Sandhya Choubey Harish-Chandra Research Institute ...lss.fnal.gov/conf/C0606131/6.2Choubey.pdf ·...
Transcript of Sandhya Choubey Harish-Chandra Research Institute ...lss.fnal.gov/conf/C0606131/6.2Choubey.pdf ·...
WHAT WE CAN LEARN FROM ATMOSPHERIC NEUTRINOS
Sandhya Choubey
Harish-Chandra Research Institute, Allahabad, India
Neutrino 2006XXII International Conference on Neutrino Physics and Astrophysics
Santa Fe, 14-19 June 2006
Goals for the Future / Plan of Talk
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.1/41
Goals for the Future / Plan of Talk
Confirmation of oscillations of atmospheric neutrinos
Precision measurement of ∆m231 and θ23
Measuring the deviation of θ23 from its maximal value
Determining the octant of θ23
Determining the sign of ∆m231
Compare and contrast the capabilities of large water Cerenkov(SK50) and magnetized iron detectors (INO-ICAL) for all of theabove. (See hep-ph/0604182 for discussion on Liquid Argon.)
Using atmospheric neutrinos to constrain new physics
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.2/41
Goals for the Future / Plan of Talk
Confirmation of oscillations of atmospheric neutrinos
Precision measurement of ∆m231 and θ23
Measuring the deviation of θ23 from its maximal value
Determining the octant of θ23
Determining the sign of ∆m231
Compare and contrast the capabilities of large water Cerenkov(SK50) and magnetized iron detectors (INO-ICAL) for all of theabove. (See hep-ph/0604182 for discussion on Liquid Argon.)
Using atmospheric neutrinos to constrain new physics
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.2/41
Goals for the Future / Plan of Talk
Confirmation of oscillations of atmospheric neutrinos
Precision measurement of ∆m231 and θ23
Measuring the deviation of θ23 from its maximal value
Determining the octant of θ23
Determining the sign of ∆m231
Compare and contrast the capabilities of large water Cerenkov(SK50) and magnetized iron detectors (INO-ICAL) for all of theabove. (See hep-ph/0604182 for discussion on Liquid Argon.)
Using atmospheric neutrinos to constrain new physics
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.2/41
Goals for the Future / Plan of Talk
Confirmation of oscillations of atmospheric neutrinos
Precision measurement of ∆m231 and θ23
Measuring the deviation of θ23 from its maximal value
Determining the octant of θ23
Determining the sign of ∆m231
Compare and contrast the capabilities of large water Cerenkov(SK50) and magnetized iron detectors (INO-ICAL) for all of theabove. (See hep-ph/0604182 for discussion on Liquid Argon.)
Using atmospheric neutrinos to constrain new physics
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.2/41
Goals for the Future / Plan of Talk
Confirmation of oscillations of atmospheric neutrinos
Precision measurement of ∆m231 and θ23
Measuring the deviation of θ23 from its maximal value
Determining the octant of θ23
Determining the sign of ∆m231
Compare and contrast the capabilities of large water Cerenkov(SK50) and magnetized iron detectors (INO-ICAL) for all of theabove. (See hep-ph/0604182 for discussion on Liquid Argon.)
Using atmospheric neutrinos to constrain new physics
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.2/41
Goals for the Future / Plan of Talk
Confirmation of oscillations of atmospheric neutrinos
Precision measurement of ∆m231 and θ23
Measuring the deviation of θ23 from its maximal value
Determining the octant of θ23
Determining the sign of ∆m231
Compare and contrast the capabilities of large water Cerenkov(SK50) and magnetized iron detectors (INO-ICAL) for all of theabove. (See hep-ph/0604182 for discussion on Liquid Argon.)
Using atmospheric neutrinos to constrain new physics
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.2/41
Goals for the Future / Plan of Talk
Confirmation of oscillations of atmospheric neutrinos
Precision measurement of ∆m231 and θ23
Measuring the deviation of θ23 from its maximal value
Determining the octant of θ23
Determining the sign of ∆m231
Compare and contrast the capabilities of large water Cerenkov(SK50) and magnetized iron detectors (INO-ICAL) for all of theabove. (See hep-ph/0604182 for discussion on Liquid Argon.)
Using atmospheric neutrinos to constrain new physics
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.2/41
Confirmation of Oscillations of Atmospheric Neutrinos
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.3/41
Confirmation of Oscillations of Atmospheric NeutrinosSmoking Gun Signal for νµ − ντ Oscillations
SK collab, Koshio talk, NANP ’05
Its important to observe the characteristic “dip” in L/E
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.4/41
Confirmation of Oscillations of Atmospheric Neutrinos
2 2.5 30
20
40
60
80
100
120
140
2 2.5 3
INO collaboration
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.5/41
Confirmation of Oscillations of Atmospheric Neutrinos
2 2.5 30
20
40
60
80
100
120
140
2 2.5 3
INO collaborationThe first oscillation dip should be clearly observable
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.5/41
Precision Measurement of ∆m231 and θ23
