TeV in the disk F. Nozzoli

To cite this version:

F. Nozzoli. TeV dark matter in the disk. Astroparticle Physics, Elsevier, 2011, 35 (4), pp.165. ￿10.1016/j.astropartphys.2011.07.004￿. ￿hal-00806360￿

HAL Id: hal-00806360 https://hal.archives-ouvertes.fr/hal-00806360 Submitted on 30 Mar 2013

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Accepted Manuscript

TeV dark matter in the disk

F. Nozzoli

PII: S0927-6505(11)00136-8 DOI: 10.1016/j.astropartphys.2011.07.004 Reference: ASTPHY 1616

To appear in: Astroparticle Physics

Received Date: 8 April 2011 Revised Date: 9 July 2011 Accepted Date: 14 July 2011

Please cite this article as: F. Nozzoli, TeV dark matter in the disk, Astroparticle Physics (2011), doi: 10.1016/ j.astropartphys.2011.07.004

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. 1 2 TeV dark matter in the disk 3 4 F. Nozzoli 5 Dipartimento di Fisica, Universit´adegli Studi di Roma “Tor Vergata” 6 Via della Ricerca Scientifica 1, I-00133 Rome, Italy 7 8 9 10 11 12 Abstract 13 14 DAMA and CoGeNT annual modulation data and, CDMS-II, EDELWEISS-II, CRESST excesses of events over the expected 15 background are reanalyzed in terms of a dark matter particle signal considering the case of a rotating halo. It is found that the 16 configurations of very high mass dark matter particles in a corotating cold flux are favored by data. A similar high-mass/low- 17 velocity solution could be of interest in the light of the positron/electron excess measured by Pamela and Fermi in cosmic rays. 18 19 Keywords: dark matter experiments, dark matter theory 20 21 LS R − 22 1. Introduction ~v⊙ = ~v⊙ ~vLS R = (10.0, 5.25, 7.17) km/s is the Sun veloc- ≃ 23 ity relative to the Local Standard of Rest (LSR), and ~vLS R 24 Since 1996 the sodium iodide experiments of DAMA col- (0, 220 ± 30, 0) km/s [22]. Therefore assuming a rotating dark 25 laboration (DAMA/NaI and DAMA/LIBRA) have measured an matter halo (~vDM , 0) one can write: ~vLS R − ~vDM ≃ (0, vlag, 0), 26 annual modulation of the single-hit counting rate which has the where vlag is the LSR velocity with respect to the dark matter 27 proper features expected for a dark matter induced signal [1]. flux. Fixing vlag = v0 ≃ 220 km/s the eq. (1) provides the 28 More recently, other experiments (CoGeNT [2], CDMS-II isothermal halo model, however, in this analysis, the v0 and vlag 29 [3, 4], EDELWEISS-II [5], CRESST [6]) have reported a pre- parameters are kept free and it is important to note that config- 30 liminary observation of some excess of events relative to the urations of v0 and vlag that are far from the isothermal halo ones 31 expected backgrounds; in particular, the CoGeNT experiment can be physically meaningful 2. 32 has reported the possible presence of a modulated signal in the To avoid parameter proliferation, only the case of dominant 33 data collected during fifteen months [7]. spin independent interaction for elastically scattering dark mat- 34 The DAMA and CoGeNT annual modulation signals and the ter will be considered and the effects of uncertainties in the val- 35 other experiment excesses, if interpreted as dark matter with ues adopted for other parameters (quenching factor, form fac- 36 dominant spin independent interaction1 in the isothermal halo tor, possible presence of channeling, etc..) will be neglected3. 