# Sinusoidal dark matter: ANAIS Edition

Title: Annual Modulation Results from Three Years Exposure of ANAIS-112.

Reference: https://arxiv.org/abs/2103.01175.

This is an exciting couple of months to be a particle physicist. The much-awaited results from Fermilab’s Muon g-2 experiment delivered all the excitement we had hoped for. (Don’t miss our excellent theoretical and experimental refreshers by A. McCune and A. Frankenthal, and the post-announcement follow-up.) Not long before that, the LHCb collaboration confirmed the $R_K$ flavor anomaly, a possible sign of violation of lepton universality, and set the needle at 3.1 standard deviations off the Standard Model (SM). That same month the ANAIS dark matter experiment took on the mighty DAMA/LIBRA, the subject of this post.

In its quest to confirm or refute its 20 year-old predecessor at Brookhaven National Lab, the Fermilab Muon g-2 experiment used the same storage ring magnet — though refurbished — and the same measurement technique. As the April 7 result is consistent with the BNL measurement, this removes much doubt from the experimental end of the discrepancy, although of course, unthought-of correlated systematics may lurk. A similar philosophy is at work with the ANAIS experiment, which uses the same material, technique and location (on the continental scale) as DAMA/LIBRA.

As my colleague M. Talia covers here and I touch upon here, an isotropic distribution of dark matter velocities in the Galactic frame would turn into an anisotropic “wind” in the solar frame as the Solar System orbits around the center of the Milky Way. Furthermore, in the Earth’s frame the wind would reverse direction every half-year as we go around the Sun. If we set up a “sail” in the form of a particle detector, this annual modulation could be observed — if dark matter interacts with SM states. The amplitude of this modulation $S_m$ is given by

$R(t) = S_m \cos(\omega (t - t_0)) + R_0 \phi_{\rm bg}(t)~,$

where

$R(t)$ is the rate of event collection per unit mass of detector per unit energy of recoil at some time $t$,

$\omega = 2\pi/(365 \ {\rm days})$,

$R_0$ captures any unmodulated rate in the detector with $\phi_{\rm bg}$ its probability distribution in time, and

$t_0$ is fixed by the start date of the experiment so that the event rate is highest when we move maximally upwind on June 02.

The DAMA/LIBRA experiment in Italy’s Gran Sasso National Laboratory, using 250 kg of radiopure thallium-doped sodium-iodide [NaI(Tl)] crystals, claims to observe a modulation every year over the last 20 years, with $S_m = 0.0103 \pm 0.0008$ /day/kg/keV in the 2–6 keV energy range at the level of $12.9 \sigma$.

It is against this serious claim that the experiments ANAIS, COSINE, SABRE and COSINUS have mounted a cross-verification campaign. Sure, the DAMA/LIBRA result is disfavored by conventional searches counting unmodulated dark matter events (see, e.g. Figure 3 here or this recent COSINE-100 paper). But it cannot get cleaner than a like-by-like comparison independent of assumptions about dark matter pertaining either to its microscopic behavior or to its phase space distribution in the Earth’s vicinity. Doing just that, ANAIS (for Annual Modulation with NaI Scintillators) in Spain’s Canfranc Underground Laboratory, using 112.5 kg of radiopure NaI(Tl) over 3 years, has a striking counter-claim summed up in this figure:

ANAIS’ error bars are unsurprisingly larger than DAMA/LIBRA’s given their smaller dataset, but the modulation amplitude they measure is unmistakably consistent with zero and far out from DAMA/LIBRA. The plot below is visual confirmation of non-modulation with the label indicating the best-fit $S_m$ under the modulation hypothesis.

The ANAIS experimenters carry out a few neat checks of their result. The detector is split into 9 pieces, and just to be sure of no differences in systematics and backgrounds among them, every piece is analyzed for a modulation signal. Next they treat $t_0$ as a free parameter, equivalent to making no assumptions about the direction of the dark matter wind. Finally they vary the time bin size in analyzing the event rate such as in the figure above. In every case the measurement is consistent with the null hypothesis.

Exactly how far away is the ANAIS result from DAMA/LIBRA? There are two ways to quantify it. In the first, ANAIS take their central values and uncertainties to compute a 3.3 $\sigma$ (2.6 $\sigma$) deviation from DAMA/LIBRA’s central values $S_m^{\rm D/L}$ in the 1–6 keV (2–6 keV) bin. In the second way, the ANAIS uncertainty $\sigma^{\rm AN}_m$ is directly compared to DAMA using the ratio $S_m^{\rm D/L}/\sigma^{\rm AN}_m$, giving 2.5 $\sigma$ and 2.7 $\sigma$ in those energy bins. With 5 years of data — as scheduled for now — this latter sensitivity is expected to grow to 3 $\sigma$. And with 10 years, it could get to 5 $\sigma$ — and we can all go home.

[1] Watch out for the imminent results of the KDK experiment set out to study the electron capture decay of potassium-40, a contaminant in NaI; the rate of this background has been predicted but never measured.

[2] The COSINE-100 experiment in Yangyang National Lab, South Korea (note: same hemisphere as DAMA/LIBRA and ANAIS) published results in 2019 using a small dataset that couldn’t make a decisive statement about DAMA/LIBRA, but they are scheduled to improve on that with an announcement some time this year. Their detector material, too, is NaI(Tl).

[3] The SABRE experiment, also with NaI(Tl), will be located in both hemispheres to rule out direction-related systematics. One will be right next to DAMA/LIBRA at the Gran Sasso Laboratory in Italy, the other at Stawell Underground Physics Laboratory in Australia. ParticleBites’ M. Talia is excited about the latter.

[4] The COSINUS experiment, using undoped NaI crystals in Gran Sasso, aims to improve on DAMA/LIBRA by lowering the nuclear recoil energy threshold and with better background discrimination.

[5] Testing DAMA, article in Symmetry Magazine.

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#### Nirmal Raj

Nirmal Raj is a postdoc at TRIUMF National Lab whose research is centered beyond the Standard Model, mostly on dark matter and new physics at the electroweak scale, and occasionally within the Standard Model in the form of supernova neutrinos. His favorite things include neutron stars, underground experiments, and particle colliders. Also, cryptic crosswords, writing short stories, and hiking in the Pacific Northwest.