The CoGeNT experiment has been running continuously since December 2009,and might collect enough data to search for the annual modulation signal. In figure6 we show results for the annual modulation amplitude predicted for the CoGeNTexperiment. Interestingly we see that there is a change of sign for the annual modula-tion amplitude at low energies E R ≈ . − . more events during the(northern) winter/fall than the (northern) summer/spring. This might provide auseful means of experimentally distinguishing this dark matter theory from otherpossible explanations. 19 S m c oun t s / ( k g k e V ee da y ) Energy [keVee] v rot = 254 km/s C o G e N T T h r e s ho l d -2-1.5-1-0.5 0 0.5 1 0 0.5 1 1.5 2 2.5 3 S m c oun t s / ( k g k e V ee da y ) Energy [keVee] v rot = 254 km/s C o G e N T T h r e s ho l d -2-1.5-1-0.5 0 0.5 1 0 0.5 1 1.5 2 2.5 3 S m c oun t s / ( k g k e V ee da y ) Energy [keVee] v rot = 254 km/s C o G e N T T h r e s ho l d -2-1.5-1-0.5 0 0.5 1 0 0.5 1 1.5 2 2.5 3 S m c oun t s / ( k g k e V ee da y ) Energy [keVee] v rot = 254 km/s C o G e N T T h r e s ho l d Figure 6: CoGeNT annual modulation amplitude versus recoil energy. For somerepresentative parameters: ǫ √ ξ A ′ = 7 . × − , m A ′ /m p = 18 (solid line), ǫ √ ξ A ′ =6 . × − , m A ′ /m p = 20 (dashed line), ǫ √ ξ A ′ = 6 . × − , m A ′ /m p = 22 (dottedline). All for v rot = 254 km/s. The figure assumes 100% detection efficiency. In addition to nuclear recoils, electron recoils from mirror electron scattering offbound atomic electrons in the target volume can also occur. The e ′ component ofthe halo is expected to be distributed with Maxwellian velocity distribution, andsince m e ′ ≪ ¯ m , we expect v [ e ′ ] ≫ v rot . In fact, from Eqs.(11,12) we can estimatethat v [ e ′ ] is in the range: (cid:20) m p m e (cid:21) − ξ He ′ < ∼ v [ e ′ ] v rot < ∼ (cid:20) m p m e (cid:21) A ′ A ′ / . (33)Since v [ e ′ ] ≫ v rot we can, to a good approximation, neglect v rot when dealing with e ′ − e scattering. This means that electron recoils give a negligible contribution to theannual modulation signal, however they can contribute significantly to the absoluterate at energies below 2 keVee. Interestingly such a rise at low energies was observedin the CDMS electron scattering data[6] and is compatible with ǫ ∼ − [11]. Recallthat the DAMA experiment doesn’t discriminate against electron recoils, so theDAMA experiment is also sensitive to electron recoils through their contribution tothe absolute rate as we now discuss. 20he DAMA experiment constrains the absolute event rate to be less than around1 cpd/kg/keVee in the region near threshold. We shall here examine the implicationsof this constraint for mirror dark matter. As discussed above, we expect both nuclearrecoils and electron recoils to contribute to the absolute rate from dark matterinteractions. The nuclear recoil contribution can easily by calculated as in Eq.(25).The electron recoil contribution is more complicated. An accurate treatment ofthe cross section would require knowledge of the wavefunctions of all the electronsin the N a and I atoms. A rough estimate of the electron scattering contributioncan be made by[11] considering only the contribution of the loosely bound (bindingenergy less than 0.1 keV) outer shell electrons in N a and I . The number of suchloosely bound atomic electrons is 9 for N a and 17 for I . We further approximatethese electrons as free and at rest, and compute the elastic scattering rate on theseelectrons. Thus, within this approximation the cross section has the form given inEq.(6), with λ e = 2 πǫ α /m e . The predicted differential interaction rate is then: dRdE R = gN T n e ′ Z dσdE R f e ′ ( v ) k | v | d v = gN T n e ′ λ e E R Z ∞| v | >v min ( E R ) f e ′ ( v ) k | v | d v (34)where N T is the number of target N aI pairs per kg of detector and k = ( πv [ e ′ ]) / is the Maxwellian distribution normalization factor. The quantity g = 26, is thenumber of loosely bound atomic electrons per N aI pair as we discussed above.Also, n e ′ is the halo e ′ number density. Assuming the halo is fully ionized it isstraightforward to show that n e ′ = " − ξ He ′ − ξ A ′ ρ dm m p . (35)Note that the lower velocity limit in Eq.(34), v min ( E R ), is given by the kinematicrelation: v min = s E R m e . (36)The velocity integral in Eq.(34) can be analytically solved leading to: dRdE R = gN T n e ′ λ e E R e − x √ πv [ e ′ ] ! (37)where x = v min /v [ e ′ ]. Finally, to compare with the experimentally measured ratewe convolve this rate, with a Gaussian [as in Eq.(25)] to take into account the finitedetector resolution.There are many potential systematic uncertainties in the absolute rate, and weconsider the following: the uncertainty in the measured detector resolution [i.e.21aking a 2 σ variation of the measured σ res given in Eq.(26)], a ∼
30% uncertainty inthe e ′ − e scattering cross section, and a 0 .
