Searching for the dark universe by the DAMA experiment

ELSkER Nuclear Physics A719 (2003) 257~265~ www.elsevier.com/locate/npe

Searching for the Dark Universe by the DAMA experiment

R. Bernabei”, M. Amatob, P. Belli”, F. Cappella”, R. Cerulli”, C.J. Daic; G. Ignestib, ,4. Incicchittib, H.H. Kuang’, J.M. Mac, F. Montecchia”, F. Nozzoli”, Z.P. Ye” and D. Prosperib

aDip. di Fisica and INFN, sez. Roma2, Universita’ di Roma “Tor Vergata”, I-00133 Rome; Italy

bDip. di Fisica and INFN, sez. Roma, Universita’ di Roma “La Sapienza”, I-00185 Rome, Italy

CIHEP, Chinese Academy, P.O. Box 918/3, Beijing 100039, China

DAMA is searching for rare processes by developing and using several kinds of radiopure scintillators. In particular, here the results released so far on the WIMP annual modulation signature are discussed and next perspectives are shortly addressed.

1. INTRODUCTION

The DAMA experimental activity is devoted to the investigation of rare processes such as WIMPS direct detection, /3/3 decay processes, charge-non-conserving processes, Pauli exclusion principle violating processes, nucleon instability, solar axions and exotics [I-13] by developing and using low radioactive scintillators. As an example of the performed activities in these fields, Fig. 1 resumes the main results achieved by this experiment in the search for p/3 decay processes.

We remind that the realized experimental set-ups are: the N 100 kg NaI(T1) set- up [6] (which has completed its data taking in July 2002), the N 6.5 kg liquid Xenon (LXe) set-up [2], th e so-called “R&D” apparatus and the new LIBRA (Large sodium Iodine Bulk for RAre processes; 2~ 250 kg of ultra-radiopure NaI(T1)) set-up now under installation. Moreover, a low-background germanium detector is operative underground to select materials for radiopurity since many years.

This paper summarizes the results obtained in the search for WIMPS by exploiting the annual modulation signature with the p 100 kg NaI(T1) set-up, including the most recent analyses. This set-up [6] can effectively exploit such a signature because of its well known technology, of its high intrinsic radiopurity, of its mass, of its suitable control of all the operational parameters and of the deep underground experimental site.

2. MODEL INDEPENDENT EVIDENCE

The WIMPS are embedded in the galactic halo, thus our solar system, which is moving with respect to the galactic system, is continuously hit by a WIMP “wind”. It can be

0375-9474/03/$ - see front matter 8 2003 Elsevier Science B.V. All rights reserved. doi:lO.l016/S0375-9474(03)00929-l

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Figure 1. Summary of the results achieved by DAMA in the search for pp decay processes in various isotopes [l]. Dark gray: previous best limits; light gray: DAMA best limits.

mainly searched for by the WIMP elastic scattering on the target nuclei of the detector. Moreover, since the Earth rotates around the Sun, which is moving with respect to the galactic system, it would be crossed by a larger WIMP flux in June (when its rotational velocity is summed to the one of the solar system with respect to the Galaxy) and by a smaller one in December (when the two velocities are subtracted). This gives rise to an annual modulation of the WIMP-nucleus elastic scattering rate measured by a suitable set-up located deep underground [14], offering in this way a model independent signature for the presence of a WIMP component in the galactic halo. This signature is very distinctive since a WIMP-induced seasonal effect must simultaneously satisfy all the following requirements: the rate must contain a component modulated according to a cosine function (1) with one year period (2) and a phase that peaks around N 2”d June (3); this modulation must be found in a well-defined low energy range, where WIMP induced recoils can be present (4); it must apply to those events in which just one detector of many actually “fires”, since the WIMP mul’i-scattering probability is negligible (5); the modulation amplitude in the region of maximal sensitivity must be 57% (6). Only systematic effects able to fulfil these 6 requirements could fake this signature; no one able to do that has been found or suggested [lo].

The results obtained by investigatin g the annual modulation signature in the data collected during four independent experiments of one year cycle each one (57986 kg . day total statistics) have been released [5,7-131. All the peculiarities required by the signature are satisfied. In particular, a model independent analysis of the data offers an immediate evidence of the presence of an annual modulation of the rate of the single hit events in the lowest energy interval (2 - 6 keV) as shown in Fig. 2. No known systematic effect

R. Bernabei et al. /Nuclear Physics A719 (2003) 257c-265~ 259~

or side reaction able to mimic a WIMP induced effect has been found as quantitatively discussed in detail in ref. [lo]. In conclusion, a WIMP contribution to the measured rate is candidate by the result of the model independent approach independently on the nature and coupling with ordinary matter of the possible WIMP particle.

