- Email: [email protected]
Search for solar axions by Primakoff effect in NaI crystals
23 August 2001
Physics Letters B 515 (2001) 6–12 www.elsevier.com/locate/npe
Search for solar axions by Primakoff effect in NaI crystals R. Bernabei a , P. Belli a , R. Cerulli a , F. Montecchia a , F. Nozzoli a , A. Incicchitti b , D. Prosperi b , C.J. Dai c , H.L. He c , H.H. Kuang c , J.M. Ma c , S. Scopel d a Dipartimento di Fisica, Universita’ di Roma “Tor Vergata” and INFN, sezione di Roma2, I-00133 Rome, Italy b Dipartimento di Fisica, Universita’ di Roma “La Sapienza” and INFN, sezione di Roma, I-00185 Rome, Italy c IHEP, Chinese Academy, P.O. Box 918/3, Beijing 100039, China d Dipartimento di Fisica Teorica, Universita’ di Torino and INFN, sezione di Torino, I-10125 Torino, Italy
Received 31 May 2001; accepted 25 June 2001 Editor: K. Winter
Abstract The results of a search for possible signal due to Primakoff coherent conversion of solar axions into photons in NaI(Tl) are presented. The experiment has been carried out at the Gran Sasso National Laboratory of INFN; the used statistics is 53 437 kg day. The presently most stringent experimental limit on gaγ γ from this process is obtained: gaγ γ < 1.7 × 10−9 GeV−1 (90% C.L.). In particular, the axion mass window ma 0.03 eV, not accessible by other direct methods, is explored and KSVZ axions with mass larger than 4.6 eV are excluded at 90% C.L. 2001 Elsevier Science B.V. All rights reserved. PACS: 95.35+d; 14.80.Mz; 61.10.Dp Keywords: Dark matter; Axions; Bragg scattering
1. Introduction In 1977 the axion was introduced as the Nambu– Goldstone boson of the Peccei–Quinn (PQ) symmetry proposed to explain CP conservation in QCD [1]. The scale, fa , of the Peccei–Quinn symmetry breaking fixes the axion mass: ma 0.62 eV ×(107 GeV/fa ). The theory does not provide restrictions on fa , therefore in the past the axion has been searched in a large extent, without success. Various experimental and theoretical considerations have restricted at present the axion mass to the range 10−6 eV ma 10−2 eV and ma ∼ eV. It has also been noted that axions with a similar mass could be E-mail address: [email protected] (R. Bernabei).
candidate as a possible component of the Dark Matter in the Universe. In this Letter, we present an experimental search for axions from the Sun by exploiting the Primakoff effect. In fact, as a consequence of the coupling between the axion field and the electromagnetic tensor, conversion of the axion into a photon is allowed with the coupling constant ma E 2(4 + z) −9 − gaγ γ 0.19 10 GeV−1 . eV N 3(1 + z) Here E/N is the Peccei–Quinn symmetry anomaly; in particular, E/N = 8/3 for the GUT–DFSZ axion model [2] and E/N = 0 for the KSVZ one [3]. The second term in parenthesis in the given expression of gaγ γ determines the chiral symmetry breaking correction with z ≡ mu /md 0.56 (note, however,
0370-2693/01/$ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 2 6 9 3 ( 0 1 ) 0 0 8 4 0 - 1
R. Bernabei et al. / Physics Letters B 515 (2001) 6–12
that this value suffers of some theoretical uncertainties [4]). Axions can efficiently be produced in the interior of the Sun by Primakoff conversion of the blackbody photons in the fluctuating electric field of the plasma. The outgoing axion flux has an average energy, Ea , of about 4 keV since the temperature in the Sun core is T ∼ 107 K. Assuming absence of direct coupling between the axion and the leptons (hadronic axion) and including helium and metal diffusion in the solar model, the flux of solar axions can be written as [5,6]: √ Φ0 (Ea /E0 )3 dΦ = λ , dEa E0 eEa /E0 − 1
(1)
where λ = (gaγ γ × 108 GeV−1 )4 is a suitable dimensionless coupling, Φ0 = 5.9 × 1014 cm−2 s−1 and E0 = 1.103 keV. Solar axions can produce detectable X-rays in crystal detectors via a coherent effect when the Bragg condition is fulfilled (depending on the direction of the incoming axion flux with respect to the planes of the crystal lattice) giving a strong enhancement of the possible signal. Following this approach, a distinctive signature for solar axion can be searched for by comparing the experimental counting rate with the rate expected by taking into account the position of the Sun in the sky during the data taking [9–11]. We note that positive results or bounds on gaγ γ obtained by this approach are independent on ma and, therefore, overcome the limitations of some other techniques which are instead restricted to a limited mass range [7,8]. A new search for solar axions is presented here exploiting this approach by means of the 100 kg NaI(Tl) DAMA set-up [12–24] running deep underground in the Gran Sasso National Laboratory of INFN. The Laboratory is located at 42◦ 27 N latitude, 13◦ 11 E longitude and 940 m level with respect to the mean Earth ellipsoid.