37 model, implies that dark matter particles possess a mass in the Therefore a four-parameter space (v , v , M , ξ σ ) will be 38 0 lag W 0 p 39 range of 5-15 GeV and an elastic scattering cross section with considered here, where MW is the particle mass, σp is the proton nucleons in the order of 10−4 pb [13, 14, 15, 16, 17, 18, 19, 20, cross section and ξ = ρDM is the density of the considered 40 0 0.3GeV/cm3 41 21]. dark matter component4 in units of 0.3 GeV/cm3. 42 In this paper the same data are reanalyzed relaxing the hy- 43 pothesis of isothermal halo model, however it is assumed that 2. Experimental observables 44 the dark matter local velocity distribution can still be approxi- mated as a single Maxwellian flux: 45 In this section the data used in the analysis are listed for each 46 2 experiment under consideration: 47 1 − ~v+~v /v2 f (~v,~v ) = e ( e) 0 . (1) 48 e 3/2 πv2 2.1. DAMA/NaI and DAMA/LIBRA 49  0 50 The total exposure of 1.17 ton×yr of NaI(Tl) provides three Here the Earth velocity relative to the dark matter flux is 51 LS R complementary observables: given by: ~v = ~v⊕(t) + ~v⊙ − ~v = ~v⊕(t) + ~v + ~v − ~v ; 52 e DM ⊙ LS R DM 53 where: ~v⊕(t) is the Earth velocity in the solar system frame; 54 2In particular, it is plausible that the whole dark halo has a not negligible an- 55 gular momentum [23, 24, 25], moreover ΛCDM halo simulations with baryons [email protected] ∼ / ∼ / 56 Email address: () predict also a corotating dark disk having v0 50 km s and vlag 50 km s 1Many other possible Dark Matter candidates have been suggested for the [26, 27] 57 interpretation of DAMA and of the other direct detection experiments. Some 3it is important, however, to keep in mind the possible relevant role of some 58 examples are (beyond the WIMPs class): -like particles [8], sterile neu- of these uncertainties. 4 59 trino or [9], leptophilic dark matter [10], inelastic dark matter ξ0 << 1 could be possible if the considered dark matter population is a 60 [11], [12], etc. subdominant component of a multicomponent . 61 Preprint submitted to Astroparticle Physics July 9, 2011 62 63 64 65 1 a) A modulated time behavior in the 2-6 keV window (see data in fig. (3) taken from fig. (4) of ref. [1]) 2 300 3 b) The energy distribution of the observed modulation ampli- 4 tude, assuming a fixed phase t0 = 152.5 d (see data in fig. (4) 5 taken from fig. (6) of ref. [1]). In the following analysis the 250 6 data in the 2-8 keV interval will be considered. 7 c) The energy distribution of the unmodulated counting rate 8 (see data in fig. (5) taken from fig. (27) of ref. [28]). This 200 9 energy distribution provides a limit for the sum of background 10 and unmodulated dark matter induced signal and therefore the 11 × 150 limit of 0.25 cpd/(kg keV) for the possible unmodulated dark (km/s) 0

