Transcript スライド 1

III International Pontecorvo Neutrino Physics School
Alushta, Ukraine, Sep. 2007
Takaaki Kajita (ICRR, U.of Tokyo)
• Production of atmospheric neutrinos
• Some early history (Discovery of atmospheric
neutrinos, Atmospheric neutrino anomaly)
• Discovery of neutrino oscillations
• Studies of atmospheric neutrino oscillations
• Sub-dominant oscillations –present and future-
Introduction
We know that neutrinos have mass:
Future experiments
3
2
1
e 

q23=45±8
Atmospheric
LBL
q13 < 11
 e 
 1 
 
 
    U   2 
 
 

 3
 
q12=34±3
Solar
KamLAND
3
e 

2
1
Small q13 and Dm122 << Dm232  OK to interpret the present data with 2 flavor
oscillation framework: P(a  b)=1-sin22qij・sin2(1.27Dmij2・L/E)
Event statistics in atmospheric
neutrino experiments
TK and Y.Totsuka, RMP73, 85 (2001) Sorry: MINOS not included yet.
More than 20,000 now.
Super-Kamiokande: history and plan
today
19
96
97
98
SK-I
99
20
00
01
02
accident
03
04
05
06
07
08
SK-II
09
20
10
11
SK-III
SK full
reconstruc
tion
The following discussion: based on the SK-I+II (or SK-I) data
2
(Dm ,
2
sin 2q)
SK-I+II atmospheric neutrino data
CC e
CC 
SK-I: hep-ex/0501064
+ SK-II 800 days
SK-I: 92 kton・yr
SK-II: 49 kton・yr
Total: 141 kton・yr
No osc.
Osc.
Estimating the oscillation parameters
Downgoing
Transition point
(as a function of energy)
 Dm2
Upgoing
Up
 1  sin 2 2q
Down
Confirmation of non-oscillated flux
Accurate measurement
possible due to small syst.
in up/down (2% or less)
 2-flavor oscillation analysis
(SK-I + SK-II combined analysis)
Sub-GeV
Multi-GeV
Plep
CC
e
CC

FC
FC
FC
FC
PC
PC
1ring multi-r 1ring multi-r stop thru
e-like e-like -like -like
UP through
showering
UP through
non-showering
UP
stop
Each box has 10
zenith-angle bins
38 event type and
momentum bins
x
10 zenith bins
 380 bins
Various detector related systematic errors are different between
SK-I and SK-II.  SK-I and SK-II data bins are not combined.
380 bins for SK-I + 380 bins for SK-II  760 bins in total
Definition of
Number of
data bins
760
L ( N exp , N obs )  
n 1
exp( N
n
exp
)(N
n
N obs
!
2
c
Number of syst
error terms
n
N obs
n
exp
)
  e i2 
  exp 2 
i 1
 2s i 
70
Poisson with systematic errors
2
n 
760 
70



