Captures of Hot and Warm Sterile Antineutrino Dark Matter on EC-decaying Ho-163 Nuclei
aa r X i v : . [ a s t r o - ph . C O ] A ug Captures of Hot and Warm Sterile Antineutrino Dark Matteron EC-decaying
Ho Nuclei
Y.F. Li a 1 and
Zhi-zhong Xing a b 2a
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China b Center for High Energy Physics, Peking University, Beijing 100080, China
Abstract
Capturing low-energy electron antineutrinos on radioactive
Ho nuclei, whichdecay into
Dy via electron capture (EC), is a noteworthy opportunity to detectrelic sterile antineutrinos. Such hypothetical particles are more or less implied bycurrent experimental and cosmological data, and they might be a part of hot darkmatter or a candidate for warm dark matter in the Universe. Using the isotope
Hoas a target and assuming reasonable active-sterile antineutrino mixing angles, wecalculate the capture rate of relic electron antineutrinos against the correspondingEC-decay background in the presence of sterile antineutrinos at the sub-eV or keVmass scale. We show that the signature of hot or warm sterile antineutrino darkmatter should in principle be observable, provided the target is big enough and theenergy resolution is good enough.
Keywords: sterile antineutrinos; isotope Ho ; hot dark matter; warm dark matter E-mail: [email protected] E-mail: [email protected] Introduction
Although the existence of dark matter (DM) in the Universe has been established, whatit is made of remains a fundamental puzzle [1]. Within the standard model (SM) threekinds of active neutrinos and their antiparticles, whose masses lie in the sub-eV range,may constitute hot DM. Beyond the SM one or more species of sterile neutrinos andantineutrinos at a similar mass scale may also form hot DM, if they were thermalized in theearly Universe as their active counterparts. Such light sterile particles are hypothetical,but their existence is more or less implied by current experimental and cosmological data.On the one hand, the long-standing LSND antineutrino anomaly [2], the more recentMiniBooNE antineutrino anomaly [3] and the latest reactor antineutrino anomaly [4] canall be interpreted as the active-sterile antineutrino oscillations in the assumption of twokinds of sterile antineutrinos whose masses are close to 1 eV [5]. On the other hand,an analysis of the existing data on the cosmic microwave background (CMB), galaxyclustering and supernovae Ia favors some extra radiation content in the Universe and oneor two species of sterile neutrinos and antineutrinos at the sub-eV mass scale [6] . We aretherefore open-minded to conjecture that hot DM may in general consist of both activeand sterile components. These relics of the Big Bang form the unseen cosmic neutrinobackground (C ν B) and cosmic antineutrino background (C ν B), whose temperature T ν isslightly lower than the CMB temperature T γ (i.e., T ν = q / T γ ≃ .
945 eV today).But hot DM only has a tiny contribution to the total matter density of the Universe.A careful analysis of the structure formation indicates that most DM should be cold(nonrelativistic) or warm (semirelativistic) at the onset of the galaxy formation, when thetemperature of the Universe was about 1 keV [8]. A number of candidates for cold DM,such as weakly interacting massive particles and axions [9], have so far been investigated.In comparison, warm DM is another interesting possibility of accounting for the observednon-luminous and non-baryonic matter content in the Universe. Its existence may allowus to solve or soften several problems that we have recently encountered in the DMsimulations [10] (e.g., to damp the inhomogeneities on small scales by reducing the numberof dwarf galaxies or to smooth the cusps in the DM halos). A good candidate for warmDM should be sterile neutrinos and antineutrinos, if their masses are in the keV range andtheir lifetimes are much longer than the age of the Universe [11]. They could be producedin the early Universe in several ways [12], and should be able to suppress the formation ofdwarf galaxies and other small-scale structures and have impacts on the X-ray spectrum,the velocity distribution of pulsars and the formation of the first stars [13]. Hence it islikely to constrain their masses and mixing angles by measuring the Lyman- α forest andX-ray fluxes [14]. In this connection some preliminary hints of keV sterile neutrinos andantineutrinos have recently been discussed [15].On the theoretical side, there are some interesting models which can accommodatesterile neutrinos and antineutrinos at either keV [16] or sub-eV [17] mass scales. A model-independent argument [18] is also supporting the conjecture of warm DM hiding out inthe “flavor desert” of the SM fermion mass spectrum [19]. Here our main concern ispurely phenomenological: how can one directly probe the sterile component of the C ν Band the keV sterile antineutrino
