Atmospheric Neutrinos

11 Pages·0.36 MB·

by  F. Ronga

Atmospheric neutrinos
F. Ronga a
a INFN LaboratoriNazionali di Frascati,
P.O. Box 13 I-00044 Frascati Italy
The results of experiments on atmospheric neutrinos are summarized, with the important exception of Su-
perkamiokande. The main emphasis is given to the Soudan-2 and MACRO experiments. Both experiments
observe atmospheric neutrino anomalies in agreement with νµ → ντ oscillations with maximum mixing. The
νµ→νs oscillation is disfavored bythe MACRO experiment.
0
0
0 1. INTRODUCTION NUSEX[6] (in the Mont Blanc tunnel between
2 France and Italy) and Frejus[7] (in another tun-
Atmospheric neutrinos are produced in the nel under the Alps) andthere wasthe suggestion
n
cascade originated in the atmosphere by a pri-
a that the anomaly was due to the differences in
J mary cosmic ray. Underground detection of at- the neutrino cross sections in water and in iron
mosphericneutrino-inducedeventswaspioneered
7 not taken into account in the Fermi gas model
2 by the Kolar Gold Field KGF[1] experiment in
usedintheoriginalcalculations. Acalculationby
India and the CWI2[2] experiment in a mine
Engel[8]showedthatthiseffectshouldbenegligi-
1 in South Africa. The field gained new interest
v ble for the energies of interest. Later, the results
when the large underground detectors for pro-
8 from another fine-grained iron detector Soudan-
ton decay experiments were put in operation. At
5 2[9]haveshownthatprobablythere wasa statis-
0 the beginning atmospheric neutrinos were stud- tical fluctuation in the NUSEX and Frejus data.
1 ied mainly as possible sourcesof backgroundsfor
In 1994 another anomaly was observed by the
0 proton decay searches. But very soon, the wa-
Kamiokande experiments[10]: the distortion of
0
ter Cherenkov experiments, IMB in the United
0 the angular distribution of the events with a sin-
StatesandKamiokandeinJapan,discoveredthat
/ gle muon in the so-called internally produced
x the ratio between events with a muon and those
e Multi-GeV data sample with a reduction of the
with an electron was lower than expected.
- flux of the vertical up-going events.
p The first historical observation of the anomaly
Therewereseveralattemptstolookforpossible
e
was in 1986 in the IMB paper ”Calculation of
h angular distortion in other categories of events,
AtmosphericNeutrino-InducedBackgroundsin a
: for example in the neutrino externally produced
v Nucleon Decay Search”[3]. It was observed in
upward-going muons. Results were produced at
i
X this paper that ”The simulation predicts that
that time by the IMB experiment[11], the Bak-
34% 1% of the events should have an identified
r ± san[12]experimentinURSSandtheKamiokande
a muon decay while our data has 24% 3%”. The
± experiment itself[13]. The results were inconclu-
importance of this discrepancy as possible signa-
sive or in contradiction with the neutrino oscil-
ture for neutrino oscillations in the path length
lation hypothesis, particularly for what concerns
between the production point and the detector
theanalysisofthestoppingmuon/through-going
(in the range 10 -13000 km) was not fully rec-
muon ratio in the IMB experiment[11] .
ognized at the beginning. In 1988[5] there was
The MACRO tracking experiment in the Gran
the first paper by the Kamiokande collaboration
Sassolaboratorybegantheoperationforneutrino
dedicatedtothisanomalyfollowedbytwopapers
physics in 1989 with a small fraction of the final
from the IMB collaboration[4].
detector. ThefirstresultsofMACRO[14]in1995
However, this anomaly was not confirmed by
showedthatthere wasa deficit ofevents particu-
the proton decay iron fine-grained experiments
larlyintheverticaldirection. Howeverthestatis-
tics was not enough at that time to discriminate
unambiguously between the oscillation and the
no-oscillation hypothesis.
