Transcript スライド 1

Accelerator Neutrino Oscillations
Results and Prospects
III International Pontecorvo Neutrino Physics School
16-26 September, 2006
Koichiro Nishikawa
Institute for Particle and Nuclear Studies
KEK
1
• The present observations are good at discovering a surprise (if it is a large
effect) for which small scale (controlled) experiments do not have enough
sensitivity.
– Long baseline (100 – 108 km) size of earth, Sun size by luck
• They are however not good at measuring underlying parameters very precisely.
• Inherent uncertainties exist in calculation of various observables:
– Fluxes of solar neutrinos on Earth
• Nuclear reaction cross sections, chemical compositions, opacity, etc.
– Fluxes of atmospheric neutrinos
• Primary cosmic ray flux, nuclear interactions, etc.
• Find model-independent observables
– Solar neutrinos:
• Comparison of NC and CC interactions
• Spectral shape, day/night effect, etc
– Atmospheric neutrinos
• m/e ratio
• Zenith angle distribution
2
Accelerator experiment
• Neutrinos can be measured more than once
– Relative change of spectrum
• Effect of oscillation depend only on neutrino energy (fixed
distance)
2
1
.
27

m
L
2
2
prob.  sin 2  sin (
)
E
• Beam energy can be chosen
– Type of detector
– Neutrino energy determination method can be chosen
3
Critical issues
• Only the product F(Ei) x s(Ei) are measurable
– Flux times cross section as a function of E
near
N obs
( E  )  Fnear ( E  )  s( E  )
far
N far
(
E
)

F
( E  )  P( a  b )  s( E  )
obs

• The P(a→b) must be determined by minimizing the followings
– s(E) poorly known at low-medium energy
• Two measurements at different distances can reduce the the
effect of ambiguities of cross sections
– Fnear(E) , Ffar(E) different from 1/r2 unless decay at rest
• Different spectrum due to finite decay length and
acceptance at two distances – decay volume and distance
– PID and E determination of observed events
• background processes (eps. NC, etc.) different in near, far
4
Neutrino beams from accelerator
with existing technologies
Produce mesons by strong int. and let them decay in weak int.
1. Neutrinos from stopping p’s and m’s
(LSND KARMEN) unique spectrum of m, m, e
no problem of Far/Near, cross section, energy determination
2. Neutrinos from in-flight decays
• Wide Band Beam - sign selected by horn system but wide p
band accepted, the highest intensity of m
(CHORUS, NOMAD,K2K, MiniBooNE, MINOS, CGSN…..)
– Off-axis beam
• Dichromatic beam-momentum selected by B and Q mangets
– clean but the acceptance beam line limits  intensity
5
Decay at Rest (DAR)
Inverse beta decay well known s
Small intrinsic e contamination
few x 10-4
p- decay in flight contamination ?
6
LSND/KARMEN Experiments
• 800MeV LINAC
– 1mA
– 600 msec width
– 10msec rep.
• Mineral oil (Cherenkov
pattern)
• prompt e and g(2.2 MeV)
p(n,g)d
• 800MeV Rapid cycling syn
– 200mA
– 200 nsec width
– 20msec rep.
• Gd loaded scintillator
• prompt e and g(7.8MeV)
Gd(n,g)
•single measurement at one position
•E e+ from anti-e + p→e+ +n
•unique spectrum for anti-m, m, e
7
Signal and Background
8
Gamma Ray Distribution
9
LSND Final Results
10
KARMEN Distributions
11
With NOMAD and reactor experiments
12
It is impossible to have only 3 neutrinos
involved if all of the effects are the
result of neutrino oscillations.
m2 (eV2)
‘Evidence’ of oscillations
me
Either some of the data are not due to
oscillations,
mt
or there must be at least one
undiscovered “sterile” neutrino
em,t
or there must be CPT violation in the
neutrino sector.
sin2 2
or exotic processes
2
2
m221  m32
 m13
0
m -m m -m m -m
2
2
2
1
2
3
2
2
2
3
13
3
1
14
15
Experimental issue
• ‘MiniBooNE’ single detector
– compare the results with MC only
• signal = no muon, shower like events, not p0
• Backgrounds = NC p0 production, e in the beam
• PID e, m, p0
•
Hadron production knowledge
– p production by 8 GeV proton →normalization and HE
components to interact with NC p0
– K to give Ke3 decay (K→p e+ e)
16
A neutrino interaction model
s/E (10-38cm2/GeV)
Total
(NC+CC)
CC Total
CC quasi-elastic
DIS
CC single p
NC single p0
E (GeV)
17
Background
Approximate number of events
and Background expected in
MiniBooNE
Signal
m Charged Current, Quasi-elastic
500,000 events
Intrinsic νe (from K&μ decay) :
236 events
π0 mis-ID:
294 events
(Neutral Current Interaction)
Other νμ mis-ID:
140 events
LSND-like me signal:
300 events
~10-3 of total neutrino events
18
Sensitivity to a Signal
Signal
Mis-ID
Intrinsic νe
Δm2 = 1 ev2
Δm2 = 0.4 ev2
19
20
HARP data
on p, K
NUANCE adjustment
photon propagation
in oil simulation
PID
e m seperation
e-p0 seperation
21
22
23
24
25
26
27
Checking the
reproducibility
of s’s,
detector sim.
28
29
~10-3 of total neutrino events
30
31
Accelerator-based Long Baseline Neutrino
Oscillation Experiments
Long = distance>>decay region
32
Wide Band Beam
•
•
•
•
•
•
•
Maximum available neutrino intensity
Protons hit target
Pions (p) produced at wide range of angles
Magnetic horn to focus p
Rock shield range out m
 beam travels through earth to the experiment
m decay / p decay ~10-2 ,, Ke3→~1% e contamination
33
Horn in K2K
p+Al  p+ m+ + m
Need measurements of high energy (muon monitor)
and low energy (neutrino events at near detector)
secondary particle direction
LE
34
Neutrino Beam