L
(
N
,
N
)
 ei 
N obs 
exp
obs
2
n
n
n



c  2 ln
 2( N exp  N obs )  2 N obs ln n     
 N  i 1 s
 L (N , N )  
n

1

obs
obs
 i
 exp 



70
N exp  N MC  P(    ( for CC  ))  (1   f j  e j )
j 1
Nobs : observed number of events
Nexp : expectation from MC
ei : systematic error term
si: sigma of systematic error
c2 minimization at each parameter point (Dm2, sin22q, …).
Method (c2 version): G.L.Fogli et al., PRD 66, 053010 (2002).
70 systematic error terms
● (Free parameter) flux absolute normalization
● Flux; (nu_mu + anti-nu_mu) / (nu_e + anti-nu_e) ratio ( E_nu < 5GeV )
● Flux; (nu_mu + anti-nu_mu) / (nu_e + anti-nu_e) ratio ( E_nu > 5GeV )
● Flux; anti-nu_e / nu_e ratio ( E_nu < 10GeV )
● Flux; anti-nu_e / nu_e ratio ( E_nu > 10GeV )
● Flux; anti-nu_mu / nu_mu ratio ( E_nu < 10GeV )
● Flux; anti-nu_mu / nu_mu ratio ( E_nu > 10GeV )
● Flux; up/down ratio
● Flux; horizontal/vertical ratio
● Flux; K/pi ratio
● Flux; flight length of neutrinos
● Flux; spectral index of primary cosmic ray above 100GeV
● Flux; sample-by-sample relative normalization ( FC Multi-GeV )
● Flux; sample-by-sample relative normalization ( PC + Up-stop mu )
● Solar activity during SK1
● Solar activity during SK-II
Flux (16)
● MA in QE and single-p
● QE models (Fermi-gas vs. Oset's)
● QE cross-section
● Single-meson cross-section
● DIS models (GRV vs. Bodek's model)
● DIS cross-section
● Coherent-p cross-section
● NC/CC ratio
● nuclear effect in 16O
● pion spectrum
● CC  cross-section
 interaction (12)
Detector, reduction
and reconstruction (21×2)
(SK-I+SK-II, independent)
● Reduction for FC
● Reduction for PC
● Reduction for upward-going muon
● FC/PC separation
● Hadron simulation (contamination of NC in 1-ring -like)
● Non- BG ( flasher for e-like )
● Non- BG ( cosmic ray muon for mu-like )
● Upward stopping/through-going mu separation
● Ring separation
● Particle identification for 1-ring samples
● Particle identification for multi-ring samples
● Energy calibration
● Energy cut for upward stopping muon
● Up/down symmetry of energy calibration
● BG subtraction of up through 
● BG subtraction of up stop 
● Non-e contamination for multi-GeV 1-ring electron
● Non-e contamination for multi-GeV multi-ring electron
● Normalization of multi-GeV multi-ring electron
● PC stop/through separation
   2 flavor analysis
1489 days (SK-1)+ 800 days (SK-II)
Best Fit: Dm2 = 2.5 x 10-3 eV2
sin2 2q = 1.00
c2 = 839.7 / 755 dof (18%)
1.9 x 10-3 eV2 < Dm2 < 3.1 x 10-3 eV2
sin2 2q > 0.93
at 90% CL
Dc2 distributions
Allowed Parameter Space from atmospheric
and Accelerator Long Baseline experiments
Accuracy: Dm2: Atm LBL, sin22q: still atm.
L/E analysis
Motivation: Really oscillation ?
Before 2004, what we knew was that neutrinos change flavor if they
propagate long enough distances.
Other mechanisms were proposed to change the neutrino flavor. For
example, they were neutrino decay or neutrino decoherence models.
oscillation
-like multi-GeV
+ PC
decay
decoherence
These models explained the atmospheric
neutrino data well.
L/E analysis
SK collab. hep-ex/0404034
oscillation
L
1
P = 1 – 2 sin22q ・ (1 – exp(–g0
))
E
decoherence
decay
L 2
P = (cos2q  sin2q ・ exp(– m
))
2 E
Should observe this dip!
 Further evidence for oscillations
 Strong constraint on oscillation parameters, especially Dm2
L/E plot in 1998 SK evidence paper…
Due to the bad L/E resolution events,
the dip was completely washed out.
(Or neutrinos decay….)
Something must be improved….
Selection criteria
FC single-ring -like
Select events with
high L/E resolution
1/2
oscillation
D(L/E)=70%
(D(L/E) < 70%)
Events are not used,
if:
★horizontally going
events
★low energy events
Similar cut for: FC multi-ring -like,
OD stopping PC, and
OD through-going PC
L/E distribution
SK-I+II, FC+PC, prelim.
(Preliminary)
MC (no osc.)
MC (osc.)
Mostly
down-going
Mostly
up-going
Osc.
The oscillation dip is observed.
Allowed oscillation parameters from the
SK-I+II L/E analysis
SK-I+II
(preliminary)
2.0 x 10-3 eV2 < Dm2 < 2.8 x 10-3 eV2
sin2 2q > 0.93
at 90% CL
Consistent with the zenith-angle analysis
Slightly unphysical
region (Dc2=0.5)
SK-I+II L/E analysis and non-oscillation
models
SK-I+II
decoherence
decay
(preliminary)
Decoh.
Decay
c2(osc)=83.9/83dof
c2(decay)=107.1/83dof
c2(decoherence)=112.5/83dof
Oscillation gives the best fit to the data.
Decay and decoherence models were
disfavored by 4.8 and 5.3 s, resp.
Osc.
Seach for CC  events
Search for CC  events (SK-I)
CC  events