2. Experimental set-up The detailed description of the highly radiopure 100 kg NaI(Tl) DAMA set-up and its performances have been given in Refs. [15,23]. Here we only remind that the data considered in the following have been collected with nine 9.70 kg NaI(Tl) crystal scintillators —
7
(10.2 × 10.2 × 25.4) cm3 each one — enclosed in suitably radiopure Cu housings. Each detector has two 10 cm long tetrasil-B light guides directly coupled to the opposite sides of the bare crystal; two photomultipliers EMI9265-B53/FL work in coincidence and collect light at single photoelectron threshold; 2 keV is the software energy threshold. The detectors are enclosed in a low radioactive copper box inside a low radioactive shield made by 10 cm copper and 15 cm lead. The lead is surrounded by 1.5 mm Cd foils and about 10 cm of polyethylene. A high purity (HP) nitrogen atmosphere is maintained inside the copper. The whole shield is enclosed in a sealed plexiglas box also maintained in HP nitrogen atmosphere as well as the glovebox which is located on the top of the shield to allow the detectors calibration in the same running conditions without any contact with external environment. The installation is subjected to air conditioning. The typical energy resolution is σ/E = 7.5% at 59.5 keV. As of interest here, the energy, the identification of the fired crystal and the absolute time occurrence are acquired for each event.
3. Data analysis 3.1. Evaluation of the expected solar axion rate For a discussion of Primakoff coherent conversion of solar axions into photons via Bragg scattering in crystals one can refer, e.g., to [11] and references quoted therein. Here we only recall that the counting rate ˆ — integrated in the energy window R(E1 , E2 , k) (E1, E2 ) — expected in a crystal from this process can be written in the form: ˆ R(E1 , E2 , k) = πV
√ (h¯ c)2 λ
1016
2
Θ(Ea )
1 dΦ (Ea ) G2 dEa
GeV G 2 2
× &(G) S(G) sin2 (θ )W (Ea , E1 , E2 ), (2)
where kˆ is the unitary vector of the axion momentum, which identifies the Sun position in the sky; V is the
is a vector of the reciprocal lattice; crystal volume; G Θ(Ea ) is the Heaviside function, which ensures that
corresponding to positive axion energy only vectors G
8
R. Bernabei et al. / Physics Letters B 515 (2001) 6–12
contribute to the sum;
= S(G)
1 1 i G·
e xi = , V va i
where the x i are the lattice vectors and va is the volume of the primitive cell;
=
&(G) ei G·dj,k Fj (G), j,k
is the atomic form factor of the j th where Fj (G) atomic specie and d j,k is the kth basis vector of the j th atom; θ is the scattering angle. Finally, W (Ea , E1 , E2 ) 1 Ea − E2 Ea − E1 = erf √ − erf √ 2 2∆ 2∆ takes into account the finite energy resolution (∆) of x 2 the detector (erf(x) = √2π 0 e−t dt). Note that the dependence of the expected counting rate from solar axions on kˆ and, therefore, on the Sun position is given by θ and by Ea ; in fact: Ea = h¯ ˆcG and sin θ2 = kˆ · G. 2k·G In conclusion, the expected rate for solar axion in a crystalline detector — given in Eq. (2) — is directly proportional √ to the adimensional constant λ. In fact, a factor λ is explicitly given in Eq. (2) and another dφ one is present in the term dE (Ea ) (see Eq. (1)). a Let us now specify the formula to the NaI case of interest here. The Bravais lattice of sodium iodide is the facedcentered cubic crystal structure generated by the primitive vectors [25]: a a ˆ b = (yˆ + zˆ ), a = (xˆ + y), 2 2 a
and c = (xˆ + zˆ ), 2 where x, ˆ yˆ and zˆ define a orthonormal basis. The size of the corresponding primitive cell is a = 6.47 Å, its volume is va = ( a ∧ b ) · c = a 3 /4 and the considered vectors of basis are: d 0 = 0 (sodium) and d 1 = a2 zˆ (iodium). In this case the quantities which appear in Eq. (2) are, respectively:
= 2π [nx xˆ + ny yˆ + nz zˆ ], G a
2 θ θ cos sin θ = 2 sin 2 2
2 ˆ 2 , ˆ = 4 G · k 1 − (G · k) 4 (ZNa − 1) &(G)
2 = Ea 4πα hc ¯ 4 2 (h¯ c) G2 + 1/rNa 2
(3)
+ (−1)nz
(ZI + 1) 1 1 + 2 − (−1)nz 2 2 2 G G G + 1/rI
(4)
2 ,
(5)
where nx , ny and nz are integers with the same parity (3 even or 3 odd numbers); G = ch¯ G ; Ea = ck = ch¯ θ · kˆ 2 sin 2 2G ZNa = 11; ZI = 53; rNa ∼ 100 pm; rI ∼ 200 pm [26]. Let us now introduce the coordinates θz , angle between the vector pointing to the Sun and one crystallographic axis (here the growth symmetry axis, gsa), and φaz , angle between the horizontal plane and the plane containing both the Sun and gsa. They are related to kˆ by the expression: kˆ = −xˆ sin(θz ) cos(φaz )− yˆ sin(θz ) sin(φaz ) − zˆ cos(θz ). To be the most conservative on the used crystals features (that is considering only a symmetry around gsa), in the present analysis the expected counting rate is calculated by averaging over the φaz coordinate. This average reduces the amplitudes expected for the typical structures of the coherent solar axion conversion in the crystals, lowering at the same time the sensitivity achievable here with respect to the case when three crystalline axes orientations are taken into account. In Fig. 1 the expected counting rate for solar axions in NaI(Tl) when λ = 1 — averaged over the whole solid angle — is shown as a function of the detected energy. Since the mean value of the expected counting rate in energy intervals above 10 keV is significantly lower than at low energy, in the present analysis the energy range 2 keV (software energy threshold of our experiment) to 10 keV has been considered. In Fig. 2 the counting rate (averaged over φaz ) expected in the detectors is shown as a function of θz considering 2 keV energy bins. In fact, the data have been analysed as a function of θz instead of the time since the expected counting rate shows a clear periodicity as a function of θz and not of the time (the path of the Sun in the sky differs from day to day).
