The Observable Universe and Beyond

Dark Matter (2018 Update for DAMA and SABRE)

It seems that the Big Bang Theory has been validated conclusively with all these supporting evidences. However, recent observations in the last few years reveal that there is something amiss. It is noticed that even though there is not enough mass to hold the stars, galaxies and galaxy clusters in place, they are still moving around and would not disperse. It looks as if there is some kind of invisible force (gravity from the dark matter) to hold them together. The situation is similar to a puppet show, where the audience can safely assume that someone behind is manipulating the movements. It is suggested that the mass of dark matter within the lunar orbit can be computed by subtracting the total mass (Earth + Dark Matter) within the lunar orbit from the mass of the Earth measured by a gravity-sensing satellite (Figure 02-10aa). It turns out to be no more than 1.5x10¹⁵ kg or about one billion times lower than the

Figure 02-10aa Earth-Moon System [view large image]

mass of the Earth. It means that the difference is too small to be measured by the 2008 technology. All that can be found is the upper bound, which is just another way of saying that there is no difference up to the current level of accuracy.

A 19 April 2012 report in Nature News indicates that a survey found only about 1/10 of the dark matter around the Solar system. The researchers measured the velocity of more 400 stars within 13000 light years of the Sun (in a 15-degree cone) below the disk of the Milky Way, and then extrapolate the result to the other side of the disk above the plane. It is found that only about 1/10 the amount of dark matter predicted by models shown in Figure 02-10ab as a blue haze around the spiral Milky Way. Since the modeling involves many assumptions, further observations are required to arrive at a definite conclusion.

Figure 02-10ab Dark Matter, Deficiency of

Figure 02-10b shows the large-scale distribution of dark matter mapped by the Hubble's Cosmic Evolution Survey in early 2007. Since light will follow the deformed path created by massive object, the quantity and location of the dark matter can be estimated by the amount of the bending. However, it should be cautioned that such image represents only a small facet of the whole picture. Just like representing the distortion of space-time as a piece of stretched rubber sheet, or the probability density of an electron (in the atom) by some foggy orbital, the dark matter distribution map does not include the other interesting properties such as its lack of interaction with other matter except via gravity.

Figure 02-10b Dark Matter Distribution [large image]

Note the increasing clumpiness from distant past to more recent epoch in the picture.

The map of dark matter forms a filamentous 'skeleton' upon which visible matter congregates, eventually producing stars and galaxies. Baryonic structures are expected to form only inside the dark-matter scaffold. But as shown in Figure 02-10ca, the concentrations of dark matter (mapped in contours) usually - but not always - match up with normal matter (coloured). The discrepancies could be a simple error resulting from the way the observations were made. Alternatively it is suggested that dark matter, if the clump is small enough, could have any accumulating visible matter blown out of it by a high-energy phenomenon such as a quasar or a supernova, for

Figure 02-10ca Dark Matter and Baryonic Matter

example. The collision of two galaxies could also blow an amount of visible matter out as a faint satellite galaxy that has no associated dark matter.

Some General Properties of Dark Matter from observations and simulations (Figure 02-10cb) :

It must be cold (meaning moving with speed much slower than that for light), otherwise it could not clumped together to form structure such as the halo of galaxy.
As it does not absorb or emit electromagnetic radiation, it must be electrically neutral.
It also does not interact with strong interaction as high energy cosmic rays fail to produce anything from the dark matter.
Since there is no known mechanism to replenish dark matter, it must be stable on cosmic timescales. Theorists propose that dark matter possesses a conserved quantity, e.g., dark-parity = +1, while all the non-dark matters have a value of -1. Thus, it is forbidden to decay to non-dark matter. However, both kinds can still interact provided the total dark-parity is unchanged after the interaction.

Figure 02-10cb Dark Matter Properties

Thus, dark matter could interact with non-dark matter gravitationally and probably via weak interaction as well.

Neutrino - It is a reasonable candidate for dark matter because of its unreactive nature. Theoretical calculations indicate that there should be as many as 100 million neutrinos for every atom in the universe. However, the recent estimates of neutrino mass is so slight that it could account for only about 0.1 - 7 per cent of the mass of the universe.

