Model independent result on possible diurnal effect in DAMA/LIBRA-phase1

Abstract

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image)

The results obtained in the search for possible diurnal effect in the single-hit low energy data collected by DAMA/LIBRA-phase1 (total exposure 1.04 ton ...... year) deep underground at the Gran Sasso National Laboratory (LNGS) of the INFN are presented. At the present level of sensitivity the presence of any significant diurnal variation and of diurnal time structures in the data can be excluded for both the cases of solar and sidereal time. In particular, the diurnal modulation amplitude expected, because of the Earth diurnal motion, on the basis of the DAMA dark matter annual modulation results is below the present sensitivity.

Eur. Phys. J. C (2014) 74:2827DOI 10.1140/epjc/s10052-014-2827-1

Regular Article - Experimental Physics

Model independent result on possible diurnal effect in DAMA/LIBRA-phase1

R. Bernabei1,2,a, P. Belli2, F. Cappella3,4, V. Caracciolo5, S. Castellano5, R. Cerulli5, C. J. Dai6, A. dAngelo3,4,S. dAngelo1,2, A. Di Marco1,2, H. L. He6, A. Incicchitti4, H. H. Kuang6, X. H. Ma6, F. Montecchia2,7, D. Prosperi3,4,b,X. D. Sheng6, R. G. Wang6, Z. P. Ye6,8

1 Dip. di Fisica, Universit di Roma Tor Vergata, 00133 Rome, Italy

2 INFN, sez. Roma Tor Vergata, 00133 Rome, Italy

3 Dip. di Fisica, Universit di Roma La Sapienza, 00185 Rome, Italy

4 INFN, sez. Roma, 00185 Rome, Italy

5 Laboratori Nazionali del Gran Sasso, INFN, Assergi, Italy

6 Institute of High Energy Physics, Chinese Academy of Sciences, P.O. Box 918/3, Beijing 100049, China

7 Dip. di Ingegneria Civile e Ingegneria Informatica, Universit di Roma Tor Vergata, 00133 Rome, Italy

8 University of Jing Gangshan, Jiangxi, China

Received: 6 December 2013 / Accepted: 18 March 2014 / Published online: 27 March 2014 The Author(s) 2014. This article is published with open access at Springerlink.com

Abstract The results obtained in the search for possible diurnal effect in the single-hit low energy data collected by DAMA/LIBRA-phase1 (total exposure 1.04 ton year) deep

underground at the Gran Sasso National Laboratory (LNGS) of the INFN are presented. At the present level of sensitivity the presence of any signicant diurnal variation and of diurnal time structures in the data can be excluded for both the cases of solar and sidereal time. In particular, the diurnal modulation amplitude expected, because of the Earth diurnal motion, on the basis of the DAMA dark matter annual modulation results is below the present sensitivity.

1 Introduction

The present DAMA/LIBRA [18] experiment, as the former DAMA/NaI [811], has the main aim to investigate the presence of dark matter (DM) particles in the galactic halo by exploiting the model independent DM annual modulation signature (originally suggested in Ref. [12,13]). In particular, they have cumulatively reached a model independent evidence at 9.3 C.L. for the presence of DM particles in the galactic halo on the basis of the exploited DM annual modulation signature [4].

In the present work the DAMA/LIBRA-phase1 data (total exposure 1.04 ton year) are analysed in terms of possi

a e-mail: [email protected]

b Deceased

ble diurnal variation of the rate of the single-hit events1 in

low energy regions, both where the DM annual modulation signal is observed (26 keV, see Ref. [24] and references therein) and in the region just above (614 keV) for comparison. Actually a diurnal effect with the sidereal time is expected for DM because of Earth rotation. In Sect. 2 the diurnal modulation of the DM signal as a function of the sidereal time due to Earth rotation velocity contribution will be discussed and some relevant formulae will be presented; this effect is model-independent and has several requirements as the DM annual modulation effect does. Thus, in Sect. 4 the data have been analyzed using the sidereal time referred to Greenwich, also sometimes called GMST. Since potential environmental backgrounds can be in principle correlated with the solar time, the analysis has been also performed in terms of solar time referred to the LNGS site.