R. Bernabei et al. / Physics Letters B 515 (2001) 6–12
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Fig. 1. Expected counting rate for solar axions in NaI(Tl) for λ = 1 — averaged over the whole solid angle — as a function of the detected energy.
3.2. Comparison of the experimental data with the expected counting rate The data analysed here refer to a statistics of 53 437 kg day. A preliminary simple approach — which does not exploit the time dependence of the possible solar axion signal — is based on the comparison of the expected rate averaged over the whole solid angle (Fig. 1) with the measured one. Notwithstanding its simplicity, this method can give the right scale of the sensitivity of the experiment. In the present case, since the average experimental counting rate at low energy −1 (see, for example, is roughly ∼ 1 cpd kg−1 keV Ref. [21,23]), an upper limit on the coupling of axions to photons: λ < 2 × 10−2 (90% C.L.), can be derived and, consequently: gaγ γ < 4 × 10−9 GeV−1 (90% C.L.). To investigate with high sensitivity the possible presence of a solar axion signal or to achieve upper limit on λ (and, consequently, on gaγ γ ), we exploit the time dependence of the solar axion signal. For this purpose the distribution of the experimental data as a function of θz is investigated. A code using the NOVAS (Naval Observatory Vector Astrometry Subroutines) routines [27] has been developed to evaluate the distribution of the experimental data as a
Fig. 2. Expected counting rate for solar axions in NaI(Tl) evaluated for λ = 1 as a function of θz in the energy intervals: 0–2 keV, 2–4 keV, 4–6 keV, 6–8 keV, 8–10 keV, 10–12 keV, 12–14 keV, 14–16 keV. The rate is averaged over φaz .
function of θz . Then, a standard maximum likelihood analysis has been carried out by accounting for the fired crystal and for the year of the data taking, using 1 keV bins for the energy and 1◦ bins for θz . In fact, the experimental number of counts Ny,j,k,i (the index y
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R. Bernabei et al. / Physics Letters B 515 (2001) 6–12
Fig. 3. Value of λ for each possible configuration of the nine gsa’s in the set-up (see text). The arrow identifies the most conservative upper limit obtained for λ which has cautiously been considered in the following to evaluate the bound on gaγ γ .
identifies the year of data taking, j the detector, k the energy bin and i the θz bin) are Poissonian variables with expected values equal to: µy,j,k,i = Wy,j,k,i · (by,j,k + λ · Rk,i ). Here Wy,j,k,i is the “generalized statistics” for the (y, j, k, i) cell, that is the products of the exposure for this cell times the efficiency times the energy bin. Furthermore, by,j,k are free parameters representing the background terms, which include contributions from whatever process other than the one induced by solar axions; finally, λ · Rk,i are expected solar axion signals as a function of the Sun position and of the energy. As usual, to extract the possible signal, the loglikelihood function: Fy,j,k (λ, by,j,k ) + const −2 ln(L) = y,j,k
can be minimized. Here: (i) the terms which do not depend on the free parameters have been included in the constant; (ii) Fy,j,k (λ, by,j,k ) by,j,k Wy,j,k,i + λRk,i Wy,j,k,i =2 i
− Ny,j,k,i ln(by,j,k + λRk,i ) .
