SEARCH FOR NEUTRALINO DARK MATTER WITH NAI DETECTORS

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Physics Letters B 295 (1992) 330-336

North-Holland PHYSICS LETTERS B

Search for neutralino dark matter with NaI detectors

A. Bottino, V. de Alfaro, N. Fornengo, G. Mignola, S.

Scopel

Dipartimento di Fisica Teorica dell'Universiff7 di Torino and INFIV, Sezione di Torino, Turin, Italy

Beijing- R o m a - Saclay (BRS) Collaboration

C. Bacci a, p. Belli b, R. Bernabei b, Dai Changjiang c, Ding Linkai c, E. Gaillard d, G. Gerbier d,

Kuang Haohuai c, A. Incicchitti a, j. Mallet a, R. Marcovaldi a, L. Mosca d, D. Prosperi a,

C. Tao 1,¢,d

and Xie Yigang ¢

a Dipartimento di Fisica, Universitgt di Roma "La Sapienza" andlNFN, Sezione di Roma, 1-00185 Rome, Italy b Dipartimento di Fisica, Universit& di Roma "'Tor Vergata" and INFN, Sezione di Roma 2, 1-00173 Rome, Italy ¢ Beijing, China (IHEP), Academia Sinica, P.O. Box 918/3, Beijing, China

d DSM/DAPNIA/SPP, C.E. Saclay, F-91191 Gifsur- Yvette, France

Received 23 September 1992

Theoretical predictions for neutralino dark matter in the framework of the minimal SUSY standard model are compared with recent results of a direct search for dark matter with NaI detectors. Perspectives for a future investigation by this kind of detectors are also discussed.

1. Introduction

An experimental for direct detection o f weakly in- teracting massive particles ( W I M P s ) using NaI crystals is in progress and preliminary results have been reported [ 1 ]. In the present paper we c o m p a r e the experimental data o f ref. [ 1 ] with the theoretical expectations based on one o f the favourite particle can- didates for cold dark matter: the neutralino. In the light of the theoretical predictions we discuss the perspectives o f future experimental searches o f neutralino dark matter employing NaI detectors.

For the general theoretical aspects o f the neutralino as dark matter candidate and for other (indirect) ways o f searching for it we refer to refs. [ 2 - 4 ]. The simplest version o f the SUSY theories is the minimal supersymmetric standard model ( M S S M ) , appro- priately implemented by some G U T assumptions. This constitutes the theoretical framework employed in the present paper.

l Also at LPC, Coll~ge de France, IN2P3/CNRS, France.

For the direct search of the W I M P s the most useful quantity is the nuclear recoil spectrum [5,6 ]

viax

dEadR = N T rn--~zPz d v f ( v ) v ~ - ~ a (v, ER) . (1) Vmin(ER)

ArT is the n u m b e r density o f the detector nuclei, Px/

rn z is the local n u m b e r density o f the dark matter particles (here neutralinos, denoted by Z) and f ( v ) is their galactic velocity distribution in the Earth rest frame, d e / d E a is the differential neutralino-nucleus cross section, where E a is the nucleus recoil energy

2 ,2

ER=mreoV ( 1 - - c o s O * ) / m N . Here 0* denotes the scattering angle in the neutralino-nucleus center o f mass frame; rnN is the nucleus mass and rnrea the neutralino-nucleus reduced mass.

The velocity Vmin(Ea) is given by Vmin(ER)=

( m N E R / 2 r n ~ , o ) ~/2 and Vmax is the maximal neutralino velocity in the halo (i.e. the galaxy escape velocity) c o m p u t e d in the Earth reference frame.

In the following we use for da(v, E R ) / d E a its low energy approximation, i.e.

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Volume 295, number 3,4 PHYSICS LETTERS B 3 December 1992

d a (v, ER) = d e

dE~-~

-~R (v, O)F2(ER)

, (2)

where F ( E R ) denotes a form factor due to the finite size o f the nucleus, and

(da/dER)

(v, 0) m a y be con- veniently expressed as

dr7 o"

- - ( v , O ) = - - ( 3 )

dER E ~ ~x "

Here E ~ ~x =

2m2r~dV2/mN

and a is the total elastic cross section c o m p u t e d for a pointlike nucleus and for zero threshold recoil energy. Then eq. ( 1 ) can be rewritten as

dR Ro

m

d E R < E ~ ax >

- -

F2(ER)I(ER) ,

(4)

where ( E ~ ~x ) is the average o f E ~ ~ over the velocity distribution, Ro is a total rate defined as

Ro=NT&a(v),

(5)

m x and

I(ER )

- -V m a x ( v 2 )

f

dv f ( v ) .