25 keVee uncertainty in energy calibration.In figure 7 we give an example of the absolute rate predicted for the DAMAexperiment showing both electron and nuclear recoil contributions separately, usingthe aforementioned systematic uncertainties to minimize the rate. Since the databelow 2 keVee is formally below the DAMA threshold we do not attempt to fit thisdata, and must await the forthcoming DAMA upgrade which is designed to lowerthe energy threshold. The rise in event rate below 2 keVee, which is illustrated infigure 7, is a prediction of this model which DAMA can potentially confirm whenthey lower their energy threshold. C oun t s / ( k g k e V da y ) Energy [keVee] v rot = 222 km/s D A M A T HR ES H O L D C oun t s / ( k g k e V da y ) Energy [keVee] v rot = 222 km/s D A M A T HR ES H O L D C oun t s / ( k g k e V da y ) Energy [keVee] v rot = 222 km/s D A M A T HR ES H O L D C oun t s / ( k g k e V da y ) Energy [keVee] v rot = 222 km/s D A M A T HR ES H O L D C oun t s / ( k g k e V da y ) Energy [keVee] v rot = 222 km/s D A M A T HR ES H O L D Figure 7: DAMA absolute rate from nuclear recoils with negligible channeling (dot-ted line), electron recoils (dashed line) and combined (solid line) for the parameters: m A ′ /m p = 20, ǫ √ ξ A ′ = 5 . × − and ǫ = 1 . × − ( ⇒ ξ A ′ = 0 . v rot = 222km/s has been assumed. 22n figure 8, we given an example of the electron scattering rate predicted forthe CDMS Germanium electron scattering experiment[6], for the same parame-ters as chosen for figure 7, together with a simple linear model for the background( R ( background ) = 1 . − . E R ). For the Germanium experiment the resolution isgiven by[6] σ = q (0 . + (0 . E R /keV keV (38)and the rate as in Eq.(37) but with g = 14[11]. . C oun t s / ( k g k e V da y ) Energy [keVee] v rot = 222 km/s 0 2 4 6 8 10 1 2 3 4 5 6 7 8 C oun t s / ( k g k e V da y ) Energy [keVee] v rot = 222 km/s
Figure 8: CDMS/Ge absolute rate from electron recoils for the same parameters asfigure 7, together with a simple linear background model.The rise in event rate seen below 2 keV in both DAMA and CDMS electronscattering data is very interesting, but is formally below the threshold of both ofthese experiments, and therefore needs to be confirmed by future measurements.Conservatively, the only limit that we can obtain is by looking at the data above 2keV. Demanding that the total rate in the first energy bin above threshold be lessthan 1 cpd/kg/keV, suggests an upper limit for ǫ . This upper limit depends quitesensitively on the value of v [ e ′ ] (and hence also on v rot and ξ A ′ ). If ξ A ′ ≪
1, then In ref.[11], we assumed a cutoff at E R = 0 . E R = 0 . E R →
23e find: ǫ < ∼ . × − , if v rot = 222 km / s ǫ < ∼ . × − , if v rot = 254 km / s ǫ < ∼ . × − , if v rot = 286 km / s (39)If ξ A ′ ≈ ǫ < ∼ . × − , if v rot = 222 km / s ǫ < ∼ . × − , if v rot = 254 km / s ǫ < ∼ . × − , if v rot = 286 km / s . (40)In computing these upper limits we have allowed for some of the systematic un-certainties by including: the uncertainty in the measured detector resolution [i.e.taking a 2 σ variation of the measured σ res given in Eq.(26)], a ∼
30% uncertainty inthe e ′ − e scattering cross section, and a 0 .