12 matter induced signal, is cautiously assumed in the following v 13 analysis; this choice allows large space for the presence of a 100 14 low energy background component in the measured counting 15 rate. 16 50 17 18 2.2. CoGeNT 19 The data of fig. (1) and (4) of ref. [7] are considered for 0 20 the exposure of 330g × 442d collected by CoGeNT germanium 0 50 100 150 200 250 300 350 400 450 500 v (km/s) 21 detector. lag 22 The annual modulation data of fig. (4) of ref. [7] have been 23 considered for the evaluation of the dark matter allowed con- Figure 1: Horizontally hatched areas: allowed configurations (90% and 24 99% C.L.) for unconstrained DAMA/NaI + DAMA/LIBRA data. Cross figurations in the hypothesis that this signal is induced by dark hatched areas: allowed configurations (90% and 99% C.L.) for DAMA/NaI 25 matter elastic scattering; however the data of the inset of fig. (1) + DAMA/LIBRA data combined with CoGeNT, CDMS-II and CRESST data. 26 of ref. [7] is considered for the evaluation of the upper limit. Filled area: configurations having a C.L. better than the one of isothermal halo 27 model (v0 = 220 km/s and vlag = 220 km/s) for DAMA/NaI + DAMA/LIBRA 28 data unconstrained. 2.3. CDMS-II and EDELWEISS-II 29 30 The exposure of 969 kg × d collected by CDMS-II germa- 31 nium detectors [4] is considered. Eleven events were observed recoil are induced by dark matter elastic scattering will be con- 32 within the recoil acceptance region passing the rejection cuts in sidered; this example will be generically addressed as CaWO4. 33 the 10-150 keV energy range. The neutron background is not 34 able to explain the CDMS-II measured events; however some 35 of these events could be ascribed to surface background, in par- 3. Parameter estimation 36 ticular for the low energy region. In the following the hypothe- The joint estimation of the four parameters 37 sis that the measured event excess could be due to dark matter (v , v , M , ξ σ ) confidence interval has been obtained 38 elastic scattering is considered. Moreover the data of the very 0 lag W 0 p by solving: 39 low energy analysis of CDMS-II (see fig. (1) of ref. [29]) are 40 also considered in the evaluation of the upper limit. The re- − + = ∆ 41 2lnL(v0, vlag, MW , ξ0σp) 2lnLmax (2) cent result of EDELWEISS-II [5] (where five recoil events are 42 measured collecting the exposure of 384 kg × d) seems to be for the appropriate values of ∆ (∆ = 7.78and 13.28for 90%and 43 99% C.L. respectively). In the eq.(2) L(v , v , M , ξ σ ) is the 44 compatible with the CDMS-II data; therefore, for simplicity, 0 lag W 0 p 45 only the CDMS-II data will be considered in this analysis. global likelihood function and Lmax is the likelihood maximum 46 value over the four parameter space. In the estimation of confi- 47 2.4. CRESST dence intervals, the Gaussian approximation has been adopted / + / 48 The preliminary exposure of 564 kg × d collected by for the likelihood of DAMA NaI DAMA LIBRA data; more- over, the possible presence of unknown background explaining 49 CRESST - CaWO4 detectors is considered [6]. In the energy 50 range ∼ 15 − 40 keV (the lower threshold is different for dif- part or all of the measured events for the other experiments has 51 ferent detectors) 38 events are observed in the Tungsten recoil been considered. 52 band and 52 events in the Oxygen one. Despite the fact that In fig. (1) the projection of the confidence interval surface 53 206Pb recoils from α decay of 210Po can contribute to the back- (90% and 99% C.L.) in the plane (v0 vs vlag) is shown for two 54 ground in the higher energy part of the Tungsten recoil band cases: 55 and that the Oxygen recoil band is partially overlapped by the 56 • unconstrained DAMA/NaI + DAMA/LIBRA data (hori- 57 α recoil band, only a fraction of the observed events can be as- zontally hatched area) 58 cribed to the evaluated background. In this analysis, to account • 59 for the possible impact of a confirmed excess in CRESST data, DAMA/NaI + DAMA/LIBRA data combined with Co- 60 the case where 30 events of Tungsten recoil and 30 of Oxygen GeNT, CDMS-II and CRESST data (cross-hatched area) 61 2 62 63 64 65 1 2 0.02 3 146 d 152.5 d 0.015 4 300 a 5 0.01 6 250 7 200 0.005 8