Another big step forward in this field was due
to the Superkamiokande experiment. In 1998
at the Takayama Neutrino conference there was
the announcement of the observation of neu-
trinooscillation(ν disappearance)fromtheSu-
µ
perkamiokande experiment. It is notable that, at
the same conference, the two other running ex-
perimentsSoudan-2andMACROhavepresented
results in strong support of the same ν oscilla-
µ
tions pattern observed by SuperKamiokande[15].
2. NEUTRINO OSCILLATIONS AND
MATTER EFFECT
Neutrino oscillations[16] were suggested by B.
Pontecorvo in 1957 after the discovery of the
Figure 1. Sketch of the atmospheric neutrino pro-
K0 K0 transitions.
↔ duction in the atmosphere and of the detection in
If neutrinos have masses, then a neutrino of
an underground detetector. L is the neutrino path
definite flavor,ν ,isnotnecessarilyamasseigen-
ℓ length and θ is the zenith angle.
state. Inanalogytothequarksectortheν could
ℓ
be a coherent superposition of mass eigenstates.
The fact that a neutrino of definite flavor is a
there is a difference in the interactionsofthe two
superposition of several mass eigenstates, whose
neutrino flavors with matter[18].
differingmassesM causethemtopropagatedif-
m The neutrino weak potential in matter is:
ferently,leadstoneutrinooscillations: thetrans-
formation in vacuum of a neutrino of one fla- GFnB −2Yn+4Ye for νe,
vor into one of a different flavor as the neutrino Vweak = 2Yn for νµ,τ, (3)
moves through empty space. The amplitude for ± 2√2 ×(0− for νs,
the transformation νℓ →νℓ′ is given by: wheretheuppersignreferstoneutrinos,thelower
A(νℓ →νℓ′)= Uℓme−iM2m2 ELUℓ∗′m (1) sniBgnthtoebaanrtyinoenudtreinnsoitsy,,GYFn tihsethneeuFterromniancodnYsetatnhte,
Xm electron number per baryon (both about 1/2 in
whereU isa3 3unitarymatrixinthehypothesis normal matter). Numerically we have
×
of the 3 standard neutrino flavors (ν ,ν ,ν ). In
µ e τ G n ρ
thehypothesisofasterileneutrino[17]U isa4 4 F B =1.9 10−14 eV . (4)
× 2√2 × g cm−3
unitary matrix.
The probability P(νℓ νℓ′) for a neutrino of The weak potential in matter produces a phase
→
flavor ℓ to oscillate in vacuum into one of flavor shift that could modify the neutrino oscillation
ℓ′ is then just the square of this amplitude. For pattern if the oscillating neutrinos have differ-
two neutrino oscillations and in vacuum: ent interactions with matter. The matter effect
could help to discriminate between different neu-
L
P(νℓ νℓ′6=ℓ)=sin22θ sin2 1.27δM2 (2) trino channels. Accordingto equation3 the mat-
→ E
(cid:20) (cid:21) ter effect in the Earth could be important for
δM2(eV2),L(km),E(GeV) νµ νeandfortheνµ νsoscillations,whilefor
→ →
ν ν oscillationsthereisnomattereffect. For
µ τ
→
This simple relation should be modified when some particular values of the oscillation parame-
a neutrino propagates through matter and when ters the matter effect could enhance the oscilla-
Baksan
IMB
Figure3. Measurementsoftheatmosphericneutrino
flavor ratio[23].
Figure 2. Rate of cosmic rays as function of the
range of neutrino energies involved goes from a
depthrelative to the Gran Sasso Laboratory.
fraction of GeV up to 10 GeV or more. Both
electronneutrinosandmuon-neutrinoscanbede-
tected. Theexternallyproducedeventshaveneu-
tions originating ”resonances” (MSW effect)[18]. trino interactionvertex in the rock below the de-
The internal structure of the Earth could have tector. Typical neutrino energies involved are of
an important role in the resonance pattern [19]. the order of 100 GeV. Only muon neutrinos can
However,for maximum mixing, the only possible be detected. Figure 1 shows the basic geometri-
effect is the reductionofthe amplitude of oscilla- cal factors of the neutrino production and detec-
tions. tion in an underground detector.