pt~35MeV/c
p
p t  pcm  sin cm
Typical characteristics
pl  pcm  (coscm  b)  g
 e /m ~ 0.01~0.001 (decay vol.)
m -m
Ep
• lifetime of p/m ~ 0.01
gp 
, pcm 
~ 35MeV
mp
2m p
• production cross sectionof K/p
~ 0.1 and Ke3 ~0.01
m2p - mm2
E  (  0) 
E p  0.5E p
  divergence ~ 10mrad/E(GeV)
2
mp
• Horn focuses to about a few mrad
E (  0)
• Far/near is not scale as 1/r2
E  ()   2 2
2
p
1  g p
2
m
35
Neutrino event vertex distribution at 300m from target
LE 0.5<Em <1GeV
HE 1<Em <2.5GeV
Width
cm
HE-LE
FWHM
4m/300m~ 10 mrad
FWHM
2m/300m~ 6 mrad
divergence is dominated by decay angle at these energies
36
Critical issues (reminder)
• Only the product F(Ei) x s(Ei) are measurable
– Flux times cross section as a function of E
near
N obs
( E  )  Fnear ( E  )  s( E  )
far
N far
(
E
)

F
( E  )  P( a  b )  s( E  )
obs

• The P(a→b) must be determined by minimizing the followings
– s(E) poorly known at low-medium energy
• Two measurements at different distances can reduce the the
effect of ambiguities of cross sections
– Fnear(E) , Ffar(E) different from 1/r2 unless decay at rest
• Different spectrum due to finite decay length and
acceptance at two distances – decay volume and distance
– PID and E determination of observed events
• background processes (eps. NC, etc.) different in near,far
37
Critical issues-1
•
s(E) poorly known at low-medium energy
–
–
–
–
Nuclear physics at GeV region
Pauli blocking
Nucleon Form factor
Final state interaction inside nucleus
SciBooNE
Minerva
For several 100~1000km baseline
38
Quasi-elastic scattering cross-sections
• Two form factors
m
•MV fixed by e.m. (CVC)
10-38cm2
•Axial V form factor
mfA , fV 
W
p
n
1
2