CC 
MC
hadrons
hadrons
● Many hadrons ．．．．
(But no big difference with other (NC) events．)
BAD
- likelihood analysis
Only ～ 1.0 CC 
FC events/kton・yr
● Upward going only
GOOD
Zenith angle
(BG (other  events)
～ 130 ev./kton・yr)
Selection of  events
Pre-cuts: E(visible) >1,33GeV, most-energetic ring = e-like
Max. distance
between primary
vertex and the
decay-electron
vertex
E(visible)
Number of
ring
candidates
Sphericity in the
CM frame
Sphericity in
the lab frame
 MC
Atm. MC
data
Likelihood / neural-net distributions
Down-going (no )
Up-going
Neural-net
Zenith-angle
Likelihood
Zenith angle dist. and fit results
Number of events
Likelihood analysis
Dat
a
scaled 
MC
, e, & NC
background
cosqzenith
Fitted # of 
events
Expected # of
 events
NN analysis
Hep-ex/0607059
cosqzenith
138±48(stat) +15 / -32(syst)
134±48(stat) +16 / -27(syst)
78±26(syst)
78±27 (syst)
Zero tau neutrino interaction is disfavored at 2.4s.
Constraints on non-standard
oscillations
Oscillation to  or sterile ?
-like data show zenith-angle and energy dependent deficit of
events, while e-like data show no such effect.

or
sterile
Propagation
x
x
Interaction
sterile
Z
Difference in
P() and
P(sterile) due
to matter effect
sterile
Neutral current
interaction
Testing  vs. sterile
High E PC
events
(Evis>5GeV)
Neutral
current
Matter
effect
Up through
muons
Pure sterile excluded
Multi-ring e-like,
with Evis >400MeV
(PRL85,3999
(2000))
Limit on oscillations to sterile
(sinx・sterile+cosx・)
If pure , sin2x=0
If pure sterile, sin2x=1
SK-1 data
Consistent
with pure

SK collab. draft in
preparation
Mass Varying Neutrinos (MaVaN)?
Neutrino dark energy scenario
 Relic neutrinos with their masses varied by ambient
neutrino density (A.Nelson et al. 2004)
 Possibly their masses also varied by matter density or
electron density beyond the MSW effect
Check the MaVaN model in atmospheric data
• Dm2→Dm2×(re/r0)n
(r0=1.0mol/cm3)
mass varying with electron density
• 2 flavor Zenith angle analysis (assuming sin22q=1.0)
• SK-I dataset
Neutrino flight length
Super-K detector: 1000m underground
below the top of Mt. Ikenoyama
About 350m
above see
level
Down-going neutrinos fly in the air
except for the last 1 to (a few) km.
Excluding a pure MaVaN scenario
Standard
oscillation
n
Dm2→Dm2×(re/r0)n
c2-c2min (@Dm2=1.95x10-3)
c2-c2min
Dm2
n vs Dm2 for MaVaN model
n
Best fit : Dm2=1.95×10-3eV2
n=-0.03
c2=172.2/178 dof
Tested MaVaN scenario is strongly disfavored
Constraining decoherence parameter
Pure decoherence is
excluded at about 5s.
It might be possible that
oscillation and
decoherence co-exists.
 survival probability for
oscillation + decoherence
L
2

 r0

1 2
D
m
L 
E
 
P(     )  1  sin 2q  1  e . cos

2
2
E




Constraining the decoherence parameter with SK L/E analysis
New constraint on decoherence
parameter
SK collab. Draft in preparation
SK-I+II
c2min = 83.8/81 d.o.f
(g0,Dm2,sin22q)= (0 GeV,2.4x10-3eV2,1.0)
g0 <1.4x10-22GeV (90%C.L.)
g0
More than factor 10
improvement over the previous
upper limit (2×10-21GeV)
(×10-21GeV)
(Lisi et al, PRL 85, 1166 (2000)
Super-K
INO
MEMPHYS
UNO
Hyper-K
Present and future osc. experiments
Present: Study of dominant oscillation channels
Future: Study of sub-dominant oscillations
Known:
q12, Dm122
3
e 

q23,
|Dm232|
Unknown:
q13
Sign of Dm232
or
2
1
Solar,
Atmospheric
KamLAND
Long baseline
If q23 ≠p/4,
is it >p/4 or <p/4 ?
(CP)
 Future atmospheric exp’s
q13
Search for non-zero q13 in atmospheric
neutrino experiments
2


