Searching for the WIMP annual signature by the ~100 kg NaI(Tl) set-up

• The ~ 100 kg NaI(Tl) DAMA set-up is searching for WIMPs mainly by investigating the so-called annual modulation signature.
  
  
  
  

• The WIMPS are expected to be gravitationally trapped in the galactic halo with a peculiar velocity distribution; therefore, a WIMP "wind" would continuously hit the Earth. It can be detected by investigating the WIMP elastic scattering on the target nuclei of a detector and the nuclear recoil energy is the measured quantity.
  
  Since the Earth rotates around the Sun, it would be invested by a larger WIMP flux in June (when its rotational velocity adds up to the velocity of the whole solar system in the Galaxy) and by a smaller flux in December (when the two velocities are in opposite directions), inducing a peculiar modulation of the low energy counting rate.
  
  

  To select the modulated component of the signal, large mass apparata with suitable features and stability control are necessary, such as the ~100 kg highly radiopure NaI(Tl) DAMA set-up.
  
  As we have already pointed out this signature is quite clear requiring that all the following features are satisfied:
  
  

  1. modulation of the "single hit" rate (that is for events where only one detector fires, being negligible the probability that a WIMP will interact in more than one);
  2. for events only in a well defined low energy region;
  3. according to a cosine-like behaviour;
  4. with a one year period (T);
  5. with a phase t₀ ~ 2 June (~152.5^th day of the year);
  6. with limited modulated amplitude (less than about 7% in the region of maximal sensitivity).

  
  The satisfaction of all these requirements has to be verified in the production data to support that a WIMP induced modulation is present; therefore, as it is evident, this definitively shrinks possible spurious effects, being necessary that they also satisfy all the 1 to 6 peculiarities given above. The same is for possible "side reactions" which have been also quantitatively investigated (see references).
  
  

  The detailed description of the DAMA/NaI set-up and its performances have been presented in Il Nuovo Cim. A112 (1999) 545, where the radiopurity of all its components has also been discussed.
  
  

  A suitable stability monitoring and control is operating (see references).
  
  

  At present the lightest supersymmetric particle named neutralino is considered the best candidate for WIMP; thus, in the model dependent analyses we have included a lower bound on the WIMP mass inspired by the limit achieved at accelerators (see e.g. LEP publications). However, it is worth to note that the obtained results are not intrinsecally restricted only to this candidate.
  

  

  
  The running periods for annual modulation search
  

  period		statistics (kgday)	references
  DAMA/NAI-1		3363.8 winter + 1185.2 summer	PLB424 (1998), 195
  DAMA/NaI-2		14962 from middle november to the subsequent end of July	PLB450 (1999), 440 PRD61 (2000), 023512
  DAMA/NaI-3		22455 roughly from middle August to the end of September	PLB480 (2000), 23 Eur. Phys.J. C18 (2000) 283 PLB509 (2001), 197 Eur. Phys. J. C23 (2002) 61 hep-ph/0203242 to appear on Phys. Rev. D
  DAMA/NaI-4		16020 roughly from middle October until the second half of August	idem
  Total statistics		57986	idem

  
  
  

  In particular:

  investigation in terms of a purely spin-independent coupled WIMP in given model frameworks: PLB424 (1998), 195; PLB450 (1999), 440; PRD61 (2000), 023512 (including uncertainties on astrophysical velocities); PLB480 (2000), 23 (including the constraint arising from the measured upper limits on recoil fraction);

  systematic investigation of possible systematic effects (it has quantitatively demonstrated that not only the contribution of possible systematics to the modulated component is quantitatively negligible, but also that no known systematic effect able to mimic the signature, that is able to contemporaneously satisfy the six peculiarities mentioned above, has neither been found nor suggested by any other): Eur. Phys. J. C18 (2000) 283;

  investigation in terms of a mixed spin-independent/spin-dependent coupled WIMP in a given model framework: PLB509 (2001), 197;

  investigation of WIMP with preferred inelastic scattering in a given model framework: Eur. Phys. J. C23 (2002) 61;
  
  

  investigation of the effect of consistent halo modeling in the case of purely spin-independent coupled WIMPs in a given model framework by P. Belli, R. Cerulli, N. Fornengo and S. Scopel, hep-ph/0203242 to appear on Phys. Rev. D

  
  

  

  
  
  The time behaviour of the counting rate
  

  
  

  The rate as a function of the time shows in the 4 years of data taking released so far an annual modulation which satisfies the 6 requirements for a WIMP induced effect.
  
  
  
  
  

  Here the 2-6 keV residual rate is shown. The ² test on these data disfavours the hypothesis of unmodulated behaviour giving a probability of 4 x 10^-4. The data are well compatible with a modulation with the right period and phase expected for a WIMP induced effect. We recall that each data point in this figure has been obtained from the raw rate after subtracting the constant part (the weighted mean of the residuals must obviously be zero over one period).
  