25 keV uncertainty in energy calibration.It should be emphasized, though, that the systematic uncertainty can potentiallybe much larger in view of the large event rate at low energies which is smeared into E R > ∼ E R < ∼ ǫ . Finally, astrophysicaluncertainties in modelling the halo will add further systematic uncertainties to the e ′ − e scattering rate due to its sensitive dependence on v [ e ′ ]. Departures fromspherical symmetry or a rotating halo etc will lead to deviations from Eq.(10), andhence to v [ e ′ ]. [Note though that the A ′ scattering rate is much less sensitive touncertainties in v since v [ A ′ ] ≪ v rot , and thus such uncertainties will have littleaffect on our DAMA/CoGeNT fit]. Thus, given these systematic uncertainties ourlimits on ǫ should be viewed more as a guide, than strict upper limits.Similar limits to the above, with the same caveats regarding potentially largersystematic uncertainties, can be obtained from the CDMS electron scattering data.In combination with our estimate of ǫ √ ξ A ′ ≈ (7 ± × − from the DAMA andCoGeNT experiments, the limits given in Eq.(40) indicate ξ A ′ > ∼ − at v rot = 222km/s, with stronger bounds at higher v rot values. This suggests that the mirrorsector may have a higher metal content than the ordinary matter sector. This iscertainly possible, and might be due to a period of rapid mirror star formation andevolution during the first few billion years of the Universe (which is suspected giventhe computed high primordial Y He ′ ≈ . The CDMS/Ge and EdelweissII experiments utilize a Germanium target, and bothof these experiments have found evidence for dark matter interactions. Due to their24elatively high threshold of 10 keV nr for CDMS/Ge and 20 keV nr for Edelweiss, theseexperiments are not sensitive to the the dominant A ′ component. The light mass andnarrow velocity dispersion of the A ′ component ensure that the predicted rate forthese experiments is much less than 1 event for their net exposures of approximately200 kg-days and 322 kg-days respectively. However, these experiments are sensitiveto heavier mirror dark matter components of the halo, and provide the most sensitiveprobes of the anticipated F e ′ component.In figure 9 we have given an example of the recoil energy spectrum predicted forCDMS/Ge (figure 9a) and for EdelweissII (figure 9b). The numerical work assumedthe CDMS/Ge[5] (EdelweissII[8]) resolution was given by σ res = 0 . σ res = 1 . ef f = 0 . . E R ( ef f ≃ v [ F e ′ ]was obtained from Eq.(13) assuming that ξ A ′ ≪
1, i.e. v [ F e ′ ] = v rot [ m F e /m p ][2 − ξ He ′ ] (41)where ξ He ′ ≈ . C oun t s / ( k g k e V da y ) Energy [keV] v rot = 254 km/s CD M S / G e T h r e s ho l d C oun t s / ( k g k e V da y ) Energy [keV] v rot = 254 km/s CD M S / G e T h r e s ho l d Figure 9a: CDMS/Ge spectrum for
F e ′ dark matter with ǫ √ ξ F e ′ = 5 . × − . Wehave assumed v rot = 254 km/s. 25 C oun t s / ( k g k e V da y ) Energy [keV] v rot = 254 km/s E de l w e i ss T h r e s ho l d C oun t s / ( k g k e V da y ) Energy [keV] v rot = 254 km/s E de l w e i ss T h r e s ho l d Figure 9b: Edelweiss spectrum for