2 Expectation for DM diurnal effect because of the Earth rotation

Let us now introduce an interesting model independent effect which can induce a diurnal variation of the counting rate of the single-hit events: the diurnal modulation of the DM signal as a function of the sidereal time due to Earth rotation velocity contribution [14]. As explained below, this effect is linked with the DM model independent annual modulation signature

1 i.e. those events where only one of the 25 detectors in DAMA/LIBRA res; that is, each detector has all the others as anti-coincidence.

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(see also for example Refs. [1518]). To explain this point in this section we describe all the components of the motion of a detector placed in a terrestrial laboratory with respect to an observer xed in the galactic frame, including both the revolution of the Earth around the Sun and the rotation of the Earth around its axis.

As known, the velocity of the detector in the terrestrial laboratory can be expressed as following:

vlab(t) = vLSR + v + vrev(t) + vrot(t), (1)

where

vLSR is the velocity of the Local Standard of Rest (LSR) due to the rotation of the Galaxy;

v is the Sun peculiar

velocity with respect to LSR;

vrev(t) is the velocity of the revolution of the Earth around the Sun and

vrot(t) is the velocity of the rotation of the Earth around its axis at the latitude and longitude of the laboratory. Using the galactic coordinate frame (that is x axis towards the galactic center, y axis following the rotation of the Galaxy and the z axis towards the galactic North pole), we have

vLSR = (0, v0, 0),

with v0 = (220 50) km/s [11,1921] (uncertainty at 90 %

C.L.), and

v = (9, 12, 7) km/s [22], while the revolution

and rotation velocities of the Earth depend on the sidereal time, t.

Revolution of the Earth around the Sun. This motion can be easily worked out using the ecliptic coordinate system (ecl1,ecl2,ecl3), where theecl1 axis is directed towards the

vernal equinox andecl1 andecl2 lie on the ecliptic plane. The

right-handed convention is used. In the galactic coordinates, we can write2:

eecl1 = (0.05487, 0.49411, 0.86767), eecl2 = (0.99382, 0.11100, 0.00035), eecl3 = (0.09648, 0.86228, 0.49715). (2) The ecliptic plane is tilted with respect to the galactic plane by 60, asecl3 (0, 0, 1) = 0.49715.

The motion of the Earth in the ecliptic plane can be described as:

vrev(t) = VEarth(ecl1 sin (t) ecl2 cos (t)) (3)

where VEarth is the orbital velocity of the Earth, which has a weak dependence on time due to the ellipticity of the Earth orbital motion around the Sun; its value ranges between 29.3 km/s and 30.3 km/s. For most purposes it can be assumed constant and equal to its mean value 29.8 km/s. On the other

hand, when more accurate calculations are necessary, the routines in Ref. [23] can be used: they also take into account the ellipticity of the Earth orbit and the gravitational inuence

2 The coordinates of these versors are rstly worked out in the equatorial coordinate system by using the routines given in Ref. [23] and then in the galactic coordinate system by using the R A and the DE of the galactic North pole and of the galactic center (see also later).

of other celestial bodies (Moon, Jupiter, and etc.)3. Moreover, the phase in Eq. 3 can be written as (t) = (t tequinox);

here = 2/T with T = 1 y, t is the sidereal time and

tequinox is the spring equinox time ( March 21).

Rotation of the Earth around its axis. The simplest way to express this motion is in the equatorial coordinate system (ecs1,ecs2,ecs3), where theecs1 axis is directed towards

the vernal equinox andecs1 andecs2 are on the equato

rial plane; theecs3 axis is towards the North pole. The

right-handed convention is used. To work out the galactic coordinates of these versors, we use the equatorial coordinates of the galactic North pole: R A = 192.859508 and

DE = 27.128336 (R A is the right ascension and DE is

declination); and of the galactic center: R A = 266.405100

and DE = 28.936175, evaluated at the Epoch J2000.0.

In the galactic coordinates, these versors can be written as:

eecs1 = (0.05487, 0.49411, 0.86767), eecs2 = (0.87344, 0.44483, 0.19808), eecs3 = (0.48384, 0.74698, 0.45599). (4) Therefore, we can write:

vrot(t) = Vr(ecs1 sin (t) ecs2 cos (t)) (5) where Vr is the rotational velocity of the Earth at the given latitude, 0, of the laboratory: Vr = Veqcos0. The equato

rial rotational velocity, Veq, is equal to 0.4655 km/s. Hence, at LNGS (0 = 4227 N and longitude 0 = 1334 E):

Vr = 0.3435 km/s. The angle (t) = rot(t + 0), where

rot = 2/Td with Td = 1 sidereal day.

