Prospects to Determine the
Neutrino Mass Hierarchy
Sandhya Choubey
KTH Royal Institute of Technology, Sweden
Harish-Chandra Research Institute, India
Electroweak Interactions and Unified Theories
Recontres de Moriond, La Thuile, Italy
Plan of talk
Current understanding of the neutrino mass hierarchy
Future prospects:
Atmospheric neutrino experiments
Long baseline experiments
Reactor experiments
Conclusions
Neutrino Mass Hierarchy
How to measure:
1. Matter effects in nu oscillation
(i) Long baseline experiments
(ii) Atmospheric nu experiments
(iii)Supernova neutrinos
2. Interference effects in nu oscillation
(i) Reactor nu experiments at
intermediate baselines
Absolute nu mass: 0vbb,cosmology
3
Current Status (SK)
Statistically insignificant…can they be called hints?
R. Wendell, Talk at Neutrino 2014
4
Numbe
0
>2000
500
1000
1500
Reconstructed neutrino energy (MeV)
0
negligibly small.
Constraints on δCP are obtained by combining our r
sults with the θ13 value measured by reactor experiment
The additional likelihood constraint term on sin2 2θ13
defined as exp{−(sin2 2θ13 − 0.098)2/(2(0.0132))}, whe
0.098 and 0.013 are the averaged value and the error
sin2 2θ13 from PDG2012 [8]. The −2∆ ln L curve as
function of δCP is shown in Figure 6, where the like
hood is marginalized over sin2 2θ13 , sin2 θ23 and ∆m23
The combined T2K and reactor measurements pref
δCP = −π/2. The 90% CL limits shown in Figure
are evaluated by using the Feldman-Cousins method [3
in order to extract the excluded region. The data e
cludes δCP between 0.19π and 0.80π (−π and −0.97
and −0.04π and π) with normal (inverted) hierarchy
o
90% CL.
The maximum value of −2∆ ln L is 3.38 (5.76)
δCP = π/2 for normal (inverted) hierarchy case. Th
value is compared with a large number of toy MC expe
iments, generated assuming δCP = −π/2, sin2 2θ13 = 0.
Talk by E.Lisi−3
2
2
sin θ23 = 0.5 and ∆m32 = 2.4 × 10
eV2 . The M
averaged value of −2∆ ln L at δCP = π/2 is 2.20 (4.1
for normal (inverted) hierarchy case, and the probab
Gerardi,Meloni,Petcov (2014)
ity of obtaining a value greater or equal to the observe
value is 34.1% (33.4%). With the same MC setting
the expected 90% CL exclusion region is evaluated to b
between 0.35π and 0.63π (0.09π and 0.90π) radians f
normal (inverted) hierarchy case.
Conclusions—T2K has made the first observation
electron neutrino appearance in a muon neutrino bea
with a peak energy of 0.6 GeV and a baseline of 295 km
With the fixed parameters |∆m232 | = 2.4 × 10−3 eV
Current Status (T2K)
δCP (π)
FIG. 4. The Eνrec distribution for νe candidate events with
the MC prediction at the best fit of sin2 2θ13 = 0.144 (normal
hierarchy) by the alternative binned Eνrec analysis.
1
Is NH favored?
0.5
∆m232>0
0
68% CL
90% CL
Best fit
PDG2012 1σ range
δCP (π)
-0.5
Is delta_cp=-90 favored?
Is non-maximal th23 favored?
-1
1
0.5
Is there NSI?
