talk @ PPC at KIAS 2012.11.07

1. Determina)on
of
mass
hierarchy
with
reactor
neutrino
experiment
Yoshitaro
Takaesu
KIAS/KNRC
arXiv:
1210.8141
1
In
collabora)on
with
S.F.
Ge,
N.
Okamura
and
K.
Hagiwara
PPC2012@KIAS
Yoshitaro
Takaesu

2. IntroducDon
• DayaBay
and
RENO
observed
large
• There
is
a
possibility
that
neutrino
mass
hierarchy
is
determined
by
observing
reactor
neutrino
oscillaDon
at
km
away
• In
this
talk,
I
discuss
the
sensiDvity
of
the
future
medium
baseline
reactor
experiments
for
determining
mass
hierarchy
arXiv:
1210.8141
2
13
O(10)
PPC2012@KIAS
Yoshitaro
Takaesu

3. Mass
Hierarchy
arXiv:
1210.8141
3
If
we
assume
there
are
3
types
of
netrinos,
there
are
6
possible
mass
hierarchies.
We
know
There
are
two
possibiliDes
leX,
NH
and
IH.
Which
one
is
realized
in
Nature?
Long
standing
and
big
ISSUE.
PPC2012@KIAS
Yoshitaro
Takaesu
m2
21 = m2
2 m2
1 7.5 10 5
m2
21 < | m2
31| 2.3 10 3
m1
m2
m3
m1
m2
m3
Normal
Hierarchy
(NH)
Inverted
Hierarchy
(IH)
| m2
31|
m2
21

4. OscillaDon
arXiv:
1210.8141
4
Mass
Hierarchy
difference
e e
PPC2012@KIAS
Yoshitaro
Takaesu

5. Reactor
neutrino
experiment
arXiv:
1210.8141
5
e
PPC2012@KIAS
Yoshitaro
Takaesu
Flux
@
Reactor
Pee
@
far
detector
e
e + p e+
+ n

6. Energy
distribuDon
@
far
detector
arXiv:
1210.8141
PPC2012@KIAS
Yoshitaro
Takaesu
6
10000
20000
30000
40000
30 km NH
IH
2000
6000
10000
14000 40 km NH
IH
1000
3000
5000
7000
dN/dE[1/MeV]
50 km NH
IH
0
1000
2000
3000
4000
2 3 4 5 6 7 8
E [MeV]
60 km NH
IH
e
We
want
to
observe
the
NH-­‐IH
difference
in
the
energy
distribuDon
at
a
far
detector
Let’s
observe
it!
…
but
There
are
obstacles…

7. Obstacle1:
arXiv:
1210.8141
PPC2012@KIAS
Yoshitaro
Takaesu
7
@
<
30
km,
the
NH-­‐IH
difference
is
totally
absorbed
by
a
small
shiX
of
within
its
uncertainty.
@
L
>
30
km,
the
NH-­‐IH
difference
cannot
be
totally
absorbed.
We
need
a
far
detector
at
L
>
30
km
There
is
the
opDmal
baseline
length
to
determine
mass
hierarchy.
| m2
31|
| m2
31|

8. Obstacle2:
finite
Energy
ResoluDon
arXiv:
1210.8141
PPC2012@KIAS
Yoshitaro
Takaesu
8
b: systematic error part
a: statistical error part
AXer
smearing
with
the
detector
Energy
resoluDon,
the
NH-­‐IH
difference
Can
be
absorbed
again.
E
E
=
a
E/MeV
2
+ b2
Upper
limit
on
the
Energy
ResoluDon

9. We
esDmate
– OpDmal
baseline
length
– Energy
resoluDon
required
– Expected
uncertainDes
of
neutrino
parameters
Assuming
an
experiment
with
20
GW
5kton
(12%
free
proton)
5
years
exposure.
arXiv:
1210.8141
PPC2012@KIAS
Yoshitaro
Takaesu
9

10. Analysis
method
arXiv:
1210.8141
10
PPC2012@KIAS
Yoshitaro
Takaesu
We
calculate
the
neutrino
energy
distribuDon
for
NH
or
IH,
Energy
ResoluDon
smearing
(Gaussian)
We
then
perform
the
standard
analysis
to
this
“data”
(next
slide).
dNNH(IH)
dEobs
=
NpT
4 L2
dE
dN
dE
Pee(L, E ) IBD(E )G(Etrue
Eobs
, E)
*
corresponds
to
the
averaged
observed
distribuDon.
We
don’t
consider
the
fluctuaDon
of
data
from
experiment
to
experiment
in
this
talk.
dNNH(IH)
dEobs
We
introduce
bining
and
prepare
“data”,
the
number
of
events
in
each
bin.
N
NH(IH)
i =
Eobs
i+1
Eobs
i
dEobs dNNH(IH)
dEobs (i = 1, · · · , nbins)
2

11. Analysis
method
cont.
arXiv:
1210.8141
11
The
sensiDvity
to
determine
MH:
PPC2012@KIAS
Yoshitaro
Takaesu
*
We
consider
zero
bin-­‐size
limit.
The
sensiDvity
should
be
considered
as
the
maximum
sensiDvity.