q
1 2

M
A,V





2
s/E (10-38cm2/GeV)
Cross-section (m)
magenta Old MC
red
new MC
39
1
10
100 GeV
Data on charged current processes
• Not well
known
• Especially 2~3
GeV
→SciBooNE
→Minerva
40
Neutrino spectrum and the far/near ratio (in K2K)
 beam
300m
250km
beam MC w/
PION Monitor
Far/Near Ratio
Angular acceptance
(well collimated for HE)
10-6
Finite decay volume length
(shorter for HE,
Near better accep. for MH )
1.0
2.0
E (GeV)
41
Accelerator Neutrinos
Present Status
K2K (1999-2005 Completed)
MINOS (2005-)
OPERA (2006-)
42
Brief history of K2K
• 1995
– Proposed to study neutrino oscillation for atmospheric neutrinos anomaly.
• 1999
– Started taking data.
• 2000
– Detected the less number of neutrinos than the expectation at a distance of
250 km. Disfavored null oscillation at the 2s level.
• 2002
– Observed indications of neutrino oscillation.
The probability of null oscillation is less than 1%.
• 2004
– Confirm neutrino oscillation at the 4s level with both a deficit of m and the
distortion of the E spectrum.
• 2004 Nov.6
– Terminated K2K due to horn trouble and high residual radiation level
43
K2K experiment
~1 event/2 days
~105 /2 days
~1011 m/2.2sec
(/10m10m)
12GeV protons
p+
~106 m/2.2sec
m (/40m40m)
SK t
m
Target+Horn
p monitor
200m
decay pipe
m monitor
100m
~250km
Near  detectors
(ND)
(monitor the beam center)
1.27  m2  L
P  sin 2  sin
E
2
Signal of  oscillation at K2K
Reduction of m events
 Distortion of m energy spectrum

44
E
GPS
Particle detection at 250km
away
Tspill
SK
TOF=0.83msec
TSK
Decay electron cut.
500msec
20MeV Deposited Energy
No Activity in Outer Detector
Event Vertex in Fiducial Volume
More than 30MeV Deposited Energy
5msec Analysis Time Window
112 events
-0.2<TSK-Tspill-TOF<1.3msec
(BG: 1.6 events within 500ms
2.4×10-3 events in 1.5ms)
TDIFF. (ms)
45
Analysis Overview
KEK
Observation
#, pm and m
 interaction MC
Measurement
F(E),  int.
Far/Near Ratio
(beam MC with p mon.+ HARP )
SK
Observation
# and E rec.
(sin22, m2)
Expectation
# and E rec.
46
Overall normalization error on Nsk for Nov99~
Errors
(Event)
KT: dominated
by FV error
SK: also.
Stat
0.28
0.37%
KT
3.32
4.37%
SK
2.28
3.00%
Flux
+2.81
-2.59
F/N
+4.26
-5.55
NC/CC
+0.15
-0.23
nQE/QE
+0.38
-0.61
CT
Total
0.46
+6.53
-7.37
HARP~1 %
0.60%
5.34%
47
Pion Monitor: pion distribution after horn
Measure Momentum / Angle Dist.
of π’s Just after Horn/Target
+Well known π Decay Kinematics
+Well Defined Decay Volume Geometry
⇒Predict
νμ Energy Spectrum at Near Site
Far Site
Ring Image Gas Cherenkov Detector
(Index of Refraction is Changeable)
To Avoid Severe Proton Beam Background,
νμ Energy Information above 1GeV is Available
(β of 12GeV Proton ~ β of 2GeV π)
48
index of refraction : pp threshold 
p
position of ring : p
pp, p gives two C-light peaks
fit with S (wi • C-light)
: :
w1 w2 w3 w4
…..
: :
pp
Good agreement with
old data. (Cho et.al.)
Beam MC based
on Cho et al.
Error assignment
based on this
measurements
49
Thin target data need assumption of secondary interaction in target
Total cross section of p-Al
Horn magnetic field ambiguity
50
Proton beam profile
HARP, Pion monitor and MC comparison
p spectrum shape
Far/Near ratio vs E
51
NEUT: K2K Neutrino interaction MC
•
CC quasi elastic (CCQE)
– Smith and Moniz with MA=1.1GeV
•
s/E (10-38cm2/GeV)
CC (resonance) single p(CC-1p)
– Rein and Sehgal’s with MA=1.1GeV
•
DIS
– GRV94 + JETSET with Bodek and
Yang correction.
•
CC coherent p
– Rein&Sehgal with the cross section
rescale by J. Marteau
•
NC
Total (NC+CC)
CC Total
CC quasi-elastic
DIS
CC single p
NC single p0
+ Nuclear Effects
E (GeV)
52
Near detector measurements
•
•
•
•
•
1KT Water Cherenkov Detector (1KT)
Scintillating-fiber/Water sandwich Detector (SciFi)
Lead Glass calorimeter (LG) before 2002
Scintillator Bar Detector (SciBar) after 2003
Muon Range Detector (MRD)
Muon range detector
53
1KT Flux measurement
• The same detector technology as Super-K.
– Sensitive to low energy neutrinos.
– Sensitive for NC
N
exp
SK
N
obs
KT
F


