Bounds on Dark Matter from the ``Atmospheric Neutrino Anomaly''
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UNDPDK-97-01Bounds on Dark Matter from the “Atmospheric Neutrino Anomaly”J.M.LoSecco University of Notre Dame,Notre Dame,Indiana 46556(April 151997)Abstract Bounds are derived on the cross section,?ux and energy density of new par-ticles that may be responsible for the atmospheric neutrino anomaly.4.6×10?45cm 2<σ<2.4×10?34cm 2Decay of primordial homogeneous dark matter can be excluded.Subject headings:Cosmology —Elementary Particles —Dark Matter
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The atmospheric neutrino anomaly[1–3]refers to indications that the ratio of muon neutrinos to electron neutrinos observed in underground detectors is signi?cantly less than expected.Expectations are based on calculations of neutrino?uxes derived from pions produced by primary cosmic ray interactions in the upper atmosphere.Since the earth’s atmosphere is not particularly dense the pions decay to produce muons and neutrinos and a good fraction of the muons also decay to produce neutrinos.Estimates based on detailed production models put the ratio of muon neutrino?ux to electron neutrino?ux close to2 [4].The overall normalization of these models is uncertain and so,it is the ratio for which one has the highest con?dence.
The most popular explanation for the de?ciency is that neutrino oscillations have con-verted some of the muon neutrinos to some other type so that the muon neutrino?ux observed is much closer to the electron neutrino?ux.The neutrino oscillation hypothesis has failed to be con?rmed by a number of experiments[5,6]that use other,independent por-tions of the atmospheric neutrino spectrum.But these results themselves are at odds with the Kamioka multi GeV results[7].While the oscillation hypothesis can not be completely ruled out it is reasonable to seek alternative explanations for the observations.
These experiments are sensitive to extremely low energy densities,which have never been probed before.Since there is no way to tell whether the observed signal is actually attributable to neutrinos,nor if they are neutrinos if they are produced in the atmosphere it is prudent to consider other possible alternatives.In particular a?ux of any particle that interacts in a way that does not produce the distinctive energetic muon in the?nal state would contribute to an increase in the relative rates of observed“electron”like events to muon neutrino induced events.
This note explores a number of constraints that can be placed on sources of non muon type interactions in underground detectors.
These events are observed in deep underground detectors.This means that whatever is producing them must have penetrated the earth(or have been present in the detector beforehand).There is no evidence for any directional dependence to the event rates so that the upward going?ux must be comparable to that from all other directions.The interaction length must be comparable to the earth’s diameter,or greater.
1
L=
component this enhancement must account for from20%to30%of all of the observed events. The event rate in a3.3kiloton water detector is about1event per day[8],which is about R=5.8×10?39events/second/Nucleon.This yields a?ux limit of
F DM>P R/σ
where P is the fraction of all events attributable to new physics and F DM is the?ux of new (dark)matter.
Here any possible nuclear shadowing has been neglected.It is assumed that all of the target nucleons available for neutrino interactions are available for this new interaction too. While one might argue that the lack of a signi?cant observed atmospheric neutrino anomaly in iron detectors[9]might imply some shadowing in the heavier iron nucleus the upper bound we have found for the cross section,in the earth,makes this unlikely.
The limit on?ux obtained from these arguments is F DM>P×2.4×10?5 particles/cm2/second.With P=0.25this is F DM>6×10?6particles/cm2/second.
Recall that the?ux is inversely proportional to the cross section.These additional particles could be electron neutrinos that are not of atmospheric https://www.wendangku.net/doc/b53246204.html,ing an average neutrino cross section ofσνe=3.4×10?39cm2,
Only a lower bound on the?ux of new particles can be obtained from this argument since if it is a new interaction of a new particle the cross section is not known.
IV.ENERGY DENSITY
A continuous?ux of new particles would indicate the presence of an energy density.The energy density can be estimated from
?=F DM
where
detector is usually a fraction of the energy of the incident particle.Forνe interactions the visible energy is equal to the energy of the electromagnetic shower produced but on average this is only1/2of the neutrino energy.The observed visible energy distribution of the excess events seems to be?at below about600MeV[10].We will take
x MeV/cm3.This is about4×10?19P
MeV is conservative.It is possible that the anomaly does
x
not extend to higher energies.Even if the evidence presented in reference[7]is correct the mean energy of the?ux will only be higher.Higher mean energies for this“dark matter”would lead to tighter bounds than those presented here.It is possible that if the new matter responsible for the anomaly has a cross section that drops rapidly with energy there could be considerably more of it present than as sampled by the observed e?https://www.wendangku.net/doc/b53246204.html,ing a,possibly low,energy estimate based on observations makes the limits obtained conservative.
V.CROSS SECTION LOWER BOUND
Given a bound on the energy density of the universe we can get a lower limit on the cross section if this energy density is manifesting itself via these excess underground events.The
relationship between energy density and cross section can be summarized by?=P R
v where R is the number of events observed per nucleon per second,P is the fraction of events attributable to the new particle,σis the interaction cross section,
One can expect an upper bound on the energy density to be enough to close the universe,
?closure.Under these conditions one?ndsσmin>P R
v
With?closure=10?8ergs/cm3 [11,12]this yieldsσmin>4.6×10?45cm2/Nucleon for P=0.25,
A crude?ux bound can be obtained from some of these ideas.It is dependent only on the observed energy and the closure bound on energy density.
F DM
To be conservative we take v=c and
VI.DECAYS
It is possible that the excess events observed as the anomaly come from the decay of particles in the detector rather than interactions with an ambient?ux.This hypothesis is attractive since the anomaly is not con?rmed by dense detectors but only by the relatively low density water detectors.Neutrino interactions(and proton decay)should depend of the ?ducial mass of the device.But if one is observing the decay of an ambient dark matter?ux the rate should depend on the volume of the detector and not its mass.The low density water detectors observe a signi?cantly large volume,by a factor of3to4relative to the mass viewed.So the anomalous fraction of decay events found in dense detectors should be greatly suppressed relative to neutrino interactions.
The observed decay rate should be R u=ρN V
τ=
?
V
?
V
Here
(
?
τ<
?closure
The decay of a primordial homogeneous component can be ruled out.The absence of any apparent point sources,in terrestrial or celestial coordinates,in the data implies either a di?use local source,or a cosmological one.It is di?cult to understand how natural processes could populate the several hundred MeV energy region with electron neutrinos or other penetrating particles.
ACKNOWLEDGEMENTS
I would like to thank John Poirier for comments on the manuscript.
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