,; / / / -0.’ L 1 ’ J ” ’

500 ? oco 1500 time (days)

Figure 2. Model independent residual rate for single hit events, in the 2-6 keV cumu- lative energy interval, as a function of the elapsed time. The expected behaviour of a WIMP signal is a cosine function with minimum roughly at the dashed vertical lines and with maximum roughly at the dotted ones. As it can be seen, the data give consistent results with proper period and phase and the x2 test largely disfavours the hypothesis of unmodulated behaviour (probability: 4 . 10e4).

3. MODEL DEPENDENT ANALYSES OF THE ANNUAL MODULATION DATA

To investigate the nature and coupling with ordinary matter of the WIMP candidate, a suitable energy and time correlation analysis is necessary as well as the assumption of one among the many possible model frameworksi.

3.1. WIMPS with dominant SI interaction in a given model framework For simplicity, initially we have considered the particular case of purely spin-independent

(SI) coupled WIMP above 30 GeV. In fact, often the spin-independent interaction with ordinary matter is assumed to be dominant since e.g. most of the used target-nuclei are practically not sensitive to SD interactions as on the contrary 23Na and 1271 are and the theoretical calculations are even more complex when including also this latter kind of interaction. Moreover, the simplest model scenario has been considered as well as fixed parameters values [5,7]. Then, this case has been extended by considering the many uncertainties which exist on the astrophysical velocity distribution [8,9] and the physical constraint which arises from the upper limits on recoils measured by the same set-up [9]. Moreover, more recently an investigation on the effect induced on the result by different

‘We remark that a model framework is identified not only by general astrophysical, nuclear and particle physics assumptions, but also by the set of values used for all the parameters needed in the model itself and in related quantities (for example WIMP local velocity, 210; form factor parameters, etc.).

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possible consistent halo models still for the particular case of purely SI coupled WIMPS has also been carried out in ref. 1131.

A standard maximum likelihood method has been used. Note that different model frameworks vary the theoretical expectations and, therefore, the best fit values of cross section and mass (as well as the allowed region) also vary2. In particular, the inclusion of the uncertainties associated to the models and to every parameter in the models them- selves as well as other possible scenarios largely enlarges the allowed region as discussed e.g. in ref. [8] for the particular case of the astrophysical velocities3.

In Fig. 3 is shown the superposition of all the 30 C.L. allowed regions obtained by analysing the four annual cycles data in a class of possible different non-rotating galactic halo models when considering purely SI coupled WIMPS [13]; for simplicity, no other uncertainties on the theoretical and experimental parameters have been considered there, thus obviously their inclusion in the calculations will further enlarge the given region.

In conclusion, the observed effect investigated in terms of a WIMP candidate with dominant SI interaction and mass above 30 GeV in the simplified model framework considered in ref. [9], supports allowed WIMP masses up to about 105 GeV (1 CT C.L.); this is extended up to about 250 GeV (1 a C.L.) w h en considering a class of possible different non-rotating halo models [13]. The DAMA annual modulation data give results well embedded in theoretical estimates for a neutralino candidate with dominant SI interactions, as discussed in [15,16]; moreover, in ref. j17] the case for an heavy neutrino of the fourth family has been considered.

3.2. WIMPS with mixed coupling in given model framework Since the 23Na and ia71 nuclei are sensitive to both SI and SD couplings - on the contrary

e.g. of natGe and natSi which are sensitive mainly to WIMPS with SI coupling (only 7.8 % is non-zero spin isotope in “atGe and only 4.7% of 2sSi in n”tSi) - the analysis of the data has been extended considering the more general case of a WIMP having not only a spin- independent, but also a spin-dependent coupling different from zero (as it is also possible e.g. for the neutralino) [ll]. Then, the log-likelihood function has been minimized ~ properly accounting also for the physical constraint set by the measured upper limit on recoils [4] - with respect to the [asr, (0s~ and rnw parameters for each given B value; thus, parameters’ regions allowed at given confidence level have been obtained. Here, also is the point-like SD WIMP cross section on nucleon and tg6’ is the ratio between the effective SD coupling constants on neutrons, a,, and on proton, ap; therefore, 0 can assume values between 0 and r depending on the SD coupling.

