A New Possible Way to Explain the DAMA Results

At present there is an effort to reconcile the results of the DAMA experiment with those from other Dark Matter experiments such as CoGeNT, CRESST, CDMS, and all LXe experiments. The author suggests a new model describing the Dark Matter signal as the result of collisions of very light (1-to-few GeV/c^2) WIMPs with hydrogen, and compares it with currently accepted models of collisions with heavy nuclei (Na, Ge or Xe). The hydrogen target would come from H-contamination of NaI(Tl), Ge and CaWO4 crystals. Initial tuning indicates that one can explain the modulation amplitude of DAMA and CoGeNT with this model, assuming a WIMP-proton cross section between 10^33 and 10^32 cm^2. This paper should be considered to be a new idea which will need substantial new experimental input from all involved experiments.


Introduction
The DAMA experiment clearly observes a small oscillatory signal. The observed signal is a peculiar modulation of the counting rate of the 2-6 keV single-hit events (i.e. those in which only one of the many detectors in the set up fires) satisfying all the many requirements of the Dark Matter annual modulation signature. The observed yearly modulation is in phase with the Earth's motion around the Sun. It has been discussed in the literature that the possible positive hints observed by the DAMA oscillatory signal can also be all explained in terms of a lower mass than originally expected Dark matter particle scattering off nuclei. DAMA is the first experiment to observe a clear oscillatory signal [Bernabei, 2013], as shown on Fig. 1.
CoGeNT (see Fig. 2) also measures a sign of oscillation; CRESST-II and CDMS experiments observe a hint of a signal. However, there is no hint of signal from any LXe Dark Matter searching experiments, such as Xenon-10, Xenon-100 or LUX. Figure 3 presents a model-dependent status of the Dark matter search (Snowmass, 2013). Nominally, none of these experiments was designed to search for ∼1 GeV/c 2 mass. As Fig. 3 Fig. 1. DAMA data: residual rate of the single-hit scintillation events, measured by DAMA/LIBRA over six annual cycles in the (2-6) keV energy intervals as a function of the time [Bernabei, 2013]. The modulation amplitude is ∼0.01 counts/day/kg/keV. CoGeNT data: counts per 30 day bins from the 0.5-2.5 keVee energy window [Aalseth, 2013]. The modulation amplitude is ∼0.3 counts/day/kg/keV. The graph also shows the low limit, below which, experiments will have to deal with the neutrino background. One can see clearly, that a WIMP mass below ∼5 GeV/c 2 would not be detected by most of present experiments. indicates there is a great opportunity to explore a cross-section of 10 −30 − 10 −44 cm 2 if the mass is indeed low.