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.6/41
Precision Measurement of ∆m231 and θ23
Experiment |∆m231| sin2 θ23
Current 30% 34%
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.7/41
Precision Measurement of ∆m231 and θ23
Experiment |∆m231| sin2 θ23
Current 30% 34%MINOS+CNGS 13% 38%
T2K (5 yrs) 6% 22%NOνA (5 yrs) 13% 42%Combination 4.5% 20%
Huber et al hep-ph/0403068
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.7/41
Precision Measurement of ∆m231 and θ23
Experiment |∆m231| sin2 θ23
Current 30% 34%MINOS+CNGS 13% 38%
T2K (5 yrs) 6% 22%NOνA (5 yrs) 13% 42%Combination 4.5% 20%
SK20 (1.84 MTy) 17% 24%
Huber et al hep-ph/0403068
Gonzalez-Garcia et al, hep-ph/0408170
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.7/41
Precision Measurement of ∆m231 and θ23
Experiment |∆m231| sin2 θ23
Current 30% 34%MINOS+CNGS 13% 38%
T2K (5 yrs) 6% 22%NOνA (5 yrs) 13% 42%Combination 4.5% 20%
SK20 (1.84 MTy) 17% 24%
INO (250 kTy) 10% 30%
Huber et al hep-ph/0403068
Gonzalez-Garcia et al, hep-ph/0408170
INO Collaboration
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.7/41
Three Generation Oscillation Probabilities
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.8/41
Muon Neutrino Survival Probability
lim∆m2
21→ 0
Pµµ(L, E) = 1 − P 1
µµ(L, E) − P 2
µµ(L, E) − P 3
µµ(L, E)
P 1
µµ(L, E) = sin2 θM13 sin2 2θ23 sin2 (A + ∆m2
31) − (∆m231)
M
8EL
P 2
µµ(L, E) = cos2 θM13 sin2 2θ23 sin2 (A + ∆m2
31) + (∆m231)
M
8EL
P 3
µµ(L, E) = sin2 2θM13 sin4 θ23 sin2 (∆m2
31)M
4EL
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.9/41
Muon Neutrino Survival Probability
lim∆m2
21→ 0
Pµµ(L, E) = 1 − P 1
µµ(L, E) − P 2
µµ(L, E) − P 3
µµ(L, E)
P 1
µµ(L, E) = sin2 θM13 sin2 2θ23 sin2 (A + ∆m2
31) − (∆m231)
M
8EL
P 2
µµ(L, E) = cos2 θM13 sin2 2θ23 sin2 (A + ∆m2
31) + (∆m231)
M
8EL
P 3
µµ(L, E) = sin2 2θM13 sin4 θ23 sin2 (∆m2
31)M
4EL
Dependence on θ23 in the form sin4 θ23
Octant sensitivity is expected to be good
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.9/41
Large Matter Effects in νµ Survival Probability
1 3 5 7 9E (GeV)
0
0.2
0.4
0.6
0.8
P µµ
0
0.2
0.4
0.6
0.8
P µµ
0
0.2
0.4
0.6
0.8
1
P µµ sin2θ23=0.50 (matter)
sin2θ23=0.50 (vacuum)
sin2θ23=0.36 (matter)
sin2θ23=0.36 (vacuum)
L=1000 km
L=3000 km
L=5000 km
L=7000 km
L=9000 km
L=11000 km
1 3 5 7 9 11E (GeV)
S.C. and P. Roy, hep-ph/0509197
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.10/41
Large Matter Effects in νµ Survival Probability
1 3 5 7 9E (GeV)
0
0.2
0.4
0.6
0.8
P µµ
SPMAX
SPMIN2SPMIN1
0
0.2
0.4
0.6
0.8
P µµ
0
0.2
0.4
0.6
0.8
1
P µµ sin2θ23=0.50 (matter)
sin2θ23=0.50 (vacuum)
sin2θ23=0.36 (matter)
sin2θ23=0.36 (vacuum)
L=1000 km
L=3000 km
L=5000 km
L=7000 km
L=9000 km
L=11000 km
1 3 5 7 9 11E (GeV)
S.C. and P. Roy, hep-ph/0509197
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.10/41
Large Matter Effects in νµ Survival Probability
1 3 5 7 9E (GeV)
0
0.2
0.4
0.6
0.8
Pµ
µ
SPMAX
SPMIN2SPMIN1
0
0.2
0.4
0.6
0.8
Pµ
µ
0
0.2
0.4
0.6
0.8
1
Pµ
µ sin2θ23=0.50 (matter)
sin2θ23=0.50 (vacuum)
sin2θ23=0.36 (matter)
sin2θ23=0.36 (vacuum)
L=1000 km
L=3000 km
L=5000 km
L=7000 km
L=9000 km
L=11000 km
1 3 5 7 9 11E (GeV)
Max effect for L ' 7000 km andE ' 5 GeV ⇒ (ESPMAX ' Eres)
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.10/41
Large Matter Effects in νµ Survival Probability
1 3 5 7 9E (GeV)
0
0.2
0.4
0.6
0.8
Pµ
µ
SPMAX
SPMIN2SPMIN1
0
0.2
0.4
0.6
0.8
Pµ
µ
0
0.2
0.4
0.6
0.8
1
Pµ
µ sin2θ23=0.50 (matter)
sin2θ23=0.50 (vacuum)
sin2θ23=0.36 (matter)
sin2θ23=0.36 (vacuum)
L=1000 km
L=3000 km
L=5000 km
L=7000 km
L=9000 km
L=11000 km
1 3 5 7 9 11E (GeV)
Max effect for L ' 7000 km andE ' 5 GeV ⇒ (ESPMAX ' Eres)
Pµµ decreases (increases) at SP-MAX (SPMIN) due to matter effects
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.10/41
Large Matter Effects in νµ Survival Probability
1 3 5 7 9E (GeV)
0
0.2
0.4
0.6
0.8
Pµ
µ
SPMAX
SPMIN2SPMIN1
0
0.2
0.4
0.6
0.8
Pµ
µ
0
0.2
0.4
0.6
0.8
1
Pµ
µ sin2θ23=0.50 (matter)
sin2θ23=0.50 (vacuum)
sin2θ23=0.36 (matter)
sin2θ23=0.36 (vacuum)
L=1000 km
L=3000 km
L=5000 km
L=7000 km
L=9000 km
L=11000 km
1 3 5 7 9 11E (GeV)
Max effect for L ' 7000 km andE ' 5 GeV ⇒ (ESPMAX ' Eres)
Pµµ decreases (increases) at SP-MAX (SPMIN) due to matter effects
Sign of the earth matter effectsdepends on both E and L
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.10/41
Large Matter Effects in νµ Survival Probability
1 3 5 7 9E (GeV)
0
0.2
0.4
0.6
0.8
Pµ
µ
SPMAX
SPMIN2SPMIN1
0
0.2
0.4
0.6
0.8
Pµ
µ
0
0.2
0.4
0.6
0.8
1
Pµ
µ sin2θ23=0.50 (matter)
sin2θ23=0.50 (vacuum)
sin2θ23=0.36 (matter)
sin2θ23=0.36 (vacuum)
L=1000 km
L=3000 km
L=5000 km
L=7000 km
L=9000 km
L=11000 km
1 3 5 7 9 11E (GeV)
Max effect for L ' 7000 km andE ' 5 GeV ⇒ (ESPMAX ' Eres)
Pµµ decreases (increases) at SP-MAX (SPMIN) due to matter effects
Sign of the earth matter effectsdepends on both E and L
Matter effects depend on thevalue of sin2 θ23
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.10/41
Large Matter Effects in νµ Survival Probability
1 3 5 7 9E (GeV)
0
0.2
0.4
0.6
0.8
Pµ
µ
SPMAX
SPMIN2SPMIN1
0
0.2
0.4
0.6
0.8
Pµ
µ
0
0.2
0.4
0.6
0.8
1
Pµ