Note that Fy,j,k depend only on one by,j,k parameter at time and on λ; in particular, when varying by,j,k at
fixed λ, one can define Y (λ) as the sum of the minima of the Fy,j,k . The information on the orientations of the gsa’s of the nine crystals, used in this experiment, was not required at time of construction several years ago; 1 therefore, they are at present unknown. Two cases are possible: either each gsa is parallel to the longest side of the crystal (namely, to z direction) or it is perpendicular to that. In the first case only one configuration is possible for the set of the nine gsa’s in the set-up, while in the second case — since we did not take any care of the gsa’s orientations during the assembling of the set-up — there are two possibilities for each crystal (namely either x or y direction) and, therefore, 29 possible configurations for the nine gsa’s in the set-up. Thus, the calculation of λ has been repeated for every possible configuration of the nine gsa’s in the set-up; the obtained values are depicted in Fig. 3. As it can be inferred, all the data points are compatible with absence of signal. In particular, in this figure an arrow emphasizes the most conservative upper limit obtained for λ. This has cautiously been considered in the following to evaluate the bound on gaγ γ . This strategy is somehow similar to one followed in Ref. [10] for the case of a single Ge crystal.
1 The crystals were built for other purposes.
R. Bernabei et al. / Physics Letters B 515 (2001) 6–12
11
Fig. 5. Logarithmic likelihood function Y (λ) as a function of λ.
Fig. 4. Distribution of the ξ variable built by using the experimental data; see text. The Gaussian fit is superimposed.
Considering this conservative configuration, we can also give a simple evidence of the absence of solar axion signal in the experimental data by calculating for each crystal, for each year, for each energy bin (here 1 keV) and for each θz bin (here 10◦ , to assure a sufficient number of counts in each interval) the variable: ξy,j,k,i =
Ty,j,k,i − Ty,j,k,i i , σy,j,k,i
(6)
where Ty,j,k,i is the measured counting rate, σy,j,k,i is the standard deviation and Ty,j,k,i is the average over θz . By definition ξ is a gaussian variable with ξ = 0 and ξ 2 = 1 under the assumption that the behaviour of the experimental counting rate is independent on θz , that is under the hypothesis of absence of signal from solar axions. In Fig. 4 the ξ distribution of the experimental data is shown. There ξ = 0.03, ξ 2 /d.o.f. = 1.04, ξ 2 = 0.98 and χ 2 /d.o.f. = obtaining further evidence for absence of signal. Similar results are achieved for every other of the possible configurations. Finally, for the same most conservative configuration, the behaviour of the Y (λ) function (the arbitrary constant has been chosen so that Y (0) = 0) is shown in Fig. 5 around its minimum; the obtained conservative value for λ is (4.3 ± 3.1) × 10−4 . According to the standard procedure [28], this result gives an upper limit on the coupling of axions to photons:
Fig. 6. Exclusion plot for gaγ γ versus ma . The limit achieved by the present experiment (gaγ γ 1.7 × 10−9 GeV−1 at 90% C.L.) is shown together with the expectations of the KSVZ and DFSZ models. The results of previous direct searches for solar axions by Solax [11] — exploiting the same technique as our experiment — and by the Tokyo helioscope [8] are also shown for comparison.
λ 8.4 × 10−4 (90% C.L.), which corresponds to the limit: gaγ γ 1.7 × 10−9 GeV−1 (90% C.L.). In Fig. 6 the region in the plane gaγ γ versus ma excluded at 90% C. L. by this experiment is shown.
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R. Bernabei et al. / Physics Letters B 515 (2001) 6–12
4. Conclusions The present experiment has searched for axions with direct detection technique without restrictions on their mass, since — as previously mentioned — bounds on gaγ γ obtained by this approach are independent on ma . The obtained limit on λ is about one order of magnitude more stringent than the one set by the SOLAX and COSME Collaborations [10,11], while the limit on the coupling constant gaγ γ has been improved by a factor 1.6 with respect to these experiments. The obtained result is at present the best direct limit on solar axions conversion in crystals and for axion masses larger than 0.1 eV is better also than the limit set by the Tokyo helioscope. In conclusion, this experiment has explored the axion mass window ma ∼ eV still open in the KSVZ a model (where gaγ γ = 3.7 × 10−10 GeV−1 m eV ) and has allowed to exclude KSVZ axions for ma > 4.6 eV at 90% C.L.