New idea to explain DAMA data
The author discusses a new idea explaining the DAMA signal as a scattering of a light ∼0.5-3 GeV/c 2 Dark matter particle with a light nucleus; specifically hydrogen present as a small OH or H 2 O contaminations in NaI(Tl) crystals. Table 1 shows maximum calculated nuclear recoil energy as a function of the WIMP mass, for two targets, hydrogen and sodium, and assuming that the WIMP velocity relative to Earth is between 0 and the Galactic escape velocity of 800 km/sec, all modulated by the Earth's velocity of 230±30km/sec in the Galactic coordinate system. The Table 1 shows the calculated kinematical limit. To estimate the measured energy one has to include the quenching factor. For sodium one can assume 25 % [Gerbier,1999], for hydrogen it is larger, close to ∼ 97 % [Ninkovic,2006]. Notice in Table 1 that the nuclear recoil of sodium is exceeding the DAMA detection threshold only if the WIMP mass is above ∼3 GeV/c 2 , if one includes the Naquenching factor. On the other hand, WIMP masses between 0.5 and 2.5 GeV/c 2 are possible to detect by the DAMA threshold if the hydrogen target is involved in the collision since the H-quenching factor is almost 1; in other words, if the target is hydrogen nucleus, most of the calculated recoil energy can also be measured. The exact tuning of the right mass within between 0.5 and 2.5 GeV/c 2 should be done with a proper fit [Profumo,2014], [Queiroz, 2014].
DAMA NaI(Tl) crystals are made of Ultra-Low-Background (ULB) materials to guarantee low radioactive background. DAMA experiment does not quote the H-contamination in their Fig. 4. FTIR spectrum of NaI(Tl) crystals showing the OHcontamination in a crystal located in the protective enclosure (green) and the H 2 O contamination when exposed to air (brown) [Shiran, 2014].
crystals. In fact, the H-contamination is usually not quoted by producers as it does not affect the spectroscopic qualities in small amounts. OH-molecules represent likely contamination of the primary NaI salt; it requires a prolonged pumping at elevated temperature to be removed [Kudin, 2011]. Fig. 4 shows a typical OH-contamination in NaI(Tl) crystals [Getkin, 2014]; the FTIR spectrum shows the OH-contamination in a crystal located in the protective enclosure (green) just after its production, and the H 2 O contamination when it was exposed to air (brown). The exact level of the OH or H 2 O contamination in NaI(Tl) crystals is a proprietary information, as indicated by Saint-Gobain Co. However, we learned from Hilger Co. that the OH-contamination at a level of a 1-3 ppm is likely. According to [Getkin, 2014], the final H-contamination may end up to be worse than 1-3 ppm, which was indicated by Hilger Co. Even at a level of ∼10 ppm, spectroscopic properties of NaI(Tl) crystals are not affected [Getkin, 2014]. Generally, these companies keep air humidity to less than ∼2% when machining the crystal and assembling the NaI(Tl) detector, although again this is proprietary knowledge. But, knowing how hard it is to keep humidity low in gases without appropriate filtration, it would seem to us that water contamination at a level of a few ppm is easily possible. Once in the detector, DAMA NaI(Tl) crystals are of course protected against the moisture by boil-off nitrogen; however, the sealed chamber is opened from time to time. The exact history of each crystal is probably not known, i.e., there may be variation among crystals.
In our calculations we will assume the H-contamination at a level of ∼1 ppm.
A low mass WIMP of 0.5-2.5 GeV/c 2 represents a real experimental challenge at present, as it requires a low mass hydrogen target to be detectable. So far, existing experiments are providing the hydrogen target only as a small "unwanted" contamination, which limits the measured rate. For example, when such WIMP strikes a hydrogen atom, a resulting proton projectile may strike an electron, which gets excited into the conduction band of the NaI(Tl) crystal structure until it finds an activator (Tl), with a very low ionization potential of 6.108 eV, where the deexcitation occurs via small photonic emissions, mostly in visible spectrum [Knoll, 2010]. To avoid noise, DAMA sets the thresh-old to 2 keVnr, which is equivalent to about 3-5 photoelectron signal.
The alkali halide inorganic crystals, such as NaI(Tl) or CsI(Tl), may have a unique advantage over other methods to detect the very low mass WIMP, if they have sufficiently high OH-contamination and if the threshold is above a single photoelectron PMT noise. This requirement may cut a large fraction of a good dark matter signal but it is necessary at the moment in the non-accelerator based searches.
The WIMP-proton scattering cross-section is not known at all at present. We will treat it as an independent variable.
We calculate the rate per day as follows:

Other Dark matter searching experiments
If the proposed H-contamination mechanism works for the DAMA experiment, it must also work for CDMSlite [Agnese,2013], CoGeNT [Aalseth,2013], and CRESST-II [Angloher,2011]. The peak amplitude for DAMA is ∼300 events/30 days, for CoGeNT it is ∼10 events/30 days; CDMSlite hints ∼2.9 counts/keV/kg-day (no clear oscillation measured yet). Both CDMSlite and CoGeNT experiments are using ultra-pure Ge-crystals [Hansen,1982]. Hydrogen is the only gas which has been successfully used for high-purity Ge crystal growth. All commercial detector grade germanium is grown exclusively in hydrogen. Therefore, even the ultra-pure Ge has a H-contamination at a level of ∼2x10 15 atoms/cm 3 , or ∼50 ppb [Hansen,1982], [Brink,2014]. No real measurement was made on the actual crystals from these two experiments, which we encouradge to do. The CRESST-II experiment is using CaWO 4 crystals of total weight ∼ 10 kg, which has also the H-contamination as these crystals are grown in the oxygen/air atmosphere that contain certain level of water, OH and other components [Getkin,2014].
If the target is hydrogen from the H-contamination, the measured signal rate in all these experiments should scale as a ratio of the H-contamination level 1 , the weight of detector 2 , and detection efficiency (DE) 3 . Table 2 shows the expected number of events per 30 days in the modulation peak amplitude. One can begin to get a hint of a possible agreement between this simple scaling model and data if one assumes that the WIMP-proton cross-section is between ∼10 −31 and ∼10 −32 cm 2 . Figure 5 shows our prediction for the modulation peak rate in several experiments as a function of cross-section, assuming the H-contamination as indicated on the graph, as a function of the WIMP-proton cross-section. One can see that to get the DAMA modulation peak of ∼300/30 day period one needs a cross-section in the range ∼10 −31 -10 −32 cm 2 . There is a hint that one could explain the count rate in CoGeNT with the same range of cross-sections as DAMA experiment, simply scaling the rate by the H-contamination level, weight and detection efficiency. The calculation in this paper is too simple (a correct way to do  . This paper's prediction for the modulation peak rate in several experiments as a function of cross-section, assuming the H-contamination as indicated, WIMP-proton scattering hypothesis, Dark matter density ∼0.3 GeV/cm 3 in our nearby Universe [Catena, 2011]. The modulation amplitude peak was caculated from a differential rate based on these two extreme values of dark matter particle velocities: 1030 km/sec and 1060 km/secsee Table 1). it would be to have a Monte Carlo Dark matter model of the Galaxy with the corect distribution of velocities).
To work it out quantitatively and convince ourselves that the proposed model is correct, all these four experiments should perform the H-contamination analysis of their crystals used in experiments. DAMA should also find out if there is a correlation between rates/crystal and the H-contamination in each crystal (if there is a variation in rates/crystal).
LXe or LAr experiments do not have the hydrogen contamination, and therefore any DM signal detected by these methods would directly contradict the proposed model.