2.1 The time dependence of | vlab(t)|

In most evaluations of dark matter candidates the expected counting rate depends on the module of the detectors velocity in the Galaxy, vlab(t). The time-independent contribution is | vs| = |

vLSR + v | 232 50 km/s, while a Taylor

expansion can be performed in the smaller time-dependent contributions | vrev(t)| 30 km/s and | vrot(t)| 0.34 km/s.

Thus, to the rst order, that reads:

vlab(t) vs + vs vrev(t) + vs vrot(t). (6)

The higher order terms with no time dependence and with higher harmonics of

2

| vs| , and the

contributions arising from the ellipticity of the Earth orbit are omitted for simplicity, having frequencies well separated from the diurnal one.

3 For completeness, we remind the discussion about the ellipticity of the Earth orbit in Ref. [18], which overcomes the description given in Ref. [24].

vrev(t): 12 V

2 Earth

| vs| 12 (vs vrev(t))

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232.5

245

v s+ V Ea rthA mcos(t-t 0) (km/s)

v s+ V rA dcos rot(t-t d) (km/s)

232.4

240

235

232.3

230

232.2

225

232.1

220

0 50 100 150 200 250 300 350 0 2 4 6 8 10 12 14 16 18 20 22 24

Sidereal time (d)

Sidereal time (h)

Fig. 1 Left velocity of the Earth in the galactic frame as a function of the sidereal time, with starting point March 21 (around spring equinox). The contribution of diurnal rotation (the third term in Eq. 6) has been dropped off. The maximum of the velocity (vertical line) is about 73 days after the spring equinox. Right sum of the Sun velocity in the galactic frame

(vs) and of the rotation velocity of a detector at LNGS (vs vrot(t)) as

a function of the sidereal time. The maximum of the velocity is about at 14 h (vertical line). These velocities have been calculated assuming v0 = 220 km/s by using the routines of Ref. [23]

The second term in Eq. 6 is responsible for the DM annual modulation of the signal and can be written as:

vs vrev(t) = VEarth(vs ecl1 sin (t) vs ecl2 cos (t)).

Dening vs ecl1 = Amsinm and vs ecl2 = Amcosm

(equal to 0.465 and to 0.149, respectively, for the case v0 =

220 km/s), one can write:

vs vrev(t) = VEarth Am cos((t) m)

= VEarth Am cos((t t0)),

with Am 0.489, this conrms that the ecliptic is tilted with

respect to the galactic plane of 60, and m 1.260 rad

(both values are calculated for v0 = 220 km/s). The phase of

the DM annual modulation is determined at the time when the argument of cosine is null:

t0 = tequinox + m/ = tequinox + 73.25 solar days,

for v0 = 220 km/s; it corresponds to June 2nd (see Fig. 1,

left). The term in the previous equation ranges from 71.76 solar days (for v0 = 170 km/s) to 74.20 solar days (for v0 =

270 km/s).

The same procedure can be followed to determine the phase of the diurnal modulation due to the Earth rotation around its axis, described by the third term in Eq. 6:

vs vrot(t) = Vr(vs ecs1 sin (t) vs ecs2 cos (t)). Dening vs ecs1 = Adsind and vs ecs2 = Adcosd

(equal to 0.465 and to 0.484, respectively, for the case v0 =

220 km/s), one can write:

vs vrot(t) = Vr Ad cos((t) d) = Vr Ad cos[rot(t td)],

with Ad 0.671 and d 3.907 rad (both values are cal

culated for v0 = 220 km/s). The phase of the DM diurnal

modulation is determined at the time when the argument of cosine is null:

td = d/rot 0.

It corresponds to td 14.02 h sidereal time for the case of

a detector at the Gran Sasso longitude4 and v0 = 220 km/s

(see Fig. 1, right); actually this value ranges from 13.94 h (v0 = 170 km/s) to 14.07 h (v0 = 270 km/s).