DM? In Ref. [20] it has been shown that the sterilecomponent of the C ν B can in principle be detected by means of the thresholdless reaction If the Big Bang nucleosynthesis (BBN) bound is taken into account, however, only one species oflight sterile neutrinos and antineutrinos is allowed [7]. e + H → He + e − , because the mass eigenstates of sub-eV sterile neutrinos contributeto ν e and thus leaves a distinct imprint on the electron energy spectrum when they arecaptured on H nuclei . The same idea has also been used to capture the keV sterileneutrino DM on radioactive β -decaying H and
Ru nuclei [19, 27]. However, thisapproach does not directly apply to the capture of light sterile antineutrinos , simplybecause it is ν e (instead of ν e ) that is involved in the capture reaction.A possible way out is to make use of some radioactive nuclei which can decay viaelectron capture (EC) [28]. It has recently been pointed out that the isotope Ho, whichundergoes an EC decay into
Dy with a small energy release ( Q ≃ . ν B [29]. This method also worksin the presence of flavor effects, which are found to be appreciable and even important insome cases [30]. Here we shall adopt the same idea to probe the sterile component of theC ν B and the keV sterile antineutrino
DM. The EC decay of
Ho [31] can be written as
Ho + e − i (shell) → Dy ∗ i + ν e → Dy + E i + ν e , (1)and a thresholdless capture of the incoming ν e on the EC-decaying Ho may happen via ν e + Ho + e − i (shell) → Dy ∗ i → Dy + E i , (2)where e − i (shell) is an orbital electron from the i -th shell of Ho, and E i is the correspondingbinding energy of the electron hole in Dy. Our main purpose is to identify a signalshown in Eq. (2) from the background described by Eq. (1) in the presence of relicsub-eV or keV sterile antineutrinos. Such a study has not been done before and makessense at least in the following three aspects. First, it is a useful and nontrivial extensionof the discussions about the active component of the C ν B in Refs. [29] and [30] and mayprovide us with a novel approach towards the direct detection of relic sterile antineutrinos,which should be compared with relic sterile neutrinos. Second, it illustrates a commonway to probe hot and warm sterile antineutrino DM. Although this way is extremelychallenging and its prospect is rather remote, it is hitherto the most promising way inthis connection. Third, it may serve to highlight the importance of doing a high-statistics calorimetric experiment to measure the
Ho spectrum, probe the absolute neutrino massscale [32] and even detect the C ν B and warm sterile antineutrino DM.The remaining parts of this paper are organized as follows. In section 2 we summarizethe main formulas which can be used to calculate the energy spectrum of the EC decay inEq. (1) and the rate of the relic antineutrino capture in Eq. (2). Section 3 is devoted to thecapture of hot sterile antineutrino DM in the (3+2) scheme of active-sterile antineutrinomixing. We show that the signature is located on the right-hand side of the spectralendpoint of the EC decay, and their interval is detectable if the target is big enough,the energy resolution is good enough and the gravitational clustering of sub-eV sterileantineutrinos is significant around the Earth. Section 4 is devoted to the capture of warmsterile antineutrino DM on
Ho nuclei. We calculate the capture rate by assuming theexistence of one species of sterile antineutrinos at the keV mass scale. We find that it isin principle possible to identify a signal of this kind of warm DM, but the required targetmass is too big to be accomplishable in the foreseeable future. We conclude in section 5. This approach was first proposed by Weinberg [21] and by Irvine and Humphreys [22] to detect theactive component of the C ν B. It has recently attracted more interest because it seems to be the mostpromising possibility for the direct laboratory detection of relic neutrinos (see Refs. [20] and [23]—[26]). Relic antineutrino captures
The key point of relic antineutrino captures on the EC-dcaying
Ho nuclei is to capturethe relic electron antineutrinos no matter how low their kinetic energies are. In thepresence of N s species of light sterile neutrinos and antineutrinos, the flavor eigenstates | ν e i and | ν e i can be written as | ν e i = X k V ∗ ek | ν k i , | ν e i = X k V ek | ν k i , (3)where | ν k i (or | ν k i ) stands for the mass eigenstate of an active (for 1 ≤ k ≤
3) or sterile (for4 ≤ k ≤ N s ) neutrino (or antineutrino), and V ek denotes an element in the first row of the(3 + N s ) × (3 + N s ) neutrino mixing matrix V [33]. Given current experimental constraintson sterile antineutrinos [5], it is reasonable to assume that the light sterile antineutrinosunder consideration do not significantly affect the values of two mass-squared differencesand three mixing angles of three active antineutrinos extracted from solar, atmospheric,reactor and accelerator neutrino oscillation data [8]. In this assumption we shall use∆ m ≃ . × − eV and | ∆ m | ≃ . × − eV together with θ ≃ ◦ and θ ≃ ◦ as typical inputs for our analysis. Depending on the sign of ∆ m , there aretwo possible mass patterns for active antineutrinos: m < m < m (normal hierarchy) or m < m < m (inverted hierarchy). In either case the absolute mass scale is unknown,but its upper bound is expected to be of O (0 .