References [1] R.D. Peccei, H.R. Quinn, Phys. Rev. Lett. 38 (1977) 1440. [2] M. Dine, W. Fishler, M. Srednicki, Phys. Lett. B 104 (1981) 199; A.P. Zhitnitskii, Sov. J. Nucl. 31 (1980) 260. [3] J.E. Kim, Phys. Rev. Lett. 43 (1979) 103;
[4] [5] [6] [7]
[8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
M.A. Shifman, A.I. Vainshtein, V.I. Zakharov, Nucl. Phys. B 166 (1980) 493. T. Moroi, H. Murayama, Phys. Lett. B 440 (1998) 69. K. van Bibber, P.M. McIntyre, D.E. Morris, G.G. Raffelt, Phys. Rev. D 39 (1989) 2089. A.O. Gattone et al., Nucl. Phys. B Proc. Suppl. 70 (1999) 59. C. Hagmann et al., Phys. Rev. Lett. 80 (1998) 2043; S. Matsuki, Talk given at the II International Workshop on the Identification of Dark Matter IDM98, Buxton, England, 7–11 September 1998. S. Moriyama et al., Phys. Lett. B 434 (1998) 147. E.A. Pascos, K. Zioutas, Phys. Lett. B 323 (1994) 367. A. Morales et al., hep-ex/0101037. S. Cebrián et al., Astropart. Phys. 10 (1999) 397. R. Bernabei et al., Phys. Lett. B 389 (1996) 757. R. Bernabei et al., Phys. Lett. B 408 (1997) 439. R. Bernabei et al., Phys. Lett. B 424 (1998) 195. R. Bernabei et al., Nuovo Cimento A 112 (1999) 545. R. Bernabei et al., Phys. Lett. B 450 (1999) 448. P. Belli et al., Phys. Lett. B 460 (1999) 236. R. Bernabei et al., Phys. Rev. Lett. 83 (1999) 4918. P. Belli et al., Phys. Rev. C 60 (1999) 065501. R. Bernabei et al., Nuovo Cimento A 112 (1999) 1541. R. Bernabei et al., Phys. Lett. B 480 (2000) 23. P. Belli et al., Phys. Rev. D 61 (2000) 023512. R. Bernabei et al., Eur. Phys. J. C 18 (2000) 283. R. Bernabei et al., Phys. Lett. B 509 (2001) 197. N.W. Ashcroft, N.D. Mermin, Solid State Physics, Saunders College, Philadelphia, 1976. http://www.webelements.com. http://aa.usno.navy.mil/software/novas/. Particle Data Group, R.M. Barnett et al., Phys. Rev. D 54 (1996) 1.
Physics Letters B 515 (2001) 6–12 www.elsevier.com/locate/npe
Search for solar axions by Primakoff effect in NaI crystals R. Bernabei a , P. Belli a , R. Cerulli a , F. Montecchia a , F. Nozzoli a , A. Incicchitti b , D. Prosperi b , C.J. Dai c , H.L. He c , H.H. Kuang c , J.M. Ma c , S. Scopel d a Dipartimento di Fisica, Universita’ di Roma “Tor Vergata” and INFN, sezione di Roma2, I-00133 Rome, Italy b Dipartimento di Fisica, Universita’ di Roma “La Sapienza” and INFN, sezione di Roma, I-00185 Rome, Italy c IHEP, Chinese Academy, P.O. Box 918/3, Beijing 100039, China d Dipartimento di Fisica Teorica, Universita’ di Torino and INFN, sezione di Torino, I-10125 Torino, Italy
Received 31 May 2001; accepted 25 June 2001 Editor: K. Winter
Abstract The results of a search for possible signal due to Primakoff coherent conversion of solar axions into photons in NaI(Tl) are presented. The experiment has been carried out at the Gran Sasso National Laboratory of INFN; the used statistics is 53 437 kg day. The presently most stringent experimental limit on gaγ γ from this process is obtained: gaγ γ < 1.7 × 10−9 GeV−1 (90% C.L.). In particular, the axion mass window ma 0.03 eV, not accessible by other direct methods, is explored and KSVZ axions with mass larger than 4.6 eV are excluded at 90% C.L. 2001 Elsevier Science B.V. All rights reserved. PACS: 95.35+d; 14.80.Mz; 61.10.Dp Keywords: Dark matter; Axions; Bragg scattering
1. Introduction In 1977 the axion was introduced as the Nambu– Goldstone boson of the Peccei–Quinn (PQ) symmetry proposed to explain CP conservation in QCD [1]. The scale, fa , of the Peccei–Quinn symmetry breaking fixes the axion mass: ma 0.62 eV ×(107 GeV/fa ). The theory does not provide restrictions on fa , therefore in the past the axion has been searched in a large extent, without success. Various experimental and theoretical considerations have restricted at present the axion mass to the range 10−6 eV ma 10−2 eV and ma ∼ eV. It has also been noted that axions with a similar mass could be E-mail address: [email protected] (R. Bernabei).