Finally, the detectors velocity in the Galaxy can be written as:

vlab(t) vs + VEarth Am cos[(t t0)]

+Vr Ad cos[rot(t td)]. (7)

2.2 The time dependence of the counting rate

In most evaluations of dark matter candidates the expected counting rate depends on the module of the detectors velocity in the Galaxy, vlab(t). Applying a Taylor expansion, as done in the previous section, the expected signal counting rate in a given k-th energy bin can be written as:

Sk[vlab(t)] Sk[vs] + [bracketleftbigg]

Sk vlab

[bracketrightbigg]vs [

VEarth Am cos (t t0)

+Vr Ad cos rot(t td)]. (8) The higher order terms with no time dependence and with higher harmonics of are omitted for simplicity. In Eq. 8 the

4 Note that in terms of local sidereal time the phase of the DM diurnal modulation is given by td + 0 = d/rot 14.92 h and it is the same

for each laboratory independently of its longitude.

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rst term is the constant part of the signal (S0), the second term is the annual modulation term with amplitude Sm =

[bracketleftBig]

Sk vlab

vs VEarth Am, and the third term provides a diurnal

modulation with amplitude Sd = [bracketleftBig]

Sk vlab

vs Vr Ad.

The interest in this signature is that the ratio Rdy of this diurnal modulation amplitude over the annual modulation amplitude is a model independent constant; considering the LNGS latitude one has:

Rdy =

SdSm =

Vr Ad

VEarth Am 0.016 (9)

Taking into account Rdy and the annual modulation effect evidenced by DAMA/LIBRA-phase1 for single-hit events in the low energy region, it is possible to derive the diurnal modulation amplitude expected for the same data. In particular, when considering the (26) keV energy interval, the observed annual modulation amplitude in DAMA/LIBRA-phase1 is: (0.0097 0.0013) cpd/kg/keV [4] and the

expected value of the diurnal modulation amplitude is

1.5 104 cpd/kg/keV.

3 The experimental set-up

The results presented in the following have been obtained by analysing the data collected in seven annual cycles by DAMA/LIBRA-phase1 (1.04 ton year exposure) [24]

at LNGS. The description, radiopurity and main features of the DAMA/LIBRA-phase1 setup are discussed in details in the dedicated Ref. [1]. The sensitive part is made of 25 highly radiopure NaI(Tl) crystal scintillators organized in a (5 5) matrix; each NaI(Tl) detector has 9.70 kg mass

and a size of (10.2 10.2 25.4) cm3. The bare crystals

are enveloped in Tetratec-teon foils and encapsulated in radiopure OFHC Cu housing. In each detector two 10 cm long special quartz light guides act also as optical windows on the two end faces of the crystal and are coupled to two low background photomultipliers (PMT) working in coincidence at single photoelectron level. The detectors are housed in a sealed low-radioactive copper box installed in the center of a low-radioactive Cu/Pb/Cd-foils/polyethylene/parafn shield; moreover, about 1 m concrete (made from the Gran Sasso rock material) almost fully surrounds (mostly outside the barrack) this passive shield, acting as a further neutron moderator. The copper box is maintained in HP Nitrogen atmosphere in slightly overpressure with respect to the external environment; it is part of the threefold-level sealing system which excludes the detectors from the environmental air of the underground laboratory. The light response of the detectors in DAMA/LIBRA-phase1 typically ranges from5.5 to 7.5 photoelectrons/keV, depending on the detector. The hardware threshold of each PMT is at single photo-

electron, while a software energy threshold of 2 keV electron equivalent (hereafter keV) is used [1]. Energy calibration with X-rays/ sources are regularly carried out in the same running condition down to few keV [1]. Moreover, the whole DAMA/LIBRA installation is under air conditioning to assure a suitable and stable working temperature for the electronics; in addition, the huge heat capacity of the multi-ton passive shield ( 106 cal/C) further assures a relevant

stability of the detectors operating temperature. The DAQ system records both single-hit events (where just one of the detectors res) and multiple-hit events (where more than one detector re) up to the MeV region despite the optimization is performed for the lowest one. A hardware/software system is operative to monitor the running conditions, and self-controlled computer processes automatically control several parameters and manage alarms. For the radiopurity, the electronic chain, the data acquisition system and for all the other details see Ref. [1]; for completeness we recall that during DAMA/LIBRA-phase1 new transient digitizers and DAQ system have been installed at fall 2008 before the start of the sixth annual cycle.

