23 August 2001

Physics Letters B 515 (2001) 6–12www.elsevier.com/locate/npe

Search for solar axions by Primakoff effect in NaI crystals

R. Bernabeia, P. Bellia, R. Cerullia, F. Montecchiaa, F. Nozzolia, A. Incicchitti b,D. Prosperib, C.J. Daic, H.L. Hec, H.H. Kuangc, J.M. Mac, S. Scopeld

a Dipartimento di Fisica, Universita’ di Roma “Tor Vergata” and INFN, sezione di Roma2, I-00133 Rome, Italyb 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, Chinad Dipartimento di Fisica Teorica, Universita’ di Torino and INFN, sezione di Torino, I-10125 Torino, Italy

Received 31 May 2001; accepted 25 June 2001Editor: 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 statisticsis 53 437 kg day. The presently most stringent experimental limit ongaγ γ from this process is obtained:gaγ γ < 1.7 ×10−9 GeV−1 (90% C.L.). In particular, the axion mass windowma � 0.03 eV, not accessible by other direct methods, isexplored and KSVZ axions with mass larger than 4.6 eV are excluded at 90% C.L. 2001 Elsevier Science B.V. All rightsreserved.

PACS: 95.35+d; 14.80.Mz; 61.10.DpKeywords: Dark matter; Axions; Bragg scattering

1. Introduction

In 1977 the axion was introduced as the Nambu–Goldstone boson of the Peccei–Quinn (PQ) symme-try proposed to explain CP conservation in QCD [1].The scale,fa , of the Peccei–Quinn symmetry breakingfixes the axion mass:ma � 0.62 eV×(107 GeV/fa).The theory does not provide restrictions onfa , there-fore in the past the axion has been searched in a largeextent, without success.

Various experimental and theoretical considerationshave restricted at present the axion mass to the range10−6 eV � ma � 10−2 eV andma ∼ eV. It has alsobeen noted that axions with a similar mass could be

E-mail address: rita.bernabei@roma2.infn.it (R. Bernabei).

candidate as a possible component of the Dark Matterin the Universe.

In this Letter, we present an experimental searchfor axions from the Sun by exploiting the Primakoffeffect. In fact, as a consequence of the couplingbetween the axion field and the electromagnetic tensor,conversion of the axion into a photon is allowed withthe coupling constant

gaγ γ � 0.19ma

eV

∣∣∣∣EN − 2(4+ z)3(1+ z)

∣∣∣∣10−9 GeV−1.

HereE/N is the Peccei–Quinn symmetry anomaly;in particular,E/N = 8/3 for the GUT–DFSZ axionmodel [2] andE/N = 0 for the KSVZ one [3]. Thesecond term in parenthesis in the given expressionof gaγ γ determines the chiral symmetry breakingcorrection withz ≡ mu/md � 0.56 (note, however,

0370-2693/01/$ – see front matter 2001 Elsevier Science B.V. All rights reserved.PII: S0370-2693(01)00840-1

R. Bernabei et al. / Physics Letters B 515 (2001) 6–12 7

that this value suffers of some theoretical uncertainties[4]).

Axions can efficiently be produced in the interiorof the Sun by Primakoff conversion of the blackbodyphotons 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 coreis T ∼ 107 K. Assuming absence of direct couplingbetween the axion and the leptons (hadronic axion)and including helium and metal diffusion in the solarmodel, the flux of solar axions can be written as [5,6]:

(1)dΦ

dEa= √

λΦ0

E0

(Ea/E0)3

eEa/E0 − 1,

whereλ = (gaγ γ × 108GeV−1)4 is a suitable dimen-sionless coupling,Φ0 = 5.9 × 1014 cm−2 s−1 andE0 = 1.103 keV.

Solar axions can produce detectable X-rays incrystal detectors via a coherent effect when the Braggcondition is fulfilled (depending on the direction ofthe incoming axion flux with respect to the planesof the crystal lattice) giving a strong enhancementof the possible signal. Following this approach, adistinctive signature for solar axion can be searchedfor by comparing the experimental counting rate withthe rate expected by taking into account the position ofthe Sun in the sky during the data taking [9–11]. Wenote that positive results or bounds ongaγ γ obtainedby this approach are independent onma and, therefore,overcome the limitations of some other techniqueswhich are instead restricted to a limited mass range[7,8].