1) eV as constrained by current cosmologicaldata [34]. We shall specify the values of m k and | V ek | (for k = 4 , · · · , N s ) when wenumerically calculate the capture rates of relic sterile antineutrinos in sections 3 and 4.Now let us consider the EC decay of Ho in Eq. (1). If the Q -value of this reactionis defined as the mass difference between Ho and
Dy, then the energy spectrumof the outgoing neutrinos will be given by a series of lines at Q − E i . For the timebeing Q has been constrained to the range 2 . ≤ Q ≤ . Q ≃ . Honuclei in Eq. (2), the de-excitation energy of unstable Dy ∗ i is in principle monoenergeticfor each antineutrino mass eigenstate ν k (i.e., T k ≡ E ν k + Q ). Convoluted with a finiteenergy resolution in a realistic experiment, the ideally discrete energy lines of the finalstates in Eq. (2) must spread and then form a continuous spectrum. As usual, we adopta Gaussian energy resolution function defined by R ( T, T k ) = 1 √ π σ exp " − ( T − T k ) σ , (4)where T is the overall energy of an event detected in the experiment. Using ∆ to denotethe experimental energy resolution (i.e., the full width at half maximum of a Gaussianenergy resolution for the detected events), we have ∆ = 2 √ σ ≃ . σ . Then thedifferential antineutrino capture rate reads [30]d λ ν d T = G β X i X k n ν k | V ek | R ( T, T k ) n i C i β i B i Γ i π · T k − E i ) + Γ i / , (5)4here G β ≡ G F cos θ C with θ C ≃ ◦ being the Cabibbo angle of quark flavor mixing, n ν k denotes the number density of ν k , n i is the fraction of occupancy of the i -th electronshell, C i stands for the nuclear shape factor, β i represents the Coulomb amplitude of theelectron radial wave function, B i is an atomic correction for the electron exchange andoverlap, and Γ i denotes the finite natural width of the i -th atomic level. The Q -value ofthe EC decay in Eq. (1) is so small that only those electrons from M , M , N , N , O , O and P levels can be captured [29]. In accordance with Eq. (5), the energy spectrumof the EC decay should also be convoluted with the Gaussian energy resolution [30]:d λ EC d T = Z Q − min( m k )0 d T c " G β π R ( T, T c ) ( Q − T c ) × X k | V ek | q ( Q − T c ) − m k Θ( Q − T c − m k ) × X i n i C i β i B i Γ i π · T c − E i ) + Γ i / , (6)where the theta function Θ( Q − T c − m k ) has been introduced to ensure the kinematicrequirement. One may use Eqs. (5) and (6) to calculate the rate of the relic antineutrinocapture on the EC-decaying Ho nuclei against the corresponding background (i.e., theEC decay itself) in the presence of active and sterile flavor effects, which are characterizedby both the antineutrino masses m k and the antineutrino mixing matrix elements | V ek | (for k = 1 , , · · · N s ). It is therefore possible to probe the existence of relic sterile antineutrinosat either sub-eV or keV mass scales.In our numerical calculations we shall input the values of those parameters relevantto the atomic levels of Dy given in Ref. [29] and references therein. The energy levelsof the captured electrons are assumed to be fully occupied (i.e., n i ≃
1) and their bindingenergies and widths can be found in Table 1 of Ref. [29]. The atomic corrections for theelectron exchange and overlap are neglected (i.e., B i ≃ β i /β ) can be found in Table 2 of Ref. [29]. Becausethe nuclear shape factors C i are approximately identical in an allowed transition [31], theycan be factored out from the sum in Eqs. (5) and (6). Note that the numerical resultsof λ ν and λ EC can be properly normalized by using the half-life of Ho via the relation λ EC T / = ln 2, where T / ≃ N S d T = 1 λ EC · d λ ν d T · ln 2 T / N T t , d N B d T = 1 λ EC · d λ EC d T · ln 2 T / N T t (7)for a given target factor N T (i.e., the number of Ho atoms of the target) and for a givenexposure time t in the experiment. To be explicit, let us focus on the capture of hot sterile antineutrino DM in the (3+2)flavor mixing scheme with two species of sub-eV sterile neutrinos and antineutrinos [5].5he absolute mass scale of three active antineutrinos is characterized by m (normalhierarchy) or m (inverted hierarchy), and its value is typically taken to be 0.0 eV, 0.05eV or 0.1 eV in our numerical analysis. In addition, we choose m ≃ . m ≃ . θ ≃ θ ≈ ◦ for two sterile antineutrinos . Accordingly, we have | V e | ≃ . | V e | ≃ . | V e | ≃ . | V e | ≃ .