0
∆m232<0
-0.5
-1
0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
sin22θ13
T2K Collaboration, arXiv:1311.4750
FIG. 5. The 68% and 90% CL allowed regions for sin2 2θ13 ,
as a function of δCP assuming normal hierarchy (top) and
5
Atmospheric Neutrino Experiments
Megaton-class Water Cerenkov Detectors
Good zenith angle resoln
e vs mu discrimination
low E threshold
statistical separation of
nue vs anti-nue
large statistics
6
Atmospheric Neutrino Experiments
50
sin2
sin2
sin2
sin2
sin2
sin2
sin2
sin2
sin2
45
40
30
= 0.04
= 0.08
13
= 0.16
13
= 0.04
13
= 0.08
13
= 0.16
13
= 0.04
13
= 0.08
13
= 0.16
13
13
3 sigma discovery in
less than 5 years
Normal mass hierarchy
25
HK fiducial mass: 560 kTon
2
(
2 - 2 )
IH NH
35
sin2 2
sin2 2
sin2 2
sin2 2
sin2 2
sin2 2
sin2 2
sin2 2
sin2 2
= 0.4
= 0.4
23
= 0.4
23
= 0.5
23
= 0.5
23
= 0.5
23
= 0.6
23
= 0.6
23
= 0.6
23
23
20
15
10 3
5
0
1
2
3
4
5
6
7
8
9
10
Hyper-K years
7
HK LOI, 1109.3262
Atmospheric Neutrino Experiments
Multi-megaton Ice/Water Detectors
e vs mu discrimination
very large statistics
8
Atmospheric Neutrino Experiments
Hierarchy sensitivity : PINGU
Initial baseline geometry : 40 new
optical modules in the deep core r
3 sigma discovery in
about 3 years
3
in
~
PINGU LOI, 1401.2046
3 yrs for 1st octant (multichannel)
Including Cascades important
9
Atmospheric Neutrino Experiments
Large Magnetized Iron Detectors
Good E and θ resoln
99% charge-id
good statistics
10
Hierarchy Sensitivity : Atmospheric Neutrinos
Atmospheric Neutrino Experiments
Incorporation of Hadron information : event by event analysis in E ,cos
Improves the hierarchy sensitvity significantly : 40 % increase in
0.22
0.2
∆χ2=6
∆χ2=10
∆χ2=14
∆χ2=7
∆χ2=11
∆χ2=15
∆χ2=8
∆χ2=12
∆χ2=16
0.22
∆χ2=9
∆χ2=13
0.2
∆χ2=11
∆χ2=15
∆χ2=19
∆χ2=12
∆χ2=16
∆χ2=20
0.16
σEµ/Eµ
0.16
σEµ/Eµ
∆χ2=10
∆χ2=14
∆χ2=18
0.18
0.18
0.14
0.12
0.14
Devi,Tha
Dighe (2
0.08
0.08
0.06
0.06
0.04
0.04
0.65
0.7
0.75
0.8
0.85
Reconstruction efficiency
0.9
0.95
1
3D an
Inform
hadro
0.12
0.1
0.1
0.02
0.6
∆χ2=9
∆χ2=13
∆χ2=17
2
0.02
0.6
0.65
0.7
0.75
0.8
0.85
Reconstruction efficiency
0.9
0.95
Talk by
1 ICHEP 2
S.C.,Ghosh, arXiv:1306.1423
Devi,Thakore,Agarwalla,Dighe,arXiv:1406.3689
Sensitivity can increase if
2
3 sigma
discovery
in 10 years for
2
3
sensitivity
in
2
sinmuon
2 and
(
true
)
0.1
energy
resolution
is
P
~
sin
Figure 6: Constant ∆χ contours in the reconstruction efficiency
energy
resolution
plane.
The
left
13
e
about
10
years
panels shows the contours from the analysis which uses only improved
the muon data from the experiments. The
Hierarchy sensitivity more for higher octant
and higher
13 were included
40%shows
improvement
abovefor
muon
analysis
right panels
the contours
the only
analysis
in which both the muon and hadron data
Ribordy, Smirnov, arXiv:1303.0758
in the
combinedS.C.,arXiv:1212.1305
statistical analysis.
Ghosh,Thakore,
PINGU
Include inelasticity y, increase sensitivity by 20-50%
Srubabati Goswami
Neutrino Phenomenology
present results for both 80 bins as well as 20 bins between
1 GeV and 11 GeV.
11
Atmospheric Neutrino Experiments
Hierarchy sensitivity of atmospheric neutrino
experiments is almost independent of delta_cp
12
of θ23 and δCP comes primarily from the νµ → νe oscillation probability Pµe . An approximate analytical formula
for this probability can be derived perturbatively [63–65]
in terms of the two small parameters α = ∆21 /∆31 and
sin θ13 .
Prospects at T2K & NOvA
2
2
Pµe = 4 sin θ13 sin θ23
NORMAL HIERARCHY
20
NoVA
18
LBL+reactors
sin2 [(1 − Â)∆]
(1 − Â)2
+α sin 2θ13 sin 2θ12 sin 2θ23 cos (∆ + δCP ) ×
sin Â∆ sin [(1 − Â)∆]
Â
(1 − Â)
+ O(α2 ) .
(1)
16
Here, ∆ = ∆31 L/4E is the oscillating term, and the effect of neutrinos interacting with√matter in the earth is
14
given by the matter term  = 2 2GF ne E/∆31 , where
12
ne is the number density of electrons in the earth. Note
that this expression is valid in matter of constant density.