WIMP - Many new particles with heavy mass appear in the supersymmetry formulation. These are referred to as weakly interacting

massive particles, or WIMPs. For example, the photino (the fermionic partner of photon) has a mass about 10 to 100 times that of the proton. Most of these electrically neutral particles would, like neutrino, go straight through Earth. On rare occasion, however, one might interact with an atom in the material they pass through. So far, the only claimed detection of a dark matter particle (by an Italian team in 2000) has been strongly disputed. One particularly interesting WIMP is the lightest supersymmetric particle (LSP) - the neutralino, which could be a Majorana fermion (a particle which is its own antiparticle) and thus has more chance to produce the electron-

Figure 02-10cc Dark Matter Constraints

positron pair. Figure 02-10cc shows the region excluded in the dark-matter-mass vs WIMP-Nucleon-Cross-Section (via gravitational interaction) by various observations in the past or in the future (if nothing shows up).

Nonluminous matter - Ordinary hidden matter consists of atoms that emit little or no light. It includes a host of celestial objects such as planets, dark gas clouds, brown dwarfs, neutron stars, and black holes. The Massive Compact Halo Objects Project (MACHO) has been looking for them in the halo of the Milky Way. A search for microlensing has turned up four candidates toward the Large Magellanic Cloud and 45 toward the Galactic Bulge.

The case has been built up for some time that light from some quasar gravitational lensings vary in long time interval (in years and decades) not characterized by the quasars. It is also noticed that the lensing images vary independently (Figure 02-10da). These observations together can be explained by additional micro-lensing of un-seen objects weighing about the mass of the sun and not much bigger than a village. Such objects match closely with the hypothetical primordial black holes formed when the universe was about 10^-5 sec old. Observations over a period of 7 years by the MACHO Collaboration yield a low value of such objects (less than 20% of dark matter estimated in the Milky Way halo). It is argued that more data is required to rule out the option of MACHO.

Figure 02-10da Primordial BH

The case for primordial black holes (PBHs) as dark matter has been revived in 2017 due the lack of progress in the searches. The new model avoids the mass constraints of PBH (should be lower than 10 M_sun according to the original idea). The wider range of PBH mass allows only a smaller fraction to be detected by microlensing experiments. And if the PBHs are grouped in clusters, it would evade detection even more by a probability of less than 1 in 1000 to be along the line of sight (see Figure 02-10da). Thus, the search for PBHs has to be aimed further out (say at distance to Andromeda and beyoud) by probing much larger volume of galactic halos (Figure 02-10db).

Figure 02-10db Primordial BH as Dark Matter {view large image]

According to the 2017 Scientific American article on "Black Holes from the Beginning of Time", there is a list of observations which can be used to determine the viability of the PBH origin :

Gravitational Waves - Large number of black hole mergers (via the detection of gravitational waves) would be a hint for PBH origin. Detection of black holes with mass below the Chandrasekhar limit of 1.45 M_sun in addition would strongly indicates the primordial origin, since such black holes cannot be generated by stellar collapses.

Ultra-faint Dwarf Galaxies - PBHs would produce large number of ultra-faint dwarf galaxies in galactic halo. They could be detected by future generation of space telescopes.

Stellar Position Variation - PBH can alter position of stars by tiny amount. ESA's Gaia mission is surveying about one billion stars in the Milky Way. The measurements could reveal the presence or absence of PBHs.

Neutral Cosmic Hydrogen - During the cosmic dark age, the universe was mostly composed of neutral hydrogen, which produces 21 cm radio line emission. If PBHs also coexisted in that period, there would be x-ray radiation produced by its accretion of matter imprinting signatures on the 21 cm all-sky map by the Square Kilometer Array (SKA) scheduled to commence operation in early 2020s.

Distortions of CMBR - The same x-ray radiation from PBHs could also induce distortions on CMBR. NASA,s Primordial Inflation Explorer (PIXIE) may include such kind of measurement in the mission (still in talking stage as of 2017).

