No role for muons in the DAMA annual modulation results
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- Bernabei, R., Belli, P., Cappella, F. et al. Eur. Phys. J. C (2012) 72: 2064. doi:10.1140/epjc/s10052-012-2064-4
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This paper gathers arguments and reasons why muons surviving the Gran Sasso mountain cannot mimic the Dark Matter annual modulation signature exploited by the DAMA/NaI and DAMA/LIBRA experiments. A number of these items have already been presented in individual papers. Further arguments have been addressed here in order to present a comprehensive collection and to enable a wider community to correctly approach this point.
The DAMA/NaI and DAMA/LIBRA experiments at the Gran Sasso underground laboratory (LNGS) of the I.N.F.N. have been and are, respectively, investigating the presence of the Dark Matter (DM) particles in the galactic halo by exploiting the model independent DM annual modulation signature, originally suggested in the middle of ’80s in Refs. [1, 2]. In fact, as a consequence of the Earth annual revolution around the Sun, which is moving in the Galaxy traveling with respect to the Local Standard of Rest towards the star Vega near the constellation of Hercules, the Earth should be exposed to a higher flux of Dark Matter particles around ∼2 June (when the Earth orbital velocity is added to the one of the solar system with respect to the Galaxy) and by a smaller one around ∼2 December (when the two velocities are subtracted).
the event rate must contain a component modulated according to a cosine function;
with period equal to one year;
with a phase roughly around June 2nd in case of usually adopted halo models (slight variations may occur in case of presence of non thermalized DM components in the halo);
this modulation must be present only at low energy, where DM particles can induce signals;
it must be present only in those events where just a single detector, in a multi-detector set-up, actually “fires” (single-hit events), since the probability that DM particles experience multiple interactions is negligible;
the modulation amplitude in the region of maximal sensitivity has to be ≲7 % in case of usually adopted halo distributions, but it may be significantly larger in some particular scenarios.
Thus, this signature has a different origin and peculiarities than effects correlated with seasons on the Earth.
To mimic such a signature spurious effects or side reactions should be able not only to account for the observed modulation amplitude but also to simultaneously satisfy all the requirements of the signature; thus, no other effect investigated so far in the field of rare processes offers a so stringent and unambiguous signature.
Let us now briefly describe the DAMA/LIBRA experiment , recalling its model independent annual modulation results [4, 5]. The present DAMA/LIBRA set-up, installed at the Gran Sasso underground laboratory, is made of 25 highly radiopure NaI(Tl) crystal scintillators in a 5-rows 5-columns matrix. Each NaI(Tl) detector has 9.70 kg mass and a size of (10.2×10.2×25.4) cm3. The scintillation light (decay time ≃240 ns) of each crystal is collected (through two 10 cm long highly radiopure quartz light guides, which also act as optical windows being directly coupled to the bare crystal) by two low-background photomultipliers working in coincidence at single photoelectron threshold. The software energy threshold in the present data taking is 2 keV electron equivalent (hereafter keV) and the measured light response is 5.5–7.5 photoelectrons/keV depending on the detector. In order to reject afterglows, Cherenkov pulses in the light guides and Bi-Po events, a 500 μs veto occurs after each event . The detectors are housed in a low radioactivity sealed copper box installed in the center of a low-radioactive Cu/Pb/Cd-foils/polyethylene/paraffin shield; moreover, about 1 m concrete (made from the Gran Sasso rock material) almost fully surrounds (mostly outside the barrack) this passive shield, acting as a further neutron moderator. In particular, the neutron shield reduces by a factor larger than one order of magnitude the thermal neutrons flux . The copper box is maintained in HP Nitrogen atmosphere in slight overpressure with respect to the external environment; it is part of the 3-levels sealing system which prevents environmental air reaching the detectors. The experiment takes data up to the MeV scale despite the optimization is made for the lowest energy region. The linearity and the energy resolution of the detectors at low and high energy have been investigated using several sources as discussed in Ref. ; routine calibrations are carried out in the same conditions as the production runs, by using the glove-box installed in the upper part of the apparatus .