F e ′ dark matter with ǫ √ ξ F e ′ = 5 . × − . Wehave assumed v rot = 254 km/s.The CDMS/Ge experiment finds two events at energies 12.3 and 15.5 keV whichare clearly compatible with the shape of the predicted recoil energy spectrum forCDMS/Ge. Edelweiss finds 2 events in their acceptance region with energy justabove threshold, which is also compatible with the shape of the predicted recoilenergy spectrum for EdelweissII. It is therefore plausible that both of these exper-iments have detected F e ′ dark matter. Under this assumption, we can obtain anestimate of the parameter: ǫ √ ξ F e ′ for each of these experiments: ǫ √ F e ′ = (3 . +2 . − . ) × − from CDMS / Ge ǫ √ F e ′ = (1 . +1 . − . ) × − from EdelweissII . (42)Here we have only included the statistical errors at 95% C.L. The systematic uncer-tainties can be quite large, given the rapidly rising event rates towards lower E R .For example, we find that a 20% systematic uncertainty in energy scale would leadto a ∼
20% uncertainty in the estimate for ǫ √ ξ F e ′ from CDMS/Ge and a 50% in theestimate for ǫ √ ξ F e ′ from EdelweissII. Also note that the systematic uncertaintiesin the form factor begin to be quite significant for Edelweiss due to the large recoilenergy threshold. Clearly systematic uncertainties can reconcile the two estimatesof ǫ √ F e ′ from CDMS/Ge and EdelweissII. The XENON100 experiment, with ananticipated net exposure of over 1000 kg-days should be able to confirm the presenceof a F e ′ signal in the near future. 26ombining the above estimate for ǫ √ ξ F e ′ with our earlier fit for ǫ √ ξ A ′ suggestsa ξ F e ′ /ξ A ′ fraction of around ∼ − which is plausible. Also note that such a small ξ F e ′ component does not significantly affect the fit of the DAMA and CoGeNTexperiments.The CRESSTII experiment using a CaW O target has recently reported 32 darkmatter candidate events, with a background of around 9 events in their signal region,which suggests a statistically significant low energy excess of around 23 events. Thethreshold of CRESSTII is 10 keV nr , with the excess of events reported in the oxygenband near threshold. The CRESSTII experiment is potentially sensitive to both the A ′ component and the F e ′ component. We illustrate this in figure 10, where we givethe predicted CRESST recoil energy spectrum for an example with parameters closeto the DAMA/CoGeNT best fit. As this figure illustrates, the A ′ component is onlyimportant in the region near threshold, while the F e ′ contribution is somewhat morespread out. Thus, in principle these two components can be distinguished from theobserved energy distribution of events (so long as they both contribute significantlyto the signal). C oun t s / ( k g k e V da y ) Energy [keV] CR ESS T II T h r e s ho l d v rot = 254 km/s 0 5 10 15 20 8 10 12 14 16 18 20 C oun t s / ( k g k e V da y ) Energy [keV] CR ESS T II T h r e s ho l d v rot = 254 km/s 0 5 10 15 20 8 10 12 14 16 18 20 C oun t s / ( k g k e V da y ) Energy [keV] CR ESS T II T h r e s ho l d v rot = 254 km/s 0 5 10 15 20 8 10 12 14 16 18 20 C oun t s / ( k g k e V da y ) Energy [keV] CR ESS T II T h r e s ho l d v rot = 254 km/s Figure 10: CRESSTII spectrum in the oxygen band for A ′ , F e ′ dark matter assuming v rot = 254 km/s. The dashed line is the A ′ contribution with parameters ǫ √ ξ A ′ =6 × − , m A ′ = 22 .