Marcos - The discovery of pentaquark in July 2015 by the LHCb experiment at LHC has fueled the speculation that dark matter could be in the form of dense agglomerations of very many quarks called "macros" (Figure 02-10fb). They might be extremely dense (similar to the neutron star) and tiny. Their characteristics are constraint by astronomical observations such that they should have no effect on gravitational lensing (already accounted for by clusters of galaxies), and they should not interfere with the formation of galaxies (a process already known). The proponents have been searching for shred of evidence from gravitational wave and cosmic detectors, ancient minerals, Skylab plastic, seismic records from the Moon, ... - all in vain. The negative results limit the mass of macros to between roughly 50 gm and the mass of Mount Everest (~ 10¹⁶ gm) giving a range in size between 10^-4 - 3 cm (at neutron star density of ~ 10¹⁴ gm/cm³). See detail in "Strangely Familiar".

Figure 02-10fb Quark Agglomerations

Axion - see "Axion".

Wimpzilla - This type is superheavy produced during the period of inflation (Figure 02-10fa). It could be the decay product of the "inflaton" driving the inflation. There are not many of such Wimpzilla around as a lot of mass-energy is packed into each one. Detection of Wimpzilla depends on whether they decay naturally or interact with non-dark matter occasionally. One possibility is that they are stable, i.e., neither decay nor interact - a scenario explaining all the futile searches of the dark matter.

Figure 02-10fa Wimpzilla
[view large image]

BTW, dark matter does interact with non-dark matter via gravity, such interaction would not produce elementary particles, which are used as signature to verify its identity.

MOND - It is proposed that instead of looking for the dark matter, slight altering of Newton's second law will account for the discrepancy. The formula F = ma is amended in such a way that lower acceleration would experience weaker gravitational force (see Figure 02-10ea).

		Figure 02-10eb shows the MOND prediction on mass discrepancy for many astronomical objects. Its main failure occurs in the cores of large galaxy clusters. Since its proposal in 1983, MOND has become a controversial subject among astronomers. It is considered as a rather ad hoc invention to fit this special problem of dark matter. Even if it is correct, the new formula should be derived from a more fundamental theory.
Figure 02-10ea MOND Theory	Figure 02-10eb MOND Prediction [view large image]

According to MOND (Modified Newtonian Dynamics), a test particle at a distance r from a large mass M is subject to the acceleration a by the following formula:

(a/a₀) a = G M / r²

where G is the gravitational constant, a₀ ~ cH₀ ~ 6.5x10^-8 cm/sec² is the MOND parameter, H₀ is the Hubble constant, and

(a/a₀) is a function of a/a₀ such that

(a/a₀) ~ a/a₀ for a/a₀ << 1, and

(a/a₀) ~ 1 for (a/a₀) >> 1. In fact,

(a/a₀) is just the ratio of the inertia mass m_a to the gravitational mass m_g, i.e.,

= m_a/m_g, which is equal to 1, i.e., m_a = m_g, according to the Principle of Equivalence and has been verified to be the case without exception from 1589 (via the Galileo's leaning tower experiment) up till today. Anyway,

	BTW, the cosmic acceleration at the current epoch is about 1/2 of a₀ as defined above. So the point at a ~ a₀ is where the inward acceleration is roughly balanced by the cosmic
Figure 02-10ec MOND and Competitors [view large image]	expansion. (See Figure 02-10ec). Such transition point is about 3,000 A.U. from the Sun. Voyager 1 is about 138 A.U. away on 28 March, 2017 and will not be able to test MOND in my lifetime.

See "Spiral Flow" for a fluid dynamic treatment of galactic disk, "Modified Newtonian Dynamics" for further detail on MOND, and a 2017 article on "Rules of Attraction: Why it's Time to Rethink how Gravity Works".

Another possibility is to identify a₀ to the acceleration of the cosmic expansion. Astronomical observations reveal that the effect of matter and dark energy canceled out (i.e., no acceleration at this point) at an epoch corresponding to 7 billion light years. Therefore, a₀ should become zero at this point and the behavior of the galactic rotational curve should be following the normal Newtonian mechanics. Current observational data are about 1 or 2 order magnitude below the threshold of 7x10⁹ lys as shown in Figure 02-10ed. Some of the samples have a vague similarity to the Newtonian curve (see Figure 02-10ec). More data from galaxies further away is required to make a definite claim.