171 and | V e | ≃ . h n ν k i ≃ h n ν k i ≃
56 cm − today for each species ofactive and sterile neutrinos and antineutrinos.For our purpose, however, we are mainly concerned about the number density of relicantineutrinos around the Earth because its value n ν k may be more or less enhanced bythe gravitational clustering effect. A detailed analysis of gravitational clustering of relicneutrinos and antineutrinos in our local neighborhood has been done in Ref. [37]. Here wetake account of this effect by conjecturing a simplified power law relation between the relicantineutrino overdensity parameter ζ k ≡ n ν k / h n ν k i and the corresponding antineutrinomass m k (for k = 1 , , · · · , N s ): ζ k ≃ A (cid:18) m k (cid:19) Ω , (8)where A and Ω are independent of the subscript k . Note that the size of ζ k for a givenvalue of m k should lie between the results obtained in two extreme cases as summarizedin Table 2 of Ref. [37]. For simplicity, here we take the average of every pair of thoseextreme values as the central input of ζ k and one half of their difference as the errorbar of ζ k . Then we have ζ k = { . ± . , . ± . , . ± . , ± } corresponding to m k = { . , . , . , . } eV extracted from Table 2 in Ref. [37]. After a least squareanalysis of the relation between m k and ζ k as illustrated in Fig. 1, we find that the best-fitvalues of A and Ω are log A ≃ . ≃ .
4. One may easily see that the deviationof ζ k from one becomes significant only when m k is larger than 0.1 eV (e.g., ζ k ≃ m k ≃ . Ho nuclei against the rateof the corresponding EC decay by means of Eqs. (5), (6) and (7). Our numerical resultsare presented in Figs. 2 and 3. Some discussions are in order.(1) Fig. 2 illustrates the relic antineutrino capture rate as a function of the overallenergy release T in the case of ∆ m >
0. In the left panel ζ k = 1 (i.e., n ν k = h n ν k i ) isassumed, and in the right panel the gravitational clustering effect (i.e., ζ k >
1) has roughlybeen taken into account with the help of Eq. (8). The impact of different values of m on the capture rate can be vertically seen in each panel. Note that the value of the finiteenergy resolution ∆ is taken in such a way that only the signal of hot sterile antineutrinoDM can be observed, since the signal of hot active antineutrino DM has already beendiscussed in Ref. [30]. We find that it is in principle possible to distinguish the signalfrom the background when ∆ is smaller than 0 . m increases from 0 The values of two sterile antineutrino masses taken here are more favored by current cosmologicaldata [6], but they are somewhat smaller than those values extracted from a global fit of the LSND,MiniBooNE and reactor antineutrino anomalies [5]. It is simply a matter of taste for us to take thecosmological hints on sub-eV sterile neutrinos and antineutrinos more seriously. Since the chosen valuesof m and m are mainly for the purpose of illustration, they do not qualitatively affect our conclusions.