candidate as a possible component of the Dark Matter in the Universe. In this Letter, we present an experimental search for axions from the Sun by exploiting the Primakoff effect. In fact, as a consequence of the coupling between the axion field and the electromagnetic tensor, conversion of the axion into a photon is allowed with the coupling constant ma E 2(4 + z) −9 − gaγ γ 0.19 10 GeV−1 . eV N 3(1 + z) Here E/N is the Peccei–Quinn symmetry anomaly; in particular, E/N = 8/3 for the GUT–DFSZ axion model [2] and E/N = 0 for the KSVZ one [3]. The second term in parenthesis in the given expression of gaγ γ determines the chiral symmetry breaking correction with z ≡ mu /md 0.56 (note, however,
0370-2693/01/$ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 2 6 9 3 ( 0 1 ) 0 0 8 4 0 - 1
R. Bernabei et al. / Physics Letters B 515 (2001) 6–12
that this value suffers of some theoretical uncertainties [4]). Axions can efficiently be produced in the interior of the Sun by Primakoff conversion of the blackbody photons in the fluctuating electric field of the plasma. The outgoing axion flux has an average energy, Ea , of about 4 keV since the temperature in the Sun core is T ∼ 107 K. Assuming absence of direct coupling between the axion and the leptons (hadronic axion) and including helium and metal diffusion in the solar model, the flux of solar axions can be written as [5,6]: √ Φ0 (Ea /E0 )3 dΦ = λ , dEa E0 eEa /E0 − 1
(1)
where λ = (gaγ γ × 108 GeV−1 )4 is a suitable dimensionless coupling, Φ0 = 5.9 × 1014 cm−2 s−1 and E0 = 1.103 keV. Solar axions can produce detectable X-rays in crystal detectors via a coherent effect when the Bragg condition is fulfilled (depending on the direction of the incoming axion flux with respect to the planes of the crystal lattice) giving a strong enhancement of the possible signal. Following this approach, a distinctive signature for solar axion can be searched for by comparing the experimental counting rate with the rate expected by taking into account the position of the Sun in the sky during the data taking [9–11]. We note that positive results or bounds on gaγ γ obtained by this approach are independent on ma and, therefore, overcome the limitations of some other techniques which are instead restricted to a limited mass range [7,8]. A new search for solar axions is presented here exploiting this approach by means of the 100 kg NaI(Tl) DAMA set-up [12–24] running deep underground in the Gran Sasso National Laboratory of INFN. The Laboratory is located at 42◦ 27 N latitude, 13◦ 11 E longitude and 940 m level with respect to the mean Earth ellipsoid.
2. Experimental set-up The detailed description of the highly radiopure 100 kg NaI(Tl) DAMA set-up and its performances have been given in Refs. [15,23]. Here we only remind that the data considered in the following have been collected with nine 9.70 kg NaI(Tl) crystal scintillators —
7
(10.2 × 10.2 × 25.4) cm3 each one — enclosed in suitably radiopure Cu housings. Each detector has two 10 cm long tetrasil-B light guides directly coupled to the opposite sides of the bare crystal; two photomultipliers EMI9265-B53/FL work in coincidence and collect light at single photoelectron threshold; 2 keV is the software energy threshold. The detectors are enclosed in a low radioactive copper box inside a low radioactive shield made by 10 cm copper and 15 cm lead. The lead is surrounded by 1.5 mm Cd foils and about 10 cm of polyethylene. A high purity (HP) nitrogen atmosphere is maintained inside the copper. The whole shield is enclosed in a sealed plexiglas box also maintained in HP nitrogen atmosphere as well as the glovebox which is located on the top of the shield to allow the detectors calibration in the same running conditions without any contact with external environment. The installation is subjected to air conditioning. The typical energy resolution is σ/E = 7.5% at 59.5 keV. As of interest here, the energy, the identification of the fired crystal and the absolute time occurrence are acquired for each event.
3. Data analysis 3.1. Evaluation of the expected solar axion rate For a discussion of Primakoff coherent conversion of solar axions into photons via Bragg scattering in crystals one can refer, e.g., to [11] and references quoted therein. Here we only recall that the counting rate ˆ — integrated in the energy window R(E1 , E2 , k) (E1, E2 ) — expected in a crystal from this process can be written in the form: ˆ R(E1 , E2 , k) = πV
√ (h¯ c)2 λ
1016
2
Θ(Ea )
1 dΦ (Ea ) G2 dEa
GeV G 2 2
× &(G) S(G) sin2 (θ )W (Ea , E1 , E2 ), (2)
where kˆ is the unitary vector of the axion momentum, which identifies the Sun position in the sky; V is the
is a vector of the reciprocal lattice; crystal volume; G Θ(Ea ) is the Heaviside function, which ensures that
corresponding to positive axion energy only vectors G
8
R. Bernabei et al. / Physics Letters B 515 (2001) 6–12
contribute to the sum;
= S(G)
1 1 i G·
e xi = , V va i
where the x i are the lattice vectors and va is the volume of the primitive cell;
=
&(G) ei G·dj,k Fj (G), j,k
is the atomic form factor of the j th where Fj (G) atomic specie and d j,k is the kth basis vector of the j th atom; θ is the scattering angle. Finally, W (Ea , E1 , E2 ) 1 Ea − E2 Ea − E1 = erf √ − erf √ 2 2∆ 2∆ takes into account the finite energy resolution (∆) of x 2 the detector (erf(x) = √2π 0 e−t dt). Note that the dependence of the expected counting rate from solar axions on kˆ and, therefore, on the Sun position is given by θ and by Ea ; in fact: Ea = h¯ ˆcG and sin θ2 = kˆ · G. 2k·G In conclusion, the expected rate for solar axion in a crystalline detector — given in Eq. (2) — is directly proportional √ to the adimensional constant λ. In fact, a factor λ is explicitly given in Eq. (2) and another dφ one is present in the term dE (Ea ) (see Eq. (1)). a Let us now specify the formula to the NaI case of interest here. The Bravais lattice of sodium iodide is the facedcentered cubic crystal structure generated by the primitive vectors [25]: a a ˆ b = (yˆ + zˆ ), a = (xˆ + y), 2 2 a