  The results of the investigation of known sources of possible systematics and side reactions have been quantitatively discussed in the reference. As mentioned above, there it has been also pointed out that no one of them is able to satisfy all the 6 requirements given above. For details see e.g. the dedicated paper Eur. Phys. J. C18 (2000), 283-292.
  
  The presence of a WIMP contribution to the experimental rate is candidate by these data independently on its nature and coupling with ordinary matter.
  
  

  

  
  
  To investigate the nature and coupling with ordinary matter of a possible candidate, an effective energy and time correlation analysis is necessary as well as to fix a model framework. Note that a model framework is identified not only by the 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 (the same is e.g. when comparing a quoted rate with expectation to evaluate exclusion plots).
  
  Full correlation analysis has been performed in different cases:
  
  

  In term of spin-independent (SI) coupled WIMPs;

  + extended analysis including the effect of consistent halo modeling (from hep-ph/0203242 to appear on PRD) (click here);

  
  
  

  In term of mixed (SI+SD) coupling WIMPs.

  
  
  

  In term of WIMPs with preferred inelastic scattering.

  
  
  

  What next?

  
  
  

  Proofs and disproofs

  
  
  

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  Results of the full correlation analysis
  in term of purely spin-independent coupled WIMPs
  
  Often the spin-independent (SI) interaction with ordinary matter is assumed to be dominant, both because most of the considered target-detectors are largely insensitive to WIMPs with purely spin-dependent interactions and because the theoretical calculations related to spin-dependent interaction are in practice more difficult. In the pure SI framework, full correlation analysis, which takes into account the time occurrence and the energy of each event, has been performed. The free parameters are: WIMP mass (m_w), _p (WIMP halo fraction in unit of 0.3 GeVcm^-3 times the WIMP-proton cross section) and background contributions. Limits achieved at accelerators have been included. Moreover, the constraint arising from the upper limits on recoils measured by the same set-up has also been included, as well as the uncertainties on the local WIMP velocity. In this purely SI model framework, the global analysis favours the presence of an annual modulation with proper feature for a spin-independent candidate with mass above 30 GeV at ~ 4 C.L. Alternative analyses with other methods, such as e.g. the ² and the Feldman and Cousins approaches always give consistent results.
  
  

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  This figure shows the region at 3 C.L. in the given model framework. The uncertainties on the local velocity have been included (Solid contour). It is also shown the region at 3 C.L. obtained when including possible bulk halo rotation. (Dashed contour).
  
  

  The proper inclusion in the calculations of the existing uncertainties on some other of the values used there for astrophysical and nuclear/particle physics parameters can further extend the allowed region in the same framework as well as different assumption e.g for the halo model.
  
  

  
  

  The implication of this result in term of neutralino candidate has been extensively discussed by A. Bottino et al.. See also R.W. Arnowitt and P. Nath and E. Gabrielli et al.
  
  

  
  

  The interpretation of the observed annual modulation in term of an heavy neutrino of the fourth family has been discussed by D. Fargion et al.
  
  

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  Including the effect of consistent halo modeling
  (from hep-ph/0203242 to appear on PRD)
  The previous analysis for the case of a WIMP with a purely spin-independent coupling has been extended by discussing in details the implications on the results of the uncertainties on the dark matter galactic velocity distribution. Possible departures from the isothermal sphere model, which is the parameterization usually adopted to describe the halo, have been studied in a systematic way. Specifically modifications arising from various matter density profiles, effects due to anisotropies of the velocity dispersion tensor and rotation of the galactic halo have been considered.
  
  (for details and references see hep-ph/0203242)
  
  The hypothesis of WIMP annual modulation, already favoured in the previous analysis using an isothermal sphere, is confirmed in all the investigated scenarios, and the effects of the different halo models on the determination of the allowed maximum--likelihood region in the WIMP mass and WIMP-nucleon cross section have been derived and discussed.
  
  In the following a summary of results obtained for the considered halo modeling is shown:
  
  
  As it evident the allowed region, when accounting for different consistent halo modeling, is greatly enlarged. If all the uncertainties in model assumptions and parameters would be included the region will be further enlarged.
  
  
  
  Results of the full correlation analysis
  in term of a WIMP with mixed coupling
  
  
  Since Na and I - on the contrary e.g. of ^natGe - are fully sensitive also to the spin-dependent coupling, the analysis of the data has been extended considering the more general case for a WIMP having both spin-independent and spin-dependent couplings. This is also the case of the neutralino candidate since in supersymmetric theories both the squark and the Higgs bosons exchanges give contribution to the coherent (SI) part of the neutralino cross section, while the squark and the Z⁰ exchanges give contribution to the spin-dependent (SD) one. Anyhow, also this model dependent analysis is intrinsecally not restricted to the case of the neutralino candidate alone. In this case, the free parameters are: WIMP mass (m_W), SI (SD) cross section on nucleon, _SI (_SD), a mixing angle for SD interaction () and background contributions.
  
  Allowed parameters' regions at given confidence level have been obtained. Note that here we have included not only the uncertainties on v₀ (between 170 and 270 km/s), but also the effect of the uncertainties on the form factors parameters and on the measured quenching factors.
  