The DAMA/LIBRA data released so far correspond to six annual cycles for an exposure of 0.87 ton×yr [4, 5]. Considering these data together with those previously collected by the former DAMA/NaI over 7 annual cycles (0.29 ton×yr) [6, 7], the total exposure collected over 13 annual cycles is 1.17 ton×yr. Several analyses on the model-independent DM annual modulation signature have been performed (see Refs. [4, 5] and references therein). A clear modulation is present in the (2–6) keV single-hit events and fulfills all the requirements of the DM annual modulation signature. In particular, no modulation is observed either above 6 keV or in the (2–6) keV multiple-hits events.
The results provide a model independent evidence of the presence of DM particles in the galactic halo at 8.9σ C.L. on the basis of the investigated DM signature. In particular, with the cumulative exposure the modulation amplitude of the single-hit events in the (2–6) keV energy interval, measured in NaI(Tl) target, is (0.0116±0.0013) cpd/kg/keV; the measured phase is (146±7) days (corresponding to May 26±7 days) and the measured period is (0.999±0.002) yr, values well in agreement with those expected for the DM particles.
Careful investigations on absence of any significant systematics or side reaction able to account for the measured modulation amplitude and to simultaneously satisfy all the requirements of the signature have been quantitatively carried out (see e.g. Refs. [3–13], refs therein); none has been found or suggested by anyone over more than a decade. In particular, the case of muons has been deeply investigated.
This paper will further demonstrate that neither muons nor muon-induced events can significantly contribute to the DAMA observed annual modulation signal. In addition, some of the already-published arguments [3–13] are summarized here.
2 The muon flux at LNGS
The muons surviving the coverage of the Gran Sasso laboratory either can have direct interactions in the experimental set-up or can produce in the surroundings and/or inside the set-up secondary particles, such as fast neutrons, γ’s, electrons, spallation nuclei, hypothetical exotics, etc., possibly depositing energy in the detectors. Such direct or indirect events are a potential background for low count rate experiments, as DAMA is. In this paper, the muon induced background in DAMA/LIBRA will be investigated and any possible role in the DAMA results will be quantitatively ruled out.
The surviving muon flux (Φμ) has been measured in the deep underground Gran Sasso Laboratory (3600 m w.e. depth) by various experiments with very large exposures [14–19]; its value is Φμ≃20 muons m−2 d−1 , that is about a factor 106 lower than the value measured at sea level. The measured average single muon energy at the Gran Sasso laboratory is 270±3 (stat) ± 18 (syst) GeV ; this value agrees with the predicted values using different parametrizations . A ≃2 % yearly variation of the muon flux was firstly measured years ago by MACRO; when fitting the data of the period January 1991–December 1994 all together, a phase around middle of July was obtained . It is worth noting that the flux variation of the muons is attributed to the variation of the temperature in the outer atmosphere, and its phase changes each year depending on the weather condition. Recently, other measurements have been reported by LVD, quoting a lower amplitude (about 1.5 %) and a phase, when considering the data of the period January 2001–December 2008 all together, equal to (5 July ± 15 days) . Finally, Borexino, has quoted a phase of (7 July ± 6 days), still considering the data taken in the period May 2007–May 2010 all together [16, 17]. More recently, the Borexino collaboration presented a modified phase evaluation (29 June ± 6 days),1 with a still lower modulation amplitude: about 1.3 % [18, 19], by adding the data collected in a further year; the appreciable difference in the fitted values further demonstrates the large variability of the muon flux feature year by year.
3 Why muons cannot play any role
The measured muon variation at LNGS has no impact on the DAMA annual modulation results, recalled in Sect. 1. In the following sections we summarize the key items. It is worth noting the arguments reported in Ref. , where no evidence for a correlation between cosmic rays and DAMA result has been found and it is shown that the two phenomena differ in their power spectrum, phase, and amplitude.
3.1 Intrinsic inability of muons to mimic the DM annual modulation signature
it would induce variation in the whole energy spectrum.
it would induce variation in the multiple-hits events (events in which more than one detector “fires”),
it would induce variation with a phase and amplitude distinctively different from the DAMA measured one (see later).
3.2 Inconsistency between the phase of muons and of the muon-induced effect and the DAMA phase
This simple approach does not consider that the experimental errors in the muon flux are not completely Gaussian; however, it gives the right order of magnitude of the confidence level for the incompatibility between the DAMA phase and the phase of muons and of the muon-induced effects. Analyses carried out by different authors confirm these outcomes; for example, a disagreement in the correlation analysis between the LVD data on muon flux and the DAMA residuals with a confidence level greater than 99.9 % is reported in Ref. .