6o 0.1 eV, the signal curve moves towards the higher T − Q region while the backgroundcurve moves towards the lower T − Q region. Hence the interval between the peak of asignal and the background becomes larger for a larger value of m , making it easier todetect this signal. If the heights of two neighboring signals are quite different and theirlocations satisfy m i − m j ∼ ∆, it will be difficult to distinguish between them because thehigher signal is much broader and may essentially overwhelm the lower one. This featurecan be seen in Fig. 2(e) and Fig. 2(f), where the signal of ν and the signal of three activeantineutrinos with nearly degenerate masses merge into a single one. In this case onlythe signal of much heavier ν is clearly distinguishable. In the right panel of Fig. 2 onemay observe that the gravitational clustering effect can enhance the capture rate, and thiseffect is more significant for heavier sterile antineutrinos. If the gravitational clustering ofrelic antineutrinos were much more significant around the Earth, it would be very helpfulfor us to detect the C ν B by means of the capture reaction under consideration.(2) Fig. 3 shows the numerical results obtained from an analogous analysis of therelic antineutrino capture rate in the case of ∆ m <
0. We see that it is quite similarto Fig. 2, and their main differences appear in the location of the signal of three activeantineutrinos and that of the endpoint of the EC-decay background. The first differencearises from the fact that the location of the signal of active antineutrinos is dominatedby the mass eigenstates ν and ν which have slightly larger eigenvalues in the ∆ m < m > Ho is located at a smaller T − Q region in the ∆ m < ν hiding out in ν e is associated with the smallestactive antineutrino mixing matrix element | V e | . So we conclude that it is somewhateasier to observe the signals of hot active and sterile antineutrino DM when three activeantineutrinos have an inverted mass hierarchy.(3) Besides the energy resolution, another factor that obviously affects the observabilityof hot antineutrino DM is the absolute capture rate which depends on the number densityof relic antineutrinos n ν k , the flavor mixing matrix elements | V ek | and the number of thetarget particles N T . By using the default values of | V ek | taken above, we illustrate theiso-rate curves for the sterile antineutrino overdensity parameter ζ versus the target massin Fig. 4 . Because of | V e | ∼ | V e | and m ∼ m ≪ Q − E i , one may obtain very similariso-rate curves for ζ versus the target mass. These curves are simply straight lines in thedouble logarithmic scale, which can easily be understood with the help of Eqs. (5) and(7). Given ζ k = 10, for example, a target with 10 kg (or 10 kg) Ho could be enoughto give a capture rate of one event per year (or ten events per year).Finally, let us give a brief comment on the properties of the capture signals of hotsterile antineutrinos against the corresponding EC decays by taking the masses of sterileantineutrinos to be consistent with the values of ∆ m and ∆ m extracted from a globalfit of the LSND, MiniBooNE and reactor antineutrino anomalies (i.e., ∆ m ≃ .
47 eV and ∆ m ≃ .
87 eV [5]). In this case the dependence of the capture rates on theenergy resolution, antineutrino number densities and target factors is quite similar to theone discussed above. The only change is the location of each sterile antineutrino signal.Because of m ≃ q ∆ m ≃ .
69 eV and m ≃ q ∆ m ≃ .
93 eV in the present situation, Instead of using Eq. (8), here we treat ζ as a free parameter independent of the neutrino masses m k . In the literature there are some different neutrino overdensity models which can actually predictvery large values of ζ k (see, e.g., Ref. [38]).
7t will be much easier to identify the sterile antineutrino signals on EC-decaying
Honuclei if the magnitudes of the mixing matrix elements | V e | and | V e | keep unchanged. Now we turn to the capture of warm sterile antineutrino DM in the (3+1) flavor mixingscheme with one species of keV sterile neutrinos and antineutrinos. To be explicit, wefix m ≃ . | V e | ≃ . × − in our numerical analysis, just for the purposeof illustration [19]. Because our main concern is to observe a possible signal of the relicantineutrino capture in the keV mass region, we simply assume three active antineutrinosto have a normal mass hierarchy with m = 0. A very similar signal can also be obtainedfor the inverted or nearly degenerate mass pattern of three active antineutrinos. Onemay also consider the gravitational clustering effect on the C ν B as described in Eq. (8),but it is insignificant in the present scenario where only active antineutrinos contributeto the C ν B. As for the keV sterile neutrinos and antineutrinos, we follow Ref. [12] toassume that they were produced in the early Universe through active-sterile neutrinoor antineutrino oscillations and their number densities are able to account for the totalamount of DM. Given the average density of DM in our Galactic neighborhood (i.e., ρ localDM ≃ . − [39]), it is straightforward to estimate the number density of ν or ν . We obtain n ν ≃ n ν ≃ × (3 keV /m ) cm − .We calculate the capture rate of warm sterile antineutrino DM on Ho nuclei againstthe corresponding EC-decay background by using Eqs. (5), (6) and (7). Our numericalresult is shown in Fig. 5. Some discussions are in order.(1) In obtaining Fig. 5 we have chosen a typical value of the finite energy resolution ∆to distinguish the signal from the background. The endpoint of the background is sensitiveto ∆, while the peak of the signal is always located at T = Q + m . So a comparisonbetween ∆ and m can easily reveal the signal-to-background ratio. The required energyresolution to identify the signal of warm sterile antineutrino DM is of O (0 .