and c = (xˆ + zˆ ), 2 where x, ˆ yˆ and zˆ define a orthonormal basis. The size of the corresponding primitive cell is a = 6.47 Å, its volume is va = ( a ∧ b ) · c = a 3 /4 and the considered vectors of basis are: d 0 = 0 (sodium) and d 1 = a2 zˆ (iodium). In this case the quantities which appear in Eq. (2) are, respectively:
= 2π [nx xˆ + ny yˆ + nz zˆ ], G a
2 θ θ cos sin θ = 2 sin 2 2
2 ˆ 2 , ˆ = 4 G · k 1 − (G · k) 4 (ZNa − 1) &(G)
2 = Ea 4πα hc ¯ 4 2 (h¯ c) G2 + 1/rNa 2
(3)
+ (−1)nz
(ZI + 1) 1 1 + 2 − (−1)nz 2 2 2 G G G + 1/rI
(4)
2 ,
(5)
where nx , ny and nz are integers with the same parity (3 even or 3 odd numbers); G = ch¯ G ; Ea = ck = ch¯ θ · kˆ 2 sin 2 2G ZNa = 11; ZI = 53; rNa ∼ 100 pm; rI ∼ 200 pm [26]. Let us now introduce the coordinates θz , angle between the vector pointing to the Sun and one crystallographic axis (here the growth symmetry axis, gsa), and φaz , angle between the horizontal plane and the plane containing both the Sun and gsa. They are related to kˆ by the expression: kˆ = −xˆ sin(θz ) cos(φaz )− yˆ sin(θz ) sin(φaz ) − zˆ cos(θz ). To be the most conservative on the used crystals features (that is considering only a symmetry around gsa), in the present analysis the expected counting rate is calculated by averaging over the φaz coordinate. This average reduces the amplitudes expected for the typical structures of the coherent solar axion conversion in the crystals, lowering at the same time the sensitivity achievable here with respect to the case when three crystalline axes orientations are taken into account. In Fig. 1 the expected counting rate for solar axions in NaI(Tl) when λ = 1 — averaged over the whole solid angle — is shown as a function of the detected energy. Since the mean value of the expected counting rate in energy intervals above 10 keV is significantly lower than at low energy, in the present analysis the energy range 2 keV (software energy threshold of our experiment) to 10 keV has been considered. In Fig. 2 the counting rate (averaged over φaz ) expected in the detectors is shown as a function of θz considering 2 keV energy bins. In fact, the data have been analysed as a function of θz instead of the time since the expected counting rate shows a clear periodicity as a function of θz and not of the time (the path of the Sun in the sky differs from day to day).
R. Bernabei et al. / Physics Letters B 515 (2001) 6–12
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Fig. 1. Expected counting rate for solar axions in NaI(Tl) for λ = 1 — averaged over the whole solid angle — as a function of the detected energy.
3.2. Comparison of the experimental data with the expected counting rate The data analysed here refer to a statistics of 53 437 kg day. A preliminary simple approach — which does not exploit the time dependence of the possible solar axion signal — is based on the comparison of the expected rate averaged over the whole solid angle (Fig. 1) with the measured one. Notwithstanding its simplicity, this method can give the right scale of the sensitivity of the experiment. In the present case, since the average experimental counting rate at low energy −1 (see, for example, is roughly ∼ 1 cpd kg−1 keV Ref. [21,23]), an upper limit on the coupling of axions to photons: λ < 2 × 10−2 (90% C.L.), can be derived and, consequently: gaγ γ < 4 × 10−9 GeV−1 (90% C.L.). To investigate with high sensitivity the possible presence of a solar axion signal or to achieve upper limit on λ (and, consequently, on gaγ γ ), we exploit the time dependence of the solar axion signal. For this purpose the distribution of the experimental data as a function of θz is investigated. A code using the NOVAS (Naval Observatory Vector Astrometry Subroutines) routines [27] has been developed to evaluate the distribution of the experimental data as a
Fig. 2. Expected counting rate for solar axions in NaI(Tl) evaluated for λ = 1 as a function of θz in the energy intervals: 0–2 keV, 2–4 keV, 4–6 keV, 6–8 keV, 8–10 keV, 10–12 keV, 12–14 keV, 14–16 keV. The rate is averaged over φaz .
function of θz . Then, a standard maximum likelihood analysis has been carried out by accounting for the fired crystal and for the year of the data taking, using 1 keV bins for the energy and 1◦ bins for θz . In fact, the experimental number of counts Ny,j,k,i (the index y
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R. Bernabei et al. / Physics Letters B 515 (2001) 6–12
Fig. 3. Value of λ for each possible configuration of the nine gsa’s in the set-up (see text). The arrow identifies the most conservative upper limit obtained for λ which has cautiously been considered in the following to evaluate the bound on gaγ γ .
identifies the year of data taking, j the detector, k the energy bin and i the θz bin) are Poissonian variables with expected values equal to: µy,j,k,i = Wy,j,k,i · (by,j,k + λ · Rk,i ). Here Wy,j,k,i is the “generalized statistics” for the (y, j, k, i) cell, that is the products of the exposure for this cell times the efficiency times the energy bin. Furthermore, by,j,k are free parameters representing the background terms, which include contributions from whatever process other than the one induced by solar axions; finally, λ · Rk,i are expected solar axion signals as a function of the Sun position and of the energy. As usual, to extract the possible signal, the loglikelihood function: Fy,j,k (λ, by,j,k ) + const −2 ln(L) = y,j,k
can be minimized. Here: (i) the terms which do not depend on the free parameters have been included in the constant; (ii) Fy,j,k (λ, by,j,k ) by,j,k Wy,j,k,i + λRk,i Wy,j,k,i =2 i
− Ny,j,k,i ln(by,j,k + λRk,i ) .