Figure 02-10ed MOND and Cosmic Expansion

Anyway, MOND has another problem with failing to explain the separation of normal and dark matters when two galactic clusters collide such as the case of the Bullet Cluster.

2012 Update - The status of dark matter research up to the beginning of 2012 is rather confusing both experimentally and theoretically. The results from several observations are inconsistent, and there are a number of theories and suggestions trying to explain the discrepancy as shown in the followings:

The DAMA experiment at the Gran Sasso underground laboratory in Italy had claimed the discovery of dark matter back in 2008. The detection depends on the seasonal difference in registration of events as the Earth ploughing through dark matter (see "Figure 02-10gf,a"). The amount of dark matter particles hitting Earth should rise in June, when the planet is moving through the galaxy in the same direction as the sun, and fall in December when it is moving in the opposite direction.
The problem arose when another Gran Sasso experiment called XENON100 (because it uses liquid xenon instead of sodium iodide) did not detect such seasonal variation. This is particularly disturbing as the two detectors are located nearby (see "Figure 02-10ge").

Figure 02-10fc Dark Matter, 2012 Update

Then a third experiment in Gran Sasso, and the CoGeNT team (using a germanium detector) reported sighting of similar annual modulation to DAMA. Their estimates point to a dark matter mass of 10 Gev, which is too light according to an updated calculation with Higgs mass ~ 125 Gev (Figure 02-10fc).

If the WIMP mass is that light, the LHC should be able to detect them by now. So far none have shown up.
The WIMP and axion (another dark matter favorite) are "cold dark matter" as they are slow-moving. The trouble with such kind is that they all tend to assemble a lot of small-scale structures (such as dwarf galaxies), contrary to observations.
Thus warm (hot) dark matter such as sterile neutrino (another hypothetical particle) is proposed to replace the WIMPs. This particle is supposed to interact with normal matter through gravity only and moves fast enough to resist clumping on smaller scale.

A novel idea suggests dark atom to resolve the problems. The alleged dark atom is similar to hydrogen atom except that it is made from dark electron, dark proton and emits or absorbs dark photon. The discrepancy in detections is the result of whether the detecting material

can change the dark atom's energy level; while the interaction with dark photon would rise the temperature of the dark matter preventing them to clump together (to form dwarf galaxies). However, the dark photons must behave differently, otherwise the spherical structure (of the dark matter halo surrounding the galaxy) would disappear as they would carry away energy and the halo collapses to a disk. Theorists now consider more and more complex dark matter with all kinds of composition to suit the observational data - a most brazenly contrived approach. See "Insignifficance" for a philosophical view of the whole thing.

Figure 02-10ga WIMP, Complex

See also "Hints of Dark Matter from Cosmic Rays", and "Dark Matter Debate" on the contentious results.

A webcast by LUX (Large Underground Xenon) on October 30, 2013 reports no sign of any dark matter. This dark matter detector has five times the sensitivity of XENON-100. It captured only 160 events in 110 days of data-taking - a level consistent with background noise. The result suggests that the WIMPs may simply have a lower mass, or it may be even more weakly interacting than originally antticipated. The same team announced at a conference on July 2016 that they had failed to make a single WIMP detection in 20 months.

Observation by AMS (Alpha Magnetic Spectrometer) - AMS is sort of a compensation by the US Congress for the cancellation of the Superconducting Supercollider (SSC) in 1993. It was finally attached to the ISS in May 2011 (Figure 02-10gb). Since then it has collected a total of 25 billion cosmic ray interactions, of which nearly seven million involved electrons and positrons having energies between 0.5 and 350 GeV. Analysis indicates that the positrons appear to arrive equally from all directions. Despite the large number of measurements, at energies larger than 250 GeV there are not yet sufficient particles detected on which to produce trustworthy data. The measurement mainly confirm the previous observations but with higher accuracy (Figure 02-10gc, Graph b). It shows that the positron fraction (the number of positrons detected divided by the total number of electrons and positrons detected at that same energy) decreases steadily for positron energy more than about one GeV, and then the positron fraction roughly doubles as the energy approaches 100 GeV. At this point the positron fraction is over ten percent, which is quite a lot of antimatter, suggesting that another source of high energy positrons (other than those from the interaction of high energy cosmic rays colliding with interstellar gas and dust) must be active in our galactic neighborhood.