( 6 ) ( v ) v V m i n ( E R )

Taking for the Z's a maxwellian velocity distribution (in the galactic rest frame) o f root mean square velocity w and putting Vmax = o9,

I(ER)

becomes

I(ER)

= xf~ 3 + 2~/2

2 xfn(1 +2r/2)erf(~/)+2~/exp(--r/2) × [erf(Xmin +r/) -- erf(Xmin --r/) ] , ( 7 ) where

3 ~ Ea-~h Xmin = 3If 3 ~ N E R

r/=X/ 2w 2 ' N / ~ 2'

i e x p ( - t

2) dt ;

2

e f t ( x ) =

o

here VEarth denotes the Earth velocity in the galactic frame. In our calculations we take I VEarth[ = 2 4 5 km s - 1 (here the effect o f the flux annual modulation due to the E a r t h - S u n relative m o t i o n is neglected), w = 300 km s - 1 which implies ( v ) = 361 km s - 1. We notice that all the averages over the velocity distri-

bution introduced here are meant to be evaluated in the Earth rest frame.

To obtain the recoil spectrum in the case o f neutralino DM, in eqs. (4), (5) we need to evaluate the quantities Pz and a in an appropriate SUSY model.

2. Theoretical framework

As mentioned above, our framework is the MSSM. The neutralino is defined to be the lowest-mass linear superposition o f photino, zino and higgsinos,

z=a,

~+a2 Z + a f t 1 ° + a4/-I ° . (8)

We adopt the usual definitions o f ~ and 2~ in terms o f the neutral U ( 1 ) , S U ( 2 ) gauginos (/~ and if'3, respectively ):

~ = c o s 0w/~+ sin 0w I~3,

2 = - s i n 0w/~+cos 0w rV3, (9)

where 0w is the Weinberg angle.

In the MSSM the coefficients ai and the neutralino mass are functions o f a restricted n u m b e r o f parameters, which may be chosen to be the/~ mass parameter M1, the # 3 mass parameter M2, the Higgs mixing mass parameter # and the ratio o f the VEVs o f the two Higgs doublets

v2/vl

= t a n fl (Vl and v2 are the VEVs o f the doublets which give masses to the down- type quarks and to the up-type quarks, respectively). The standard G U T condition M1 = ~M2 tan20w is assumed to hold. Further parameters are the masses of the two neutral CP-even Higgs bosons (h, H ) and o f the CP-odd one (A). If one o f the Higgs masses, say rnh, is taken to be a free parameter, the other two masses

mA, rnn

m a y be expressed in terms o f

mh,

o f the mass o f the top quark m, and o f the mass rh o f its SUSY partners (taken to be degenerate). This last property relies on recent results about one-loop ra- diative corrections to the Higgs masses [ 7 ].

As for the values of the Z mass, m z, the range con- sidered in this paper is 20 GeV

<mz<mw,

which is above the present experimental lower b o u n d [8] ~l

~ It has recently been shown [ 9 ] that a model of non-linear evo- lution of initial density fluctuations in the universe, under the further assumption that the average Z density in the universe is 70% of the critical density, points to lower limits on rn x much larger than those obtained at accelerators.

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Volume 295, number 3,4 PHYSICS LETTERS B 3 December 1992 but within the reach of the next future accelerators.

Extension of the present analysis to neutralinos heav- ier than the Wboson is under way.

In the MSSM the total cross section a can be evaluated as described in refs. [2-4]. The relevant am- plitudes are due to Higgs boson exchange and Zo exchange in the t-channel and to squark exchange in the s-channel. The crucial properties are the following: (1) Higgs boson exchange contributes a coherent ( C H ) cross section which is non-zero only for a ;( whose composition contains a zino-higgsino mixture [ 10 ]; (2) Zo exchange provides a spin-dependent (SD) cross section which takes contribution only from the higgsino components of Z; (3) squark exchange contributes a CH cross section (due to zino- higgsino mixing) as well as a SD cross section (mainly due to the gaugino components in Z) [ 11 ]. Because of the relative size of the various couplings and of the fact that the squark mass is already severely con- strained by present accelerator data (fit > 150 GeV), in what follows we disregard the squark-exchange diagrams (see below for a further c o m m e n t on this point).