The neutrino events could have background
3. ATMOSPHERIC NEUTRINOS connectedwiththeproductionofhadronsbypho-
toproductionduetothedown-goingmuons. This
Inthehadroniccascadeproducedfromthepri- background has been measured by the MACRO
mary cosmic ray we have the production of neu- experiment[21]. Thephotoproducedneutronscan
trinos with the following basic scheme : simulate internal events and the pions can simu-
P+N π+K.. late stopping or through-going muons. The rate
−→
π/k µ+(µ−)+ν (ν ) of this background depends on the rate of the
µ µ
−→
µ+(µ−) e+(e−)+ν (ν )+ν (ν ) down-going muons and therefore on the depth.
e e µ µ
−→
From these decay channels one expects at low As it his shown in Figure 2 this effect could be
energies about twice muon neutrinos respect to important for detectors of shallow depth and it
electron neutrinos. This result doesn’t change could be one of the reason for some past results
very much with a detailed calculation. The cal- in contradiction with the current oscillation sce-
culationof the absolute neutrino fluxes is a more nario.
complicated matter, with several sources of un-
certainty[20] due to the complicated shower de- 4. THE SOUDAN-2 EXPERIMENT
velopmentintheatmosphereandtothelargeun-
certainties in the cosmic ray spectrum. TheresultsoftheSoudan-2experimentaredis-
There are two basic topologies of neutrino in- cussed in detail in another talk at this confer-
duced events in a detector: internally produced ence[22]. Here I want to stress the importance of
events and externally produced events. The in- this experiment for the Sub-GeV events (events
ternally produced events have neutrino interac- having energies of the order of 1 GeV or less)
tion vertices inside the detector. In this case all where a possible contradiction between the iron
thesecondariescanbeinprincipleobserved. The sampling calorimeters and the water Cherenkov
detector was suggested in the past. Figure 3
showsthecurrentexperimentalsituationtogether
with the new results of Soudan-2[23][24]with 4.6
Ktons/year of data.
Recently the Soudan-2 group has been able to
study the L/Edistributionfora sampleofevents
selected to have an high energy resolution. The
distributions are shown in Figure 4. After back-
ground subtraction they have 90.5 ν CC events
µ
and 116.4 ν CC (153.6 predicted) events.
e
Due to the nuclear effects and to the limited
statistics it is not possible to see the sinusoidal
pattern of equation (2) with the first minimum
at Log(L) = 2.5 predicted in the case of oscilla-
E
tions with δm2 3 10−3eV2. One of the main
∼ ×
goal of the next generationatmospheric neutrino
experiments is the measurement of this pattern
that could provide a precise measurement of the
oscillation parameters and a way to discriminate
alternative hypothesis with neutrino decays[25].
However, from the study of the χ2 of the L/E Figure 4. L distribution for the Soudan-2 experi-
E
distribution as function of the oscillation param- ment[23][22]. Top: νe with data normalized to the
eters the Soudan-2 group has been able to set a prediction. Bottom : νµ with normalization taken
90% confidence region for the oscillation param- from νe.
eters, reported together with the other experi-
ments in figure 12. The best χ2 is for δm2 =
0.8 10−2eV2 and sin22θ =0.95.
×
Soudan-2 measures a flux of νe neutrinos The Up Through tracks come from νµ inter-
smaller than the one expected (with an old ver- actions in the rock below MACRO. The muon
sion of the Bartol flux), while SuperKamiokande crosses the whole detector (Eµ > 1 GeV). The
has agreement between predictions and data. time information provided by scintillator coun-
Thisdisagreementcouldbedueortoastatistical terspermitstoknowtheflightdirection(time-of-
fluctuation or to some physical effect due to the flight method). The typical neutrino energy for
differentgeomagneticcutsortodifferencesinthe this kind of events is of the order of 100 GeV.
neutrino samples (Soudan-2 accepts events with The data have been collected in three periods,
a smaller energy and accepts multiprong events). with different detector configurations starting in
1989 with a small fraction of the apparatus.