  In this case an allowed volume in the four dimensional space (m_W, _SI, _SD, ) is obtained.
  
  For simplicity, next figure shows slices (colored areas) for some m_W of the region allowed at 3 C.L. in the ( _SI, _SD, m_W) space at fixed value. Four particular SD couplings have been considered here: i) = 0 (a_n=0 and a_p0 or |a_p||a_n|); ii) =/4 (a_p=a_n); iii) =/2 (a_n0 and a_p=0 or |a_n| |a_p|); iv) =2.435 rad (a_n/a_p=-0.85, pure Z⁰ coupling). The case a_p= -a_n is nearly similar to the case iv).
  
  

  The dashed lines given for the case m_W = 50 GeV represent the limit curves calculated for v₀ = 220 km/s from the data of the DAMA liquid Xenon experiment ; regions above these dashed lines could be considered excluded at 90% C.L. for the case of this v₀ value and overall astrophysical, nuclear and particle physics assumptions used in the model framework of each different nucleus. Moreover, since the ¹²⁹Xe nucleus - on the contrary of the ²³Na and of the ¹²⁷I - has the neutron as odd nucleon, only the case /2 would be - under these hypotheses - affected; similar results are obtained for all m_W. We take this opportunity to further remark that the comparison of results achieved by different experiments - even more when different target nuclei and/or different techniques have been used - is affected by intrinsic uncertainties. In addition no quantitative comparison can be directly performed between the results obtained in direct and indirect searches because it even more strongly depends on assumptions and on the considered model framework; moreover, the indirect searches themselves suffer of large uncertainties.

  When the SD contribution goes to zero (y axis), an interval not compatible with zero is obtained for _SI.

  Similarly, when the SI contribution goes to zero(x axis), finite values for the SD cross section are obtained.

In our study we have also shown that:

finite values can be allowed for _SDeven when _SI 3 x 10^-6 pb as in the region allowed in the pure SI scenario considered above;

regions not compatible with zero in the _SDversus m_W plane are allowed even when _SIvalues much lower than those allowed in the dominant SI scenario previously summarized are considered;

minima with both _SIand _SD different from zero are present for some m_W and pairs; the related confidence level ranges between 3 and 4.

In conclusion, this analysis has shown that the DAMA data of the four annual cycles, analysed in terms of WIMP annual modulation signature, can also be compatible with a mixed scenario where both _SIand _SDare different from zero.
Further investigations are in progress on model dependent analyses. As an example we recall that for the SD form factor an universal formulation is not possible since the internal degrees of the WIMP particle model (e.g. supersymmetry in case of neutralino) cannot be completely separated from the nuclear ones. In the calculations presented here we have adopted the SD form factors of ref. M.T. Ressell et al., Phys. Rev. C56 (1997), 535 estimated by considering the Nijmengen nucleon-nucleon potential. Other formulations are possible for SD form factors and can be considered. Moreover, the inclusion of the effect of consistent halo modeling as shown for the case of purely spin-independent coupled WIMPs in a given model framework (hep-ph/0203242, see above) will further enlarge the allowed volume in this scenario.

Results of the full correlation analysis
in term of a WIMP with preferred inelastic scattering

The DAMA annual modulation data have also been analysed in the framework of WIMP with preferred inelastic scattering according to the model by D. Smith and N. Weiner (PRD64(2001),043502). They consider as WIMP candidate a two states particle ( ), with mass splitting. The interaction of this WIMP with a target-nucleus can occur only if the energy transferred to is greater than . In this case a transition from to can take place. In this scenario a kinematical constraint arises which favours this process for heavy nuclei (such as ¹²⁷I) with respect to lighter ones (such as ^natGe).

This model scenario, with respect to the case of WIMP elastically scattering, gives rise to an enhanced modulated component, S_m, with respect to unmodulated one, S₀, and to largely different behaviours with energy for both S₀ and S_m (both show a higher mean value). In the following results of the energy and time correlation analysis in this model framework are presented. There uncertainties on WIMP local velocity, on WIMP escape velocity in the galactic frame, on nuclear Form Factor parameters and on the measured quenching factors have been included.

Slices of the volume allowed in the space at given WIMP mass (3 C.L.) for a WIMP with preferred inelastic scattering by the DAMA annual modulation data. The regions allowed in this model framework largely lie in sections where detection by experiments with light target-nuclei (such as e.g. Ge) are disfavoured. Also in this case the inclusion of the effect of consistent halo modeling and of uncertainties on assumptions and parameters values would enlarge the allowed volume.

What next?

The data taking of a 7-th annual cycle has been completed at end of July 2002.

The work needed to improve the installation and to built the new LIBRA set-up (target mass ~ 250 kg of highly radiopure NaI(Tl)) has been started. Full installation foreseen at end 2002.

Further work on model dependent analyses in progress.

The data of the 5-th, 6-th and 7-th annual cycles are at hand and the model independent and models dependent analyses will be completed after the LIBRA installation.