F
( E )s ( E )dE
M SK  SK


M KT  KT
KT ( E )s ( E ) dE
SK
Far/Near Ratio (by MC)~1×10-6
M: Fiducial mass MSK=22,500ton, MKT=25ton
: efficiency SK-I(II)=77.0(78.2)%, KT=74.5%
+11.6
exp
NSK =158.4 -10.0
NSKobs=112 54
Near Detector Spectrum Measurements
• 1KT
– Fully Contained 1 ring m (FC1Rm) sample.
• SciBar
– 1 track, 2 track QE (p≤25), 2 track nQE (p>25)
where one track is m.
• SciFi
– 1 track, 2 track QE (p≤25), 2 track nQE (p>30)
where one track is m.
(pm,m) for 1track, 2trackQE and 2track nQE samples
 F(E), nQE/QE
55
m (MeV/c)
E
KT data
QE (MC)
nQE(MC)
MC templates
0-0.5 GeV
0.5-0.75GeV
0.75-1.0GeV
Pm (MeV/c)
•  flux FKEK(E) (8 bins)
•  interaction (nQE/QE)
1.0-1.5GeV
•
•
•
•
56
Flux measurements
c2=638.1 for 609 d.o.f
–
–
–
–

–
–
–
–
F1 (
E < 500) = 0.78  0.36
F2 ( 500 E < 750) = 1.01  0.09
F3 ( 750 E <1000) = 1.12  0.07
F4 (1000 E <1500) = 1.00
F5 (1500 E <2000) = 0.90  0.04
F6 (2000 E <2500) = 1.07  0.06
F7 (2500 E <3000) = 1.33  0.17
F8 (3000 E
) = 1.04  0.18
nQE/QE
= 1.02  0.10
The nQE/QE error of 10% is assigned based on
the sensitivity of the
fitted nonQE/QE value by varying the fit
criteria.
 >10(20 ) cut: nQE/QE=0.95 0.04
• standard(CC-1p low q2 corr.): nQE/QE=1.02
0.03
• No coherent: p=nQE/QE=1.06 0.03
F(E) at KEK
E
57
Super-K oscillation analysis
• Total Number of events
• Erec spectrum shape of FC-1ring-m events
• Systematic error term
L(m 2 , sin 2 , f x )
 Lnorm (m 2 , sin 2 , f x )  Lshape (m 2 , sin 2 , f x )  Lsyst ( f x )
f x : Systematic error parameters
Normalization, Flux, and nQE/QE ratio are in fx
Near Detector measurements, Beam constraint,
beam MC estimation, and Super-K systematic
58
uncertainties.
Log Likelihood difference from the minimum.
lnL
lnL
- 68%
- 90%
- 99%
m2[eV2]
- 68%
- 90%
- 99%
sin22
59
m disappearance versus E shape distortion
E shape
m2[eV2]
m2[eV2]
NSK (#m)
sin22
Both disappearance of m and the distortion of
E spectrum have the consistent result.
sin22
60
Allowed region
Distortion of the neutrino spectrum
Normalized by area
Best fit
sin22 =1
m2 =2.77 x 10-3
0.006
0.004
0.002
0.0 0.2 0.4 0.6 0.8 1.0
Rate
Nobs=112 +9.4
Nexp=158.4 -8.7
sin22
Null oscillation hypothesis excluded at 4.4s
61
K2K upper bounds on m→e
K2K-I+II (#obs.=1, #B.G.=1.70)
upper limit (90% CL)
sin22me=0.13 @2.8e-3 eV2
limit
sensitivity
62
Conclusion
•
K2K Oscillation analysis on June99 ~November 6 , 05 full
data
1.
2.
Long Baseline experiment can be done!
Both SK rate reduction and Erec shape distortion has been
observed
3. Null oscillation hypothesis has been excluded by 4.41s
4. m2=1.88~3.48x10-3eV2 for sin22=1 @ 90%CL
5. sin22, m2 are consistent with atmospheric neutrino results
6. e-appearance search is limited by statistics, upper limit
(90% CL) sin22me=0.13 @2.8ｘ10-3 eV2
7. Many studies on low energy neutrino interaction continue
63
MINOS experiment
• Two neutrino detectors
• Long baseline neutrino oscillation
experiment
• Fermilab’s NuMI beamline
735 km
64
Neutrino beamline
π+
•
•
•
•
νμ
μ+
120 GeV protons hit graphite target
Two magnetic horns focus positive pions and kaons
Mesons decay in flight in evacuated decay pipe giving rise to almost pure υμ beam
Adjustable neutrino beam energy
65
Adjustable beam energy
• Changing target position
changes neutrino beam energy
• 10 cm most favorable for
oscillation analysis
• Data in other configurations
used for systematic studies
• LE event composition:
– 92.9% υμ
– 5.8% υμ
– 1.3% υe / υe
Target position:
- 10 cm
- 100 cm
- 250 cm
• After target replacement run at
9cm
66
MINOS Detectors
• Functionally identical
– 2.54cm thick steel planes
– 4.1×1cm scintillator strips
– Multianode PMT readout
– Magnetized B~1.3T
Coil
Far Detector
• Near Detector:
– 1 km from target
– 1 kton
– 282 steel and 153 scintillator
planes
Near Detector
• Far Detector:
– 735 km from target
– 5.4 kton
– 484 steel/scinitllator planes67
Neutrino interactions
υμ
μ
υ
υ
X
m
CC Event
X
NC Event
Monte Carlo
• Likelihood
procedure used to
differentiate
between NC and
CC events
• NC contaminations
in lowest energy
bins
Monte Carlo
3.5m
•long m track + hadronic
activity at vertex
1.8m
•short event, often
diffuse
Eυ =
Eshower+Pμ
68
Event classification
y=Eshw/Eυ
• Good agreement between data and MC for input variables