(km/s) 150 0 b d 9 0 v 10 100 unconstrained -0.005 11 50 12 -0.01 13 0

500 (2-6) keV Residuals (cpd/kg/keV) 14 450 -0.015 c 400 2 15 350 constrained 10 v 300 250 10 -0.02 16 lag (km/s)200 -1 1 -100 0 100 200 300 400 150 -2 10 100 10 time (d) 17 50 Mass (TeV) 18 0 19 Figure 3: Expected modulation behavior for NaI(Tl) in the 2-6 keV region for 20 the models listed in table (1). Data points are taken from fig. (4) of ref. [1]. Figure 2: Allowed configurations in the volume (v0, vlag, MW ). The confidence 21 levels and the cases of unconstrained/constrained DAMA data adopt the same 22 palette code used for fig. (1). The configurations of very heavy dark matter 23 particles are favored. 24 In fig. (3) the expected modulation behavior in the 2-6 keV 25 energy region of DAMA for the four considered models is nd 26 shown. The vertical lines mark the time of 152.5d ∼ 2 of It can be noted that DAMA/NaI+DAMA/LIBRA data favor 27 configurations having low velocity dispersion (low v ) and rel- 28 0 atively low v which would imply a relatively cold and coro- 29 lag 0.05 30 tating dark matter flux in the Galaxy. Combining the DAMA data with the constraints from other 31 0.04 b 32 experiments further strengthens this indication. As a comparison, in fig. (1), the projection of the config- 33 d 34 urations having a C.L. better than the one of isothermal halo 0.03 35 model (v0 = 220 km/s and vlag = 220 km/s) for unconstrained 36 DAMA/NaI + DAMA/LIBRA data, is reported. 0.02 c 37 In fig. (2) the allowed configurations in the volume (cpd/kg/keV) m

38 (v0, vlag, MW ) are shown. The confidence levels and the cases of S 0.01 a 39 unconstrained/constrained DAMA data adopt the same palette 40 code used for fig. (1). It may be noted that configurations hav- 41 0 ing low v0 and low vlag require a very high MW ; only a similar 42 configuration would provide a flux of dark matter particles with 43 -0.01 enough kinetic energy to allow nuclear recoils events beyond 0 2 4 6 8 10 12 14 44 the experimental thresholds. Energy (keV) 45

46 Figure 4: Expected energy distribution of modulation amplitudes (S m) for the 47 4. Comparison of the annual modulation signal with re- models listed in table (1). Data points are taken from fig. (6) of ref. [1]. 48 spect to the case of isothermal halo model 49 50 Here, the expected dark matter annual modulation signal fea- June (where the maximum of the modulation amplitude is ex- 51 tures in NaI(Tl) are compared assuming the four different mod- pected for a non-rotating halo model) and 146 d where a max- 52 els listed in table (1). imum can be easily achieved, for example, assuming a coro- 53 tating flux. The data points are taken from fig. (4) of ref. 54 Model v0 (km/s) vlag (km/s) MW ξ0σp (pb) [1] and represent the annual modulation signal measured by 55 − a) 220 220 60GeV 1.3 × 10 5 DAMA/NaI + DAMA/LIBRA. The measured time of maxi- 56 −5 b) 220 220 10GeV 9.3 × 10 mum of the modulation in DAMA is 146 ± 7d, which is com- 57 × −4 c) 10 95 90 TeV 5.8 10 patible both with non-rotating as well as with many of the ro- 58 d) 20 75 90 TeV 4.6 × 10−4 59 tating halo models. It is important to note that the modulation 60 Table 1: Models adopted in fig. (3), (4) and (5). behavior is roughly sinusoidal but for some extremal models 61 3 62 63 64 65 1 -1 2 10 v0 = 220 km/s 3 CDMS -2 vlag = 220 km/s 4 1 10 (low energy)

5 -3 6 10 0.25 cpd/(kg x keV) DAMA 7 -4 8 c 10 (pb)

p CaWO 9 -1 4 σ -5 10 0 10 10 ξ (cpd/kg/keV) 0 S 11 -6 12 10 d b 13 a -7 10 14 CoGeNT