0. The dotted line is for the
F e ′ contribution with parameters ǫ √ ξ F e ′ = 1 . × − . The solid line is the sum of the two contributions. [100%detection efficiency has been assumed, and a resolution of 0 . A ′ contribution has a very large annual modulation inthe energy region above threshold. In fact, dR dE mR ≈ . dR dE mR . (43)The large annual modulation results because the interactions arise from A ′ particlesin the tail of the narrow Maxwellian distribution and therefore can be greatly affectedby small changes in the velocity of the Earth. Thus, if A ′ does contribute significantlyto the signal, an examination of events in the Ethreshold < E < Ethreshold +3 keV bin should show a statistically significant annual modulation with just 1-2 years ofdata. The annual modulation predicted for the F e ′ events is smaller, but still quitelarge: dR dE mR ≈ . dR dE mR (44)and could also be eventually seen provided that a significant proportion of the eventsare due to F e ′ interactions. In conclusion, we have confronted the mirror dark matter theory with the mostrecent experimental data. We examined the DAMA experiments allowing for thepossibility of a negligible channeling fraction and showed that under that assump-tion the impressive DAMA signal can be fully explained. Mirror dark matter cansimultaneously explain the CoGeNT low energy excess, and remains compatiblewith the results of the other experiments, including interesting hints of dark matterdetection from CDMS/Ge, EdelweissII and CRESSTII. Taking into account someof the possible systematic uncertainties in quenching factor, detector resolution,galactic rotational velocity and velocity dispersion, we have mapped out the allowedregions of parameter space in the m A ′ , ǫ √ ξ A ′ plane [Figures 4,5]. The net resultis that the mirror dark matter candidate can explain all of the existing direct de-tection experiments, with parameters ǫ √ ξ A ′ = (7 ± × − , m A ′ /m p = 22 ± ξ A ′ > ∼ − , ξ F e ′ /ξ A ′ ∼ − .Importantly this theory will soon be more stringently tested by: a) Further datafrom DAMA: in the near future the DAMA collaboration plan to upgrade theirexperiment with the aim of lowering their energy threshold. As illustrated in figure1, they should see a change in sign of their modulation amplitude between 1.0-2.0keVee. b) The CRESSTII experiment, with light target element O ′ and threshold10 keV is potentially sensitive to both A ′ and F e ′ components. They should find arapidly falling energy spectrum with most of their events between 10 and 14 keV,with a very large annual modulation. c) The CDMS/Si experiment is sensitive tothe dominant mirror metal component, A ′ . This experiment currently provides the28trongest constraint from the null experiments and limits m A ′ /m p < ∼
30. Furtherdata from CDMS/Si should either see a signal, or produce tighter constraints on m A ′ . d) More data from the CoGeNT experiment should be helpful. Of particularnote, is that mirror dark matter predicts a detectable annual modulation signal forCoGeNT (figure 6) with the distinctive feature that it changes in sign at energiesaround E R ≈ . − . ∼ F e ′ component which should exist at some level. The two events seenin CDMS/Ge and in EdelweissII are consistent with this component, and suggests ξ F e ′ /ξ A ′ ∼ − . f) In the longer term, directional experiments will be importantdue to the low velocity dispersion of mirror dark matter [ v [ A ′ ] ≪ v rot ]. Mirror dark matter is not expected to show up in collider experiments throughthe photon-mirror photon kinetic mixing induced interactions. However, the Higgs- mirror Higgs quartic interaction [Eq.(3)] leads to modifications of the properties ofthe Higgs boson[14] which can potentially be observed at the LHC and Tevatron[39].Sensitive orthopositronium studies[40], might be able to directly probe ǫ ∼ − andthus provide further tests of the mirror dark matter scenario. Such an experimenthas been proposed recently in ref.[41]. Acknowledgments