1
.
27
D
m
2
2
2
23 L 

P(    e )  sin q 23  sin 2q13  sin 

E


Since e is involved,
the matter effect
must be taken into
account.
(Dm122=0 and vacuum
oscillation assumed)
Earth
model
Simulation
Core
Mantle
Search for non-zero q13 in atmospheric
neutrino experiments
2


1
.
27
D
m
2
2
2
23 L 

P(    e )  sin q 23  sin 2q13  sin 

E


Assuming 3 is
the heaviest:
P(   e )
(Dm122=0 and vacuum
oscillation assumed)
Monte Carlo, SK 20yrs
1+multi-ring, e-like,
2.5 - 5 GeV
cosQ
Electron appearance
s213=0.05
s213=0.00
null oscillation
E(GeV)
cosQ
Electron appearance in the multi-GeV upward going events.
SK-I multi-GeV e-like data
Multi-GeV, single-ring e-like
Multi-GeV, multi-ring e-like
(special)
No evidence for excess of upward-going e-like events
 No evidence for non-zero q13
q13 analysis from Super-K-I
Hep-ex/0604011
Normal
3
2
1
Inverted
2
1
3
c2 distributions
SK-1
CHOOZ limit
If the shape of c2 continues to be like this, (factor ～2) more
data might constrain the interesting q13 region at 90%CL.
Future sensitivity to non-zero q13
 1.27Dm23 2 L 

P(    e )  sin q 23  sin 2q13  sin 

E


2
20yrs SK
(450kton・yr)
2
2
Approximate CHOOZ limit
s22q12=0.825
s2q23=0.40 ~ 0.60
s2q13=0.00~0.04
dcp=45o
Dm212=8.3e-5
Dm223=+2.5e-3
sin2q23=0.60
0.55
0.50
3s
0.45
0.40
3s for 80yrs SK
~4yrs HK
(1.8Mton・yr)
Positive signal for nonzero q13 can be seen if
q13 is near the CHOOZ limit and sin2q23 > 0.5
But probably
after
T2K/Nova…
Search for non-zero q13 with 
disappearance in atmospheric  exp.
INO/2006/01
Project report
But I was unable to fine the
sensitivity plots for magnetized
iron detectors. Sorry…
Sign of
2
Dm
Sign of Dm2
If Dm232 is positive, resonance for 
Very important to
measure the
charge of leptons
 If Dm232 is negative, resonance for anti-
q13
(With resolution)
 Magnetized
detector
INO/2006/01
Project report
q13 (sin2q13)
Significance
(1.12Mtonyr)
7 deg (0.015) 1.6 s
Blue = normal
Red = inverted
9
(0.025) 2.5
11
(0.036)
3.5
13
(0.05)
4.5
 If Dm232 is positive,
resonance for 
 If Dm232 is negative,
resonance for anti-
+
s(total) and ds/dy are
different between
 and anti-.
P (    e )
or
P (    e )
ds/dy
Can we discriminate positive and
negative Dm2 in water Ch.?


y=(E-E)/E
SK atm.  MC
Fraction
1-ring e-like
Others
CC e
CC e
Multi-ring e-like
CC e
Others
CC e
E(GeV)
Electron appearance for positive and
negative Dm2
Single-ring e-like
Relatively high anti-e
fraction
Multi-ring e-like
Lower anti-e fraction.
Positive Dm2
Negative Dm2
null oscillation
cosQ
cosQ
Small (Large) effect for
Dm2 <0 (>0).
c2 difference (true – wrong hierarchy)
Dm2: fixed, q23: free, q13: free
Exposure: 1.8Mtonyr = 80yr SK = 3.3yr HK
True=
3
2
1
True=
2
1
3
3s
 Water Ch. and magnetized muon detectors have similar sensitivity
3s
Octant of q23
Solar oscillation effect in
atmospheric neutrinos
3
e 