Note that the results of ref. [ll] have been obtained by considering a simple isothermal sphere for the galactic halo model and a maxwellian WIMP velocity distribution with

‘It is worth to note that the exclusion plots (quoted by experiments exploiting approaches unable to investigate a model independent signature) are always dependent on the used model frameworks and several assumptions; thus, they have not an “universal” validity and must be considered cautiously in comparison with other results. 3For example, in the particular model framework and assumptions of ref. [9] by varying the WIMP local velocity, ue; from 170 km/s to 270 km/s to account for its present uncertainty, we obtained the best fit values rnw = (722::) GeV and (0s~ = (5.7 i 1.1) 1O-6 pb for ‘ue = 170 km/s and mw = (43’;‘) GeV and Eosr = (5.4 It 1.0) 10v6 pb for ~10 = 220 km/s. Here, < is the WIMP local density in 0.3 GeV cmp3 unit, CJS~ is the point-like SI WIMP-nucleon generalized cross section and mw is the WIMP mass.

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Figure 3. A purely SI case: superposition of all the 3 0 allowed regions in the plane <asI versus mu, for a WIMP with dominant SI interaction and mass above 30 GeV when considering all the (non-rotating) galactic halo models discussed in ref. [13] (note that - only in this figure - < indicates the fractional amount of WIMP in the galactic halo). As always in similar analyses, it accounts for many sets of “most likely” values; moreover the inclusion of present uncertainties on some other astrophysical, nuclear and particle physics parameters would enlarge the region (varying again consequently the “most likely” values for each considered set).

inclusion of the uncertainties on uo, on the nuclear radius and the nuclear surface thickness parameter in the SI form factor, on the b parameter in the used SD form factor and on the quenching factors [4] measured for the detectors. For completeness, we mention in particular that an universal formulation is not possible for the SD form factor since the internal degrees of the WIMP particle model (e.g. supersymmetry in case of neutralino) cannot be completely separated; other formulations than the one adopted here are possible and can be considered with evident implications on the obtained allowed regions.

For simplicity, as an example Fig. 4 left pmel shows slices for some rnw of the region allowed at 3 g C.L. in the (<a~~, [aso, mw) space for two particular couplings. As it can he seen, purely SD, purely SI as well as mixed configuations are allowed. Some quantita- tive discussions are given in ref. [ll]. Further investigations are in progress to account for other known parameters uncertainties and for possible different model assumptions such as on the halo models and their parameters, as already done for the purely SI case.

3.3. Inelastic Dark matter It has been suggested in ref. [18] that the observed annual modulation effect could

be induced by possible inelastic Dark Matter: relic particles that prefer to scatter inelastically off of nuclei. The inelastic Dark Matter could arise from a massive complex scalar split into two approximately degenerate real scalars or from a Dirac fermion split into two approximately degenerate Majorana fermions, namely x+ and x-, with a b mass

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100 300 'O 0 200 0 100 200 300

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Figure 4. Left panel: some mixed SI/SD cases; examples of slices of the volume allowed at 3 0 C.L. in the (< oSI; EcrsD, mw) space for some mw and 0 values in the model framework considered in ref. [ll]. Only two particular couplings are reported here for simplicity: i) 0

77/2; ii) B = 2.435 rad. Right panel: some inelastic cases; slices at fixed WIMP masses rf the volume allowed at 3 v C.L. in the space ([a,, 6, mu,) obtained for the model framework considered in ref. [12]. Note that e.g. Ge experiments are sensitive mainly only to SI coupling and, therefore, cannot explore most of the DAMA allowed regions in these scenarios. Moreover, these allowed regions would be further enlarged by taking into account the uncertainties existing on the halo models, on the SD form factor which has a not universal formulation and on some other experimental and theoretical parameters.

splitting. In particular, a specific model featuring a real component of the sneutrino; in which the mass splitting naturally arises, has been given in ref. [lS]. It has been shown that for the x- inelastic scattering on target nuclei a kinematical constraint exists which favours heavy nuclei (such as 1271) with respect to lighter ones (such as e.g. natGe) as target-detectors media. In fact, x- can only inelastically scatter by transitioning to x+ (slightly heavier state than x-) and this process can occur only if the x- velocity is larger than ‘r& = c- * where 1*1~~ is the WIMP-nucleus reduced mass (c = 1). This kinematical constraint becomes increasingly severe as the nucleus mass, mN, is decreased [lS]. Moreover, t,his model scenario gives rise - with respect to the case of WIMP elastically scattering - to an enhanced modulated component, S,, with respect to the unmodulated one, Se, and to largely different behaviours with energy for both So and S, (both show a higher mean value) [18]. A dedicated energy and time correlation analysis of the DAMA annual modulation data has been carried out [la] handling aspects other than the interaction type as in ref. [ll] (in this way a particular model framework is fixed). Also here for simplicity an isothermal sphere for the galactic halo model and a maxwellian WIMP