This work was supported by the Australian Research Council.
References [1] R. Bernabei et al . (DAMA Collaboration), Riv. Nuovo Cimento. 26, 1 (2003)[astro-ph/0307403]; Int. J. Mod. Phys. D13, 2127 (2004); Phys. Lett. B480, 23(2000).[2] R. Bernabei et al . (DAMA Collaboration), Eur. Phys. J. C56: 333 (2008)[arXiv:0804.2741].[3] R. Bernabei et al . (DAMA Collaboration), arXiv: 1002.1028.[4] C. E. Aalseth et al. (CoGeNT Collaboration), arXiv:1002.4703.[5] Z. Ahmed et al. (CDMS Collaboration), arXiv: 0912.3592.[6] Z. Ahmed et al. (CDMS Collaboration), Phys. Rev. D81: 042002 (2010) [arXiv:0907.1438].[7] W. Seidel (for the CRESST collaboration), Talk given at IDM2010, July 2010. A dark matter detection experiment in the southern hemisphere would be very useful because,due to the Earth’s orientation, it could sensitively probe the possible diurnal variation if there areaccumulated mirror particles in the Earth’s core. et al. (MACHO collaboration), ApJ, 542, 281 (2000) [arXiv: astro-ph/0001272]; P. Tisserand et al. , (EROS Collaboration) Astron. Astrophys,469, 387 (2007) [arXiv: astro-ph/0607207].[20] D. Clowe et al. , Astrophys. J. 648, L109 (2006) [astro-ph/0608407].[21] Z. K. Silagadze, arXiv:0808.2595.[22] R. Foot, A. Yu. Ignatiev and R. R. Volkas, Phys. Lett. B503, 355 (2001)[arXiv: astro-ph/0011156]; R. Foot, Int. J. Mod. Phys. A19 3807 (2004) [astro-ph/0309330]; R. Foot and Z. K. Silagadze, Int. J. Mod. Phys. D14, 143 (2005)[astro-ph/0404515]; P. Ciarcelluti and R. Foot, Phys. Lett. B679, 278 (2009)[arXiv: 0809.4438]. See also, S. Davidson, S. Hannestad and G. Raffelt, JHEP5, 3 (2000) [arXiv: hep-ph/0001179].[23] G. Raffelt,
Stars as Laboratories for Fundamental Physics,
Chicago UniversityPress (1996).[24] P. Ciarcelluti and R. Foot, Phys. Lett. B690, 462 (2010) [arXiv:1003.0880].[25] Z. Berezhiani et al. , Astropart. Phys. 24, 495 (2006) [astro-ph/0507153].3026] Z. Berezhiani, D. Comelli and F. L. Villante, Phys. Lett. B503, 362 (2001) [hep-ph/0008105]; L. Bento and Z. Berezhiani, Phys. Rev. Lett. 87, 231304 (2001)[hep-ph/0107281]; A. Yu. Ignatiev and R. R. Volkas, Phys. Rev. D68, 023518(2003) [hep-ph/0304260]; R. Foot and R. R. Volkas, Phys. Rev. D68, 021304(2003) [hep-ph/0304261]; Phys. Rev. D69, 123510 (2004) [hep-ph/0402267]; Z.Berezhiani, P. Ciarcelluti, D. Comelli and F. L. Villante, Int. J. Mod. Phys.D14, 107 (2005) [astro-ph/0312605]; P. Ciarcelluti, Int. J. Mod. Phys. D14,187 (2005) [astro-ph/0409630]; Int. J. Mod. Phys. D14, 223 (2005) [astro-ph/0409633].[27] R. H, Helm, Phys. Rev. 104, 1466 (1956).[28] J. D. Lewin and P. F. Smith, Astropart. Phys. 6, 87 (1996).[29] M. J. Reid et al. , Astrophys. J. 700, 137 (2009) [arXiv: 0902.3913].[30] A. K. Drukier, K. Freese and D. N. Spergel, Phys. Rev. D33, 3495 (1986); K.Freese, J. A. Frieman and A. Gould, Phys. Rev. D37, 3388 (1988).[31] R. Bernabei et al . (DAMA Collaboration), Nucl. Instrum. Meth. A592: 297(2008) [arXiv: 0804.2738].[32] N. Bozorgnia, G.B. Gelmini and P. Gondolo, arXiv: 1006.3110.[33] R. Bernabei et al . (DAMA Collaboration), Eur. Phys. J. C53, 205 (2008)[arXiv: 0710.0288].[34] D. Hooper, J. I. Collar, J. Hall and D. McKinsey, arXiv: 1007.1005.[35] C. E. Aalseth et al. (CoGeNT Collaboration), Phys. Rev. Lett. 101, 251301(2008) [arXiv: 0807.0879].[36] J. P. Filippini, Ph.D thesis, 2008.[37] E. Aprile et al. (XENON100 Collaboration), arXiv: 1005.0380 (2010).[38] J. I. Collar and D. N. McKinsey, arXiv:1005.0838; arXiv: 1005.3723; TheXenon Collaboration, arXiv: 1005.2615; J. I. Collar, arXiv: 1006.2031; P.Sorensen, arXiv: 1007.3549.[39] A. Yu. Ignatiev and R. R. Volkas, Phys. Lett. B487, 294 (2000) [hep-ph/0005238]; R. Barbieri, T. Gregoire and L. J. Hall, hep-ph/0509242; W.Li, P. Yin and S. Zhu, Phys. Rev. D76, 095012 (2007) [arXiv: 0709.1586].[40] S. L. Glashow, Phys. Lett. B167, 35 (1986); R. Foot and S. N. Gninenko, Phys.Lett. B480, 171 (2000) [hep-ph/0003278].[41] P. Crivelli et al.et al.