4 Model independent experimental results

In order to point out the presence of a possible diurnal effect, the low energy single-hit DAMA/LIBRA-phase1 data have been grouped in 1 hour bin using either the sidereal or solar time, respectively. We dene N(jky)i,d as the number of events collected in the ith hour of the day d (for the two cases of sidereal and solar time); as regards the other indexes: i) j identies the detector; ii) k identies the energy bin within the considered energy interval; iii) y identies the annual cycle. Hence, the single-hit rate in ith hour is written as:

r(jky)i = [summationtext]

d N(jky)i,d

d Mj t(y)i,d E (jky)

,

where Mj is the mass of the jth detector, t(y)i,d is the detector running time during the ith hour of the dth day of the yth annual cycle, E is the energy bin and (jky) is the overall efciency [1].

Therefore, the residual rate has been calculated according to: r(jky)i f lat(jky) jky, where the average is made on all

the detectors ( j index), on all the considered energy bins (k index), and on all the DAMA/LIBRA-phase1 annual cycles (y index). The f lat(jky) is the rate averaged over the day: f lat(jky) = r(jky)i i, which is of the order of 1 cpd/kg/keV

[1]. Here, the possible time-dependent contribution due to the annual modulation signal is not considered since it is washed out by the almost uniform data collection along the day and along the year; its estimated effect is much lower than 104

of f lat(jky).

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Fig. 2 Experimental model-independent diurnal residual rate of the single-hit scintillation events, measured by DAMA/LIBRA-phase1 in the (24), (25) and (26) keV energy intervals as a function of the hour of the solar (left) and sidereal (right) day. The experimental points present the errors as vertical bars and the associated time bin width (1 h) as horizontal bars. The cumulative exposure is 1.04 ton

year. See textSolar Time (h)

0.03

0.03

2-4 keV

2-4 keV

0.02

0.02

0.01

0.01

cpd sol/kg/keV

0

cpd si d/kg/keV

0

-0.01

-0.01

-0.02

-0.02

-0.03

-0.03

0 5 10 15 20

0 5 10 15 20

Sidereal Time (h)

0.03

0.03

2-5 keV

2-5 keV

0.02

0.02

0.01

0.01

cpd sol/kg/keV

0

cpd si d/kg/keV

0

-0.01

-0.01

-0.02

-0.02

-0.03

-0.03

0 5 10 15 20

0 5 10 15 20

Solar Time (h)

Sidereal Time (h)

0.03

0.03

2-6 keV

2-6 keV

0.02

0.02

cpd si d/kg/keV

0.01

0.01

cpd sol/kg/keV

0

0

-0.01

-0.01

-0.02

-0.02

-0.03

-0.03

0 5 10 15 20

0 5 10 15 20

Solar Time (h)

Sidereal Time (h)

Figure 2 shows the time and energy behavior of the experimental residual rates of single-hit events both as a function of solar (left) and of sidereal (right) time, in the (24), (25) and (26) keV energy intervals5 and in Fig. 3 those in the (614) keV interval for the solar (left) and sidereal (right) case. The used time bin is 1 (either solar or sidereal, respectively) hour.

5 We recall that the annual modulation signal has been pointed out only in these energy intervals; see Ref. [24] and references therein.

The null hypothesis (absence of residual rate diurnal variation) has been tested by a 2 test, obtaining the results given in Table 1; there the upper tail probabilities (P-values), calculated by the standard 2 distribution, are also reported. Thus, no diurnal variation with a signicance of 95 % C.L. is found.

In addition to the 2 test, another independent statistical test has been applied: the run test (see e.g. Ref. [25]); it veries the hypothesis that the positive and negative data points are randomly distributed. The lower tail probabilities

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Fig. 3 Experimental model-independent diurnal residual rate of the single-hit scintillation events, measured by DAMA/LIBRA-phase1 in the (614) keV energy interval as a function of the hour of the solar (left) and sidereal (right) day.The experimental points present the errors as vertical bars and the associated time bin width(1 h) as horizontal bars. The cumulative exposure is 1.04 ton

year. See text

Solar Time (h)

0.03

0.03

6-14 keV

6-14 keV

0.02

0.02

0.01

0.01

cpd sol/kg/keV

0

cpd si d/kg/keV

0

-0.01

-0.01

-0.02

-0.02

-0.03

-0.03

0 5 10 15 20 0 5 10 15 20

Sidereal Time (h)

Table 1 Test of absence of diurnal effect in the DAMA/LIBRA-phase1 data. The P values, calculated by the standard 2 distribution, are also shown. As it can be seen, the 2 test applied to the data supports the hypothesis that the residual rates are simply uctuating around zero