1) keV, whichshould be easily reachable in a realistic experiment.(2) The main problem which makes the observability of keV sterile antineutrino DMrather dim and remote is the tiny capture rate. The latter is strongly suppressed for twosimple reasons. On the one hand, the mixing factor between three active antineutrinosand the keV sterile antineutrino is too small [11]. On the other hand, the Breit-Wignerdistribution function is too small when the signal of ν is located far away from theresonance energies E i . In Fig. 6 we depict the iso-rate curves for the mixing matrixelement | V e | versus the target mass. One can see that a target with 600 ton Ho isneeded for | V e | ∼ O (10 − ), so as to obtain a capture rate of one event per year. Henceit is almost hopeless to capture warm sterile antineutrino DM on the EC-decaying Honuclei in the foreseeable future. In comparison, it seems somewhat more hopeful to detectwarm DM in the form of keV sterile neutrinos on radioactive beta-decaying H and
Runuclei in the long term [19].Finally, let us give some brief comments on the detection prospects for three kinds ofrelic antineutrinos (i.e., hot active antineutrino DM, hot sterile antineutrino DM and warmsterile antineutrino DM). Given a target made of the isotope
Ho, the capture of eachkind of DM in a realistic experiment crucially relies on its energy resolution and targetmass. Because three active antineutrinos have relatively large mixing angles and relatively8mall masses, the corresponding hot active antineutrino DM has the largest capture ratebut requires the most stringent energy resolution (∆ ≃ .
015 eV or smaller, as discussedin Ref. [30]) for us to distinguish a signal from its background. In contrast, the situationfor capturing warm sterile antineutrino DM is just the opposite. Here ∆ ∼ O (0 .
1) keVis good enough because of m ∼ O (1) keV, and this energy resolution requirement canbe satisfied even today. But the capture rate of ν on the EC-decaying Ho nuclei is sosmall that the desired target mass has to be formidably large. As we have seen in theabove analysis, the capture of hot sterile antineutrino DM at the sub-eV (or eV) massscale requires a relatively mild energy resolution and a reasonably large target mass ascompared with the situations for detecting hot active antineutrino DM and warm sterileantineutrino DM in the same way. So it might be possible to probe the sterile componentof the C ν B by using the isotope
Ho as a target in the future.
To pin down what DM is made of has been one of the most important and most challengingproblems in particle physics and cosmology. In this paper we have addressed ourselves tothe direct laboratory detection of possible contributions of light sterile antineutrinos toDM. Such hypothetical particles might be a part of hot DM if their masses are in the sub-eV (or eV) range, or a good candidate for warm DM if their masses lie in the keV range.Choosing the isotope
Ho as a target and assuming reasonable active-sterile antineutrinomixing angles, we have calculated the capture rate of relic electron antineutrinos againstthe corresponding EC-decay background in the presence of sterile antineutrinos at eithersub-eV or keV mass scales. Our analysis shows that the signature of hot or warm sterileantineutrino DM should in principle be observable, provided the target is big enough,the energy resolution is good enough and the gravitational clustering effect is significantenough. We admit that our numerical results are quite preliminary and mainly serve forillustration, but we stress that such a direct laboratory search for hot and warm sterileantineutrino DM is fundamentally important and deserves further attention and moredetailed investigations.Why has one chosen the EC-decaying
