GeV WIMPs scattering off of OH impurities cannot explain the DAMA signal

In the presence of OH impurities in the DAMA crystals, GeV-scale WIMPs elastically scattering off of hydrogen nuclei with a spin independent cross section of $\sim 10^{-33}\ {\rm cm}^2$ might explain the annual modulation observed by the DAMA experiment, while being consistent with other direct dark matter searches, as scattering would occur at energies below the energy threshold of other detectors. In this work we examine this possibility and show that, independent of the level of OH impurities in the DAMA crystals, for several reasons this scenario does not provide a viable explanation to the DAMA signal.

The particle nature of the dark matter (DM) remains one of the most troubling mysteries of our universe. Weakly interacting massive particles, or WIMPs, are form many reasons leading particle candidates, and, as such, they are being very actively searched in a broad variety of experiments. In the recent past, a variety of puzzling signals have been gathered from several direct detection experiments, tentatively pointing, if interpreted as originating from WIMP-nuclei scattering, towards a mass window in the 5-10 GeV range. Such WIMPs, light compared to standard theory-driven expectations, might for example provide an interpretation to the excess events reported by CDMS-SI [2], CoGeNT [3][4][5], CRESST [6] and DAMA [7].
Whether or not all the putative signals listed above can be made consistent with each other is matter of some contention [5,8]. More importantly, null results from the XENON [9] and LUX [10] collaborations are entirely incompatible, at last at face value, with a light WIMP interpretation, with the possible exception of highly tuned iso-spin violation scenarios [11], or if the scintillation properties of LXe are fiercely changed from the assumptions used by the LUX experiment [10].
Recently, Ref. [1] argued that 1 GeV WIMP might provide a possible explanation to the DAMA signal. Ref. [1] advocates that a contamination of OH-molecules is likely to be present in the NaI(Tl) crystals used by the DAMA collaboration. The precise level of such contamination is unknown, but, if at all at a reasonable level, it would be supposedly sufficient to cause a 1 GeV WIMP to strike a Hydrogen nucleus, which in turn would produce photons then captured by the PMTs in the DAMA detector. Ref. [1] utilizes a putative 1 ppm contamination level; In what follows we will assume this same value.
The DAMA/LIBRA experiment in the INFN Gran Sasso National Laboratory in Italy, makes use of a large mass detector of about 250 kg highly radio pure NaI(Tl). The experiment is set up to detect nuclear recoil events through scintillation light, and is designed to search for time variations in the event rate rather than to identify dark matter scattering on an event-by-event basis. The strategy of looking for an annual modulation can used to distinguish a dark matter signal from most possible backgrounds sources, although one may worry * profumo@ucsc.edu † fdasilva@ucsc.edu about possible sources of background which could potentially also exhibit seasonal variation. However, DAMA claims that no such background satisfies all of the following criteria: (i) having a cosinusoidal modulation rate; (ii) existing only in a definite low energy range;(iii) having exactly a one year period; (iv) possessing the proper phase; (v) producing singlehit events; (vi) having the proper modulation amplitude. So far no background seems to fulfill all these criteria, and the DAMA/LIBRA collaboration has so far released results corresponding to a total exposure of 1.17 ton yr over 13 annual cycles supporting the detection of a signal possibly due to dark matter at the ∼ 9σ level [7]. Ref. [1] states that the DAMA signal can be explained by a 1 GeV WIMP dark matter particle. We give here several arguments as to why this is not a viable possibility.
First, Ref. [1] assumes that such a dark matter particle would scatter off of Hydrogen, but not off of Na. This, if at all possible, would definitely make for highly peculiar particle properties. However, even if one could neglect the Na recoils and consider Hydrogen scattering only, we find that one can fit the DAMA signal with spin-independent scattering only down to a mass of 2.5 GeV, at the 99% C.L., as we show in fig. 1, assuming a quenching  contours that this setup provides a very poor fit to the DAMA modulation. Indeed, the best fit point is excluded at the 3.9σ level. In other words, a very light WIMP as a candidate to explain the DAMA modulation is excluded at almost ∼ 4σ.
There are other lines of reasoning as to why a 1 GeV with a large scattering cross section is strongly disfavored. Such a light and strongly interactive particle would quite likely violate bounds from high-altitude detectors [14]. In addition, if as expected the WIMP pair-annihilated, it would over-heat the Earth grossly violating the measured heat flow [15].
In conclusion, we showed that a 1 GeV WIMP scattering off of Hydrogen nuclei from residual OH contamination in the DAMA NaI(Tl) crystals is highly disfavored, for the following reasons: (i) under the unmotivated assumption that the WIMP only scatter off of Hydrogen but not Na, we showed that the favored mass range would place the proton-WIMP cross section in a region grossly ruled out by current experiments; (ii) if scattering off of Na exists concurrently with H, the resulting signal does not provide a good fit to the DAMA signal, and is ruled out to almost the 4σ level; (ii) if scattering off of Ge exists concurrently with H, then CDMSlite limits eliminate the favored WIMP candidate mass; (iv) indirect constraints such as limits from high-altitude detectors and from the Earth heat flow are generically incompatible with the proposed mass and cross section.