10
This approximate formula is useful for understanding the
8
physics of neutrino oscillations. However in our simulations, we use the full numerical probability calculated by
6
GLoBES.
In the analyses that follow, we have evaluated the χ2
4
for determining the mass hierarchy, octant of θ23 and
2
CP violation using a combination of LBNE and the curMarginalized
rent/upcoming experiments T2K, NOνA and ICAL. For
0
0
50
100
150
200
250
300
350
each set of ‘true’ values assumed, we evaluate the χ2
δcp(true)
marginalized over the ‘test’ parameters. In our simulations, we have used the effective atmospheric parameters
Ghosh,Thakore, S.C.,arXiv:1212.1305
corrected for three-flavour effects [66–68]. The true valf δCP (true) on the mass hierarchy sensitivity. The sensitivity
change
NOνA
due are: sin2 θ12 = 0.304,
ues assumed
forofthe
parameters
2
−5
n by the green solid line. The ∆χ2 for the wrong mass13
hierarchy
expected
from
|∆
× 10−3 eV
, ∆the
eV2 and
31 | = 2.4
21 = 7.65 × 10
∆ χ2
All expts
3 sigma sensitivity expected if
NH true and delta_cp is -90 deg
or if
IH true and delta_cp is 90 deg
Addition of 10 years INO data
gives 3 sigma sensitivity for
both hierarchies and all delta_cp
w
h
k
t
t
w
m
t
p
e
1
a
o
o
s
m
is
s
w
fo
e
fo
Sensitivity
LBNE+NOνA+T2K+ICAL LBNE+NOνA+T2K LBNE
Hierarchy(χ2 = 25)
22(22)
39(39)
95(106
Octant(χ2 = 25)
35(37)
65(50)
84(76)
CP(40% at χ2 = 9)
65(36)
65(36)
114(90
Future Long Baseline Experiments
TABLE I: Adequate exposures for hierarchy, octant and CP in units of MW-kt-yr for
Sensitivity at ELBNF
50 sensitivity possible for all
5
sig
LBNE(FD)
LBNE(FD)
60
LBNE(FD+ND)
LBNE(FD+ND)
LBNE(FD)+Others
LBNE(FD)+Others
values
of
delta_cp
if one adds the
LBNE(FD+ND)+Others
LBNE(FD+ND)+Others
40
LBNE: 37T2K,
MW-kt-yr NOvA and INO
data from
True IH
30
25
20
LBNE: 22 MW-kt-yr
30
2
WO INO, the exposure needs to go
20
up by almost a factor of two (39)
χ
χ
2
True IH
χ2
40
15
10
20
10
0
-180
L
LBNE: 65 M
True NH
-120
-60
0
60
δCP(True)
120
Ghosh,Ghoshal,Goswami,Raut, arXiv:1412.1744
ELBNF alone needs 95 MW-kty
0
180 data
-180for
-1205 sigma
-60
0
60
120
180
5
0
-180
-120
δCP(True)
Sample figure. I apologise to all whose fig I could not show.
FIG. 2: Hierarchy/Octant/CP violation discovery sensitivity χ2 vs true δCP in the left/middle/right panel. T
effect of including a near detector on the sensitivity14of LBNE alone and LBNE combined with the other exper
0
0
10
20
30
40
Exposure (x 1021 pot kt)
Future Long Baseline Experiments
Figure 3: Hierarchy sensitivity χ2 vs LBNO exposure, for both baselines and hierarchies under consideration. The value of exposure shown here is adequate to exclude the wrong hierarchy for all values of δCP .
The additional axis along the upper edge of the graph shows the required total pot assuming a detector
mass of 10 kt.
LBNO
80
80
NOvA+T2K
+LBNO, exp = 7.5
+ICAL+LBNO, exp = 7.5
+LBNO, exp = 11.2
21
(in 10 pot-kt)
70
60
Along with T2K and NOvA,
one gets 5 sig sensitivity either
with exposure of 11.2x1021pot-kt
OR with INO added with
exposure of 7.5x1021pot-kt
60
40
50
χ2
2
χ
70
L=2290 km
IH true
50
30
40
30
20
20
10
0
-180
NOvA+T2K
+LBNO, exp = 22.5
+ICAL+LBNO, exp = 22.5
+LBNO, exp = 37.5
21
(in 10 pot-kt)
10
-120
-60
0
true δCP
60
120
180
0
-180
-120
-60
0
Ghosh,Ghoshal,Goswami,Raut, arXiv:1308.5979 true δCP
60
120
180
Sample figure. I apologise to all whose fig I could not show.