Ho nuclei as a proper target for probing theantineutrino content of DM? The reason is simply that the captures of relic neutrinos andantineutrinos require different types of radioactive nuclei: ν e is involved in the capturereactions on the beta-decaying H and
Ru nuclei, while ν e is associated with the capturereactions on the EC-decaying Ho nuclei. So it makes sense to look for another ratherstable isotope which can undergo an EC decay with a much lower Q -value, in order todo a more promising experiment for the direct detection of hot and warm antineutrinoDM. Although the present experimental techniques are unable to lead us to a guaranteedmeasurement of relic neutrinos and antineutrinos in the near future, we might have achance to make a success of this great exploration in the long term.This work was supported in part by the China Postdoctoral Science Foundation undergrant No. 20100480025 (Y.F.L.) and in part by the National Natural Science Foundationof China under grant No. 10875131 (Z.Z.X.).9 eferences [1] See, e.g., Z.Z. Xing and S. Zhou, Neutrinos in Particle Physics, Astronomy andCosmology (Zhejiang University Press and Springer-Verlag, 2011).[2] A. Aguilar et al. (LSND Collaboration), Phys. Rev. D , 112007 (2001).[3] A.A. 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The four points and their error bars in this graphare extracted from Table 2 of Ref. [37]. 12 (a) m =0.00 eV =0.08 eV1.01.0 T Q (eV) R a t e [ e v en t s / ( e V y ea r) ] -0.2 0.0 0.2 0.4 0.60510 (b) m =0.00 eV =0.08 eV2.16.6 T Q (eV) R a t e [ e v en t s / ( e V y ea r) ] -0.2 0.0 0.2 0.4 0.60510 (c) m =0.05 eV =0.08 eV1.01.0 T Q (eV) R a t e [ e v en t s / ( e V y ea r) ] -0.2 0.0 0.2 0.4 0.60510 m =0.05 eV =0.08 eV2.16.6 (d) T Q (eV) R a t e [ e v en t s / ( e V y ea r) ] -0.2 0.0 0.2 0.4 0.60510 (e) m =0.10 eV =0.08 eV1.01.0 T Q (eV) R a t e [ e v en t s / ( e V y ea r) ] -0.2 0.0 0.2 0.4 0.60510 m =0.10 eV =0.08 eV2.16.6 (f) T Q (eV) R a t e [ e v en t s / ( e V y ea r) ] Figure 2: The relic antineutrino capture rate as a function of the overall energy release T in the case of ∆ m >
0, where ζ k = 1 in the left panel and ζ k > ν B signature and its background, respectively.The value of the finite energy resolution ∆ is taken in such a way that only the signal ofthe sterile component of the C ν B can be seen.13 (a) m =0.00 eV =0.08 eV1.01.0 T Q (eV) R a t e [ e v en t s / ( e V y ea r) ] -0.2 0.0 0.2 0.4 0.60510 (b) m =0.00 eV =0.08 eV2.16.6 T Q (eV) R a t e [ e v en t s / ( e V y ea r) ] -0.2 0.0 0.2 0.4 0.60510 (c) m =0.05 eV =0.08 eV1.01.0 T Q (eV) R a t e [ e v en t s / ( e V y ea r) ] -0.2 0.0 0.2 0.4 0.60510 (d) m =0.05 eV =0.08 eV2.16.6 T Q (eV) R a t e [ e v en t s / ( e V y ea r) ] -0.2 0.0 0.2 0.4 0.60510 (e) m =0.10 eV =0.08 eV1.01.0 T Q (eV) R a t e [ e v en t s / ( e V y ea r) ] -0.2 0.0 0.2 0.4 0.60510 (f) m =0.10 eV =0.08 eV2.16.6 T Q (eV) R a t e [ e v en t s / ( e V y ea r) ] Figure 3: The relic antineutrino capture rate as a function of the overall energy release T in the case of ∆ m <
0, where ζ k = 1 in the left panel and ζ k > ν B signature and its background, respectively.The value of the finite energy resolution ∆ is taken in such a way that only the signal ofthe sterile component of the C ν B can be seen.14 event / year Target Mass (kg)
Figure 4: The iso-rate curves of hot sterile antineutrino DM for the overdensity parameter ζ versus the target mass. Here ζ is treated as a free parameter and m ≃ . | V e | ≃ .
174 have been input. m =0.00 eV =0.40 keV T Q (keV) R a t e [ e v en t s / ( k e V y ea r) ] Figure 5: The rate of capturing warm sterile antineutrino DM as a function of the overallenergy release T in the (3+1) flavor mixing scheme with ∆ m > m ≃ -9 -8 -7 -6 -5 -4 event / year | V e4 | Target Mass (t)
Figure 6: The iso-rate curves of warm sterile antineutrino DM for the mixing matrixelement | V e | versus the target mass. Here n ν ≃ n ν ≃ × (3 keV /m ) cm −3