		The theoretical model with WIMP seems to fit quite well with the AMS data (Figure 02-10gc, Graph a). It has generated considerable hype in the media since the press release about the observation in April 2013.
Figure 02-10gb AMS [view large image]	Figure 02-10gc AMS Data [view large image]	Closer examination reveals that it is far short of a discovery (of dark matter) for the following reasons :

The dark matter signature of (positron fraction) peaking at certain energy and then falling off abruptly (after reaching the mass of WIMP) is absent.
The excess in positron fraction can be explained by other causes. Many astronomical objects such as supernovae, pulsars, neutron stars, black hole accretion discs, quasars, and even planetary thunderstorms would produce antimatter via high-energy particle collisions.
The WIMP would have enough energy to produce equal amount of proton-antiproton pairs, but AMS shows essentially no antiprotons.
The theoretical fit involves the theory of supersymmetry and the conjecture of Majorana fermion, but there is no observational evidence for both.
Most dark matter appears to be located in the galactic halos, or in filaments connecting galaxies and galactic clusters, rather than amongst the stars in the spiral arms. If the dark matter annihilation mechanism for the positron excess is correct, then there are also a large density of extremely high energy electrons and positrons in intergalactic space resulting in a specific form of the extragalactic gamma ray spectrum which is not observed. The absence of such feature strongly constrains the electron-positron density, and along with it the density of dark matter, in the galactic halo.

BTW, AMS-01 is the prototype for the test run in 1998. The real thing is designed as AMS-02. Figure 02-10gd1 below is a 2014 update on the various experiment/observations to detect dark matter :

Figure 02-10gd1 Dark Matter Update, 2014

2018 Update : By 2018, there is a growing sense of "crisis" in the search for dark matter as all attempts fail to unveil its true nature. It is now advocated that diversifying the experimental efforts and incorporating astronomical surveys could provide the best hope of making progress on the problem. Figure 02-10gd2 identifies the possible nature of dark matter, while Table 02-01a summarizes the six coresponding categorials in the search as illustrated in the review article "A New Era in the Search for Dark Matter".

Category	Motivation	Example (Energy/Mass)	Exp/Obs
Weak Scale (WIMP)	This is the CDM based on naturalness such as SUSY with "natural" cancellation of high energy virtual particle contributions to arrive at the observed mass.	neutralino (~ 200 Gev)	LHC, DAMA, etc...
Neutrinos	This class of "Hot Dark Matter" includes the SM variety and any hypothetical neutral ferminon interacting only through gravity.	Sterile Neutrino (~ 1 ev)	MiniBooNE
Light Bosons	The very small mass bosons are postulated to explain a QCD anomaly and radiation excesses from galactic center.	Axion (~ 10^-5 ev)	ADMX
Other Particles	Dark matter could be the relic of super-heavy particle created in early universe. It is the X particle predicted by GUT.	Wimpzilla (10¹⁵ Gev)	None
Macroscopic Objects	Instead of exostic particles, the so-called dark matter could be just hidden ordinary matter that emits little or no light.	MACHO (~ M_Sun)	MACHO Project
Modified Gravity	It asserts that there is no dark matter. The excessive attraction in galactic rotation can be resolved by slight altering of Newton's second law.	MOND (~ M_Galaxy)	Suggestions

Table 02-01a Dark Matter Candidates

Figure 02-10gd2 Dark Matter Update, 2018 [view large image]

Another approach suggests to give up the top-down paradigm, which starts the search from a theory with many assumptions, and instead relies on empirical data to steer the effort at each instance (see "Going Nowhere Fast", American Scientist, November-December 2018)

DAMA, 2018 - The DAMA Experiment is in one of the laboratories under the Gran Sasso Mountain (Figure 02-10ge). These 1400 meters underground facilities are supposed to shield off unwanted high energy particles from outside. However, there are still trace of radioactive elements in the soil and equipment which is very difficult to get rid off. Anyway, the claim of dark matter detection is based on the seasonal pattern of collision counts (Figure 02-10gf,d), events from other sources would just appear as background that can be subtracted away. Such modulation persists in two different incarnations over 20 years, each one has been upgraded to remove potential uncertainties. The latest result is presented in 26 March, 2018 (see "DAMA/LIBRA-Phase2"). However, nobody else can reproduce the result, the problem remains unresolved. Followings are some details and comments about the experiment.