5. NEUTRINO DETECTION IN THE The Internal Up events come from ν interac-
MACRO EXPERIMENT tions inside the apparatus. Since two scintillator
layers are intercepted, the time-of-flight method
The MACRO detector is described else- is applied to identify the upward going events.
where[14][30]. Active elements are streamer tube Thetypicalneutrinoenergyforthiskindofevents
chambersusedfor trackingandliquidscintillator is around 4 GeV. If the atmospheric neutrino
counters used for the time measurement. anomalies are the result of ν oscillations with
µ
Figure 5 shows a schematic plot of the three maximum mixing and ∆m2 between 10−3 eV2
different topologies of neutrino events analyzed and 10−2 eV2 it is expected a reduction in the
up to now: Up Through events, Internal Up fluxofthiskindofeventsofaboutafactoroftwo,
eventsandInternalDowntogetherwithUpStop withoutanydistortionintheshapeoftheangular
events. The requirementof a reconstructedtrack distribution. Onlythedatacollectedwiththefull
selects events having a muon. MACRO (live-time around 4.1 years) have been
similar to the one expected for the Internal Up.
6. UPWARD THROUGH-GOING
MUONS
The direction that muons travel through
MACRO is determined by the time-of-flight be-
tweentwodifferentlayersofscintillatorcounters.
The measured muon velocity is calculated with
the convention that muons going down through
the detector are expected to have 1/β near +1
while muons going up through the detector are
expected to have 1/β near -1.
Several cuts are imposed to remove back-
grounds caused by radioactivity or showering
events which may result in bad time reconstruc-
tion. The most important cut requires that the
position of a muon hit in each scintillator as de-
termined from the timing within the scintillator
counter agrees within 70 cm with the position
±
indicated by the streamer tube track.
In order to reduce the background due to the
photoproduced pions each upgoing muon must
cross at least 200 g/cm2 of material in the bot-
Figure 5. Sketch of different event topologies in- tom half of the detector. Finally, a large number
ducedbyneutrinointeractionsinoraroundMACRO of nearly horizontal (cosθ > 0.1), but upgoing
(see text). In the figure, thestars represent thescin- muons have been observed co−ming from azimuth
tillator hits. The time of flight of theparticle can be
angles corresponding to a direction containing a
measuredonlyfortheInternal UpandUpThrough
cliff in the mountain where the overburden is in-
events.
sufficient toremovenearlyhorizontal,downgoing
muons whichhavescatteredinthe mountainand
appear as upgoing. This region is excluded from
used in this analysis. both the observation and Monte-Carlo calcula-
The Up Stop and the Internal Down events tion of the upgoing events.
are due to external interactions with upward- There are 561 events in the range 1.25 <
−
going tracks stopping in the detector (Up Stop) 1/β < 0.75 defined as upgoing muons for this
−
and to neutrino induced downgoing tracks with data set. These data are combined with the pre-
vertex in the lower part of MACRO (Internal viously published data [14] for a total of 642 up-
Down). These events are identified by means of going events. Based on the events outside the
topologicalcriteria. The lackoftime information upgoing muon peak, it is estimated there are
preventsto distinguishthe twosubsamples. The 12.5 6 background events in the total data set.
±
datasetusedforthisanalysisisthesameusedfor In addition to these events, there are 10.5 4
±
the Internal Up search. An almost equal num- events which result from upgoing charged parti-
berofUpStopandInternalDown isexpectedif cles produced by downgoing muons in the rock
neutrinos do not oscillate. The average neutrino nearMACRO.Finally,itis estimatedthat12 4
±
energyforthiskindofeventsisaround4GeV.In events are the result of interactions of neutrinos
case of oscillations it is not expected a reduction intheverybottomlayerofMACROscintillators.
in the flux of the Internal Down events (having In the upgoing muon simulation it is used the
pathlengthsoftheorderof20km),whileitisex- neutrino flux computed by the Bartol group[26].
pectedareductioninthenumberUpStopevents The cross-sections for the neutrino interactions
bility 1 Tau neutrino
ba
o
Pr0.1
0.01
A)
Combination
0.001
1
Sterile Neutrino
0.1
Combination
0.01
B)
0.001
10-5 0.0001 0.001 0.01 0.1 D m2 1
Figure 7. A: Probabilities for maximum mixing
and oscillations νµ → ντ . B: oscillations νµ → νs.