15 -2 -8 CDMS 10 10 -3 -2 -1 16 2 3 4 5 6 7 8 10 10 10 1 10 17 Energy (keV) Mass (TeV) 18 19 Figure 5: Expected energy distribution of the unmodulated part of the counting Figure 6: Allowed configurations at 2σ C.L. obtained for the isothermal halo 20 rate (S 0) for the four models listed in table (1). Data points are taken from fig. model with v0 = 220 km/s and vlag = 220 km/s. The dark filled area inside the 21 (27) of ref. [28]. CoGeNT region marks the configurations allowed at 1σ C.L. (∆ < 2.3). 22 23 24 also large departures from a pure sinusoid can be found. In fig. -1 25 (4) the expected energy distribution of modulation amplitudes 10 26 v0 = 20 km/s (S m) for the four considered models is shown. The data points v = 75 km/s 27 -2 CDMS lag are taken from fig. (6) of ref. [1] and represent the annual mod- 10 (low energy) 28 CaWO ulation amplitude energy distribution measured by DAMA/NaI -3 4 29 10 30 + DAMA/LIBRA. In fig. (5) the expected energy distribution DAMA of the unmodulated part of the counting rate (S 0) for the four -4 31 10 considered models is shown. The data points are taken from 32 (pb) p

fig. (27) of ref. [28] and represent the measured counting rate σ -5 33 0 10 34 of DAMA/LIBRA; they are the sum of the background and of ξ 35 the possible dark matter signal. The dot-dashed line marks the -6 10 CoGeNT 36 limit of 0.25 cpd/(kg × keV) cautiously assumed for the maxi- -7 37 mum allowed S 0 value in this analysis. It is important to note 10 CDMS 38 that corotating halo models offer a large S m/S 0 ratio allowing 39 -8 the presence of a reasonable background component also in the 10 -3 -2 -1 10 10 10 1 10 40 low energy part of DAMA data. Mass (TeV) 41 42 Figure 7: Allowed configurations at 2σ C.L. obtained for a cold corotating halo 43 5. Allowed regions fixing the halo: an example. with v0 =20 km/s and vlag = 75 km/s. The dark filled area inside the DAMA (or 44 CoGeNT) region marks the configurations allowed at 1σ C.L. (∆ < 2.3). 45 In this section, as an example, the halo model will be speci- 46 fied to fixed v0 and vlag values. In this fixed halo model, the 2σ 47 confidence intervals in the (MW vs ξ0σp) plane are evaluated 48 considering configurations having ∆ < 6.18 with respect to the As an example, for v0 =20 km/s, vlag = 75 km/s, MW = 20 49 −4 maximum likelihood of the considered halo model. TeV and ξ0σp = 10 pb, one would expect: 50 In fig. (6) the allowed regions, assuming the isothermal halo 51 model (v0 = vlag = 220 km/s) are shown. 52 As a comparison, the allowed regions for the case of a cold • only a fraction of 0.5% of the total CoGeNT rate in the 53 corotating halo (v = 20 km/s and v = 75 km/s) are given in 0.4-0.9 keV window due to dark matter elastic scattering 54 0 lag fig. (7). In both figures the dashed curve is the limit that can be 55 evaluated with CDMS-II when the low energy threshold data 56 • ∼ 13 recoils measured in CDMS-II 57 are also considered [29] . It may be noted that compatibility 58 among possible positive hints for dark matter could be achieved • ∼ 60 recoils measured in CaWO (CRESST-like) mainly 59 in models of very heavy particles (MW > few TeV) forming a 4 expected to lie in Tungsten band. 60 cold corotating halo. 61 4 62 63 64 65 1 6. Conclusions [27] C.W. Purcell et al., Astrophys. J. 703, 2275 (2009). [28] R. Bernabei et al., Nucl. Instr. and Meth. A 592, 297 (2008). 2 DAMA and CoGeNT annual modulation data and, CDMS-II, [29] Z. Ahmed et al., Phys. Rev. Lett. 106, 131302 (2011); arXiv:1011.2482. 3 EDELWEISS-II, CRESST excesses of events over the expected [30] O. Adriani et al., Nature 458, 607 (2009). 