Figure 4: Hierarchy sensitivity χ for different combinations of experiments, demonstrating the synergy
15 of 2290(1540) km, assuming IH to be true. With
between them. The left(right) panel is for a LBNO baseline
2
II.
THE THREE-GENERATION ν̄e SURVIVAL PROBABILITY
Reactor Experiments
The expression for the ν̄e survival probability in the case of 3 flavor neutrino mixing and neutrino mass spectrum
with normal hierarchy II.
(NH)THE
is given
by 5 [23, 30, 35]:
THREE-GENERATION
ν̄e SURVIVAL PROBABILITY
The expression for the ν̄e survival probability in the case of 3 flavor neutrino mixing and neutrino mass spectrum
PN H(NH)
(ν̄e →is ν̄given
e)
with normal hierarchy
by 5 [23,
"
! 30, 35]:
2
∆matm L
= 1 − 2 sin2 θ cos2 θ 1 − cos
2 Eν
PN H (ν̄e → ν̄e )
#!
$ "
2
∆m
L
2
1
4
2
∆m⊙atm L
cos
−
1
−
cos
(9)
θ
sin
2θ
2
2
⊙
= 21 − 2 sin θ cos θ 1 − cos 2 Eν
!
! 2 Eν
"
"
2
2
2
#
∆m $ L ∆m⊙ L
∆matm L
1 sin24 θ cos22 θ sin2 θ⊙ cos∆m2⊙ Latm −
−
cos
,
+
2
cos θ sin 2θ⊙ 1 − cos
−
(9)
2
E
2
E
2
E
ν
ν
ν
2
2 Eν
!
!
"
"
2
2
2
L
L
∆m
∆m
∆m⊙ Lhierarchy (IH),
neutrino
is with−inverted
probability
where Eν is the ν̄e energy.
2
2
atm
atmthe ν̄e, survival
• Large
q13 open
cos
− cos
θ cos
θ sin2mass
θ⊙ spectrum
+ 2 If
sinthe
2 Eν
2 Eν
2 Eν
can be written in the form [23, 30, 35]:
Neutrino Mass Hierarchy
doors to MH
– Exploit L/E spectrum with reactors
where Eν is the ν̄e energy. If the neutrino mass spectrum is with inverted hierarchy (IH), the ν̄e survival probability
PIHform
(ν̄e →
) 35]:
can be written in the
[23,ν̄e30,
"
!
2
L
∆m
atm
= 1 − 2 sin2 θ cos2 θ 1 − cos
2 Eν
PIH (ν̄e → ν̄e )
"
#!
22 $
∆m
L
1
L
∆m
⊙atm
4
2 2 2θ⊙
2
− 1 cos
1 1−−cos
(10)
θ sin
θ
cos
θ
cos
=
−
2
sin
2
2 E2νEν
"
"
!
!
2
2
#
$
2
L ∆m⊙ L
∆matm L
2
∆m∆m
1 sin24 θ cos22 θ cos2 θ
⊙ L atm
−
cos
.
cos
−
+
2
cos θ sin 2θ⊙ 1 ⊙
−
− cos
(10)
2
E
2
E
2
E
ν
ν
ν
2
2 Eν
"
"
!
!
2
2
2
L
L
∆m
∆m
∆m⊙ Lassociated with
2
2 depend
atmthe atmospheric
atmangle
The ν̄e survival probability
not
neutrino
− cos
.
cos on the
− θatm
θ cos
θ cos2 θ⊙ either
+ 2 sindoes
2E
2 Eν
2 Eν
ν
oscillations, nor on the CP violating phase δ in the PMNS
matrix.