Figure 6. Zenith distribution of flux of upgoing The 3 lines corresponds to the probability from the
muons with energy greater than 1 GeV for data and total number of events (dotted line), the probability
Monte Carlo for the combined MACRO data. The from the chi-square of the angular distribution with
shaded region shows the expectation for no oscilla- data and prediction normalized (dashed line) and to
tions with the 17% uncertainty in the expectation. thecombinationofthetwoindependentprobabilities
The solid line shows the prediction for an oscillated (continous line)
flux with sin22θ=1 and ∆m2=0.0025 eV2.
greater than 1 GeV for all MACRO data com-
pared to the Monte Carlo expectation for no os-
havebeencalculatedusingtheGRV94[27]parton cillations and with a ν ν oscillatedflux with
µ τ
distributions set which varies by +1% respect to sin22θ =1 and ∆m2 =0→.0025 eV2.
the Morfin and Tung parton distribution used in The shapeoftheangulardistributionhasbeen
the past. The systematic error on the upgoing tested with the hypothesis of no oscillations nor-
muonfluxduetouncertaintiesinthecrosssection malizing data and predictions. The χ2 is 22.9,
including low-energyeffects[28] is 9%. The prop- for 8 degrees of freedom (probability of 0.35%
agation of muons to the detector has been done for a shape at least this different from the ex-
using the energy loss calculation of reference[29] pectation). Also ν ν oscillations are consid-
µ τ
→
for standard rock. The total systematic uncer- ered. The best χ2 in the physical region of the
tainty on the expected flux of muons adding the oscillations parameters is 12.5 for ∆m2 around
errorsfromneutrinoflux,cross-sectionandmuon 0.0025eV2 and maximum mixing (the best χ2 is
propagation in quadrature is 17%. This the- 10.6, outside the physical region).
±
oretical error in the prediction is mainly a scale To test the oscillation hypothesis, the inde-
errorthatdoesn’tchangetheshapeoftheangular pendent probabilities for obtaining the number
distribution. Thenumberofeventsexpectedinte- of events observed and the angular distribution
gratedoverallzenith angles is 824.6,givinga ra- for various oscillation parameters are calculated.
tiooftheobservednumberofeventstotheexpec- They are reported for sin22θ = 1 in Figure 7 A)
tation of 0.74 0.031(stat) 0.044(systematic) for oscillations ν ν . It is notable that the
µ τ
± ± →
0.12(theoretical). value of ∆m2, suggested from the shape of the
±
Figure 6 shows the zenith angle distribution of angulardistribution is similar to the value neces-
the measured flux of upgoing muons with energy sary in order to obtain the observedreduction in
100
Psterile =0.1 Pmax tau 1.8
Prediction nsterile
Prediction ntau
10-1 m s < mm 6 0 MPreeadsicutrieodn eVlaelcuterons
2eV)10-2 m s > mm qos ( ) <-0.q< cos ( ) < 11..46
2 (m10-3 -1 < cR=-0.6 1.2
D Statist+System Error
10-4
1
10-5 0.0001 0.001 0.01 0.1
0 0.2 0.4 0.6 0s.8in2(2 q )1 D m2 (eV2)
Figure 9. The ratio obtained binning the data in
two bins and the comparison with the νs,νe and ντ
Figure 8. Iso-probability plot for sterile neutrino oscillations with maximum mixing
showingthecontourscorrespondingtoa3.6%proba-
bility(10% of themaximumprobability for ντ). The
two regions are for positive and negative values of
∆m2 experiments. In case of oscillations it is im-
portant to take into account correctly the en-
ergy threshold of the different experiments: Su-
the total number of events in the hypothesis of perkamiokande has an average energy threshold
maximum mixing. Figure 7 B) shows the same of the order of 7 GeV while for MACRO it is 1
quantities for sterile neutrinos oscillations taking GeV. The comparison between Kamiokande[32],
into account matter effects. Superkamiokande[33]andMACROshowninFig-
The maximum of the probability is 36.6% for ure 10 is done by comparing the ratio between
oscillations ν ν . The probability for no os- the events measured and the events expected in
µ τ
→
cillation is 0.36%. case of oscillation (as computed by each experi-
The maximum probability for the sterile neu- ment). Thereis aremarkableagreementbetween
trinois8.6%inaregionof∆m2 around10−2eV2. the three experiments even if there is still some
The probabilitiesfor sterile neutrinos arecompa- possiblediscrepancyintheregionaroundthever-
rable to the one for τ neutrinos only in the small tical.