The solar system is moving at 232 km/s with respect to the halo of the Milky Way, while the Earth is revolving around the Sun in one year cycle. Thus the DAMA lab has a varying velocity profile related to the halo with a maximum at (232 + 30) km/s in June and minimum (232 - 30) km/s in December (Figure 02-10gf,a). This pattern can be translated into the interaction rate of counts for between the dark matter particles and the molecules of the detecting material, i.e., maximum encounter rate at June and minimum in December.

		In the diagram, S_k is the total count integrated over all the energy bins E (of 0.5 kev interval, see Figure 02-10gf,c), S_0,k is the average rate, and S_m,k the residual. The unit of the count rate is counts per day per unit detector mass per unit energy (cpd/kg/keV) as a function of recoil energy. Figure 02-10gf,c reveals that residual signals only show up between the energy range from 2 to 6 kev; Figure 02-10gf,d presents the pattern of modulation as detected by the last 2 upgrades.
Figure 02-10ge Gran Sasso Labs. [view large image]	Figure 02-10gf DAMA, 2018 [view large image]

The detecting material is pieces of 232 kg ULB (Ultra-Low-Background, meaning very pure) NaI(T1) doped with thallium

ion (T1⁺) to provide discrete energy levels between the valence and condutiion bands (Figure 02-10gg). The incoming Dark Matter (DM) particle scatters the atomic nucleus through gravitational interaction, which is very weak as indicated by the very small cross-section of ~ 10^-40 cm² or less (comparing to the nuclear reaction cross-section of ~ 10^-24 cm²). Anyway, it manages to scatter off the nucleus with sufficient energy to bump electrons up from the valence to the conduction band. The excited electrons then decay via "two steps" in ~ 250 ns to emit bluish photons, which trigger a cascade of electrons in the PMT (PhotoMultiplier Tube, Figure 02-10gf,b) to register the event. The nuclear recoil energy in unit of keV is actually the "electron equivalent" recoil energy (keV_ee) measured by scintillation light. The relationship between keV and keV_ee depends on the medium the scattering takes place in, and must be established empirically for each material.

Figure 02-10gg NaI Scintillation [view large image]

See more in "Basic of Scintillation Detectors".

In a 2015 PhD thesis entitled "SABRE: A Search for Dark Matter and a Test of the DAMA/LIBRA Annual-Modulation Result Using Thallium-doped Sodium-iodide Scintillation Detectors", about 1/3 of the 383 pages is spent on dissecting the DAMA modulation. It comes to the conclusion that uncertainties in the dark-matter model, the halo model, and the detector response makes it impossible to compare between DAMA and other experiments with different targets. The remaining 2/3 of the dissertation is devoted to describe SABRE (Sodium-iodide with Active Background REjection) - an experiment similar to DAMA, but with many inprovements as summarized below.

Figure 02-10gh SABRE Experiment
[view large image]

SABRE has twin sites (Figure 02-10gh,a), one in Gran SASSO (Hall C) formerly housing DarkSide across the DAMA lab (see Figure 02-10ge). The other one is the Stawell Underground Physics Laboratory (SUPL) in Victoria, Australia. Differences of the 2 sites relevant to the modulation detection include :

Seasonal effects with opposite phase.
Rock composition and radiopurity.
Independent radon, temperature, pressure control systems and power supply.

	As shown in Fiugre 02-10gh,c there are many backgrounds which can contribute to the counts of event leading to wrong conclusion. The goal is to produce Ultra-pure NaI crystals through growth procedure, independent assessment, and further R&D. Figure 02-10gi shows the improvement in ppb (part per billion) of a 2 kg crystal comparing to the
Figure 02-10gi Radio-Purity [view large image]	DAMA's. A full size crystal (5.5 kg) is under production. Larger crystal will improve the surface to volume ratio and the expected backgrounds.