Under these assumptions the coherent cross section is [ 10 ]

8G2 m 2 ~2 ~2 A2

aCH = ~ - - m----~- ~ n ... d~t , (10)

where A is the mass number of the nucleus and C~H is an effective coupling constant which depends on the MSSM parameters (the explicit expression for aH and its numerical values are given in ref. [ 3 ] ).

The SD cross section due to Zo exchange is given by [11,12]

8G2F 2 2 2 2 2 2

= - - (a3 - - a 4 ) mred(ZqT3L,qAq) ). J ( J + 1 ) .

O'SD

(11) The values of 2 z used in this paper are those obtained in the odd-group model [ 13,14 ] where only the odd nuclear species in o d d - e v e n nuclei is explicitly taken into account. Thus in eq. (11 ) Aq is the fractional spin carried by the quark q in the nucleon of the odd

species; T3L,q

denotes the third component of the quark weak isospin. Other determinations of 22 are given in ref. [ 15 ].

In ref. [2] tr has been evaluated in extended regions of the parameters space for a number of repre-

sentative points defined by fixed values of the fol-

lowing parameters: mh, tan fl, m t and fit. For each

representative point the other free parameters, M2 and ~t, have been varied in the ranges 0 < ME < 600 GeV,

- 3 0 0 < ~ t < 3 0 0 GeV.

The choice of the representative points in ref. [2 ] was meant to illustrate different physical scenarios of particular significance. Here we consider the follow-

ing values: tan f l = 2 and 8, m r = 150 GeV, fit= 1 TeV,

mh ~ 50 GeV (see LEP lower bounds for SUSY Higgs bosons [ 8 ] ).

3. Cross sections and rates for NaI target-detectors

To analyze the preliminary results from the NaI experiment mentioned in the introduction we are now focusing on the sodium and iodine target-nuclei. Ex- perimental details can be found in ref. [1], from which we quote some parameter values relevant to this analysis. The present value of the electron-equiv- alent energy threshold Et~ is about 4 keV. The scintillation efficiency is lower for a recoiling nucleus than for an electron of the same kinetic energy: the corresponding ratio, or "quenching factor", is ~ 0.25 for a

23Na and ~-0.07 for a 127I nucleus, so the recoil energy threshold is E ~ = 1 6 keV for sodium and E ~ = 57 keV for iodine. At these energies the present counting rate is about 10 e v e n t s / k g / k e V / d .

3.1. Coherent p o i n t l i k e cross section

This is maximal in the parameter-space regions where the zino-higgsino mixing is dominant, i.e. in the/~> 0 sector. Here, at tan fl= 8, c~H turns out to be in the range a l l = 1.2--1.5 GeV; this implies, from eq.

(10),

4

acH = ( 2 - 8 ) n b ( 5 0 GeV~ for 127I, (10')

\ mh /

and

aCH = (2_3) X 10-2 nb ( 5 0 Ge----~V~ ` for 23Na.

\ mh I

(1o")

For this tan fl value, in the sector/2 < 0 the cross sections are only reduced by a factor 1.5-2.0 as corn-

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Volume 295, number 3,4 PHYSICS LETTERS .q 3 December 1992 pared to the values given in eqs. ( 1 0 ' ) , (10"). How-

ever, at lower values o f tan fl, the effective coupling constant a n suppresses the coherent cross sections significantly. For instance, at tan fl= 2 the aCH values in the p > 0 ( / z < 0 ) sector are drown by one (two) orders o f magnitude with respect to the cross-sections values reported in eqs. (10'), (10").

3.2. Spin-dependent pointlike cross sections

Eq. ( 11 ), computed with the numerical values [ 14 ] 2 2 J ( j + l ) = 0 . 0 4 1 for 23Na, 2 2 J ( j + l ) = 0 . 0 0 7 for

127I; AU = 0.77, A d = - 0.49, As = -- 0.15 and our eval- uations o f the coefficients a3, a4, leads to the following estimates for the maximal contributions due to the SD effects:

O'sD< 1 × 10-4 nb for 127I (11')

and

O'SD < 2 × 10-4 nb for 23Na. (1 1") Possible SD contributions due to 0-exchange would provide cross sections o f a few 10 -4 ( m w / m ~ ) 4 nb in regions where Z is dominantly a gaugino.