A new search for solar axions is presented hereexploiting this approach by means of the� 100 kgNaI(Tl) DAMA set-up [12–24] running deep under-ground in the Gran Sasso National Laboratory ofINFN. The Laboratory is located at 42◦27′N latitude,13◦11′E longitude and 940 m level with respect to themean Earth ellipsoid.

2. Experimental set-up

The detailed description of the highly radiopure�100 kg NaI(Tl) DAMA set-up and its performanceshave been given in Refs. [15,23]. Here we only remindthat the data considered in the following have been col-lected with nine 9.70 kg NaI(Tl) crystal scintillators —

(10.2×10.2×25.4) cm3 each one — enclosed in suit-ably radiopure Cu housings. Each detector has two 10cm long tetrasil-B light guides directly coupled to theopposite sides of the bare crystal; two photomultipli-ers EMI9265-B53/FL work in coincidence and collectlight at single photoelectron threshold; 2 keV is thesoftware energy threshold. The detectors are enclosedin a low radioactive copper box inside a low radioac-tive shield made by 10 cm copper and 15 cm lead.The lead is surrounded by 1.5 mm Cd foils and about10 cm of polyethylene. A high purity (HP) nitrogen at-mosphere is maintained inside the copper. The wholeshield is enclosed in a sealed plexiglas box also main-tained in HP nitrogen atmosphere as well as the glove-box which is located on the top of the shield to allowthe detectors calibration in the same running condi-tions without any contact with external environment.The installation is subjected to air conditioning. Thetypical energy resolution isσ/E = 7.5% at 59.5 keV.

As of interest here, the energy, the identification ofthe fired crystal and the absolute time occurrence areacquired for each event.

3. Data analysis

3.1. Evaluation of the expected solar axion rate

For a discussion of Primakoff coherent conversionof solar axions into photons via Bragg scattering incrystals one can refer, e.g., to [11] and referencesquoted therein.

Here we only recall that the counting rateR(E1,E2, k) — integrated in the energy window(E1,E2) — expected in a crystal from this process canbe written in the form:

R(E1,E2, k)

= πV (hc)2√λ

1016 GeV2

∑ GΘ(Ea)

1

G2

dΦ

dEa(Ea)

(2)× ∣∣& ( G)∣∣2 ∣∣S( G)∣∣2 sin2(θ)W(Ea,E1,E2),

wherek is the unitary vector of the axion momentum,which identifies the Sun position in the sky;V is thecrystal volume; G is a vector of the reciprocal lattice;Θ(Ea) is the Heaviside function, which ensures thatonly vectors G corresponding to positive axion energy

8 R. Bernabei et al. / Physics Letters B 515 (2001) 6–12

contribute to the sum;

S( G)= 1

V

∑i

ei G· xi = 1

va,

where the xi are the lattice vectors andva is thevolume of the primitive cell;

& ( G)=∑j,k

ei G· dj,kFj ( G),

where Fj ( G) is the atomic form factor of thej thatomic specie and dj,k is the kth basis vector of thej th atom;θ is the scattering angle. Finally,

W(Ea,E1,E2)

= 1

2

[erf

(Ea −E1√

2∆

)− erf

(Ea −E2√

2∆

)]

takes into account the finite energy resolution (∆) ofthe detector (erf(x) = 2√

π

∫ x0 e

−t2 dt). Note that the

dependence of the expected counting rate from solaraxions onk and, therefore, on the Sun position is givenby θ and byEa ; in fact:Ea = hcG

2k·G and sinθ2 = k · G.In conclusion, the expected rate for solar axion in

a crystalline detector — given in Eq. (2) — is directlyproportional to the adimensional constantλ. In fact,a factor

√λ is explicitly given in Eq. (2) and another

one is present in the termdφdEa(Ea) (see Eq. (1)).

Let us now specify the formula to the NaI case ofinterest here.

