Limits on cold dark matter from underground neutrinos

12 January 1995

PHYSICS LETTERS B ELSEVIER

Physics Letters B 342 (1995) 392-396

Limits on cold dark matter from underground neutrinos J.M. LoSecco The University of Notre Dame, Notre Dame, IN 46556, USA Received 21 September 1994; revised manuscript received 11 November 1994 Editor: L. Montanet

Abstract Limits on the flux of energetic neutrinos from the direction of the Sun are used to improve the limits on cold dark matter. The model of Olive and Srednicki is used to exclude a number of dark matter candidates including photinos, Higgsinos, Majorana neutrinos, massive Dirac neutrinos and sneutrinos. New limits are placed on photino and Higgsino masses. We also quote limits on fluxes from the Earth.

1. Introduction The presence of dark matter within the solar system has the potential to produce indirect signals leading to its detection. In particular the dark matter may be absorbed by the Earth and Sun where subsequent annihilations will produce an observable neutrino signal [ 1 ]. Some of these neutrinos will be produced directly in the annihilation and others result from the prompt decay of charm and beauty particles produced in the annihilation. If the flux of dark matter is large enough the resulting flux of neutrinos will be observable in terrestrial experiments. The only significant background to these terrestrial experiments, atmospheric neutrinos, is also a convenient normalizer. The atmospheric neutrinos are present and enter the detector from all directions. A source from the Sun would be localized. The experiment can search for evidence of dark matter by comparing the neutrino interaction rate for particles coming from the direction of the Sun with the interaction rate from all other directions [ 2]. Many effects such as the detector live time and angular resolution

can be removed by such a comparison. Atmospheric neutrinos result from cosmic ray interactions in the upper atmosphere. Secondaries from these reactions decay to produce muon and electron neutrinos. To a large extent these atmospheric neutrinos are a convenient normalizer since they are alway present and are fairly uniform. Calculations can than be done to predict the relative reaction rate of dark matter produced neutrino interactions to atmospheric neutrino interactions [2]. Limits on dark matter can simply be looked up as a function of limits on the relative rate of neutrinos from the Sun. We include the raw numbers in our report since the atmospheric flux model [ 3 ] may improve at some time in the future. In this note we employ the method of Olive and Srednicki [2] and the expanded IMB 1 plus IMB 3 data set to improve previous limits [4] on a number of forms of dark matter.

2. Method Since neutrinos are only weakly interacting a very large detector and a long exposure are needed to get

0370-2693/95/$09.50 (~) 1995 Elsevier Science B.V. All rights reserved SSDI 0 3 7 0 - 2 6 9 3 ( 9 4 ) 0 1 5 2 3 - 6

J.M. LoSecco / Physics Letters B 342 (1995) 392-396

a significant signal from any natural source. A number of very large particle physics detectors, primarily looking for evidence of proton decay have observed the atmospheric background. The atmospheric background is a flux of neutrinos anywhere in the Earth. These neutrinos are caused by cosmic ray interactions in the upper atmosphere. Fluxes of neutrinos from cold dark matter are expected to be of comparable size as the observed atmospheric neutrino rate. The atmospheric neutrinos present a nonremovable background to a search for neutrinos coming from dark matter. But rather than being a problem for the search they provide a very convenient normalizer. Neutrinos from dark matter annihilation would come from celestial bodies such as the Sun and Earth. The atmospheric neutrino flux is, to a large extent, isotropic. We can search for a a component of neutrino flux coming from the direction of known celestial objects. The ambient flux, from all other directions, can be used to normalize the observations. Olive and Srednicki [2] have calculated the expected signal in terms of the ratio of excess flux from the direction of the Sun to the ambient flux. The ambient flux is a good normalizer. Detector lifetime and efficiency affect both the signal, from the Sun, and the background, from the atmosphere, so many detector details drop out of the ratio. They [2] define r90 to be the 90% confidence level upper limit on the ratio of neutrino interactions from the Sun to interactions due to the atmospheric background. The IMB detector is an 8000 metric ton imaging water Cherenkov detector located about 650 m underground near Cleveland, OH [4]. The detector records two major classes of data. Contained interaction come from interactions within the detector, such as neutrino interactions or proton decays. Upward muons come from energetic muon neutrino interactions in the rock below the detector. Only upward muons are collected, as neutrino interactions, since there is still a large flux of muons penetrating from the surface. For both of these samples the direction of the neutrino and the time of the interaction can be determined. In addition, for the contained interactions the visible energy is measured. The visible energy is the energy of an electromagnetic shower producing the equivalent Cherenkov light output. We have used an approximate expression to convert these visible energies into neutrino energies. These two classes of data span two different energy

125

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393

I ....