µ sin2θ23=0.50 (matter)
sin2θ23=0.50 (vacuum)
sin2θ23=0.36 (matter)
sin2θ23=0.36 (vacuum)
L=1000 km
L=3000 km
L=5000 km
L=7000 km
L=9000 km
L=11000 km
1 3 5 7 9 11E (GeV)
Max effect for L ' 7000 km andE ' 5 GeV ⇒ (ESPMAX ' Eres)
Pµµ decreases (increases) at SP-MAX (SPMIN) due to matter effects
Sign of the earth matter effectsdepends on both E and L
Matter effects depend on thevalue of sin2 θ23
Most important to choose the bins properly in both E and L
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.10/41
Very Large Matter Effects in νµ ↔ νe Probability
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.11/41
Very Large Matter Effects in νµ ↔ νe Probabilities
lim∆m2
21→ 0
Pµe(L, E) = sin2 θ23 sin2 2θM13 sin2 (∆m2
31)ML
4E
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.12/41
Very Large Matter Effects in νµ ↔ νe Probabilities
lim∆m2
21→ 0
Pµe(L, E) = sin2 θ23 sin2 2θM13 sin2 (∆m2
31)ML
4E
1 3 5 7 9E (GeV)
0
0.1
0.2
0.3
0.4
0.5
P µe
sin2θ23=0.5(matter)
sin2θ23=0.5(vacuum)
1 3 5 7 9E (GeV)
L=7000 km L=9000 km
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.12/41
Very Large Matter Effects in νµ ↔ νe Probabilities
lim∆m2
21→ 0
Pµe(L, E) = sin2 θ23 sin2 2θM13 sin2 (∆m2
31)ML
4E
1 3 5 7 9E (GeV)
0
0.1
0.2
0.3
0.4
0.5
P µe
sin2θ23=0.5(matter)
sin2θ23=0.5(vacuum)
1 3 5 7 9E (GeV)
L=7000 km L=9000 km
Above ∼ 3 GeV, matter effects increase Pµe for all E and L
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.12/41
Very Large Matter Effects in νµ ↔ νe Probabilities
lim∆m2
21→ 0
Pµe(L, E) = sin2 θ23 sin2 2θM13 sin2 (∆m2
31)ML
4E
1 3 5 7 9E (GeV)
0
0.1
0.2
0.3
0.4
0.5
P µe
sin2θ23=0.5(matter)
sin2θ23=0.5(vacuum)
1 3 5 7 9E (GeV)
L=7000 km L=9000 km
Sub-dominant ∆m221 oscillations in Pµe is also crucial
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.12/41
Atmospheric Neutrino Events
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.13/41
Atmospheric Neutrino EventsChange in number of muon events:
Nµ = N0
µPµµ + N0
e Peµ
= N0
µ
[
Pµµ +1
rPeµ
]
; (where r =N0
µ
N0e
)
1 −Nµ
N0µ
' (P 1
µµ + P 2
µµ) + (P 3
µµ)′s2
23(s2
23 −1
r)
(P 3
µµ)′ = sin2 2θM13 sin2 (∆m2
31)M
4EL
Can be used to study maximality and octant of θ23
Can be used to study the neutrino mass hierarchy
∆m221 and δCP bring in small effects
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.14/41
Atmospheric Neutrino EventsChange in number of electron events:
Ne
N0e
− 1 ' sin2 2θM12 sin2
(
(∆m221)
ML
4E
)
× (r cos2 θ23 − 1)
+ sin2 2θM13 sin2
(
(∆m231)
ML
4E
)
× (r sin2 θ23 − 1)
+ sin θ23 cos θ23 r Re
[
A∗
13A12 exp(−iδCP )
]
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.15/41
Atmospheric Neutrino EventsChange in number of electron events:
Ne
N0e
− 1 ' sin2 2θM12 sin2
(
(∆m221)
ML
4E
)
× (r cos2 θ23 − 1)
+ sin2 2θM13 sin2
(
(∆m231)
ML
4E
)
× (r sin2 θ23 − 1)
+ sin θ23 cos θ23 r Re
[
A∗
13A12 exp(−iδCP )
]
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.16/41
Atmospheric Neutrino EventsChange in number of electron events:
Ne
N0e
− 1 ' sin2 2θM12 sin2
(
(∆m221)
ML
4E
)
× (r cos2 θ23 − 1)
+ sin2 2θM13 sin2
(
(∆m231)
ML
4E
)
× (r sin2 θ23 − 1)
+ sin θ23 cos θ23 r Re
[
A∗
13A12 exp(−iδCP )
]
∆m221-driven oscillation effect
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.16/41
Atmospheric Neutrino EventsChange in number of electron events:
Ne
N0e
− 1 ' sin2 2θM12 sin2
(
(∆m221)
ML
4E
)
× (r cos2 θ23 − 1)
+ sin2 2θM13 sin2
(
(∆m231)
ML
4E
)
× (r sin2 θ23 − 1)
+ sin θ23 cos θ23 r Re
[
A∗
13A12 exp(−iδCP )
]
∆m221-driven oscillation effect
Brings an excess (depletion) in the sub-GeV electron eventsample for sin2 θ23 < 0.5(> 0.5)
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.16/41
Atmospheric Neutrino EventsChange in number of electron events:
Ne
N0e
− 1 ' sin2 2θM12 sin2
(
(∆m221)
ML
4E
)
× (r cos2 θ23 − 1)
+ sin2 2θM13 sin2
(
(∆m231)
ML
4E
)
× (r sin2 θ23 − 1)
+ sin θ23 cos θ23 r Re
[
A∗
13A12 exp(−iδCP )
]
∆m221-driven oscillation effect
Brings an excess (depletion) in the sub-GeV electron eventsample for sin2 θ23 < 0.5(> 0.5)
Can be used for studying maximality and octant of θ23
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.16/41
Atmospheric Neutrino EventsChange in number of electron events:
Ne
N0e
− 1 ' sin2 2θM12 sin2
(
(∆m221)
ML
4E
)
× (r cos2 θ23 − 1)
+ sin2 2θM13 sin2
(
(∆m231)
ML
4E
)
× (r sin2 θ23 − 1)
+ sin θ23 cos θ23 r Re
[
A∗
13A12 exp(−iδCP )
]
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.17/41
Atmospheric Neutrino EventsChange in number of electron events:
Ne
N0e
− 1 ' sin2 2θM12 sin2
(
(∆m221)
ML
4E
)
× (r cos2 θ23 − 1)
+ sin2 2θM13 sin2
(
(∆m231)
ML
4E
)
× (r sin2 θ23 − 1)
+ sin θ23 cos θ23 r Re
[
A∗
13A12 exp(−iδCP )
]
θ13-driven oscillation effect
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.17/41
Atmospheric Neutrino EventsChange in number of electron events:
Ne
N0e
− 1 ' sin2 2θM12 sin2
(
(∆m221)
ML
4E
)
× (r cos2 θ23 − 1)
+ sin2 2θM13 sin2
(
(∆m231)
ML
4E
)
× (r sin2 θ23 − 1)
+ sin θ23 cos θ23 r Re
[
A∗
13A12 exp(−iδCP )
]
θ13-driven oscillation effectReduces the excess (depletion) in the sub-GeV electron event
sample for sin2 θ23 < 0.5(> 0.5) – thats the bad part!!