4 [31] A.A. Abdo et al., Phys. Rev. Lett. 102, 181101 (2009). background have been reanalyzed in terms of a dark matter par- 5 [32] I. Cholis and L. Googenhough, JCAP1009:010 (2010), arXiv:1006.2089. 6 ticle signal considering the case of a rotating halo. It has been 7 found that the data favor the configurations of very high mass 8 dark matter particles in a corotating cold flux. It is important to 9 note that such a high-mass/low-velocity solution could also be 10 of interest in the light of the positron/electron excess measured 11 by Pamela [30] and Fermi [31] in cosmic rays (see e.g. [32]). 12 The proposal of a consistent model for a corotating dark halo 13 is beyond the scope of the present article, whose approach is 14 data driven; however, it could be noticed that in order to avoid 15 a rate of high energy recoils in excess of the observed one, the 16 corotating component of a TeV dark matter in the halo should 17 be dominant with respect to the non-rotating one. 18 In consequence of this consideration there are two classes 19 of halo models that could be more deeply investigated in the 20 future: 21 a) single-component models, where the whole dark halo posses 22 a net angular momentum. The estimation of the dark halo an- 23 gular momentum/angular velocity in some simulations (see e.g. 24 25 [23, 24, 25]) would allow local halo corotation velocity of the 26 order of 100 km/s. 27 b) multi-component models, where low cross-section particles 28 (e.g. or sterile neutrinos) are the dominant population 29 in the non rotating halo. In this last model (similarly to the 30 known case of the baryonic matter) a sub-dominant TeV mass 31 dark matter population could be mainly present in a corotating 32 disk, possibly due to its accretion history. 33 34 35 References 36 References 37 [1] R. Bernabei et al., Eur. Phys. J. C 67, 39 (2010). 38 [2] C.E. Aalseth et al., Phys. Rev. Lett. 106, 131301 (2011); 39 arXiv:1002.4703. 40 [3] Z. Ahmed et al., Science 327, 1619 (2010). [4] Z. Ahmed et al., Phys. Rev. D 83,112002 (2011); arXiv:1012.5078. 41 [5] E. Armengaud et al., arXiv:1103.4070. 42 [6] see e.g. Franz Pr¨obst slides at the workshop ”Dark Matter: Direct Detec- 43 tion and Theoretical Developments”, Princeton, November 15-16, 2010. 44 [7] C.E. Aalseth et al., arXiv:1106.0650. 45 [8] R. Bernabei et al., Int. J. Mod. Phys. A 21, 1445 (2006). [9] R. Bernabei et al., Mod. Phys. Lett. A 23, 2125 (2008). 46 [10] R. Bernabei et al., Phys. Rev. D 77, 203506 (2008). 47 [11] D. T. Smith and N. Weiner, Phys. Rev. D 64, 043502 (2001). 48 [12] R. Foot, Phys. Rev. D 82, 095001 (2010). 49 [13] S. Chang et al., JCAP 1008:018 (2010), arXiv:1004.0697. 50 [14] A. Bottino et al., Phys. Rev. D 81, 107302 (2010). [15] N. Fornengo et al., Phys. Rev. D 83, 015001 (2011). 51 [16] D. Hooper and C. Kelso, arXiv:1106.1066. 52 [17] P. Belli et al., arXiv:1106.4667. 53 [18] T. Schwetz and J. Zupan, arXiv:1106.6241. 54 [19] M. Farina et al., arXiv:1107.0715. 55 [20] P. Fox et al., arXiv:1107.0717. 56 [21] C. McCabe, arXiv:1107.0741. [22] C. McCabe, Phys. Rev. D 82, 023530 (2010). 57 [23] P. Bett et al., MNRAS 404, 1137 (2010); arXiv:0906.2785v2. 58 [24] S.S. McGaugh et al., Astrophys. J. 659, 149 (2007). 59 [25] J.S. Bullock et al., Astrophys. J. 555, 240 (2001). 60 [26] J.I. Read et al., MNRAS 389, 1041 (2008). 61 5 62 63 64 65 Highlights

>The data collected by different direct detection experiments are reanalyzed. >The case of a rotating halo is considered. >Dark matter particles with mass in the TeV scale are compatible with the experimental data.