12. Results
arXiv:
1210.8141
PPC2012@KIAS
Yoshitaro
Takaesu
12

13. SensiDvity
for
mass
hierarchy
arXiv:
1210.8141
13
0
2
4
6
8
10
12
14
10 20 30 40 50 60 70 80 90 100
(2
)min
L [km]
b = 0
a = 2% NH
IH
3% NH
IH
4% NH
IH
5% NH
IH
6% NH
IH
20
GW
5kton
5
years
a
<
3%
for
E
E
=
a
E/MeV
2
+ b2
OpDmal
L
~
50
km
PPC2012@KIAS
Yoshitaro
Takaesu
( 2
)min > 9

14. SystemaDc
Error
of
ResoluDon
arXiv:
1210.8141
14
0
2
4
6
8
10
12
14
10 20 30 40 50 60 70 80 90 100
(
2
)min
L [km]
(a, b) = (2, 0) NH
IH
(2, 0.5) NH
IH
(2, 0.75) NH
IH
(2, 1) NH
IH
E
E
=
a
E/MeV
2
+ b2
b
<
1%
for
20GW
5kton
5
years
Larger
b
Shorter
opDmal
L
PPC2012@KIAS
Yoshitaro
Takaesu
( 2
)min > 9

15. UncertainDes
of
Parameters
arXiv:
1210.8141
15
0.5
1.0
1.5
2.0
sin2
2 12
×10
-2
(a, b) = (3, 0.5) NH
IH
(3, 1) NH
IH
(6, 1) NH
IH
1
2
3
4 sin
2
2 13
×10
-3
0.5
1.0
1.5
StatisticalUncertainty
m2
21
×10
-6
eV
2
0
2
4
6
10 20 30 40 50 60 70 80 90 100
L [km]
| m
2
31|
×10-5
eV2
Parameter
measurements
are
not
sensiDve
to
the
Energy
resoluDon
PPC2012@KIAS
Yoshitaro
Takaesu
~
0.5%
level
of
uncertainDes
can
be
achieved
for
sin2
2 12
| m2
31|
m2
21

16. Summary
• We
study
the
sensiDvity
of
a
future
medium
baseline
reactor
neutrino
experiment
for
MH
determinaDon.
• For
20
GW
5kton
5
years
exposure,
–
opDmal
baseline
length
~
50
km
–
<
3%
staDsDcal
&
<
1%
systemaDc
errors
of
Energy
ResoluDon
is
required
–
0.5%
level
of
accuracy
for
Neutrino
Parameters
arXiv:
1210.8141
16
PPC2012@KIAS
Yoshitaro
Takaesu
*
This
study
gives
the
minimum
requirement
for
the
energy
resoluDon.
*
More
realisDc
study
is
very
sensiDve
to
the
environment,
such
as
distribuDon
of
reactors
within
~100
km
from
the
far
detector
(J.Evslin
et.al,
arXiv:1209.2227).

17. arXiv:
1210.8141
17
Thank
you
PPC2012@KIAS
Yoshitaro
Takaesu

18. arXiv:
1210.8141
18
-0.25
0
0.25
0.5 sin
2
2 12
2% NH
IH
3% NH
IH
6% NH
IH
-0.25
0
0.25
0.5 sin
2
2 13
-0.25
0
0.25
0.5
pullfactor
m
2
21
-0.25
0
0.25
0.5
| m
2
31|
-0.25
0
0.25
0.5
10 20 30 40 50 60 70 80 90 100
L [km]
fsys
PPC2012@KIAS
Yoshitaro
Takaesu

19. arXiv:
1210.8141
PPC2012@KIAS
Yoshitaro
Takaesu
19
-10 0 10 20 30
50
100
150
( 2
)min
E
E
=
2%
E/MeV
2
+ (0.5%)2
L = 50km
1000 experiments
( 2)min = 11.2
( 2
)min = 7.1

20. arXiv:
1210.8141
PPC2012@KIAS
Yoshitaro
Takaesu
20
-5
0
5
10
15
20
10 20 30 40 50 60 70 80 90 100
(2
)min
L [km]
20GWth, 5kton (12.00% proton), 5 years, ( Evis/Evis)2
= ( (a / Evis)2
+ b2
)%
(a, b) = (2, 0.5) NH
IH

21. arXiv:
1210.8141
21
PPC2012@KIAS
Yoshitaro
Takaesu

22. arXiv:
1210.8141
22
PPC2012@KIAS
Yoshitaro
Takaesu