However,
Dm232
2
1
Dm122
Diameter of the Earth (L) = 12,800km,
Typical atmospheric neutrino energy (E) =
1GeV
 (L/E)-1 = 8×10-5 (km/GeV)-1
So far, Dm122 has been
neglected, because
Dm122 (8.0×10-5) <<
Dm232 (2.5×10-3)
Solar oscillation terms
cannot be neglected !
●matter effect must be
taken into account
●q13 = 0 assumed.
Solar term effect to atmospheric 
Peres & Smirnov NPB 680
(2004) 479
Atmospheric
neutrinos oscillation
by (q12, Dm122).
P(   e )
w/o matter effect
s22q12=0.825
Dm212=8.3×10-5
Dm223=2.5×10-3
sin2q13=0
with matter effect
Solar term effect to atmospheric 
However, due to the cancellation between
e and ex, the change in the e flux is
small.
P(e  e)
= 1 – P2
P(e  ) = P(  e) = cos2q23 P2
P2 : 2 transition prob. e  x by Dm122
e flux (osc) = f(e0)・(1-P2)+f(0)・cos2q23P2
 e flux(osc)
 e flux(no osc)
Oscillation probability is different between s2q23=0.4 and 0.6
 discrimination between q23 >p/4 and <p/4 might be possible by
studying low energy atmospheric e and  events.
Effect of the solar terms to the sub-GeV /e
ratio (zenith angle dependence)
Dm212
= 8.3 x 10-5 eV2
Dm223
= 2.5 x 10-3 eV2
sin2 2q12 = 0.82
sin2q13=0
(/e) (3 flavor)
(/e) (2 flavor full-mixing)
Below 1.3GeV
P , e < 400 MeV
P , e > 400 MeV
sin2q23 = 0.6
sin2q23 = 0.5
sin2q23 = 0.4
It could be possible to discriminate the octant of q23,
if sin2q23 is significantly away from 0.5.
Constraint on sin2q23 with and without
the solar terms
Solar terms off :
w/o solar terms
best-fit : sin2 q23 = 0.50
w/ solar terms
Solar terms on :
(preliminary)
best-fit : sin2 q23 = 0.52
(sin2 2q23 = 0.9984)
Still (almost)
maximum mixing is
most favored.
Future q23 octant determination with the
(12) and (13) terms
1.8Mtonyr = SK 80 yrs = 3.3 HK yrs
90%CL
90%CL
sin22q23=0.96
s2q23=0.40 ~ 0.60
s2q13=0.00~0.04
dcp=45o
sin22q23=0.99
sin2q13
Fit result
Test point
sin2q23
Discrimination between
q23>p/4 and <p/4 is
possible for all q13.
sin2q23
Discrimination between
q23>p/4 and <p/4 is marginally
possible only for sin2q13 >0.04.
q23 octant determination and syst. errors
S.Nakayama, RCCN Int. Workshop
on sub-dom. Atm. Osc. 2004
Dm212
= 8.3 x 10-5 eV2
Dm223
= 2.5 x 10-3 eV2
sin2 2q12 = 0.82
sin2q13=0
P , e < 400 MeV
sin2q23 = 0.6
sin2q23 = 0.5
sin2q23 = 0.4
true
(/e) (3 flavor)
(/e) (2 flavor full-mixing)
0.8 Mtonyr = SK 20yr = HK 0.8yr
Summary of atmospheric neutrino-2
• Present atmospheric neutrino data are nicely
explained by    oscillations.
• L/E analysis has shown evidence for “oscillatory”
signature.
• The data are consistent with tau neutrino
appearance.
• So far, no evidence for sub-dominant oscillations.
• Future atmospheric neutrino experiments
(magnetized detector, very large water
Cherenkov) are likely to give unique contribution
to this field (especially if sin22q13 is close to the
present limit). Detecting solar oscillation effect is
also an interesting possibility.
End