regions shown in Figure 8.
Anotherwaytotrytodiscriminatebetweenthe 7. THE MACRO LOW ENERGY
oscillationofνµ inνs andtheoneinντ istostudy EVENTS
the angular distribution in two bins, computing
the ratio between the two bins as shown in Fig- The analysisoftheInternal Upeventsissimi-
ure 9. The statistical significance is higher then lar to the analysisofthe Up Through. The main
in the case of data binned in 10 bins, but some difference is due to the requirement that the in-
features of the angular distribution could be lost teraction vertex should be inside the apparatus.
using this ratio. The ratio is insensitive to most About 87% of events are estimated to be ν CC
µ
of the errors on the theoretical prediction of the interactions. The uncertainty due to the accep-
ν flux and cross section[31]. From this plot the tance and analysis cuts is 10%. After the back-
ν hypothesis is disfavored at 2σ level. groundsubtraction(5events)116eventsareclas-
s
It is interesting to check if there is agree- sified as Internal Up events
ment between the data measured by different The Internal Down and the Up Stop events
2
s
n
o
ati
cill 1.5
s
o
h
wit
n
o 1
cti
di
e
Pr
a/
dat 0.5 SuperKamiokande
o
ati MACRO
R
Kamiokande
0
-1 -0.8 -0.6 -0.4 -0.2 0
Cos(zenith)
Figure 10. Comparison of the upward-going
through-going muon data of Kamiokande[32], Su-
perkamiokande[23], MACRO. The prediction in case
of oscillation (as computed from each experiment for
the best fit point) are for different value of δm2 and
(for Kamiokande and Superkamiokande) for slightly Figure 11. Zenith angle (θ) distribution for IU
different valuesof thenormalization. and UGS + ID events. The background-corrected
data points (black points with error bars) are com-
pared with the Monte Carlo expectation assuming
no oscillation (full line) and two-flavor oscillation
are identified via topological constraints. The (dashed line) using maximum mixing and ∆m2 =
main requirement is the presence of a recon- 2.5×10−3 eV2.
structed track crossing the bottom scintillator
layer. The tracking algorithm for this search
requires at least 3 streamer hits (corresponding
roughly to 100 gr cm−2). All the trackhits must around the MACRO detector (5.3 kton). The
beatleast1mfromthedetector’sedges. Thecri- uncertainty on the expected muons flux is about
teriausedtoverifythattheeventvertex(orstop- 25%. The number of expected events was also
ping point) is inside the detector are similar to evaluated using the “NEUGEN” neutrino event
those used for the Internal Up search. To reject generator[34](developedby the SoudanandMI-
ambiguous and/or wrongly tracked events which NOS collaborations) as input to our full Monte
survived automated analysis cuts, real and simu- Carlo simulation. The NEUGEN generator pre-
lated events were randomly merged and directly dicts 6%(5%) fewer IU (ID+UGS) events de-
∼
scannedwiththe MACROEventDisplay. About tectable inMACROthan[28],wellwithinthe es-
90% of the events are estimated to be ν CC in- timatedsystematicuncertaintyforneutrinocross
µ
teractions. The main background for this search sections ( 15%).