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.17/41
Atmospheric Neutrino EventsChange in number of electron events:
Ne
N0e
− 1 ' sin2 2θM12 sin2
(
(∆m221)
ML
4E
)
× (r cos2 θ23 − 1)
+ sin2 2θM13 sin2
(
(∆m231)
ML
4E
)
× (r sin2 θ23 − 1)
+ sin θ23 cos θ23 r Re
[
A∗
13A12 exp(−iδCP )
]
θ13-driven oscillation effectReduces the excess (depletion) in the sub-GeV electron event
sample for sin2 θ23 < 0.5(> 0.5) – thats the bad part!!
Contains big earth matter effects resulting in sizable change inmulti-GeV electron event sample, with the change being sin2 θ23
dependent – thats the excellent part!!
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.17/41
Atmospheric Neutrino EventsChange in number of electron events:
Ne
N0e
− 1 ' sin2 2θM12 sin2
(
(∆m221)
ML
4E
)
× (r cos2 θ23 − 1)
+ sin2 2θM13 sin2
(
(∆m231)
ML
4E
)
× (r sin2 θ23 − 1)
+ sin θ23 cos θ23 r Re
[
A∗
13A12 exp(−iδCP )
]
θ13-driven oscillation effectReduces the excess (depletion) in the sub-GeV electron event
sample for sin2 θ23 < 0.5(> 0.5) – thats the bad part!!
Contains big earth matter effects resulting in sizable change inmulti-GeV electron event sample, with the change being sin2 θ23
dependent – thats the excellent part!!
Can be used for studying maximality and octant of θ23
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.17/41
Atmospheric Neutrino EventsChange in number of electron events:
Ne
N0e
− 1 ' sin2 2θM12 sin2
(
(∆m221)
ML
4E
)
× (r cos2 θ23 − 1)
+ sin2 2θM13 sin2
(
(∆m231)
ML
4E
)
× (r sin2 θ23 − 1)
+ sin θ23 cos θ23 r Re
[
A∗
13A12 exp(−iδCP )
]
θ13-driven oscillation effectReduces the excess (depletion) in the sub-GeV electron event
sample for sin2 θ23 < 0.5(> 0.5) – thats the bad part!!
Contains big earth matter effects resulting in sizable change inmulti-GeV electron event sample, with the change being sin2 θ23
dependent – thats the excellent part!!
Can be used for studying maximality and octant of θ23
Can be used for studying the neutrino mass hierarchy
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.17/41
Atmospheric Neutrino EventsChange in number of electron events:
Ne
N0e
− 1 ' sin2 2θM12 sin2
(
(∆m221)
ML
4E
)
× (r cos2 θ23 − 1)
+ sin2 2θM13 sin2
(
(∆m231)
ML
4E
)
× (r sin2 θ23 − 1)
+ sin θ23 cos θ23 r Re
[
A∗
13A12 exp(−iδCP )
]
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.18/41
Atmospheric Neutrino EventsChange in number of electron events:
Ne
N0e
− 1 ' sin2 2θM12 sin2
(
(∆m221)
ML
4E
)
× (r cos2 θ23 − 1)
+ sin2 2θM13 sin2
(
(∆m231)
ML
4E
)
× (r sin2 θ23 − 1)
+ sin θ23 cos θ23 r Re
[
A∗
13A12 exp(−iδCP )
]
“interference” term which depends on δCP
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.18/41
Atmospheric Neutrino EventsChange in number of electron events:
Ne
N0e
− 1 ' sin2 2θM12 sin2
(
(∆m221)
ML
4E
)
× (r cos2 θ23 − 1)
+ sin2 2θM13 sin2
(
(∆m231)
ML
4E
)
× (r sin2 θ23 − 1)
+ sin θ23 cos θ23 r Re
[
A∗
13A12 exp(−iδCP )
]
“interference” term which depends on δCP
It might cancel the effect of the ∆m221 and θ13 terms depending on
the value of δCP – bad bad bad...
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.18/41
Atmospheric Neutrino EventsChange in number of electron events:
Ne
N0e
− 1 ' sin2 2θM12 sin2
(
(∆m221)
ML
4E
)
× (r cos2 θ23 − 1)
+ sin2 2θM13 sin2
(
(∆m231)
ML
4E
)
× (r sin2 θ23 − 1)
+ sin θ23 cos θ23 r Re
[
A∗
13A12 exp(−iδCP )
]
“interference” term which depends on δCP
It might cancel the effect of the ∆m221 and θ13 terms depending on
the value of δCP – bad bad bad...