Energy (keV)

Solar time Sidereal time

24 2/d.o.f. = 35.2/24 P = 7 %

2/d.o.f. = 28.7/24 P = 23 % 25 2/d.o.f. = 35.5/24 P = 6 %

2/d.o.f. = 24.0/24 P = 46 % 26 2/d.o.f. = 25.8/24 P = 36 %

2/d.o.f. = 21.2/24 P = 63 % 614 2/d.o.f. = 25.5/24 P = 38 %

2/d.o.f. = 35.9/24 P = 6 %

are equal to: 43, 18, 7 and 26 % in the (24), (25), (26) and (614) keV energy region, respectively, for the solar case and 54, 84, 78 and 16 % in the (24), (25), (26) and (614) keV energy region, respectively, for the sidereal case. Thus, in conclusion the presence of any signicant diurnal variation and of time structures can be excluded at the reached level of sensitivity (see e.g. the error bars in Fig. 2).

4.1 Comparison with expectation for DM diurnal effect

When considering the DM diurnal effect due to the Earth rotation around its axis described in Sect. 2, only an upper limit can be derived. In particular, the residual rates of the single-hit events in the (24), (25), (26) and (614) keV energy intervals as a function of the sidereal time (see Figs. 2, right and 3, right) have been tted with a cosine function with amplitude Aexpd as free parameter, period xed at 24 h and phase at 14 h. The results are reported in Table 2: all the diurnal modulation amplitudes are compatible with zero.

Figure 4 shows the diurnal modulation amplitudes, Ad, as function of energy (the energy bin is 1 keV) obtained by tting the single-hit residual rate of the entire DAMA/LIBRA-phase1 as function of the sidereal time, with the formula Ad cos[rot(t td)]. The period is xed at 24 h and the

phase at 14 h, as expected for the DM diurnal effect (see

Table 2 Diurnal modulation amplitudes, Aexpd, for each considered energy interval obtained by tting the single-hit residual rate of the entire DAMA/LIBRA-phase1 as function of the sidereal time, (see Figs. 2, right, 3, right) with the formula Aexpd cos[rot(t td)]. The amplitude

Aexpd is a free parameter, while the period is xed at 24 h and the phase at 14 h, as expected for the DM diurnal effect. The corresponding 2 values of each t and the P-values are also reported

Energy (keV) Aexpd (cpd/kg/keV) 2/d.o.f. P (%)

24 (2.0 2.1) 103 27.8/23 22 25 (1.4 1.6) 103 23.2/23 45 26 (1.0 1.3) 103 20.6/23 61 614 (5.0 7.5) 104 35.4/23 5

A d(cpd si d/kg/keV)

0.01

0

-0.01

0 2 4 6 8 10 12 14 16 18 20

Energy (keV)

Fig. 4 Diurnal modulation amplitudes, Ad, as function of energy (the energy bin is 1 keV) obtained by tting the single-hit residual rate of the entire DAMA/LIBRA-phase1 as function of the sidereal time, with the formula Ad cos[rot(t td)]. The amplitude Ad is a free parameter,

while the period is xed at 24 h and the phase at 14 h, as expected for the DM diurnal effect. The Ad values are compatible with zero, having random uctuations around zero with 2 equal to 19.5 for 18 degrees of freedom. The cumulative exposure is 1.04 ton year. See text

above). The Ad values are compatible with zero, having random uctuations around zero with 2 equal to 19.5 for 18 degrees of freedom.

In order to compare the experimental data with the DM diurnal effect due to the Earth rotation around its axis described in Sect. 2, the (26) keV energy interval is taken

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into account for simplicity. From Table 2 one can obtain Aexpd = (1.0 1.3) 103 cpd/kg/keV (2/d.o. f. =

20.6/23). Following the FeldmanCousins [26] procedure an upper limit can be obtained for the measured diurnal modulation amplitude: Aexpd < 1.2 103 cpd/kg/keV (90 %

C.L.); thus, the present experimental sensitivity is larger than the expected diurnal modulation amplitude ( 1.5

104 cpd/kg/keV) derived above from the DAMA/LIBRA-phase1 observed effect.

In conclusion, it will be possible to investigate this diurnal effect with adequate sensitivity only when a much larger exposure will be available, provided a suitable control of the running parameters at the needed level. On the other hand, better sensitivities can also be achieved by lowering the software energy threshold; in fact an almost exponential rising of the signal rate is expected at lower energy for some DM candidates. This is one of the goals of the presently running DAMA/LIBRA-phase2.