It is also worth noting that the expected phase for DM is significantly different than the expected phase of muon flux at Gran Sasso: in fact, while the first one is always about 152.5 day of the year, the second one is related to the variations of the atmospheric temperature above the site location, Teff. In particular, the atmosphere is generally considered as an isothermal body with an effective temperature Teff; the behaviour of Teff at the LNGS location as function of time has been determined e.g. in Refs. [18, 19]. As first order approximation Teff was fitted with a cosinusoidal behaviour and the phase turned out to be (24 June ± 0.4 days) [18, 19]; this is later than e.g. the middle of June, date which is still 3σ far away from the DAMA measured phase (see Fig. 1). In addition, fitting the temperature values at L’Aquila in the years 1990–20112 with a cosinusoidal function, a period of (365.1±0.1) days and a phase of (25 July ± 0.6 days) are obtained.
Thus, in conclusion, the phase of the DAMA annual modulation signal  is significantly different than the phases of the surface temperature and of the Teff, on which the muon flux is dependent, and than the phases of the muon flux measured by MACRO, LVD and Borexino experiments.
The above argument also holds for every kind of cosmogenic product (even hypothetical exotics) due to muons.
Two extreme cases can be considered: if τ≪T/2π, one gets tside≃tμ+τ; else if τ≫T/2π, one gets tside≃tμ+T/4 (≃tμ+90 days) and the relative modulation amplitude of the effect is ≪1.5 %.
In conclusion, the phase of muons and of whatever (even hypothetical) muon-induced effect is inconsistent with the phase of the DAMA annual modulation effect.
3.3 No role for the muons interacting in the detectors directly
In addition to the previous arguments, the direct interaction of muons crossing the DAMA set-ups cannot give rise to any appreciable variation of the measured rate. In fact, the exposed NaI(Tl) surface of DAMA/LIBRA is about 0.13 m2 (and smaller in the former DAMA/NaI); thus the muon flux in the ≃250 kg DAMA/LIBRA set-up is about 2.5 muons/day. In addition, the impinging muons give mainly multiple-hits events and over the whole energy spectrum.
3.4 No role for fast neutrons produced by muon interaction
The surviving muons and the muon-induced cascades or showers can be sources of neutrons in the underground laboratory. Such neutrons produced by cosmic rays are substantially harder (extending up to several hundreds MeV energies ) than those from environmental radioactivity; their typical flux is about 10−9 neutrons/cm2/s , that is three orders of magnitude smaller than the neutron flux produced by radioactivity.
The integral neutron yield critically depends on the chemical composition and on the density of the medium through which the muons interact. The dependence on atomic weight is well described by a power law : Y=4.54×10−5A0.81 neutrons per muon per g/cm2; alternatively, it can also be expressed as : Y=1.27×10−4(Z2/A)0.92 neutrons per muon per g/cm2. Thus, the integral yield of neutrons produced by muons deep underground at LNGS is Y≃(1–7)×10−4 neutrons per muon per g/cm2 [21, 28] for relatively light nuclei and Y≃4.5×10−3 neutrons per muon per g/cm2  for lead.
We stress that—in addition—the latter value has been overestimated by orders of magnitude both because of the extremely cautious values assumed in the calculation and because of the omission of the effect of the neutron shield of the set-up.
In conclusion, any appreciable contribution from fast neutrons produced by the muon interactions can be quantitatively excluded. In addition, it also would fail some of the requirements of the DM annual modulation signature such as III, IV and V.
For completeness, in the next two sub-sections we will address the case of environmental neutrons of whatever origin (and, thus, also including those induced by muons). In the first sub-section the outcomes in Refs. [4–7, 29] will be recalled without entering in details, while in the second one the case of the neutron capture on Iodine will be analysed in depth.
