Transcript Atmospheric neutrino Oscillations in Soudan 2

Atmospheric Neutrino Oscillations in
Soudan 2
Peter Litchfield
For the Soudan 2 Collaboration
Neutrino and background data
Azimuthal, zenith and L/E distributions
Bin-free likelihood analysis
Feldman-Cousins analysis for confidence limits on m2 and sin22
Results submitted to Phys Rev D and more details in hep-ex/0307069
Soudan 2 Detector
1 kiloton fine grained drifting calorimeter
Individual tracks reconstructed, good energy and
pointing resolution
Excellent particle id, ~3% flavour misidentification
Veto shield flags cosmic ray generated events
e quasi-elastic
 inelastic
Data Sets
 5.90 kiloton years of data taken between 1989 and 2001.
 488 contained and partially contained  and e candidate events with
no activity in the surrounding veto shield.
 516 contained events with in time shield activity, produced by
secondary neutrons and gammas from cosmic ray muon interactions.
Used to simulate the background in the neutrino events.
 3624 MC neutrino events generated using the Bartol 96 flux and the
NEUGEN neutrino event generator, inserted in the data stream and
processed identically to the data events.
 Data divided into;
 high resolution sample (high energy events with reconstructed
recoil protons and pions) which have good pointing accuracy
 The rest, low energy, low resolution sample.
Backgrounds
MC+background
 Neutrino events distinguished
statistically from neutron and
gamma events via the depth
distribution in the detector
 Background depth distribution
represented by the shield tagged
sample, neutrino by the MC
 Neutron interaction length ~80cm,
gamma conversion length ~15cm
 Backgrounds dependent on event
energy and topology
 Data divided into 6 samples and
fraction of background fitted
independently in each.
 ~10% overall background
MC
Background
Zenith and Azimuthal Angles
Unoscillated MC+background
 Oscillation probability
L

P  sin 2 2 sin 2 1.27m 2 
E

 High resolution events
 L depends only on the zenith
angle, not the azimuthal angle
 e-flavor events agree with the
MC prediction up to a
normalization factor
 -flavor events show a zenith
angle dependent depletion
 Soudan is near the magnetic
pole; no geomagnetic
azimuthal dependence
Best fit oscillation parameters +background
Background contribution
L/E distribution
Unoscillated MC+background
Best fit oscillation parameters +background
Background contribution
 High resolution events
 e-flavor events follow the MC
prediction up to a ~90%
normalization factor
 -flavor events show a
depletion above log10(L/E) of
~ 1.5
 Consistent with neutrino
oscillations with m2<~0.025
eV2
Likelihood Analysis
 Data assumed to be represented by the sum of MC neutrino events,
weighted by the oscillation probability plus background represented by
the shield tagged events
 Bin-free likelihood analysis performed.
 Likelihood given by (d = depth)




k
k
k
k
L     ln Q ( L / Ei , d i )  N  ln M   M    N e ln M e  M e
k 1,5 i 1, N k



Shape factor Q given by
1
Q k  xi , d i   k AC k X k ( L / E , m 2 , sin 2 2 ) Dk (d i )  N Rk X Rk ( L / E ) DRk (d i )
M
k sums taken over the different data sets, background fraction fitted
independently in each
X is a pdf describing the L/E distributions and containing the oscillation
probability for the neutrino events
D is a pdf describing the depth distribution





Likelihood results
 Likelihood calculated on a 15x80
grid of sin22, log10m2
 Difference (L) from best
likelihood plotted.
 No oscillations gives a likelihood
rise of 11.3
 Best likelihood
 sin22=0.97
 m2=0.0052
 Normalization of MC relative
to Bartol 96=0.91
 Fraction of background=9.6%
Feldman-Cousins analysis
Proposed by Feldman and Cousins for the calculation of confidence
levels to allow for statistics, systematic errors, physical constraints and
any biases in the analysis procedure.
At each grid square MC experiments are generated and analyzed just
like the data.
Neutrino events and background events are incorporated at each grid
square according to the fitted amounts at that square in the data
Systematic effects are incorporated into the MC experiments.
For the uncertainty in energy calibration
For the uncertainty in the neutrino flux as a function of energy
For the uncertainty in the /e flux ratio
For the uncertainty in the neutrino cross-sections
Feldman-Cousins analysis
1000 experiments generated at each
grid point and the difference between the
best fit likelihood and the likelihood at the
generated grid square (LMC)
histogramed.
This is the likelihood distribution
expected if the truth was at this grid
square
The likelihood containing 90% of the
MC experiments (L90) is obtained. If the
data likelihood is less than L90 the point
is within the 90% confidence region.
The probability of the no oscillation
hypothesis is given by the fraction of
experiments at the no oscillation grid
square with likelihood > data likelihood
(5.8x10-4)
“no oscillation”
(min m2,sin22)
100000 experiments
L90 surface
Shape is mostly a function
of the background and Monte
Carlo normalization fitting.
Some contribution from the
systematic effects on the
neutrino flux, neutrino crosssections and detector energy
calibration
L90 is significantly greater
than 2.3 over most of the
surface
Confidence regions
68%,90% and 95% confidence
level contours are plotted
The 90% sensitivity (defined as
the 90% confidence contour
calculated from the MC
experiments) is slightly bigger than
the data 90% contour, more
corresponding to the 95% contour.
Due to the data electron and muon
best normalisation being slightly
different.
The contour defined by a 2.3 rise
in data likelihood corresponds
closely to the 68% FeldmanCousins confidence level contour
Comparison with other experiments
There is excellent agreement at
the 90% level between Soudan 2,
Super-K and MACRO.
At the 68% confidence level
Soudan 2 prefers the lower part of
the Super-K allowed region
The 3-d Battistoni prediction for
the neutrino flux gave very similar
results for the confidence regions
but required a normalization factor
of 1.05 to be compared with 0.91
for the Bartol 96 calculation
Summary
Soudan 2 observes a depletion of the atmospheric  flux, consistent
with  oscillations.
A bin-free likelihood analysis has been carried out using the FeldmanCousins prescription.
The probability of the no oscillation hypothesis is 5.8x10-4.
The 90% confidence level contours in the sin22,m2 plane are
consistent with those found by Super-K and MACRO.
This is the first experiment to confirm the Super-K results on fully
reconstructed neutrino events covering the full angular and L/E range.
Soudan 2 is a drifting iron calorimeter at a different site to the Super-K
water cherenkov. All detector based systematics are quite different.
The excellent agreement is a strong confirmation that neutrino
oscillations, and thus neutrino mass, exist