But it might tell us if δCP = 0 or π (Fogli et al. hep-ph/0506083)
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.18/41
Atmospheric Neutrino Events in MTon Water Detector
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.19/41
Atmospheric Neutrino Events in MTon Water Detector
−1 −0.6 −0.2 0.2 0.6 1cosξ
0
1000
2000
3000
4000
5000
even
ts (S
K50
)
∆m2
31=2.5x10−3
eV2
sin22θ23=0.91
sin2θ13=0.00
SGe SGµ
MGeMGµ
0
4000
8000
12000
16000
20000
even
ts (S
K50
)
sin2θ23=0.35
sin2θ23=0.65
∆m2
21=0
−1 −0.6 −0.2 0.2 0.6 1cosξ
0
2000
4000
6000
8000
10000
12000
even
ts (S
K50
)
0
4000
8000
12000
16000
20000
even
ts (S
K50
)
These are just 2-gen νµ → ντ oscillationsOSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.20/41
Atmospheric Neutrino Events in MTon Water Detector
−1 −0.6 −0.2 0.2 0.6 1cosξ
0
1000
2000
3000
4000
5000
even
ts (S
K50
)
∆m2
31=2.5x10−3
eV2
sin22θ23=0.91
sin2θ13=0.00
SGe SGµ
MGeMGµ
0
4000
8000
12000
16000
20000
even
ts (S
K50
)
sin2θ23=0.35
sin2θ23=0.65
∆m2
21=8x10−5
eV2
−1 −0.6 −0.2 0.2 0.6 1cosξ
0
2000
4000
6000
8000
10000
12000
even
ts (S
K50
)
0
4000
8000
12000
16000
20000
even
ts (S
K50
)
∆m221-driven oscillations bring in octant sensitivity in SGe events
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.20/41
Atmospheric Neutrino Events in MTon Water Detector
−1 −0.6 −0.2 0.2 0.6 1cosξ
0
1000
2000
3000
4000
5000
even
ts (S
K50
)
sin22θ23=0.91
sin2θ13=0.04
SGe SGµ
MGeMGµ
∆m2
31=2.5x10−3
eV2
0
4000
8000
12000
16000
20000
even
ts (S
K50
)
sin2θ23=0.35
sin2θ23=0.65
∆m2
21=8x10−5
eV2
−1 −0.6 −0.2 0.2 0.6 1cosξ
0
2000
4000
6000
8000
10000
12000
even
ts (S
K50
)
0
4000
8000
12000
16000
20000
even
ts (S
K50
)
θ13 brings in more octant sensitivity through matter effectsSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.20/41
Atmospheric Neutrino Events in INO-ICAL
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.21/41
Atmospheric Neutrino Events in INO-ICAL
1 3 5 7 9E (GeV)
−0.4
−0.3
−0.2
−0.1
0
0.1
UN/D
N −
UA/D
A
−0.4
−0.3
−0.2
−0.1
0
0.1
UN/D
N −
UA/D
A
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
UN/D
N −
UA/D
A
matter (s2
23=0.5)vacuum (s
2
23=0.5)matter (s
2
23=0.36)
1 3 5 7 9 11E (GeV)
|cξ|=|0−0.157|
|cξ|=|0.157−0.314|
|cξ|=|0.314−0.471|
|cξ|=|0.471−0.628|
|cξ|=|0.628−0.785|
|cξ|=|0.785−0.942|
S.C and P. Roy hep-ph/0509197SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.22/41
Testing Maximality of θ23
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.23/41
Testing maximality of θ23
|D| within 14%LBL combined
Antusch, et al,
hep-ph/0404268
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.24/41
Testing maximality of θ23
|D| within 14%LBL combined
Antusch, et al,
hep-ph/0404268
|D| within 19%SK50
Gonzalez-Garcia, et al,
hep-ph/0408170
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.24/41
Testing maximality of θ23
|D| within 14%LBL combined
Antusch, et al,
hep-ph/0404268
|D| within 19%SK50
Gonzalez-Garcia, et al,
hep-ph/0408170
0.25 0.35 0.45 0.55 0.65 0.75sin
2θ23(true)
1
2
3
∆m2 31
(tru
e)[1
0−3 eV
2 ]
sin2θ13(true)=0.00
500 kTy
|D| within 25%INO-ICAL 500 kTy
S.C. and P. Roy,
hep-ph/0509197
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.24/41
Testing maximality of θ23
|D| within 14%LBL combined
Antusch, et al,
hep-ph/0404268
|D| within 19%SK50
Gonzalez-Garcia, et al,
hep-ph/0408170
0.25 0.35 0.45 0.55 0.65 0.75sin
2θ23(true)
1
2
3
∆m2 31
(tru
e)[1
0−3 eV
2 ]
sin2θ13(true)=0.00
500 kTy
|D| within 25%INO-ICAL 500 kTy
S.C. and P. Roy,
hep-ph/0509197
Sensitivity to |D| ≡ |(sin2 θ23 − 0.5)| comparable to LBL expts
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.24/41
Testing Maximality of θ23
|D| within 14%LBL combined
Antusch, et al,
hep-ph/0404268
0.25 0.35 0.45 0.55 0.65 0.75sin
2θ23(true)
1
2
3
∆m2 31
(tru
e)[1
0−3 eV
2 ]
sin2θ13(true)=0.00
|D| within 20%SK50
preliminary
.
0.25 0.35 0.45 0.55 0.65 0.75sin
2θ23(true)
1
2
3
∆m2 31
(tru
e)[1
0−3 eV
2 ]
sin2θ13(true)=0.00
500 kTy
|D| within 25%INO-ICAL 500 kTy
S.C. and P. Roy,
hep-ph/0509197
Sensitivity to |D| ≡ |(sin2 θ23 − 0.5)| comparable to LBL expts
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.25/41
Testing Maximality of θ23
|D| within 14%LBL combined
Antusch, et al,
hep-ph/0404268
0.25 0.35 0.45 0.55 0.65 0.75sin
2θ23(true)
1
2
3
∆m2 31
(tru
e)[1
0−3 eV
2 ]
sin2θ13(true)=0.00
|D| within 20%SK50
preliminary
.
0.25 0.35 0.45 0.55 0.65 0.75sin
2θ23(true)
1
2
3
∆m2 31
(tru
e)[1
0−3 eV
2 ]
sin2θ13(true)=0.04
500 kTy
|D| within 23%INO-ICAL 500 kTy
S.C. and P. Roy,
hep-ph/0509197
Sensitivity to |D| in INO-ICAL improves marginally with θ13
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.26/41
Testing Maximality of θ23
|D| within 14%LBL combined
Antusch, et al,
hep-ph/0404268
0.25 0.35 0.45 0.55 0.65 0.75sin
2θ23(true)
1
2
3
∆m2 31
(tru
e)[1
0−3 eV
2 ]
sin2θ13(true)=0.04
|D| within 11%SK50
preliminary
.
0.25 0.35 0.45 0.55 0.65 0.75sin
2θ23(true)
1
2
3
∆m2 31
(tru
e)[1
0−3 eV
2 ]
sin2θ13(true)=0.04
500 kTy
|D| within 23%INO-ICAL 500 kTy
S.C. and P. Roy,
hep-ph/0509197
Sensitivity to |D| in INO-ICAL improves marginally with θ13
Sensitivity to |D| in SK50 improves remarkably with θ13
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.27/41
Resolving the θ23 Octant Ambiguity
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.28/41
Resolving the θ23 Octant Ambiguity with INO-ICAL
0.35 0.4 0.45 0.5 0.55 0.6 0.65sin
2θ23(true)
0
2
4
6
8
10
12
∆χ2 [s
in2 θ 23(true)
− sin2 θ 23(fa
lse)]
Normal Mass Ordering
0.35 0.4 0.45 0.5 0.55 0.6 0.65sin
2θ23(true)
Inverted Mass Ordering
sin2θ13(true)=0.04
sin2θ13(true)=0.03
sin2θ13(true)=0.02
sin2θ13(true)=0.01
1 MTonyr S.C and P. Roy hep-ph/0509197
sin2 θ23(false) can be excluded at 3σ if:
sin2 θ23(true) < 0.402 or > 0.592 for sin2 θ13(true) = 0.02,
sin2 θ23(true) < 0.421 or > 0.573 for sin2 θ13(true) = 0.04.
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.29/41
Resolving the θ23 Octant Ambiguity with SK50
Gonzalez-Garcia et al, hep-ph/0408170
sin2 θ23(false) can be excluded at 3σ if:sin2 θ23(true) < 0.36 or > 0.62 for sin2 θ13(true) = 0.00.