The Bravais lattice of sodium iodide is the faced-centered cubic crystal structure generated by the prim-itive vectors [25]:

a′ = a2(x + y), b′ = a

2(y + z),

and c′ = a2(x + z),

wherex, y andz define a orthonormal basis. The sizeof the corresponding primitive cell isa = 6.47 Å, itsvolume isva = ( a′ ∧ b′) · c′ = a3/4 and the consideredvectors of basis are: d0 = 0 (sodium) and d1 = a

2 z

(iodium).In this case the quantities which appear in Eq. (2)

are, respectively:

(3) G= 2π

a[nxx + nyy + nzz],

(4)

sin2 θ =[2 sin

(θ

2

)cos

(θ

2

)]2

= 4(G · k)2[1− (G · k)2],

∣∣& ( G)∣∣2 = E4a

(hc)44παhc

((ZNa − 1)

G2 + 1/r2Na

(5)+ (−1)nz(ZI + 1)

G2 + 1/r2I+ 1

G2 − (−1)nz1

G2

)2

,

wherenx , ny andnz are integers with the same parity(3 even or 3 odd numbers);

Ea = ck = ch∣∣∣∣ G

2 sinθ2

∣∣∣∣ = ch∣∣∣∣ G

2G · k∣∣∣∣;

ZNa = 11; ZI = 53; rNa ∼ 100 pm; rI ∼ 200 pm[26].

Let us now introduce the coordinatesθz, angle be-tween the vector pointing to the Sun and one crystal-lographic axis (here the growth symmetry axis,gsa),andφaz, angle between the horizontal plane and theplane containing both the Sun andgsa. They are re-lated tok by the expression:k = −x sin(θz)cos(φaz)−y sin(θz)sin(φaz)− z cos(θz). To be the most conserv-ative on the used crystals features (that is consideringonly a symmetry aroundgsa), in the present analysisthe expected counting rate is calculated by averagingover theφaz coordinate. This average reduces the am-plitudes expected for the typical structures of the co-herent solar axion conversion in the crystals, loweringat the same time the sensitivity achievable here withrespect to the case when three crystalline axes orienta-tions are taken into account.

In Fig. 1 the expected counting rate for solar axionsin NaI(Tl) when λ = 1 — averaged over the wholesolid angle — is shown as a function of the detectedenergy. Since the mean value of the expected countingrate in energy intervals above 10 keV is significantlylower than at low energy, in the present analysis theenergy range 2 keV (software energy threshold of ourexperiment) to 10 keV has been considered.

In Fig. 2 the counting rate (averaged overφaz)expected in the detectors is shown as a function ofθz considering 2 keV energy bins. In fact, the datahave been analysed as a function ofθz instead of thetime since the expected counting rate shows a clearperiodicity as a function ofθz and not of the time (thepath of the Sun in the sky differs from day to day).

R. Bernabei et al. / Physics Letters B 515 (2001) 6–12 9

Fig. 1. Expected counting rate for solar axions in NaI(Tl) forλ= 1— averaged over the whole solid angle — as a function of thedetected energy.

3.2. Comparison of the experimental data with theexpected counting rate

The data analysed here refer to a statistics of53 437 kg day.

A preliminary simple approach — which does notexploit the time dependence of the possible solaraxion signal — is based on the comparison of theexpected rate averaged over the whole solid angle(Fig. 1) with the measured one. Notwithstanding itssimplicity, this method can give the right scale of thesensitivity of the experiment. In the present case, sincethe average experimental counting rate at low energy

is roughly ∼ 1 cpd kg−1 keV−1

(see, for example,Ref. [21,23]), an upper limit on the coupling of axionsto photons:λ < 2 × 10−2 (90% C.L.), can be derivedand, consequently:gaγ γ < 4 × 10−9 GeV−1 (90%C.L.).

To investigate with high sensitivity the possiblepresence of a solar axion signal or to achieve upperlimit on λ (and, consequently, ongaγ γ ), we exploitthe time dependence of the solar axion signal. Forthis purpose the distribution of the experimental dataas a function ofθz is investigated. A code usingthe NOVAS (Naval Observatory Vector AstrometrySubroutines) routines [27] has been developed toevaluate the distribution of the experimental data as a

Fig. 2. Expected counting rate for solar axions in NaI(Tl) evaluatedfor λ = 1 as a function ofθz in the energy intervals: 0–2 keV, 2–4keV, 4–6 keV, 6–8 keV, 8–10 keV, 10–12 keV, 12–14 keV, 14–16keV. The rate is averaged overφaz.