4.2 Comparison with any hypothetical diurnal effects with cosine behaviour

In order to leave to the reader the possibility to compare the data with possible exotic models, the experimental residual rates of the single-hit events as function of both solar and sidereal time have been compared with a cosine function with a free phase. For this purpose the residual rate for each energy bin of 1 keV has been tted with the formula Ad cos[rot(t

td)]. The free parameters of the t are the 18 modulation

amplitudes (one for each energy bin) and the phase td. The period is xed at 24 h. The results are reported in Fig. 5 for both solar and sidereal time cases.

The Ad values are compatible with zero, having random uctuations around zero with 2 equal to 24.2 and 25.4 (18 degrees of freedom) for the solar time and sidereal time, respectively. The best t values for the phase are td = (6.1

1.1) h and td = (10.7 1.1) h for the solar time and sidereal

time, respectively.

4.3 Comparison with possible diurnal effects induced by cosmic rays

Solar and sidereal diurnal modulation of the underground muon rate at LNGS have been searched for by the MACRO experiment computing hourly deviations of the muon rate from 6 month averages [27]. Statistically signicant diurnal modulations with the solar and the sidereal periods have been pointed out: their amplitudes are <0.1 %, at the limit of the detector statistics. The solar diurnal modulation is due to the diurnal atmospheric temperature variations at 20 km,i.e. the altitude of primary cosmic ray interactions with the atmosphere; the sidereal diurnal modulation is due to the

-0.02

0.02

A d(cpd sol/kg/keV)

0

0 2 4 6 8 10 12 14 16 18 20

Energy (keV)

A d(cpd si d/kg/keV)

-0.02

0.02

0

0 2 4 6 8 10 12 14 16 18 20

Energy (keV)

Fig. 5 Diurnal modulation amplitudes, Ad, as function of energy (the energy bin is 1 keV) obtained by tting the single-hit residual rate of the entire DAMA/LIBRA-phase1 with the formula Ad cos[rot(t td)].

The free parameters of the t are the 18 modulation amplitudes (one for each energy bin) and the phase td. The results are reported for the solar time (top) and sidereal time (bottom) cases. The Ad values are compatible with zero, having random uctuations around zero with 2 equal to 24.2 and 25.4 (18 degrees of freedom) for the solar time and sidereal time, respectively. The best t values for the phase are td = (6.1 1.1) h and td = (10.7 1.1) h for the solar time and

sidereal time, respectively. The cumulative exposure is 1.04 ton year.

See text

ComptonGetting modulation due to solar system motion relative to the local standard of rest.

Thus, we have estimated consistency of the result, obtained with the presently reached sensitivity, with these known effects. The measured single-hit event counting rate of DAMA/LIBRA-phase1 in the low energy region is of the order of 1 cpd/kg/keV [1] and, as shown in Ref. [6], the con

tribution due to muons surviving the Gran Sasso mountain or related particles is very small ( 1 cpd/kg/keV). Therefore,

the effect due to diurnal variation of muon ux is expected to be 103 cpd/kg/keV, that is well below the present exper

imental sensitivity (see e.g. the error bars in Fig. 2).

5 Conclusions

The low energy (26) keV single-hit data collected in the whole DAMA/LIBRA-phase1 (7 annual cycles; exposure:1.04 ton year) [24] have been analyzed in terms of diur

nal effects. At the present level of sensitivity the presence of any signicant diurnal variation and of diurnal time structures in the data can be excluded for both the cases of solar and sidereal time. In particular, the diurnal modulation ampli-

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tude expectedbecause of the Earth diurnal motionon the basis of the DAMA DM annual modulation results is below the present sensitivity; it will be possible to investigate this diurnal effect with adequate sensitivity only when a much larger exposure will be available, provided a suitable control of the running parameters at the needed level. At present DAMA/LIBRA is continuously running in its new conguration (named DAMA/LIBRA-phase2) with a lower software energy threshold [5] which also can offer an alternative possibility to increase sensitivity to such an effect.

Acknowledgments It is a pleasure to thank Mr. A. Bussolotti andA. Mattei for their qualied technical work.

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Funded by SCOAP3 / License Version CC BY 4.0.

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