Transcript NNN05 workshop, Aussois, Savoie, France, April 2005 Takaaki Kajita ICRR, Univ. of Tokyo Work done with S.Nakayama, Y.Obayashi, K.Okumura, M.Shiozawa.

NNN05 workshop,
Aussois, Savoie, France, April 2005
Takaaki Kajita
ICRR, Univ. of Tokyo
Work done with
S.Nakayama, Y.Obayashi, K.Okumura, M.Shiozawa
n mass and mixing parameters:
q12, q23, q13, d, Dm122, Dm132(=Dm232)
Known:
q12, Dm122
n3
ne nm
nt
q23,
|Dm232|
Unknown:
q13
Sign of Dm232
or
n2
n1
Solar,
Atmospheric
KamLAND
Long baseline
If q23 ≠p/4,
is it >p/4 or <p/4 ?
CP ?
How much can we learn from
atmospheric neutrino experiments?
Outline
•
•
•
•
Introduction
sin2q13 ?
Sign of Dm232 ?
. q23 >p/4 or <p/4 ? (including solar
oscillation terms)
• CP phase measurement ?
• Summary
Detector and assumption
Detector: Hyper-Kamiokande
The performance of the Hyper-K detector is assumed to be
identical to Super-K.
54m
Fiducial mass = 0.54 Mton
Search for non-zero q13
2

2
2
2 1.27Dm L 

P(n m  n e )  sin q 23  sin q13  sin 


E


P(n m n e )
(Dm122=0 assumed)
0.45 Mtonyr
1+multi-ring, e-like, 2.5 - 5 GeV
cosqzenith
Electron appearance
s213=0.05
s213=0.00
null oscillation
En(GeV)
cosqzenith
Electron appearance in the multi-GeV upward going events.
Binning for this analysis (= 3flavor analysis in SK)
10 zenith angle bins
for each box.
SubGeV
MultiGeV
Up-stop
SingleRing e
En
MultiRing e
CC ne
SingleRing m
MultiRing m
PCstop
PCthrough
Up-through
CC nm
37 momentum bins x 10 zenith bins = 370 bins in total
Small number of events per bin
(or slightly smaller number
of bins for some analyses)
Poisson statistics to claculate c2 with 44 systematic error terms
Statistical significance for
non-zero q13
Importance of s2q23>0.5;
S.Pascoli et al., hepph/0305152
450 kton・yr = 0.8yr HK
Dm232 ; positive assumed
3s
3s
3s
(Dc2 is approximately
proportional to the exposure)
Sign of Dm2 ?
If Dm232 is positive, resonance for neutrinos
If Dm232 is negative, resonance for anti-neutrinos
Single-ring e-like
Relatively high anti-ne
fraction
Dm2=0.002eV2
s2q23 = 0.5
s2q13 = 0.05
(0.45 Mtonyr)
Multi-ring e-like
Relatively high ne
fraction
Positive Dm2
Negative Dm2
null oscillation
cosQ
cosQ
c2 difference (inverted-normal)
True= normal mass hierarchy assumed.
Dm2: fixed, q23: free, q13: free
Exposure: 1.8Mtonyr
(HK = 3.3 yr)
3s
3s
3s
c2 difference (normal – inverted)
True= inverted mass hierarchy assumed.
Dm2: fixed, q23: free, q13: free
Exposure: 1.8Mtonyr
(HK =3.3 yr)
3s
3s
3s
q23 >p/4 or <p/4 ?
CP phase measurement ?
Expected oscillation with solar terms (1)
P(n m n e )
Because of the LMA
solution, atmospheric
neutrinos should also
oscillate by (q12, Dm122).
However, due to
the cancellation
between nmne
and nenm, the
change in the ne
flux is small.
Peres & Smirnov
NPB 680 (2004)
479
s22q12=0.825
Dm212=8.3×10-5
Dm223=2.5×10-3
sin2q13=0
n e flux(osc)
n e flux(no osc)
s2q23=0.4
=0.5
Oscillation probability is different between s2q23=0.4 and 0.6
 discrimination between q23 >p/4 and <p/4 might be possible.
=0.6
Expected oscillation with
solar terms (2)
n e flux(osc)
n e flux(no osc)
s2q23=0.4
s2q13=0.0
In addition,
we may have
non-zero q13.
s22q12=0.825
Dm212=8.3×10-5
Dm223=2.5×10-3
(always assumed
later in this talk)
s2q23=0.4
s2q13=0.04
dcp=p/4
Effect of LMA
Effect
Interference of q
13
(CP)
e-like (3 flavor) / e-like (2 flavor full-mixing)
Effect of the solar term to sub-GeV e-like zenith
Dm
= 8.3 x 10
angle
2
12
2
Dm 23
= 2.5
2
sin 2q12 = 0.82
sin2q13=0
sub-GeV e-like
(Pe :100 ~ 1330 MeV)
(Pe :100 ~ 400 MeV)
-5
eV2
x 10-3 eV2
(Pe :400 ~ 1330 MeV)
sin2 q23 = 0.4
sin2 q23 = 0.5
sin2 q23 = 0.6
cosqzenith
(Much smaller and opposite effect for m-like events.)
m/e ratio @low energy is useful to discriminate
q23>p/4 and <p/4.
Discrimination between q23 >p/4 and <p/4
with the (12) and (13) terms s q =0.40 ~ 0.60
2 23
s2q13=0.00~0.04
1.8Mtonyr = 3.3 yrs HK
90%CL
90%CL
sin22q23=0.96
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 q13 >0.04.
Effect of dCP in atmospheric neutrino data
e-like (3 flavor) / e-like (no-osc)
no osc. with 80yrs stat.error
dCP= 45o
135o
225o
315o
s22q12=0.825
s2q23=0.5
s2q13=0.04
Dm212=+8.3e-5
Dm223=+2.5e-3
Mutli-GeV, multiring e-like
CP effect
q13 effect
cosqzenith
Sensitivity to dcp
s22q12=0.825
s2q23=0.5
s2q13=0.01~0.04
Dm212=+8.3e-5
Dm223=+2.5e-3
1.8 Mtonyr ~ 3.3yrs HK
sin2q13=0.04
Test (d, q13) point
0.1
99%CL
90%CL
sin2q13
0
sin2q13=0.02
0.1
0
0.1
0
sin2q13=0.01
0
p
2p 0
p
2p 0
CP phase d
p
2p 0
p
2p
CP phase could be seen if q13 is close to the CHOOZ limit.
• The present Monte Carlo study suggests that the
future atmospheric neutrino experiments with
very high statistics will be very interesting, if q13
is large enough.
• For large q13, atmospheric neutrino experiments
with > 2 Mtonyr exposure will;
discriminate the mass hierarchy
discriminate between q23 >p/4 and <p/4
(if sin22q23 is smaller than 0.99)
(if sin22q23 is about 0.96 or smaller,
the discrimination is possible even if q13=0)
give some information on the CP phase
End