Note that Fy,j,k depend only on one by,j,k parameter at time and on λ; in particular, when varying by,j,k at
fixed λ, one can define Y (λ) as the sum of the minima of the Fy,j,k . The information on the orientations of the gsa’s of the nine crystals, used in this experiment, was not required at time of construction several years ago; 1 therefore, they are at present unknown. Two cases are possible: either each gsa is parallel to the longest side of the crystal (namely, to z direction) or it is perpendicular to that. In the first case only one configuration is possible for the set of the nine gsa’s in the set-up, while in the second case — since we did not take any care of the gsa’s orientations during the assembling of the set-up — there are two possibilities for each crystal (namely either x or y direction) and, therefore, 29 possible configurations for the nine gsa’s in the set-up. Thus, the calculation of λ has been repeated for every possible configuration of the nine gsa’s in the set-up; the obtained values are depicted in Fig. 3. As it can be inferred, all the data points are compatible with absence of signal. In particular, in this figure an arrow emphasizes the most conservative upper limit obtained for λ. This has cautiously been considered in the following to evaluate the bound on gaγ γ . This strategy is somehow similar to one followed in Ref. [10] for the case of a single Ge crystal.
1 The crystals were built for other purposes.
R. Bernabei et al. / Physics Letters B 515 (2001) 6–12
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Fig. 5. Logarithmic likelihood function Y (λ) as a function of λ.
Fig. 4. Distribution of the ξ variable built by using the experimental data; see text. The Gaussian fit is superimposed.
Considering this conservative configuration, we can also give a simple evidence of the absence of solar axion signal in the experimental data by calculating for each crystal, for each year, for each energy bin (here 1 keV) and for each θz bin (here 10◦ , to assure a sufficient number of counts in each interval) the variable: ξy,j,k,i =
Ty,j,k,i − Ty,j,k,i i , σy,j,k,i
(6)
where Ty,j,k,i is the measured counting rate, σy,j,k,i is the standard deviation and Ty,j,k,i is the average over θz . By definition ξ is a gaussian variable with ξ = 0 and ξ 2 = 1 under the assumption that the behaviour of the experimental counting rate is independent on θz , that is under the hypothesis of absence of signal from solar axions. In Fig. 4 the ξ distribution of the experimental data is shown. There ξ = 0.03, ξ 2 /d.o.f. = 1.04, ξ 2 = 0.98 and χ 2 /d.o.f. = obtaining further evidence for absence of signal. Similar results are achieved for every other of the possible configurations. Finally, for the same most conservative configuration, the behaviour of the Y (λ) function (the arbitrary constant has been chosen so that Y (0) = 0) is shown in Fig. 5 around its minimum; the obtained conservative value for λ is (4.3 ± 3.1) × 10−4 . According to the standard procedure [28], this result gives an upper limit on the coupling of axions to photons:
Fig. 6. Exclusion plot for gaγ γ versus ma . The limit achieved by the present experiment (gaγ γ 1.7 × 10−9 GeV−1 at 90% C.L.) is shown together with the expectations of the KSVZ and DFSZ models. The results of previous direct searches for solar axions by Solax [11] — exploiting the same technique as our experiment — and by the Tokyo helioscope [8] are also shown for comparison.
λ 8.4 × 10−4 (90% C.L.), which corresponds to the limit: gaγ γ 1.7 × 10−9 GeV−1 (90% C.L.). In Fig. 6 the region in the plane gaγ γ versus ma excluded at 90% C. L. by this experiment is shown.
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4. Conclusions The present experiment has searched for axions with direct detection technique without restrictions on their mass, since — as previously mentioned — bounds on gaγ γ obtained by this approach are independent on ma . The obtained limit on λ is about one order of magnitude more stringent than the one set by the SOLAX and COSME Collaborations [10,11], while the limit on the coupling constant gaγ γ has been improved by a factor 1.6 with respect to these experiments. The obtained result is at present the best direct limit on solar axions conversion in crystals and for axion masses larger than 0.1 eV is better also than the limit set by the Tokyo helioscope. In conclusion, this experiment has explored the axion mass window ma ∼ eV still open in the KSVZ a model (where gaγ γ = 3.7 × 10−10 GeV−1 m eV ) and has allowed to exclude KSVZ axions for ma > 4.6 eV at 90% C.L.
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