3.5 … and no role for environmental neutrons
Environmental neutrons cannot give any significant contribution to the annual modulation measured by the DAMA experiments [4–7, 29]. In fact, the thermal neutron flux surviving the multicomponent DAMA/LIBRA shield has been determined by studying the possible presence of 24Na from neutron activation of 23Na in NaI(Tl). In particular, 24Na presence has been investigated by looking for triple coincidences induced by a β in one detector and by the two γ’s in two adjacent ones. An upper limit on the thermal neutron flux surviving the multicomponent DAMA/LIBRA shield has been derived as: <1.2×10−7 n cm−2 s−1 (90 % C.L.) , that is at least one order of magnitude lower than the value of the environmental neutrons measured at LNGS. The corresponding capture rate is: <0.022 captures/day/kg. Even assuming cautiously a 10 % modulation (of whatever origin3) of the thermal neutrons flux, and with the same phase and period as for the DM case, the corresponding modulation amplitude in the lowest energy region would be [4, 6]: <0.01 % of the DAMA observed modulation amplitude. Similar outcomes have also been achieved for the case of fast neutrons; the fast neutrons have been measured in the DAMA/LIBRA set-up by means of the inelastic reaction 23Na(n,n′)23Na∗ (2076 keV) which produces two γ’s in coincidence (1636 keV and 440 keV). An upper limit—limited by the sensitivity of the method—has been found: <2.2×10−7 n cm−2 s−1 (90 % C.L.) , well compatible with the value measured at LNGS; a reduction at least an order of magnitude is expected due to the neutron shield of the set-up. Even when cautiously assuming a 10 % modulation (of whatever origin) of the fast neutrons flux, and with the same phase and period as for the DM case, the corresponding modulation amplitude is <0.5 % of the DAMA observed modulation amplitude [4, 6].
Moreover, in no case the neutrons can mimic the DM annual modulation signature since some of the peculiar requirements of the signature would fail, such as III, IV and V.
3.6 No role for 128I decay
Reference  has claimed that environmental neutrons (mainly thermal and/or epithermal), occasionally produced by high energy muon interactions, once captured by Iodine might contribute to the modulation observed by DAMA through the decay of activated 128I (that produces—among others—low energy X-rays/Auger electrons). Such an hypothesis is already excluded by several arguments given above (as e.g. those in Sects. 3.1 and 3.5), moreover it has already been rejected in Refs. [11, 12]; anyhow, in the following we will focus just on its main argument avoiding to comment on several other wrong statements present in Ref. .
considering the branching ratios of the EC processes in the 128I decay, the K-shell contribution (around 30 keV) must be about 8 times larger than that of L-shell; while no modulation has been observed by DAMA above 6 keV (see [4, 5] and references therein) and, in particular, around 30 keV;
the 128I also decays by β− with much larger branching ratio (93.1 %) than EC (6.9 %) and with a β− end-point energy at 2 MeV. Again, no modulation has instead been observed in DAMA experiments at energies above 6 keV [4, 5];
the L-shell contribution would be a gaussian centered around 4.5 keV; this shape is excluded by the behaviour of the measured modulation amplitude, Sm, as a function of energy (see Fig. 6 (bottom)). The efficiencies to detect an event per one 128I decay are: 2×10−3, 6×10−3, and 2×10−3 in (2–4) keV, (4–6) keV and (6–8) keV respectively, as calculated by the Monte Carlo code. Thus, the contribution of 128I in the (2–4) keV would be similar to the one in the (6–8) keV, while the data exclude that.
3.7 No role for hypothetical phosphorescence induced by muons
In Ref.  it is argued that delayed phosphorescent pulses induced by the muon interaction in the NaI(Tl) crystals might contribute to the (2–6) keV single-hit events. Many wrong statements are put forward in that reference. We have already critically addressed Ref.  in our Ref. . We will just focus on the main argument.
such a hypothesis would imply dramatic consequences for every NaI(Tl) detector at sea level (where the μ flux is 106 times larger than deep underground at LNGS), precluding its use in nuclear and particle physics;
phosphorescence pulses (as afterglows) are single and spare photoelectrons with very short time decay (∼10 ns); they appear as “isolated” uncorrelated spikes. On the other side, scintillation events are the sum of correlated photoelectrons following the typical time distribution with mean time equal to the scintillation decay time (∼240 ns). Pulses with short time structure are already identified and rejected in the noise rejection procedure described in detail in  (the information on the pulse profile is recorded). Thus, in addition, phosphorescence pulses are not present in the DAMA annual modulation data;
because of the poissonian fluctuation on the number of muons, the standard deviation of the (2–6) keV single-hit modulation amplitude due to a similar effect would be 13 times (see Appendix) larger than that measured by DAMA, and therefore no statistically-significant effect, produced by any correlated events, could be singled out. Even just this argument (that will be further illustrated in the following) is enough to discard the hypothesis of Ref.  (similar considerations are also reported in Ref. );
the muon phase is inconsistent with the phase measured by DAMA (see Sect. 3.2).