I ....

I

. . . .

100 >

75

~

5o 25 B, 0

B

500

1000 1500 Energy(MeV)

2000

2500

Fig. 1. The neutrino energy spectra for single prong contained neutrino interactions.

ranges and have different angular resolutions. The upward muons must come from muon neutrinos with energies in excess of 2 GeV. At these high energies the direction of the muon is fairly well correlated with the direction of the initial direction of the neutrino. Previous studies [ 5 ] have shown that a reconstruction angular resolution of about 4.6 ° is achieved for these data. An angular cut of about 7 ° optimizes the signal to noise from a compact source. Neutrinos from the Sun will always qualify as a compact source. Some sources in the Earth could have a diameter in excess of 108 cm and be underestimated by this analysis. Our sample consists of 651 events. In our analysis we have compared the number of events from within 7 ° of a celestial object with the total number. This corresponds to 0.37% of the total solid angle for searches from the Sun. Since we only sample from the lower hemisphere, and the Earth does not move relative to this cut it represents 0.75% of the total solid angle for searches from the Earth. The contained events, in general, come from much lower energy neutrino interactions. Fig. 1 is a plot of the neutrino energy for all contained single prong events. The plot indicates the peak rate is for events with energies of about 600 MeV. Dark matter will tend to produce events at high energies. In particular Olive and Srednicki [2] have calculated the expected rate for contained events in the energy ranges 1-2 GeV and above 2 GeV. From the figure it can be seen that only 206 single prong contained events have been found with energies above 1 GeV. 24 events have been found with energies above 2 GeV. Our sample consists of 677 single prong events

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J.M. LoSecco / Physics Letters B 342 (1995) 392-396

Table 1 Neutrinos from the Sun Case

Energy range

Total events

Angular cut

Events near the Sun

Poisson probability

r90

90% CL upper limits

case I case 2 case 3

Eu > 0 1 GeV < Eu < 2 GeV upward muons Ev > 2 GeV

677 182 651 24

30 ° 30 ° 7° 30 °

54 11 4 2

0.090 0.560 0.099 0.219

0.031 0.036 0.009 0.184

19.84 6.20 5.78 4.08

chosen from a sample of 887 contained interactions. Single prong events are chosen since they preserve the original neutrino direction better than the multitrack events. The angular resolution is energy dependent but is about 30 °. We use a cut of 30 ° which is quite reasonable at the energies considered for cases 1 and 3. This corresponds to 6.7% of the solid angle.

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3. Limits To get a bound on the ratio of the excess neutrino flux attributable to dark matter to the atmospheric flux we measure the number of events coming from near the Sun and compare it to the total number of events collected from all directions in the same energy range. These two numbers can be turned into a 90% confidence limit upper limit on the ratio of excess flux to atmospheric flux using a formula given in Olive and Srednicki [2]. The method assumes that the two measurements are Poisson distributed and the atmospheric flux is well measured by the large solid angle off source. Fig. 2 is a plot of the energy distribution for all contained events within 30 ° of the Sun. Fig. 3 is a similar plot for events that are within 30 ° of the upward going vertical. These upward events could be coming from sources within the Earth. Table 1 lists the data for the 3 cases considered by Olive and Srednicki [2] and for the entire contained event single prong sample. Case 1 is neutrinos in the energy range 1 GeV < Ep < 2 GeV. Case 2 is upward going muons with energies in excess of 2 GeV. Case 3 is contained events with energies in excess of 2 GeV. Cases 2 and 3 rule out all masses of Majorana or Dirac neutrinos. Case 3 rules out all masses of scalar electron and muon neutrinos. Case 2 excludes photino masses

....

10

0

500

1000 1500 Energy(MeV)

2000

2500

Fig. 2. The neutrino energy spectra for single prong contained neutrino interactions within 30 ° of the Sun.

15

>

lO

0

500

1000 1500 Energy(MeV)

2000

2500

Fig. 3. The neutrino energy spectra for single prong contained neutrino interactions within 30 ° of the Earth.

of less than about 18 GeV and Higgsino masses of less than 10 GeV. Included in Table 1 is the Poisson probability of getting a background fluctuation of this magnitude or greater and a 90% confidence level upper limit on the number of excess events coming from a possible source calculated by the method of Helene [6].