F r o m the previous discussion it follows that, for scattering o f z offpoint-like 23Na and 127I nuclei, CH cross sections largely dominate over the SD cross sections, except where coherent effects are severely hindered by small values o f tan fl and by values o f mh

which are well above the present experimental bound. This happens, for example, at tan f l = 2, mh = 80 GeV; however, here the level o f the total cross sections is very low (about 8 × l0 -5 nb).

3.3. Nuclear form factors

The specific analytic expressions to be used for the form factors depend on the associated elastic nuclear cross section. In the case o f coherent cross section it may be taken o f the form [ 18 ]

F ( E R ) - 3jl (qro__..) exp( - ½siq 2) . (12)

qro

Here q i _ [ q l 2 = 2mNER is the squared three-mo- m e n t u m transfer, s ~ 1 fm is the thickness parameter for the nucleus surface, ro = (r z - 5s 2 ) l/2, r= 1.2 A 1/3

fm and Jl (qro) is the spherical Bessel function o f in- dex 1.

For heavy nuclei the suppression effect introduced by the form factor in the differential rate is notice- able at threshold already. In fact, using the values o f E~e h and o f the quenching factors given above one finds from eq. (12) that F i ( E ~ ) = 0 . 9 6 for 23Na and F i ( E ~ ) = 0.045 for t27I. For 23Na the differential rate is negligibly affected by the form factor over the whole E~ spectrum. On the contrary, for 127I the form factor plays an important role in reducing the coherent cross section also because of the first zero o f the function

Jx (qro)/qro which occurs at a rather low value o f E~e, i.e. at Eee= 7.3 keV.

For the SD cross section the relevant form factor has a smaller suppression effect in heavy nuclei, as was shown in ref. [16] for the case o f 131Xe and in ref. [ 17 ] for 93Nb. A corresponding nuclear evalua- tion for 1271 is not available at present ~2; so in this paper we have simply assumed that the form factor o f the SD amplitude in 127I and in 131Xe are roughly the same and we have used the results o f ref. [ 16 ].

3.4. Neutralino local density

We may take for it the standard value agreed for the local D M density, i.e. & = 0 . 2 - 0 . 4 G e V / c m 3, whenever the value o f the average relic density, ~xh 2,

is >0.05. When 12xh 2 is smaller than this value because the 7,X annihilation cross section, aann, is large (and so the neutralino cannot be the only c o m p o n e n t o f D M ) , Px has to be rescaled [ 19,20,2 ]; thus we take pz=~&, with ~=lixhi/O.05 whenever I i z h i < 0 . 0 5 , ( = 1 otherwise. It is worth remarking that £izh 2 is strongly suppressed a r o u n d the point mz= ½m,4 because at this value o f m z the Higgs-exchange amplitude in tran . has a pole singularity. The values o f (izh 2 used here for rescaling are taken from ref. [2] and refer to the same parameter space discussed above in connection with the cross sections.

3.5. Results

Our results are reported in figs. 1-3. Fig. 1 shows the maximal differential rate, dR/dEee, which was found for NaI by varying 342 and/1 in the ranges mentioned above, at the representative point defined by tan fl= 8, m h = 50 GeV; here the Z local density is set **2 A theoretical investigation on this subject is in progress.

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Volume 295, number 3,4 PHYSICS LETTERS B 3 December 1992 Maximal differential rate (Px=0.3 Ge¥ cm -n)

103 . . . . I . . . . I . . . . I . . . . I . . . . 102 ~ ~ ~ 101 BO 1oO - ~

'".

, 10-1 10_2 I " "" , ."" 80 10 -3 20 ". "' 1 0 - 4 . . . . l . . . . 1 .. . . . I i . . . 0 2 4 6 8 I0 E. (KeV)

Fig. 1. Maximal differential rate, dR/dEee , at tan fl= 8, mh= 50

GeV, mr= 150 GeV, r~= 1 TeV when M2 andp are varied in the

range: 0 < M2 < 600 GeV, - 300 < tz < 300 GeV. Here Pz is set equal

to the local DM density: px=p~=0.3 GeV cm -3. Dotted, dashed

and solid lines refer t o 127I, 2 3 N a and total Nal contributions, re-

spectively, at two values of the Z mass: rnx= 20 , 80 GeV.

