The Dark Matter Problem...Tomás Cruz, N.º 65725 & Luís Cebola, N.º 65701 Modulation amplitude Maximum likelihood method + Releasing the assumption of a phase t0 =152.5 day Y m,k

Article 14: First results from DAMA/LIBRA and the combined results with DAMA/NaI.

Tomás Cruz, N.º 65725 & Luís Cebola, N.º 65701

The Dark Matter Problem.

Evidence of existence of dark matter in the universe.

• The LMC spins around our galaxy faster than expected in case only

luminous matter would be present.

• The observation of X-Ray emitting gases surrounding elliptical galaxies.

• The velocity distribution of hot intergalactic plasma in clusters.

Nature of Dark Matter.

• MACHOs.

• Neutrinos.

• Black Holes.

• WIMPs.



Dark Matter annual modulation signature.

• Model independent approach.

is the local Dark Matter velocity.

Since , the expecting counting rate in first order.

Averaging this expression in a k-th energy interval:



Properties of Dark Matter annual modulation signature.

• The rate must contain a component modulated according to a cosine function.

• One year period.

• Phase that peaks roughly around 2nd June.

• Low Energy Range, where WIMP induced recoils can be present.

• Just one detector should fire, WIMP multiple scattering negligible.

• The amplitude modulation in maximal sensitivity must be



Set up requirements.

• Suitable deep underground site to reduce at most the background contribution

from cosmic rays;

• Suitable low background hard shield against electromagnetic and neutron

background;

• Deep selection of low background materials and a suitable identification of

radio-purification techniques to build a low background set-up;

• Effective Radon removal system and control on the environment nearby the

detectors;

• Good model independent signature;



Experimental set-up.





Energy threshold

Eliminate :

• PMT noise;

• Cherenkov light;

(Near the energy

threshold in the

single-hit events)

Noise is practically absent in the multiple-hit events P < 3 × 10−6

Energy threshold of the experiment - 2 keV

Results:





Residual rates and fits

<rijk – flatjk>jk

• rijk - rate i-th time interval for the j-th detector in the k-th energy bin

• flatjk - rate of the j-th detector in the k-th energy bin averaged over the cycles






• χ2/d.o.f. of the best fit of the (2–6) keV is 53.2/64

• Function: Acosω(t –t0)






Fourier analysis

• (2–6) keV (solid lines)

• (6–14) keV (dotted lines)



Various energy intervals

Lowest energy region:

• Compton electrons

• X-rays and/or Auger electrons

• Muon induced events

• Etc…

Events on the higher

energy part of the spectrum



Multiple-hits residual rate

• DM signal can be present just in

the single-hit residual rate

• Single-hit events (open circles)

• Multiple-hits events (filled triangles)

−(0.0004 ± 0.0008) cpd/kg/keV (2-4) keV

−(0.0005 ± 0.0007) cpd/kg/keV (2-5) keV

−(0.0004±0.0006) cpd/kg/keV (2-6) keV

Multiple-hits events amplitude:





Modulation amplitude

Maximum likelihood method:

• (6–20) keV - random

fluctuations around zero with

χ2/d.o.f. equal to 24.4/28.

Mean χ2/d.o.f. - 1.072 > 1

• possible systematics

Additional error:

• ≤ 5 × 10-4 cpd/kg/keV (quadratically)

• ≤ 7 × 10-5 cpd/kg/keV (linearly)

• ≤ 4.7% (quadratically)

• ≤ 0.7% (linearly)

Upper limit of possible systematic effects (on modulation amplitude)





Modulation amplitude

Maximum likelihood

method + Releasing the

assumption of a phase t0

=152.5 day

Ym,k cosω(ti –t*), or

Sm,k cosω(ti –t0) +

Zm,k sinω(ti –t0)

Fit values: (2–6) keV

• Sm,k = (0.0122 ± 0.0016) cpd/kg/keV;

• Zm,k = −(0.0019 ± 0.0017) cpd/kg/keV;

• Ym,k = (0.0123 ± 0.0016) cpd/kg/keV;

• t∗ = (144.0 ± 7.5) day;

Fit values: (6–14) keV

• Sm,k = (0.0005 ± 0.0010) cpd/kg/keV;

• Zm,k = (0.0011 ± 0.0012) cpd/kg/keV;

• Ym,k = (0.0012 ± 0.0011) cpd/kg/keV;

• t∗ obviously not determined.



Investigation on possible systematic effects and side reactions:

The Temperature:

• Full experiment is placed underground and works in an air conditioned environment.

• Multi tons metallic passive shield with huge heat capacity assures stability.

• Operating temperature is read and stored with the data.

• Mean RMS operating temperature 0.04 ºC

The maximum mod. amplitude is

that is less than of the observed modulation

amplitude.



The Background.

Neutrons.

Radon.

Side processes.

• Flux of thermal neutrons that survive the shield.

• Flux of fast neutrons that survive the shield.

• Radon can exists in the HP nitrogen atmosphere

• Percentage variations shows a cumulative

Gaussian behavior with

• Hypothetical muon flux modulation correlated to the

temperature atmosphere.

• Solar neutrinos modulation.



The Noise.

The Calibration factor and the efficiencies.

The hardware rate is significantly determined by the noise.

• In long term running conditions, periodical calibrations

were performed every 10 days.

• The energy calibration factor for each detector is known

with an uncertainty much less than 1% during data taking.

• Time behavior of efficiencies show no modulation at all.



Conclusion on possible systematic effects.

No modulation have been found in any of the possible sources of systematic or side

reactions studied. In particular, they cannot account for the measured modulation.



Conclusions.

• The model independent results achieved confirms evidence of Dark

Matter particles in the galactic halo with high confidence level.

• Considering the data from the former DAMA/NaI experiment and the

data from DAMA/LIBRA together, can be obtained a cumulative CL of

• The analysis made exclude the effect from the temperature, noise,

hardware or software procedures, background including Radon, neutrons

and cosmic rays.

Prospects for the future.

• Model dependent considerations will be presented devoted to this aspect.

• Collection of a larger exposure will allow to improve information that can

be used to derive the nature of the candidate particle and on various related

astrophysical, nuclear and particle physics scenarios.



References:

[1] R. Bernabei et al., Eur. Phys. J. C (2008) 56: 333–355

[2] R. Bernabei et al., Riv. Nuovo Cimento 26(1), 1–73 (2003)

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The Dark Matter Problem...Tomás Cruz, N.º 65725 & Luís Cebola, N.º 65701 Modulation amplitude Maximum likelihood method + Releasing the assumption of a phase t0 =152.5 day Y m,k