J.M. LoSecco / Physics Letters B 342 (1995) 392-396

395

Table 2 Neutrinos from the Earth

Case

Energy range

Total events

Angular cut

Events near the Earth

Poisson probability

r90

90% CL upper limits

case 1 case 2 case 3

Eu> 0 I GeV < E u < 2 GeV upward muons Eu > 2 G e V

677 182 651 24

30 ° 30 ° 7° 30 °

42 7 6 1

0.656 0.919 0.217 0.219

0.015 0.023 0.010 0.134

10.34 4.22 6.20 3.12

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0.9

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0.95 Cosine

Fig. 4. The angular distribution of upward muons near the Sun. Cosine of 1 is coming from the Sun.

Fig. 5. The angular distribution of upward muons near the Earth. Cosine of 1 is coming from the Earth.

In Table 2 we have carried out a similar analysis for events coming from the direction of the Earth. There is no calculation of the significance of these r90 limits. The calculation of r90 for upward going muons from sources in the Earth deviates slightly from the prescription given in Olive and Srednicki [2]. For one thing the fraction of solid angle subtended by the source is double what it is for the other searches. This is not relevant for searches from the Sun since the Sun spends equal times above and below the horizon when averaged over a year. Another problem comes from the fact that the distribution of upward muons is not uniform in cosine of the local zenith angle. The larger decay path length available near the horizon increases the flux somewhat in this direction. There is no problem near vertical. As a gauge of the non uniformity we have plotted the cosine of the angular distribution for upward muons near vertical in Fig. 5. (The distribution about the direction of the Sun is shown in Fig. 4.) This nonuniformity tends to slightly overestimate the background to any upward muon signal and so tends to reduce the

signal. We can recalculate r90 for upward muons near the vertical if we normalize to the 66 events in Fig. 5. There are then 6 events within 7 ° of the vertical out of 66 within 31.8 °. This gives r90 = 0.122 (the ratio of fluxes in only this solid angle), a Poisson probability of 0.050 and a 90% confidence level upper limit on the excess flux of 7.37. This r90 value can be scaled to give r90 = 0.006 relative to an atmospheric background from a full 4~r solid angle. Please note that by normalizing to the near vertical flux and not the total the mean background estimate has dropped to 3.28 from the value of 4.85 if we had normalized to the entire hemisphere. These data can also be used to place limits on neutralino dark matter in the context of the minimal supersymmetric model [7]. The model predicts a neutrino flux as a function of 3 mass parameters and several parameters relating to the local velocity and density of these particles. For some of these parameters the source size may be large compared to the detector resolution. The number of events in a series of angular cuts near the vertical is summarized in Table 3 and

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J.M. LoSecco / Physics Letters B 342 (1995) 392-396

Table 3 Upward muons from the Earth Angular cut

Events near the Earth

Poisson probability

r90

90% CL upper limits

7 10 15 20 25 30

6 I1 15 29 46 62

0.217 0.291 0.928 0.945 0.972 0.997

0.010 0.012 0.008 0.010 0.011 0.011

6.20 7.39 5.19 6.49 7.27 6.86

We would like to thank Morton International for the use of their Fairport mine and Keith Olive for helpful discussions.

References

m a y be used in these cases where Table 2 does not apply. The w a r n i n g s o f the previous paragraph apply to to Table 3. The calculation o f detailed limits based on these data is b e y o n d the scope o f this paper.

Acknowledgements

This work was supported in part by the U.S. D e p a r t m e n t o f E n e r g y under contract D E - A C 0 2 8 7 E R 4 0 3 6 6 . A 0 0 3 and grant D E - F G 0 2 - 9 1 E R 4 0 6 2 3 .

[ 1] J. Silk, K. Olive and M. Srednicki, Phys. Rev. Lett. 55 (1985) 257; a useful reference is M. Srednicki, ed., Current Physics - Sources and Comments, Vol. 6, Particle Physics and Cosmology: Dark Matter (North-Holland, Amsterdam, 1990). [2] K. Olive and M. Srednicki, Phys. Lett. B 205 (1988) 553. [31 L.V. Volkova, Sov. J. Nucl. Phys. 31 (1980) 784. [4] J. LoSecco et al., Phys. Lett. B 188 (1987) 388. [5] R. Svoboda et al., Astrophys. J. 315 (1987) 420; R. Becker-Szendy et al., Phys. Rev. Lett. 69 (1992) 1010; Phys. Rev. D 47 (1993) 4203. [6] O. Helene, Nucl. Instrum. Methods A 212 (1983) 319. [7] M. Mori et al., Phys. Lett. B 270 (1991) 89; Phys. Rev. D 48 (1993) 5505.