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.30/41
Resolving the θ23 Octant Ambiguity with SK50
0.3 0.4 0.5 0.6 0.7sin
2θ23(true)
0
5
10
15
∆χ2
Blue Lines: sin2θ13(true)=0.00 Red Lines: sin
2θ13(true)=0.02
Solid Lines: no priors; Dashed Lines: external priors
Prelim
inary
sin2 θ23(false) can be excluded at 3σ if:sin2 θ23(true) < 0.384 or > 0.601 for sin2 θ13(true) = 0.00.
sin2 θ23(true) < 0.438 or > 0.574 for sin2 θ13(true) = 0.02.
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.31/41
Resolving the θ23 Octant Ambiguity with SK50
0.3 0.4 0.5 0.6 0.7sin
2θ23(true)
0
5
10
15
∆χ2
Blue Lines: sin2θ13(true)=0.00 Red Lines: sin
2θ13(true)=0.02
Solid Lines: no priors; Dashed Lines: external priors
Prelim
inary
sin2 θ23(false) can be excluded at 3σ if:sin2 θ23(true) < 0.384 or > 0.601 for sin2 θ13(true) = 0.00.
sin2 θ23(true) < 0.438 or > 0.574 for sin2 θ13(true) = 0.02.
�
�
�
�
Sensitivity to octant of θ23
improves remarkably as θ13
increases from zero.
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.31/41
Resolving the sgn(∆m231) Ambiguity
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.32/41
Resolving the sgn(∆m231) Ambiguity with INO-ICAL
0 0.05 0.1 0.150
2
4
6
8
∆χ2 w
r hie
r for
400
0 ev
ents µ-like
2σ
0 0.05 0.1
true value of sin22θ
13
0
10
20
30
µ-likehigh
osc. params. fixed, external prior information, osc. params. freesolid: true hierarchy normal, dashed: true hierarchy inverted
0 0.05 0.1 0.150
5
10
15
20
3σ
3σ
e-like
4000 upward going events (Thomas Schwetz)Petcov and Schwetz, hep-ph/0511277
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.33/41
Resolving the sgn(∆m231) Ambiguity with INO-ICAL
0 0.05 0.1 0.150
2
4
6
8
∆χ2 w
r hie
r for
400
0 ev
ents µ-like
2σ
0 0.05 0.1
true value of sin22θ
13
0
10
20
30
µ-likehigh
osc. params. fixed, external prior information, osc. params. freesolid: true hierarchy normal, dashed: true hierarchy inverted
0 0.05 0.1 0.150
5
10
15
20
3σ
3σ
e-like
4000 upward going events (Thomas Schwetz)Petcov and Schwetz, hep-ph/0511277
The wrong hierarchy can be ruled out at 2σ with 4000 upwardgoing events for sin2 2θ13 = 0.1(sin2 θ13 = 0.026) and sin2 θ23 = 0.5
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.33/41
Resolving the sgn(∆m231) Ambiguity with INO-ICAL
0 0.05 0.1 0.150
2
4
6
8
∆χ2 w
r hie
r for
400
0 ev
ents µ-like
2σ
0 0.05 0.1
true value of sin22θ
13
0
10
20
30
µ-likehigh
osc. params. fixed, external prior information, osc. params. freesolid: true hierarchy normal, dashed: true hierarchy inverted
0 0.05 0.1 0.150
5
10
15
20
3σ
3σ
e-like
4000 upward going events (Thomas Schwetz)Petcov and Schwetz, hep-ph/0511277
The wrong hierarchy can be ruled out at 2σ with 4000 upwardgoing events for sin2 2θ13 = 0.1(sin2 θ13 = 0.026) and sin2 θ23 = 0.5
Polamares-Ruiz,Petcov (2003)
Indumathi, Murthy (2004)
Ghoshal,Gandhi,Goswami,Mehta,UmaSankar (2004)
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.33/41
Resolving the sgn(∆m231) Ambiguity with INO-ICAL
0 0.05 0.1 0.150
2
4
6
8
∆χ2 w
r hie
r for
400
0 ev
ents µ-like
2σ
0 0.05 0.1
true value of sin22θ
13
0
10
20
30
µ-likehigh
osc. params. fixed, external prior information, osc. params. freesolid: true hierarchy normal, dashed: true hierarchy inverted
0 0.05 0.1 0.150
5
10
15
20
3σ
3σ
e-like
4000 upward going events (Thomas Schwetz)Petcov and Schwetz, hep-ph/0511277
The wrong hierarchy can be ruled out at 2σ with 4000 upwardgoing events for sin2 2θ13 = 0.1(sin2 θ13 = 0.026) and sin2 θ23 = 0.5
Sensitivity increases with E and L resolution
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.33/41
Resolving the sgn(∆m231) Ambiguity with INO-ICAL
0 0.05 0.1 0.150
2
4
6
8
∆χ2 w
r hie
r for
400
0 ev
ents µ-like
2σ
0 0.05 0.1
true value of sin22θ
13
0
10
20
30
µ-likehigh
osc. params. fixed, external prior information, osc. params. freesolid: true hierarchy normal, dashed: true hierarchy inverted
0 0.05 0.1 0.150
5
10
15
20
3σ
3σ
e-like
4000 upward going events (Thomas Schwetz)Petcov and Schwetz, hep-ph/0511277
The wrong hierarchy can be ruled out at 2σ with 4000 upwardgoing events for sin2 2θ13 = 0.1(sin2 θ13 = 0.026) and sin2 θ23 = 0.5
Sensitivity increases if it were possible to detect electrons
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.33/41
Resolving the sgn(∆m231) Ambiguity with INO-ICAL
0 0.05 0.1 0.150
2
4
6
8
∆χ2 w
r hie
r for
400
0 ev
ents µ-like
2σ
0 0.05 0.1
true value of sin22θ
13
0
10
20
30
µ-likehigh
osc. params. fixed, external prior information, osc. params. freesolid: true hierarchy normal, dashed: true hierarchy inverted
0 0.05 0.1 0.150
5
10
15
20
3σ
3σ
e-like
4000 upward going events (Thomas Schwetz)Petcov and Schwetz, hep-ph/0511277
The wrong hierarchy can be ruled out at 2σ with 4000 upwardgoing events for sin2 2θ13 = 0.1(sin2 θ13 = 0.026) and sin2 θ23 = 0.5
Sensitivity increases with sin2 θ23
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.33/41
Resolving the sgn(∆m231) Ambiguity with SK50
0 0.01 0.02 0.03sin2θ13
0
2
4
6
8
10
12
14
16
∆χ2 IH
True Hierarchy is Normal
Prelim
inar
y
s2
23(true)=0.4 s2
23(true)=0.5 s2
23(true)=0.6solid: δCP=0
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.34/41
Resolving the sgn(∆m231) Ambiguity with SK50
0 0.01 0.02 0.03sin2θ13
0
2
4
6
8
10
12
14
16
∆χ2 IH
True Hierarchy is Normal
Prelim
inar
y
s2
23(true)=0.4 s2
23(true)=0.5 s2
23(true)=0.6solid: δCP=0 dashed: δCP=free
Sensitivity drops appreciably due to δCP
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.34/41
Resolving the sgn(∆m231) Ambiguity with SK50
0 0.01 0.02 0.03sin2θ13
0
2
4
6
8
10
12
14
16
∆χ2 IH
True Hierarchy is Normal
Prelim
inar
y
s2
23(true)=0.4 s2
23(true)=0.5 s2
23(true)=0.6solid: δCP=0 dashed: δCP=free
Sensitivity drops appreciably due to δCP
Resolving param degen:
T2K+ATM:hep-ph/0501037
βbeams+ATM:hep-ph/0603172
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.34/41
Searching for New Physics
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.35/41
Searching for New PhysicsNon-Standard neutrino-matter Interaction
Violation of Equivalence Principle
Lorentz Invariance Violation
Violation of CPT Symmetry
Neutrino Decay
Quantum Decoherence
(This list is not exhaustive.)