69
Event Classification
rejected as
NC like
Event Classification Parameter
70
Tuning hadron production MC for ND data
• Fit ND data from all beam configurations : various Target-horn
configuration
• Simultaneously fit νμ and νμ spectra
(Use MIPP data in future)
LE010/185kA
LE100/200kA
LE250/200kA
υμ LE010/185kA
71
Beam matrix method
X
=
• Construct beam matrix using
MC
• Use Near Detector data to
predict the “unoscillated”
spectrum at the Far detector
• Spectrum known at
2-4% level
72
Observed FD events
Data Sample
FD
Data
Expected
Data/Prediction
(MC)
(Matrix Method)
m All
563
738±30
0.76 (4.4 s)
m (<10 GeV)
310
496±20
0.62 (6.2 s)
m (<5 GeV)
198
350
±14
0.57 (6.5 s)
• Energy dependant deficit
73
• Time stamping of the
neutrino events is provided
by two GPS units
• Timing of neutrino
candidates consistent with
spill signal
• Easy to separate cosmic
muons (0.5Hz)
• Time distribution is as
expected
NuMI only mode
Far Detector Data
timing to spill time
74
Systematic errors
• Systematic shifts in the fitted parameters are computed using MC “data
samples” (at best fit point)
Shift in Δm2
(10-3 eV2)
Shift in
sin2(2θ)
Near/Far normalization 4%
0.065
<0.005
Absolute hadronic energy scale 10%
0.075
<0.005
NC contamination 50%
0.010
0.008
All other systematic uncertainties
0.041
<0.005
Total systematic (summed in quadrature)
0.11
0.008
Statistical error (data)
0.17
0.080
Uncertainty
75
Far spectrum
• Best fit for 2.5x1020 POT
20
| Δm32 | 2.38-00..16
10-3 eV2 / c4
2
sin 2 (2 23 )  1.00-0.08
c2 /n.d.f = 41.2/34 = 1.2
76
Allowed region
• Fit is constrained
to physical
region:
sin2(223)≤1
( c min  2.3)
2
( cmin  4.61)
2
20
| Δm32 | 2.38-00..16
10-3 eV2 / c4
sin 2 (2 23 )  1.00-0.08
2
c2 /n.d.f = 41.2/34 = 1.2
77
Unconstrained fit
Δm 2  2.26 10-3 eV2
sin 2 2  1.07
c2 /n.d.f = 40.9/34 = 1.2
78
Summary
• Analyzed data using 2.5×1020 POT
• Systematic errors well under control
• MINOS disfavors no disappearance hypothesis by 6.2σ
(<10GeV)
• Best fit to oscillation hypothesis yields:
20
| Δm32 | 2.38-00..16
10-3 eV2 / c4
2
sin 2 (2 23 )  1.00-0.08
• Forthcoming results:
– υμ → υe search
– υμ → υs search
79
Forthcoming improvements
• Use antineutrinos +
neutrinos
• Expanded FD fiducial
volume
• Improved event
reconstruction +
selection
• 3.5×1020POT through
8/07
• Next year significant
proton accelerator
improvements
– 4.6×1020ppp
(demonstrated in MI)
80
K2K and MINOS have established neutrino
oscillation in muon-neutrino disappearance
as observed in atmospheric neutrino
observation in Super-Kamiokande
81
OPERA
CNGS
Beam
730km
An Emulsion-Counter
Hybrid experiment for
Tau neutrino
Appearance
Detection.
Collaboration :
13countries 37 Institutes
CNGS First Neutrino to Gran
Sasso at 2006 August
OPERA
Detector
Current phase: Installation of
Emulsion target (ECC Bricks)
82
83
84
Expected signal and background in OPERA in
5 years
>20mrad
I.P.=5-20mm
85
First neutrino : Muons from Neutrino Interactions
2006 August
319 on-spill events
are observed
¾ muons coming from
the rock
¼ neutrino
interactions in the
detector (CC+NC)
The observed
numbers are
consistent with the
expectation
Detector live-time
~95%
Recorded "Rock Muon" event
Beam events:
~horizontal tracks
Beam angle:
3.35° from below
Cosmic rays muons
86
CERN
Tracks zenith angle (no beam timing requirement)
Summary
• First CNGS Neutino in 2006: total 8.2x1017 pot
– Electric detector's performance was confirmed.
– Succeeded to connect tagged muons from the Electric
detector to the Emulsion target (CS and ECC).
• Current status in Gran Sasso: ECC brick production and
installation is going on.
– Current production and insertion Speed ~300ECC/day about
1/3 of planned. Need speed up  700ECC/day.
– until the end of April 2007
• CNGS 2007 run is planned in this Autumn.
– OPERA will start the Physics RUN with 60,000ECC bricks.
– ~300 neutrino interaction  ~10 charm events for decay
detection and analysis. And <1 Tau neutrino event.
87
Three generation neutrinos
88
Current status of neutrino mass and mixings
Anything new?
12, m122
23, m322
13, m312
J.W.F. Valle, hep-ph/0410103
Solar + KamLAND
Atmospheric
MINOS、K2K
Only upper limit on 13
No info. on d
89
Three Flavor Mixing in Lepton Sector
Weak eigenstates
m1
e
 e 
 1 
 