Petcov,Piai
(2002),
In the convention
(we will
call A) in which the neutrino masses are not ordered in magnitude and the NH neutrino
The ν̄spectrum
probabilityto
does
notm2depend
on IH
thespectrum
angle θatm
associatedwith
withthe
theordering
atmospheric
SC,Petcov,Piai
(2003),
e survival
mass
corresponds
m1 <
< m3 , either
while the
is associated
m3 < neutrino
m1 < m2 ,
oscillations,
on the CP violating phase δ in the PMNS matrix.
it
is natural nor
to choose
In the convention (we will call A) in which the neutrino masses are not ordered in magnitude and the NH neutrino
2
mass spectrum corresponds to m1 < ∆m
m2 2⊙
<=
m3∆m
, while
is associated
0 , IH spectrum
Convention
A. with the ordering m3 < m1 < m(11)
2,
21 >the
16
it is natural to choose
Phys.Rev.D78:111103,2008
S.T. Petc
S.Choub
J. Learn
L. Zhan
PRD79:
J. Learn
…
Realisti
reactor
Neutrino Mass Hierarchy
• Large q13 open doors to MH
– Exploit L/E spectrum with reactors
Reactor Expts (JUNO, RENO-50)
Li,Cao,Wang,Zhan,PRD88,013008,2013
Neutrino Mass Hierarchy
Phys.Rev.D78:111103,2008
• Large q13 open doors to MH
S.T. Petcov et al., PLB533(2002)94
S.Choubey et al., PRD68(2003)113006
J. Learned et al., PRD78, 071302 (2008)
L. Zhan, Y. Wang, J. Cao, L. Wen, PRD78:111103, 2008,
PRD79:073007, 2009
J. Learned et al., arXiv:0810.2580
…
Realistic requirements about determining MH with
reactors will be discussed later
– Exploit L/E spectrum with reactors
Petcov,Piai (2002),
SC,Petcov,Piai (2003),
Learned,Dye,Pakvasa,Svoboda (2008)
Zhan,Wang,Cao,Wen (2008)
Zhan,Wang,Cao,Wen (2009)
Ghoshal,Petcov (2011)
Hagiwara,Okamura,Takaesu (2012)
Capozzi,Lisi,Marrone (2014)
Phys.Rev.D78:111103,2008
Figure 1: The MH discrimination ability for the proposed
3
as functions of the baseline (left panel)
and the detector en
with the method of the least squares function in Eq. (11).
!
detector energy resolution 3%/ E(MeV) as a benchmark.
be the true one (otherwise mentioned explicitly) while the
for the other assumption. The relevant oscillation paramet
global analysis [28] as ∆m221 = 7.54 × 10−5 eV−2 , (∆m231 +
2
2
13 = 0.024 and sin θ12 = 0.307. The CP-violating
S.T. Petcov etsinal.,θPLB533(2002)94
Finally, the reactor antineutrino flux model from
S.Choubey etneeded.
al., PRD68(2003)113006
in our simulation1 . Because two of the three mass-squar
J. Learned et al., PRD78,
071302 (2008)
17
and ∆m232 ) are independent, we choose ∆m221 and ∆m2ee d
Reactor Expts (JUNO, RENO-50)
Hierarchy sensitivity of reactor neutrino
experiments is completely independent of delta_cp
as well as theta_23
18
Reactor Expts (JUNO, RENO-50)
Synergy between PINGU and JUNO
Blenow,Schwetz, 1306.3988
19
Conclusions
Adapted from Blennow et al, 1311.1822
For favorable deltacp
early hints expected from
NOvA
rchy sensitvity in future experiments
y sensitvity of NOvA atmospheric experiments
NOvA
CP
Atmospheric
INO/SK 40
23
o
50o
For unfavorable deltacp values,
early hints expected from
atmospheric expts and/or Juno
After Blenow et al. 1311.1822
3
NoVA : 3
INO : arXiv:1406.3689
HK : arXiv 1109.3262
PINGU: arXiv 1401.2046
o
o
Pingu : 38.7 51.3
The lower end of the bands denote worst sensitivity
Pingu/HK huge statistics help for higher 2-3 angle
Thank you!
For favourable CP values early hint from Nova
and for unfavourable CP values from NOvA + INO
20
Backup Slide
7
7
LBNE
34kt
True NO
6
5
LBNE
10kt
4
PINGU
JUNO
3
INO
2
Median sensitivity @sD
Median sensitivity @sD
6
5
LBNE
10kt
4
PINGU
JUNO
3
INO
2
NOvA
NOvA
1
0
LBNE
34kt
True IO
1
2015
2020
2025
0
2030
Date
2015
2020
2025
2030
Date
FIG. 12: The left (right) panel shows the median sensitivity in number of sigmas
rejecting the IO
Blennow etfor
al, 1311.1822
(NO) if the NO (IO) is true for di↵erent facilities as a function of the date. The width of the bands
correspond to di↵erent true values of the CP phase for NO⌫A and LBNE, di↵erent true values
p
of ✓23 between 40 and 50 for INO and PINGU, and energy resolution between 3% 1 MeV/E
p
21