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.36/41
Searching for New Physics in INO-ICAL/SK50 like ExptsNon-Standard neutrino-matter Interaction
Violation of Equivalence Principle
Lorentz Invariance Violation
Violation of CPT Symmetry
Neutrino Decay
Quantum Decoherence
Each one has a distinctive L/E behavior
Oscillations go linearly as L/E
Atmospheric neutrinos have a very wide range of L/E
This L/E data can be used to probe new physics – INO-ICAL
Comparison of contained events and upward going muons inwater Cerenkov detectors can also be used
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.37/41
Searching for New Physics with Neutrino TelescopesNeutrino Telescopes have atmospheric ν’s as background
The atm ν’s seen will be of highest energies: (10−1-104) TeV
At these energies, standard neutrino oscillations are negligible
Any E or L dependence in the data will signify new physics
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.38/41
Searching for New Physics with Neutrino TelescopesNeutrino Telescopes have atmospheric ν’s as background
The atm ν’s seen will be of highest energies: (10−1-104) TeV
At these energies, standard neutrino oscillations are negligible
Any E or L dependence in the data will signify new physics
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.38/41
Searching for New Physics with Neutrino TelescopesNeutrino Telescopes have atmospheric ν’s as background
The atm ν’s seen will be of highest energies: (10−1-104) TeV
At these energies, standard neutrino oscillations are negligible
Any E or L dependence in the data will signify new physics
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.38/41
Searching for New Physics with Neutrino TelescopesNeutrino Telescopes have atmospheric ν’s as background
The atm ν’s seen will be of highest energies: (10−1-104) TeV
At these energies, standard neutrino oscillations are negligible
Any E or L dependence in the data will signify new physics
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.38/41
Searching for New Physics with Neutrino TelescopesNeutrino Telescopes have atmospheric ν’s as background
The atm ν’s seen will be of highest energies: (10−1-104) TeV
At these energies, standard neutrino oscillations are negligible
Any E or L dependence in the data will signify new physics
102
103
104
105
Eµ [GeV]
0.6
0.8
1
1.2
1.4
1.6
1.8
2
pho
riz /
p vert
10-2810
-2710-2610
-25
10-24
Solid=νµ+ντ Dashed=νµ only
δc/c = vary, ξ = 45
pi = Ni / Niosc
vert=[-1.0, -0.6] horiz=[-0.6, -0.2]
Gonzalez-Garcia et al, hep-ph/0502223
ICECUBE
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.38/41
Searching for New Physics with Neutrino TelescopesNeutrino Telescopes have atmospheric ν’s as background
The atm ν’s seen will be of highest energies: (10−1-104) TeV
At these energies, standard neutrino oscillations are negligible
Any E or L dependence in the data will signify new physics
Morgan et al, astro-ph/0412618
ANTARES
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.38/41
Conclusions
SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.39/41
ConclusionsOsc of atmospheric neutrinos will be confirmed by INO-ICAL
Precision on ∆m231 and θ23 can be improved to 17%(10%) and
24%(30%) respectively by SK20 and INO-ICAL(250 kTy)
|D| can to determined to within 20% (25%) by SK50(INO-ICAL(500 kTy)) if sin2 θ13(true) = 0
|D| can to determined to within 11% (23%) by SK50(INO-ICAL(500 kTy)) if sin2 θ13(true) = 0.04
Octant of θ23 can be determined with INO-ICAL(1 MTy) ifsin2 θ23(true) < 0.42 or > 0.57 for sin2 θ13(true) = 0.04
Octant of θ23 can be determined with SK50 ifsin2 θ23(true) < 0.38 or > 0.60 for sin2 θ13(true) = 0
Sensitivity to octant for SK50 improves remarkably if θ13 6= 0
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.40/41
ConclusionsOsc of atmospheric neutrinos will be confirmed by INO-ICAL
Precision on ∆m231 and θ23 can be improved to 17%(10%) and
24%(30%) respectively by SK20 and INO-ICAL(250 kTy)
|D| can to determined to within 20% (25%) by SK50(INO-ICAL(500 kTy)) if sin2 θ13(true) = 0
|D| can to determined to within 11% (23%) by SK50(INO-ICAL(500 kTy)) if sin2 θ13(true) = 0.04
Octant of θ23 can be determined with INO-ICAL(1 MTy) ifsin2 θ23(true) < 0.42 or > 0.57 for sin2 θ13(true) = 0.04
Octant of θ23 can be determined with SK50 ifsin2 θ23(true) < 0.38 or > 0.60 for sin2 θ13(true) = 0
Sensitivity to octant for SK50 improves remarkably if θ13 6= 0
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.40/41
ConclusionsOsc of atmospheric neutrinos will be confirmed by INO-ICAL
Precision on ∆m231 and θ23 can be improved to 17%(10%) and
24%(30%) respectively by SK20 and INO-ICAL(250 kTy)
|D| can to determined to within 20% (25%) by SK50(INO-ICAL(500 kTy)) if sin2 θ13(true) = 0
|D| can to determined to within 11% (23%) by SK50(INO-ICAL(500 kTy)) if sin2 θ13(true) = 0.04
Octant of θ23 can be determined with INO-ICAL(1 MTy) ifsin2 θ23(true) < 0.42 or > 0.57 for sin2 θ13(true) = 0.04
Octant of θ23 can be determined with SK50 ifsin2 θ23(true) < 0.38 or > 0.60 for sin2 θ13(true) = 0
Sensitivity to octant for SK50 improves remarkably if θ13 6= 0
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.40/41
ConclusionsOsc of atmospheric neutrinos will be confirmed by INO-ICAL
Precision on ∆m231 and θ23 can be improved to 17%(10%) and