I0 0 10-1

'•

tO-g 10-3 10_4 10-6

Spin-dependent conLribuLion maximized

(with reecallng for local density)

! . . . . J . . . . i . . . . I . . . . t . . . . ! ". zo ::z0 -'.'- '. 20 . . .. , , :.. , i"i"?":.,..,., , , , . . . j 2 4 8 8 10 z. (KEY)

Fig. 3. Differential rate when the SD contribution is maximized by varying M2,/z in the same range as in figs. 1, 2. The representative point is defined here by tanfl=2, mh----80 GeV, mr= 150 GeV, rh = 1 TeV. The conventions for the symbols are as in the previous figures.

Maximal differential raLe (with relca|ing /or local den*lty)

102 I . . . . I . . . . I . . . . I . . . . 101 ~ + + + + + ++ + + + + g" 100 ~ ' ~ 10-1 . 7 10_2 - _: 20 ~ -2,..~ "... - -- ~-'~"-- 10_3 "' "'. 80 10-4 , , , I ;'., , I . . . . I , ,',, ,1 . . . . 0 g 4 6 8 10 ¢• (KeV)

Fig. 2. The same as in fig. 1, except that here Px is rescaled (Px = ~o~ )

according to the procedure discussed in the text. The crosses de- note the experimental upper limits of ref. [ 1 ].

e q u a l to the s t a n d a r d v a l u e for t h e local D M d e n s i t y :

px=P~=0.3 G e V c m -3. T h e d o t t e d l i n e w h i c h de- n o t e s the c o n t r i b u t i o n o f i o d i n e for m x = 8 0 G e V shows a t y p i c a l d i p at E ~ 7.3 keV, d u e to a zero o f the f o r m factor i n eq. ( 1 2 ) . I n fig. 2 we r e p o r t the m a x i m a l rescaled d i f f e r e n t i a l rate d R / D E = , calcu- l a t e d in the s a m e r e p r e s e n t a t i v e p o i n t as in fig. 1. As

p r e v i o u s l y discussed, rescaling is i n t r o d u c e d i n d R / dEe¢ b y p u t t i n g px=~9~ i n eq. ( 5 ) . H e r e d R / d E ¢ ~ is d o m i n a t e d b y c o h e r e n t effects o v e r the w h o l e s h o w n r a n g e (the ratio o f the SD c o n t r i b u t i o n to t h e C H c o n t r i b u t i o n is typically O ( 1 0 - 3 ) ). H e r e the rescal- i n g suppresses t h e rex= 20 G e V curves in a v e r y sub- s t a n t i a l w a y (~_~ 8 × 10 - 3 ) , b e c a u s e t h e pole o f aann occurs at r n z = 25 G e V ( i n fact at t h e p r e s e n t repre- s e n t a t i v e p o i n t the v a l u e o f mA t u r n s o u t to be mA = 51 G e V ) . T h e d i f f e r e n t i a l rate for v a l u e s o f m x i n the r a n g e r e x = 4 0 - 8 0 G e V (the r e x = 8 0 G e V case is s h o w n i n fig. 2 ) is rescaled m u c h less, i.e. ~ 0 . 2 - 0 . 4 . I n fig. 2 the crosses d e n o t e the p r e s e n t e x p e r i m e n t a l u p p e r l i m i t s o f ref. [ 1 ].

We clearly see f r o m fig. 2 the i n t e r p l a y b e t w e e n the t w o n u c l e i , 23Na a n d ~27I, i n d e t e r m i n i n g t h e total d i f f e r e n t i a l rate. F o r i n s t a n c e , for rex= 80 GeV, u p to the v a l u e E ~ = 6 keV, d R / d E ~ ¢ is d o m i n a t e d b y scat- t e r i n g o f z off i o d i n e .

O n e m a y w o n d e r w h e t h e r S D effects c o u l d p r o v i d e a sizeable d i f f e r e n t i a l rate for a X o f s o m e a p p r o p r i a t e c o m p o s i t i o n (e.g. a Z with higgsino d o m i n a n c e i n t h e case o f a Z - e x c h a n g e g r a p h ) . O u r p r e v i o u s e s t i m a t e s for the r e l e v a n t cross sections, eqs. (11 ), s h o w t h a t the SD effects are in general v e r y s m a l l i n t h e p a r a m - eter space c o n s i d e r e d in this paper; a direct n u m e r i - cal test o f m a x i m i z a t i o n o f the S D c o n t r i b u t i o n s ( i n -

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Volume 295, number 3,4 PHYSICS LETTERS B 3 December 1992 stead o f the total, coherent plus SD, differential r a t e )

c o n f i r m s these expectations.