 
CP
 m   U MNS VM  2 
 
 
 t
 3
m
t
U PMNS
1

 0
0

0   c13

 s23  0
 c23  - s13e id
0
 c23
- s23
0
1
0
mass eigenstates
m2
m3
 s13e - id   c12

0
 - s12
 c13  0
 s12
 c12
0
0

0
1 
cij = cosij, sij=sinij
V
CP
M
eia1

  0
 0

0
e
ia 2
0
0

0
1
12, 23, 13
+ d (+2 Majorana phase)
m122,
m232,
m132
90
Present Knowledge
1 to be the larger component in e
sin 2 212  0.84  0.07
12 < p/4
2
2
dm12
 8.3  10-5 eV2 (dm12
> 0)
solar neutrino (SK,SNO), reactor (KamLAND)
Matter effect fix the sign of m2 12
sin 2 223  0.96 - 1.00
(


)

45

5
23
dm223  2.5  10-3 eV 2 ( unkown )
atm. neutrino (SK), long-baseline (K2K,MINOS)
Oscillation probability sqaured is measured
1 to be the larger component in e
sin 2 213 < 0.16(upper limit)
13 < p/4
2
dm13
 2.5  10-3 eV 2 ( unkown )
reactor neutrino exp.(CHOOZ), K2K, MINOS
91
Three ambiguities
1
dm
2
13
2
(13 , d MNS )
3
sin 2 23
2
sign of dm21３
2 fold ambiguity for mass
undetermined
23 （octant） and p/4
2 fold ambiguity for 13, d
“best fit” 23 =45 : no octant ambiguity
92
Regardless of ‘ambiguities,
only the measurements of 13 can open the
next phases of progress
93