Thus, the argument regarding a possible contribution from delayed phosphorescent pulses induced by muons can be safely rejected.
3.8 Absence of long term modulation
In Ref.  it is argued that high-energy muons measured by LVD might show a long term modulation with a period of about 6 years, suggesting that a similar long term modulation might also be present in the DAMA data. We avoid to comment here on the other arguments reported in Ref.  that are actually already addressed elsewhere in the present paper, and already discard such a suggestion. However, for completeness such a long term modulation has also been looked for in the DAMA data.
This further shows that no evidence for a long term modulation in the counting rate is present, as—on the other hand—it should already be expected on the basis of the many other arguments (and just one suffices) discussed in this paper, further demonstrating that there is no role for muons.
3.9 No role for muons from statistical considerations
The value experimentally observed by DAMA for σ(A), 0.0013 cpd/kg/keV , is shown as (red online) dashed line in Fig. 9; the σ(A) curve approaches this value just for Aeff≫50 m2, while—as we will demonstrate—even in the most cautious case the Aeff value is much smaller. In fact, to have an idea on the possible sizes of Aeff, four interesting cases are shown in Fig. 9: (i) the muons interacting directly in the NaI(Tl) DAMA/LIBRA detectors (hypothetically producing either very short range particles or phosphorescence pulses as discussed in Sect. 3.7, …), corresponding to Aeff equal to the DAMA/LIBRA exposed surface: 0.13 m2; (ii) the effective area equal to the one calculated (by a Monte Carlo simulation) just considering the 1/r2 dependence for the flux of the “products”, without including any shield effect, corresponding to Aeff≃1.65 m2; (iii) the effective area equal to the area of the heavy passive shield, Aeff≃1.75 m2; (iv) the effective area equal to the area of the heavy passive shield plus the neutron moderator, Aeff≃3 m2. In all the four cases the fluctuation, driven by the small number of muons, is much larger than that observed by DAMA. Since it is extremely safe to consider that any hypothetical mechanism would have a corresponding Aeff within the previous considered cases (that is Aeff≪50 m2), we can conclude that all (standard and exotic) mechanisms, because of the low number of the involved muons, provide too high fluctuations of the data, not observed in DAMA. Even just this argument is enough to discard any kind of hypothesis about muons.
In this paper we have compiled some of the main scientific and quantitative arguments which demonstrate that there is no room for any hypothetical contribution from muons to the (2–6) keV single-hit annual modulation amplitude measured by DAMA experiments. Some comments about incorrect arguments reported in recent papers [30, 32, 33, 36, 37] have also been addressed. In conclusion, the hypothesis of a role for muons in the DAMA observed (2–6) keV single-hit annual modulation can be safely rejected for many scientific reasons.
It is worth noting that in Refs. [18, 19] 28 June (179.0 days) is instead quoted as measured phase; actually, in our convention—coherent throughout the paper—179.0 days correspond to 00:00 of 29 June (as, for example, t=0.0 days is 00:00 of 1st of January and t=1.0 days is 00:00 of 2nd of January).
For the sake of correctness, it is worth noting that a variation of the neutron flux in the underground Gran Sasso laboratory has never been suitably proved. In particular, besides few speculations, there is just an unpublished 2003 short internal report of the ICARUS collaboration, TM03-01, that seemingly reports a 5 % environmental neutron variation in hall C by exploiting the pulse shape discrimination (PSD) in commercial BC501A liquid scintillator. However, the stability of the data taking and of the applied PSD procedures over the whole data taking period and also the nature of the discriminated events are not fully demonstrated. Anyhow, even assuming the existence of a similar neutron variation, it cannot quantitatively contribute to the DAMA observed modulation amplitude [4, 6, 7] as well as satisfy all the peculiarities of the DM annual modulation signature.