The results o b t a i n e d by a p p l y i n g this m a x i m i z a - tion p r o c e d u r e to the rescaled dR/dEee d i s t r i b u t i o n are shown in fig. 3. A p a r t from the low values o f m z

(rnx~-20 G e V ), the SD c o n t r i b u t i o n is m a x i m a l a n d d o m i n a n t over the C H c o n t r i b u t i o n in the p a r a m e t e r region where kt < 0. The overall signal shown in fig. 3 r e m a i n s rather low in the whole rn x range.

F r o m the p o i n t o f view o f the rescaling effect we r e m a r k that at the r e p r e s e n t a t i v e p o i n t o f fig. 3 ( t a n f l = 2 , m h = 80 G e V ) the value o f m A is mA= 170 GeV and then rescaling is p a r t i c u l a r l y severe for

rnx~- 80 GeV. The dR/dEe~ d i s t r i b u t i o n s is m u c h less affected by the rescaling p r o c e d u r e for values o f m z

in the ranges m z = 2 0 - 3 0 G e V (the case m z = 20 G e V is shown in fig. 3) and r e x = 5 0 - 6 0 GeV. At mz-~40 G e V a dip occurs in 12zh 2 because o f a singularity due to h-exchange in the a n n i h i l a t i o n a m p l i t u d e [ 2 ].

4. Conclusions and outlook

In the present p a p e r theoretical p r e d i c t i o n s b a s e d on M S S M are c o m p a r e d to p r e l i m i n a r y d a t a from an N a I scintillator e x p e r i m e n t . The total elastic z - N a I differential rate is m a x i m a l in the M S S M p a r a m e t e r s space region where the coherent z - n u c l e u s cross section is d o m i n a n t due to z i n o - h i g g s i n o mixing. In this case the e x p e r i m e n t a l sensitivity has to be i m p r o v e d by about t w o - t h r e e o r d e r s o f m a g n i t u d e in o r d e r to start testing the predictions o f the model in the z-mass region a r o u n d 4 0 - 8 0 GeV. Q u a n t i t a t i v e l y the situa- tion is given in fig. 2. It must be e m p h a s i z e d that the 127I c o n t r i b u t i o n , d o m i n a n t over the 23Na c o n t r i b u - tion fog m z ~ 80 GeV, directly d e p e n d s on the value o f the i o d i n e quenching factor which still needs to be d e t e r m i n e d accurately.

I f the z i n o - h i g g s i n o m i x i n g in the n e u t r a l i n o com- p o s i t i o n is very small, the coherent cross sections are strongly reduced. In this case the ratio o f the spin de- p e n d e n t c o n t r i b u t i o n to the coherent c o n t r i b u t i o n m a y be substantial (in p a r t i c u l a r for 23Na ); however the relevant differential rate is one or two orders o f m a g n i t u d e lower than the values taken by the coherent rate in the regions where this last one is m a x i m a l . F r o m the e x p e r i m e n t a l p o i n t o f view an increase o f sensitivity o f two o r d e r s o f m a g n i t u d e m a y be

reached in the next few years by a b e t t e r selection a n d p u r i f i c a t i o n o f all the d e t e c t o r c o m p o n e n t s , an im- p r o v e m e n t o f the shielding thickness a n d quality, a possible statistical s e p a r a t i o n between C o m p t o n electrons versus nuclear recoils, a n d a study o f the W I M P s flux annual m o d u l a t i o n .

Such an i m p r o v e m e n t will allow to start testing the present model. It also p r o v i d e s the o p p o r t u n i t y to ex- plore a region o f masses a n d cross sections which has never been reached so far, where o t h e r presently un- p r e d i c t e d D M c a n d i d a t e s could be present.

M o r e o v e r o t h e r scintillation crystals, in principle m o r e favourable than s o d i u m a n d i o d i n e for the spin d e p e n d e n t a n d / o r coherent couplings (like CaF2), are u n d e r investigation in the BRS C o l l a b o r a t i o n .

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