Comparison with LHC experiments
It is interesting to compare our prediction for the DAMA WIMP-nucleon cross-section range with upper limits obtained by Tevatron and LHC experiments, where WIMP is measured in "WI MP + WI MP + jets" events [Beltran, 2010]. This is shown in Figure 6. It is clear that the accelerator-based crosssection upper limits are lower than values obtained from the Hcontamination model. This may not be significant at this stage, but at some point it should be explained.

A new proposal for future experiments
One could attempt to detect diatomic molecular vibration, excited by gentle WIMP-proton "diffraction-like" scattering, and further reduce the threshold on the WIMP mass. To excite such vibtrations, a very small energy deposit at a level of 1.8-4.3 eV is Fig. 6. Upper limits of WIMP-nucleon cross-sections as a function of the WIMP mass, plotted for Tevatron [Beltran, 2010] and LHC [ATLAS, 2013], [CMS, 2013]. There is a large range of possible values of cross-section limits for ∼1 GeV/c 2 WIMP. needed and still be able to detect de-excitations by the Bialakali photocathode [Vavra, 2004]. To do this, one could use so called "wet" fused silica, which has ∼1000 ppm of OH-contamination by design. Or, one could use simply pure water, and "tune" for the OH-absorption lines. This avenue is presently not pursued because of a high single photoelectron noise. It could be, however, considered in future accelerator-triggered beam dump experiments searching for the dark matter production.

Conclusion
This paper suggests that the measured oscillation in the DAMA experiment may be caused by a scattering of the light mass WIMP (mass between ∼0.5 and ∼2.5 GeV/c 2 ) on a hydrogen nucleus, which happens to be the H-contamination in the NaI(Tl) crystal.
For our choice of parameters for the H-contamination model, and taking into account the DAMA modulation peak rate of ∼0.01 cpd/kg/keV, we can explain it with the WIMP-proton scattering cross-section in the range ∼10 −31 -10 −32 cm 2 (see Fig. 5).
We are also proposing the H-contamination model to explain signals in CDMSlite, CoGeNT, and CRESST-II experiments. There is a hint that one could explain the count rate with the same range of cross-sections as DAMA experiment, simply scaling the rate by the H-contamination level, weight and detection efficiency.
As the H-contamination may vary from crystal-to-crystal in the DAMA experiment, one may observe different rates.
To make this calculation credible, we suggest to DAMA, CDMS, CoGeNT, and CRESST-II collaborations to perform the FTIR analysis on their crystals to determine the Hcontamination.
LXe or LAr experiments do not have the hydrogen contamination, and therefore any DM signal detected by these methods would directly contradict the proposed model in this paper.

Acknowledgements
I also would like to thank CDMS people for discussing ideas of this paper, especially P. Brink, R. Partridge, G. Godfrey, and M. Kelsey. I also thank Ferilando Da Silva Queiroz for discussions regarding reconciliation of ideas of this paper and their publication [Profumo, 2014]. I would like Prof. E. Nappi for showing interest in the idea, sharing it with Prof. C. Broggini, and asking very good questions about early version of the paper. I would like to thanks Prof. E.V. Kolb for providing several references, which allowed me to enter the up-to-date status of the collider WIMP searches.