function of θz. Then, a standard maximum likelihoodanalysis has been carried out by accounting for thefired crystal and for the year of the data taking, using 1keV bins for the energy and 1◦ bins forθz. In fact, theexperimental number of countsNy,j,k,i (the indexy

10 R. Bernabei et al. / Physics Letters B 515 (2001) 6–12

Fig. 3. Value ofλ for each possible configuration of the ninegsa’s in the set-up (see text). The arrow identifies the most conservative upperlimit obtained forλ which has cautiously been considered in the following to evaluate the bound ongaγγ .

identifies the year of data taking,j the detector,k theenergy bin andi the θz bin) are Poissonian variableswith expected values equal to:µy,j,k,i = Wy,j,k,i ·(by,j,k + λ · Rk,i ). HereWy,j,k,i is the “generalizedstatistics” for the (y, j, k, i) cell, that is the productsof the exposure for this cell times the efficiency timesthe energy bin. Furthermore,by,j,k are free parametersrepresenting the background terms, which includecontributions from whatever process other than the oneinduced by solar axions; finally,λ · Rk,i are expectedsolar axion signals as a function of the Sun positionand of the energy.

As usual, to extract the possible signal, the log-likelihood function:

−2 ln(L)=∑y,j,k

Fy,j,k(λ, by,j,k)+ const

can be minimized. Here: (i) the terms which do notdepend on the free parameters have been included inthe constant; (ii)

Fy,j,k(λ, by,j,k)

= 2∑i

[by,j,kWy,j,k,i + λRk,iWy,j,k,i

−Ny,j,k,i ln(by,j,k + λRk,i )].

Note thatFy,j,k depend only on oneby,j,k parameterat time and onλ; in particular, when varyingby,j,k at

fixedλ, one can defineY (λ) as the sum of the minimaof theFy,j,k .

The information on the orientations of thegsa’sof the nine crystals, used in this experiment, wasnot required at time of construction several yearsago;1 therefore, they are at present unknown. Twocases are possible: either eachgsa is parallel to thelongest side of the crystal (namely, toz direction)or it is perpendicular to that. In the first case onlyone configuration is possible for the set of the ninegsa’s in the set-up, while in the second case — sincewe did not take any care of thegsa’s orientationsduring the assembling of the set-up — there are twopossibilities for each crystal (namely eitherx or ydirection) and, therefore, 29 possible configurationsfor the ninegsa’s in the set-up. Thus, the calculationof λ has been repeated for every possible configurationof the ninegsa’s in the set-up; the obtained valuesare depicted in Fig. 3. As it can be inferred, all thedata points are compatible with absence of signal.In particular, in this figure an arrow emphasizes themost conservative upper limit obtained forλ. This hascautiously been considered in the following to evaluatethe bound ongaγ γ . This strategy is somehow similarto one followed in Ref. [10] for the case of a single Gecrystal.

1 The crystals were built for other purposes.

R. Bernabei et al. / Physics Letters B 515 (2001) 6–12 11

Fig. 4. Distribution of theξ variable built by using the experimentaldata; see text. The Gaussian fit is superimposed.

Considering this conservative configuration, we canalso give a simple evidence of the absence of solaraxion signal in the experimental data by calculatingfor each crystal, for each year, for each energy bin(here 1 keV) and for eachθz bin (here 10◦, to assurea sufficient number of counts in each interval) thevariable:

(6)ξy,j,k,i = Ty,j,k,i − 〈Ty,j,k,i〉iσy,j,k,i

,

whereTy,j,k,i is the measured counting rate,σy,j,k,i isthe standard deviation and〈Ty,j,k,i〉 is the average overθz. By definitionξ is a gaussian variable with〈ξ〉 = 0and〈ξ2〉 = 1 under the assumption that the behaviourof the experimental counting rate is independent onθz, that is under the hypothesis of absence of signalfrom solar axions. In Fig. 4 theξ distribution ofthe experimental data is shown. There〈ξ〉 = 0.03,〈ξ2〉 = 0.98 and χ2/d.o.f. = ∑

ξ2/d.o.f. = 1.04,obtaining further evidence for absence of signal.Similar results are achieved for every other of thepossible configurations.