24%(30%) respectively by SK20 and INO-ICAL(250 kTy)
|D| can to determined to within 20% (25%) by SK50(INO-ICAL(500 kTy)) if sin2 θ13(true) = 0
|D| can to determined to within 11% (23%) by SK50(INO-ICAL(500 kTy)) if sin2 θ13(true) = 0.04
Octant of θ23 can be determined with INO-ICAL(1 MTy) ifsin2 θ23(true) < 0.42 or > 0.57 for sin2 θ13(true) = 0.04
Octant of θ23 can be determined with SK50 ifsin2 θ23(true) < 0.38 or > 0.60 for sin2 θ13(true) = 0
Sensitivity to octant for SK50 improves remarkably if θ13 6= 0
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.40/41
ConclusionsOsc of atmospheric neutrinos will be confirmed by INO-ICAL
Precision on ∆m231 and θ23 can be improved to 17%(10%) and
24%(30%) respectively by SK20 and INO-ICAL(250 kTy)
|D| can to determined to within 20% (25%) by SK50(INO-ICAL(500 kTy)) if sin2 θ13(true) = 0
|D| can to determined to within 11% (23%) by SK50(INO-ICAL(500 kTy)) if sin2 θ13(true) = 0.04
Octant of θ23 can be determined with INO-ICAL(1 MTy) ifsin2 θ23(true) < 0.42 or > 0.57 for sin2 θ13(true) = 0.04
Octant of θ23 can be determined with SK50 ifsin2 θ23(true) < 0.38 or > 0.60 for sin2 θ13(true) = 0
Sensitivity to octant for SK50 improves remarkably if θ13 6= 0
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.40/41
ConclusionsOsc of atmospheric neutrinos will be confirmed by INO-ICAL
Precision on ∆m231 and θ23 can be improved to 17%(10%) and
24%(30%) respectively by SK20 and INO-ICAL(250 kTy)
|D| can to determined to within 20% (25%) by SK50(INO-ICAL(500 kTy)) if sin2 θ13(true) = 0
|D| can to determined to within 11% (23%) by SK50(INO-ICAL(500 kTy)) if sin2 θ13(true) = 0.04
Octant of θ23 can be determined with INO-ICAL(1 MTy) ifsin2 θ23(true) < 0.42 or > 0.57 for sin2 θ13(true) = 0.04
Octant of θ23 can be determined with SK50 ifsin2 θ23(true) < 0.38 or > 0.60 for sin2 θ13(true) = 0
Sensitivity to octant for SK50 improves remarkably if θ13 6= 0
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.40/41
ConclusionsOsc of atmospheric neutrinos will be confirmed by INO-ICAL
Precision on ∆m231 and θ23 can be improved to 17%(10%) and
24%(30%) respectively by SK20 and INO-ICAL(250 kTy)
|D| can to determined to within 20% (25%) by SK50(INO-ICAL(500 kTy)) if sin2 θ13(true) = 0
|D| can to determined to within 11% (23%) by SK50(INO-ICAL(500 kTy)) if sin2 θ13(true) = 0.04
Octant of θ23 can be determined with INO-ICAL(1 MTy) ifsin2 θ23(true) < 0.42 or > 0.57 for sin2 θ13(true) = 0.04
Octant of θ23 can be determined with SK50 ifsin2 θ23(true) < 0.38 or > 0.60 for sin2 θ13(true) = 0
Sensitivity to octant for SK50 improves remarkably if θ13 6= 0SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.40/41
ConclusionsNeutrino mass hierarchy can be determined at 2σ at 4000upward going events at INO-ICAL if sin2 θ13(true) = 0.026 andsin2 θ23(true) = 0.5
Neutrino mass hierarchy can be determined at > 2σ at SK50 ifsin2 θ13(true) = 0.026 and sin2 θ23(true) = 0.5
However, the sensitivity to hierarchy at SK50 falls appreciablywhen δCP is allowed free
New Physics might be discovered/constrained usingatmospheric neutrinos
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.41/41
ConclusionsNeutrino mass hierarchy can be determined at 2σ at 4000upward going events at INO-ICAL if sin2 θ13(true) = 0.026 andsin2 θ23(true) = 0.5
Neutrino mass hierarchy can be determined at > 2σ at SK50 ifsin2 θ13(true) = 0.026 and sin2 θ23(true) = 0.5
However, the sensitivity to hierarchy at SK50 falls appreciablywhen δCP is allowed free
New Physics might be discovered/constrained usingatmospheric neutrinos
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.41/41
ConclusionsNeutrino mass hierarchy can be determined at 2σ at 4000upward going events at INO-ICAL if sin2 θ13(true) = 0.026 andsin2 θ23(true) = 0.5
Neutrino mass hierarchy can be determined at > 2σ at SK50 ifsin2 θ13(true) = 0.026 and sin2 θ23(true) = 0.5
However, the sensitivity to hierarchy at SK50 falls appreciablywhen δCP is allowed free
New Physics might be discovered/constrained usingatmospheric neutrinos
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.41/41
ConclusionsNeutrino mass hierarchy can be determined at 2σ at 4000upward going events at INO-ICAL if sin2 θ13(true) = 0.026 andsin2 θ23(true) = 0.5
Neutrino mass hierarchy can be determined at > 2σ at SK50 ifsin2 θ13(true) = 0.026 and sin2 θ23(true) = 0.5
However, the sensitivity to hierarchy at SK50 falls appreciablywhen δCP is allowed free
New Physics might be discovered/constrained usingatmospheric neutrinos
OSANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.41/41
ConclusionsNeutrino mass hierarchy can be determined at 2σ at 4000upward going events at INO-ICAL if sin2 θ13(true) = 0.026 andsin2 θ23(true) = 0.5
Neutrino mass hierarchy can be determined at > 2σ at SK50 ifsin2 θ13(true) = 0.026 and sin2 θ23(true) = 0.5
However, the sensitivity to hierarchy at SK50 falls appreciablywhen δCP is allowed free
New Physics might be discovered/constrained usingatmospheric neutrinos
I thank the organizers of Neutrino 2006, Harish-Chandra Research Institute,University of Oxford, INO collaboration, Srubabati Goswami, Michele Maltoni,Probir Roy and Thomas Schwetz.
Thank You!!SANDHYA CHOUBEY WHAT CAN WE LEARN FROM ATMOSPHERIC NEUTRINOS Neutrino 2006, 16.06.06 – p.41/41