∼
are the low energy particles produced by donwn- The angular distributions of data and predic-
going muons [21]. After background subtraction tions are comparedin Figure 11. The low energy
(7 2events)193eventsareclassifiedasInternal samples show an uniform deficit of the measured
±
Down and Up Stop events. The Montecarlosim- numberofeventsoverthewholeangulardistribu-
ulation for the low energy events uses the Bartol tion with respect to the predictions, while there
neutrino flux [26] and the neutrino low energy is good agreement with the predictions based on
cross sections reported in [28]. The simulation is neutrino oscillations.
performed in a large volume of rock (170 kton) The theoretical errors coming from the neu-
this analisys it is used the same Bartol neu-
MACRO trinofluxusedfromMACRO.Theratio measured
Low energies expected
10-1 with oscillations in the best fit point of each ex-
periment and for cos(θ) < 0.2 is 0.97 0.11
Soudan2 for SuperKamiokande in go−od agreemen±t with
10-2 Kamiokande 1.02±0.15for the MACRO IUP and 0.91±0.11
for the MACRO IDW +STOP events.
MACRO
Upmu
2V) SuperKam
2m (e10-3 Combined 8. CONCLUSIONS
D
The Soudan-2 detector is able to study at-
10-4 mospheric neutrino oscillations in the Sub-GeV
region. MACRO is able to cover the Multi-
GeV and the 100GeV region. MACRO
∼
10-5 and Soudan2 results can be compared to
0 0.2 0.4 0.6 0.8 1
Kamiokande and SuperKamiokande that covers
sin2(2 q ) all the three region. The 90% allowed confi-
Figure 12. The 90% confidence level regions of the dence regions for Kamiokande,Superkamiokande,
experimentswithpositiveindicationofoscillation for Soudan-2, MACRO for the oscillation ν ν
µ τ
atmosphericneutrinos. TheMACROlimitsarecom- are shown in Figure 12. The statistical pow→er of
putedusing theFeldman-Cousins procedure[35]
the Superkamiokande experiment is larger than
the others, but it is remarkable to note that it
is possible to see the same effect detected in Su-
perkamiokande with detectors using completely
trino flux and cross section uncertainties almost different experimental techniques and in similar
cancel if the ratio between the measured num- energy regions.
ber of events IU is comparedwith the ex- Usingthemattereffectitispossibletodiscrim-
(ID+UGS)
pected one. The partial error cancellation arises inate between different oscillation hypothesis. In
from the nearly equal energy spectra of parent particularthe oscillationν ν withmaximum
µ s
→
neutrinos for the IU and the ID+UGS events. mixing is disfavored by the MACRO experiment
The experimental systematic uncertainty on the respect the ν ν oscillation. A similar results
µ τ
ratio is 6%. The measured ratio is IU = is obtained by→Superkamiokande.
ID+UGS
0.60 0.07 , while the one expected without Although the ν ν oscillation hypothesis is
stat µ τ
± →
oscillationsis0.74 0.04 0.03 . Theprob- the most simple that fits the current data, other
sys theo
± ±
ability (one-sided ) to obtain a ratio so far from more complex scenariosexist and can fit well the
the expected one is 5%, near independent of the data. They require additional hypothesis on the
usedneutrinoflux andneutrino crosssectionsfor existence of exotic particles, such as the sterile
the predictions. neutrino, or of oscillations in more than 2 fami-
Theconfidencelevelregionsasfunctionof∆m2 lies[37].
and sin22θ are studied using a χ2 comparison of The exact determination of oscillation param-
data and Monte Carlo for the data of Fig. 11. eters and of the channels of the oscillations will
The χ2 includes the shape of the angular distri- be the main goal of the future generation exper-
bution, the IU ratio and the overall nor- iments using atmospheric neutrinos or artificial
ID+UGS
malization. Thesystematicuncertaintyis10%in neutrino beams.
each bin of the angular distributions, while it is I am greatly indebted to W. A. Mann, Maury
5%fortheratio. TheresultisshowninFigure12 Goodman and T. Kafka of the Soudan2 Group
(MACRO low energes). andallthecolleguesoftheMACROcollaboration
A direct comparison can be done with the Su- for the results presented in this Talk and for the
perkamiokande stopping muons [36], because in very useful discussions.
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