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velocity- distribution have been adopted, including the uncertainties on vo. In this scenario of Dark Matter with inelastic scattering an allowed volume in the space ([o,,mw,b) is obt.ained [12]. For simplicity, as an example Fig. 4 right panel shows slices of such an allowed volume at some given WIMP masses (3 g C.L.). The allowed regions have been obtained - as in the previous cases - by the superposition of those obtained when varying the values of the previously mentioned parameters according to their uncertainties. Note that - as in the previous cases - each set of values (within those allowed by the associated uncertainties) for the previously mentioned parameters gives rise to a different expecta- tion, thus to different “most likely” values. As an example we mention that when fixing the other parameters as in ref. [ll], the “most likely” values for a WIMP mass of 70 GeV are: i) [Ok = 2.5 x lo-’ pb and b = 115 keV when ~0 = 170 km/s, ii) ECUS = 6.3 x lop4 pb and b = 122 ke\J when u. = 220 km/s; they are in 6 region were Ge and Si experiment are disfavoured. Finally, we further note that the allowed regions are further enlarged when properly including the uncertainties on the halo models, on the experimental and theoretical paramet,ers and other assumptions.

4. PROOFS AND DISPROOFS

The claim for contradiction made by some authors 1191, which use different target nuclei and different methodological approaches, is intrinsically incorrect as we have already discussed several times (see e.g. [20]). In particular - besides the usual uncertainties which always exist in the comparison of results achieved by different experiments - a model independent comparison cannot be pursued at all and, in addition, they are not sensitive to the annual modulation signature.

We just comment here that in ref. [19] only very small/marginal statistics (with respect to several years of data taking and to the several used detectors) have been released and several strong and sometimes unsafe procedures have been applied to reduce the measured very high levels of background; however, to credit the results obtained by these procedures, a deep knowledge and control of several quantities is necessary, while - on the contrary - they are generally even not mentioned by those authors at all. Only events surviving these “reduction procedures” are considered to calculate limits on cross section for one particular model framework (astrophysical, nuclear and particle Physics assumptions and experimental and theoretical parameters at fixed values) and compared with only one particular model (of the many existing) dependent DAMA allowed region, which generally is even not one of those endorsed, for the various model frameworks, by DAMA itself.

We remark that since the target mass and the exposure time of these experiments are much lower than those of DAMA, the number of counts they can expected from the DAMA annual modulation effect varies from only a few to zero events depending on the models and on the assumptions, Few comments about the possibility of these experiments to reliably achieve such a small number of events have been addressed e.g. in ref. [20] where also a discussion about the possibility of a reliable comparison is carried out.

5. PERSPECTIVES: TOWA DS THE LIBRA SET-UP

Since fall 2002 efforts are devoted to the installation of the LIBRA set-up to increase the sensitivity of the experiment. It consists of N 250 kg of NaI(T1); in fact, new radiopure

264c R. Bevnabei et al. /Ndear Physics A719 (2003) 257~~265~

detectors have been realized in collaboration with Crismatec company as a result of a

/““I’ “I” ” 3

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\ bckq=lO~"cpd/kq/keV?

Figure 5. First panel: behaviour of C.L. achievable by LIBRA as a function of the exposure and background rate in the experimental condition as the p 100 kg NaI(T1) set-up. The shaded regions account for several model frameworks. Second panel: example of allowed regions at lo C.L., evaluated by simulating the response of LIBRA to a WIMP having mu, = 60 GeV, usI = 10e6 pb, 0s~ = 0.8 pb and 0 = 2.435 rad. In this example, for simplicity the calculation has been performed assuming the particular simplified model framework of ref. [ll], vg = 220 km/s and all the other parameters at mean or nominal values.

dedicated R&D by exploiting chemical/physical purification of NaI and TlI powders. The perspectives for LIBRA are to achieve very high confidence levels (C.L.) for the

model independent annual modulation effect and to further investigate the nature and the interaction of the WIMP candidate particle (see e.g. Fig. 5).

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Searching for the dark universe by the DAMA experiment