The most troublesome contaminant is the K-40 long half-life (~ 1 billion years) isotope of potassium. A particular decay mode transforms it to Ar-40 by capturing an electron. The Ar-40 then emits a 1.5 Mev gamma ray and an Auger electron. The electron goes on to masquerade as dark matter particle to register an event at the most sensitive energy range of 3 kev (Figure 02-10gj,a).

	By surrounding the NaI detector with Liquid Scintillator Veto (LSV), which examines the by-products of all the events (the gamma ray in this example), the false one would be rejected. In addition, the LSV can also tag incoming radiation on the way to the detector, making it unnecessary to stop the radiation completely (Figure 02-10gj,b).
Figure 02-10gj K-40 Decay Mode, and Veto Technique

		As mentioned earlier on the DAMA detector, The scintillator only measure the part of the "electron equivalent" energy E_ee in unit of keV_ee. The nuclear recoil energy E_nr is determined through experiments on the "quenching factor" Q by the formula E_nr = E_ee / Q. DAMA uses Q = 0.3 = constant for the entire range. Actually as shown in Figure 02-10gk, the value of Q depends on energy and particularly the value of Q below 1 keV_ee is undetermined. One of the SABRE's improvements is to extend the low energy threshold below
Figure 02-10gk Quenching Factor [view large image]	Figure 02-10gl POP Run [view large image]	1 keV_ee by developing high efficiency, low noise, and very low background PMT (PhotoMultiplier Tube).

Figure 02-10gl is the result of the 2018 POP (Proof Of Principle) run by SABRE to check out the background in the crystal. The inserted table shows about 10 times improvement on the K-40 background count with veto on.

An arXiv preprint with the title "Is DAMA Bathing in a Sea of Radioactive Argon?" is the most recent explanation on the DAMA modulation (as of 28 March, 2018). It attributes the cause of the DAMA pattern to radioactive Ar-37 or Ar-40. The Ar-37 could be produced by the seasonal variation of neutron flux in the atmosphere; while the Ar-40 could be excited by seasonally varying Rn-222 atoms or associated neutron and gamma-ray flux. If either interpretation is correct, the veto technique employed by SABRE should be able to reject such events and would not observe the annual modulation.

The following is a much simplified derivation of the WIMP-NaI cross section. It demonstrates the relationship between the entities mentioned previously. The variables in the target and the incident beam are identified. A formula is then derovated to link the cross section of the constituent (the NaI molecule) and the mass of the individual beam particle (the WIMP mass), see pictorial illustration in Figure 02-10gm,a.

Figure 02-10gm WIMP Mass
- S_m ~ 0.01 count/day-kg-kev (This is the # of counts from 1 kg of target mass, 1 kev bin energy in 1 day, see Figure 02-10gf).
- E = (4 kev)x(25 # of bins) = 100 kev (The total amount of kev in collecting the counts, see Figure 02-10gm,b).
- M_t = 250 kg (Mass of the target material, see Figure 02-10gm,d).
- m_t = 150 atomic weight = 249x10^-27 kg (The mass of the target NaI molecule. DAMA separates NaI into Na and I atoms of 23 and 127 atomic weight respectively. The target is either the Na or I atom, hence 2 separate WIMP mass zones in Figure 02-10gm,c).
- t = 86400 sec (The # of sec in 1 day for calculating the cross section in cm²).
- v_b = 232x10⁵ cm/sec (Local dark matter velocity - excluding seasonal and statistical variations).
- _b = 5.7x10^-25 gm/cm³ (The local dark matter density according to dark matter halo model).
- m_b = 50 Gev/c² = 9x10^-24 gm (The estimated dark matter particle mass).
- = 8x10^-42 cm² (The calculated cross section, see Figure 02-10gm,c to compare)
This is a very naive estimate of the "dark matter - nucleon" interaction cross section omitting many finer details. As shown in Figure 02-10gm,c DAMA presents 2 regions of compatible parameters when everything is taken into consideration.

Note that the 2 "Discovery" regions claimed by DAMA is inside the "WIMP Mass Exclusion Zone" ruled out by other experiments.


Figure 02-10gm WIMP Mass