Finally, for the same most conservative configura-tion, the behaviour of theY (λ) function (the arbi-trary constant has been chosen so thatY (0) = 0) isshown in Fig. 5 around its minimum; the obtained con-servative value forλ is (4.3 ± 3.1)× 10−4. Accord-ing to the standard procedure [28], this result givesan upper limit on the coupling of axions to photons:

Fig. 5. Logarithmic likelihood functionY(λ) as a function ofλ.

Fig. 6. Exclusion plot forgaγγ versusma . The limit achieved bythe present experiment (gaγγ � 1.7 × 10−9 GeV−1 at 90% C.L.)is shown together with the expectations of the KSVZ and DFSZmodels. The results of previous direct searches for solar axions bySolax [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 thelimit: gaγ γ � 1.7× 10−9 GeV−1 (90% C.L.).

In Fig. 6 the region in the planegaγ γ versusmaexcluded at 90% C. L. by this experiment is shown.

12 R. Bernabei et al. / Physics Letters B 515 (2001) 6–12

4. Conclusions

The present experiment has searched for axionswith direct detection technique without restrictionson their mass, since — as previously mentioned— bounds ongaγ γ obtained by this approach areindependent onma .

The obtained limit onλ is about one order of mag-nitude more stringent than the one set by the SOLAXand COSME Collaborations [10,11], while the limiton the coupling constantgaγ γ has been improved bya factor 1.6 with respect to these experiments. The ob-tained result is at present the best direct limit on so-lar axions conversion in crystals and for axion masseslarger than� 0.1 eV is better also than the limit set bythe Tokyo helioscope.

In conclusion, this experiment has explored theaxion mass windowma ∼ eV still open in the KSVZmodel (wheregaγ γ = 3.7×10−10 GeV−1ma

eV ) and hasallowed to exclude KSVZ axions forma > 4.6 eV at90% 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;

M.A. Shifman, A.I. Vainshtein, V.I. Zakharov, Nucl. Phys.B 166 (1980) 493.

[4] T. Moroi, H. Murayama, Phys. Lett. B 440 (1998) 69.[5] K. van Bibber, P.M. McIntyre, D.E. Morris, G.G. Raffelt, Phys.

Rev. D 39 (1989) 2089.[6] A.O. Gattone et al., Nucl. Phys. B Proc. Suppl. 70 (1999) 59.[7] C. Hagmann et al., Phys. Rev. Lett. 80 (1998) 2043;

S. Matsuki, Talk given at the II International Workshop on theIdentification of Dark Matter IDM98, Buxton, England, 7–11September 1998.

[8] S. Moriyama et al., Phys. Lett. B 434 (1998) 147.[9] E.A. Pascos, K. Zioutas, Phys. Lett. B 323 (1994) 367.

[10] A. Morales et al., hep-ex/0101037.[11] S. Cebrián et al., Astropart. Phys. 10 (1999) 397.[12] R. Bernabei et al., Phys. Lett. B 389 (1996) 757.[13] R. Bernabei et al., Phys. Lett. B 408 (1997) 439.[14] R. Bernabei et al., Phys. Lett. B 424 (1998) 195.[15] R. Bernabei et al., Nuovo Cimento A 112 (1999) 545.[16] R. Bernabei et al., Phys. Lett. B 450 (1999) 448.[17] P. Belli et al., Phys. Lett. B 460 (1999) 236.[18] R. Bernabei et al., Phys. Rev. Lett. 83 (1999) 4918.[19] P. Belli et al., Phys. Rev. C 60 (1999) 065501.

[20] R. Bernabei et al., Nuovo Cimento A 112 (1999) 1541.[21] R. Bernabei et al., Phys. Lett. B 480 (2000) 23.[22] P. Belli et al., Phys. Rev. D 61 (2000) 023512.[23] R. Bernabei et al., Eur. Phys. J. C 18 (2000) 283.[24] R. Bernabei et al., Phys. Lett. B 509 (2001) 197.[25] N.W. Ashcroft, N.D. Mermin, Solid State Physics, Saunders

College, Philadelphia, 1976.[26] http://www.webelements.com.[27] http://aa.usno.navy.mil/software/novas/.[28] Particle Data Group, R.M. Barnett et al., Phys. Rev. D 54

(1996) 1.