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Introduc)on	
  
	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  is	
  observed	
  	
  
Reactor	
  Experiments	
  (Medium	
  Baseline)	
  
will	
  determine	
  the	
  Neutrino	
  Mass	
  Hierarchy	
  .	
  
We	
  study	
  the	
  sensi:vity	
  	
  
of	
  such	
  future	
  Experiments.	
  
sin2
2 13 0.1
RENO	
  
DayaBay	
  
Neutrino	
  Mass	
  Hierarchy	
  	
  
m1	
  
m2	
  
m3	
  
Normal	
  Hierarchy	
  (NH)	
  
m3	
  
m1	
  
m2	
  
Inverted	
  Hierarchy	
  (IH)	
  
m2
21
| m2
31|
2.3 10 3
eV2
7.5 10 5
eV2
m2
21
| m2
31|
Which	
  Hierarcy	
  is	
  realized	
  in	
  Nature?	
  
m
Oscilla)on	
  
Mass	
  Hierarchy	
  difference	
  
e e
How	
  to	
  dis)nguish	
  MH	
  ?	
  (theory)	
  
±
sin2
12
2
sin2
2 13 sin(2 21) sin(2| 31|)
Pee = 1 cos4
13 sin2
2 12 sin2
( 21)
sin2
2 13 sin2
(| 31|)
sin2
12 sin2
2 13 sin2
( 21) cos(2| 31|)
Reactor	
  neutrino	
  experiment	
  
e + p e+
+ n
e
	
  Flux	
  @	
  Reactor	
   	
  @	
  Detector	
  ee
=
Baseline	
  (L	
  km)	
  
Pee
How	
  to	
  dis)nguish	
  MH	
  ?	
  (experiment)	
  
Reactor	
   Detector	
  
We	
  esImate	
  the	
  sensi)vity	
  	
  
to	
  dis)nguish	
  the	
  MH	
  difference.	
  
Method	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  analysis	
  	
  2
 	
  Baseline	
  Length	
  
MH	
  difference	
  disappears	
  aJer	
  shiJ	
  in	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  @	
  L	
  =	
  30km.	
  
| m2
31| | m2
31|+
| m2
31|+| m2
31|
| m2
31|
L	
  =	
  30km	
  
L	
  =	
  50km	
  
What	
  affects	
  the	
  sensi)vity	
  ?	
  
MH	
  difference	
  remains	
  aJer	
  shiJ	
  in	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  @	
  L	
  =	
  50km.	
  | m2
31|
Short	
  Baseline	
  (	
  L	
  <	
  50km	
  )	
  is	
  less	
  sensi)ve	
  	
  
Energy	
  Distribu)on	
  @	
  Detector	
  
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
L	
  =	
  30km	
  
L	
  =	
  40km	
  
L	
  =	
  50km	
  
L	
  =	
  60km	
  
e
 	
  	
  	
  Energy	
  Resolu)on	
  	
  
b: systematic error part
a: statistical error part
w/o	
  Resolu)on	
   a	
  =	
  6%	
  
| m2
31|+
ShiJ	
  in	
  | m2
31|
a	
  =	
  6%	
  
E
E
=
a
E
2
+ b2
E = 0
What	
  affects	
  the	
  sensi)vity	
  ?	
  
	
  	
  	
  	
  Energy	
  Resolu)on	
  affects	
  significantly.	
  
Sensi)vity	
  for	
  Mass	
  Hierarchy	
  
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
20GW	
  5kton	
  5yrs	
  
opImal	
  Baseline	
  
L	
  ~	
  50km	
  
a	
  <	
  3%	
  
is	
  required	
  for	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  .	
  	
  ( 2
)min 9
Results	
  1-­‐a	
  
	
  	
  	
  	
  Sta:s:cal	
  part	
  of	
  Energy	
  ResoluIon	
  	
  	
  
E
E
=
a
E
2
+ b2
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
b	
   opImal	
  L	
  
b	
  <	
  1%	
  
is	
  required	
  for	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  .	
  	
  ( 2
)min 9
20GW	
  5kton	
  5yrs	
  
Sensi)vity	
  for	
  Mass	
  Hierarchy	
  
Results	
  1-­‐b	
  
	
  	
  	
  	
  Systema:c	
  part	
  of	
  Energy	
  ResoluIon	
  	
  	
  
E
E
=
a
E
2
+ b2
Parameter	
  measurement	
  
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
m
2
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
eV
2
Results	
  2	
  
FiZed	
  parameter	
  values	
  are	
  not	
  so	
  sensi:ve	
  to	
  the	
  Energy	
  Resolu:on	
  
~	
  0.5%	
  accuracy	
  can	
  be	
  achieved	
  for	
  	
  sin2
2 12, m2
21, m2
31
 	
  Summary	
  
We	
  have	
  studied	
  the	
  sensi:vity	
  of	
  	
  
Medium	
  Baseline	
  Reactor	
  Experiments	
  	
  
for	
  MH	
  determina:on.	
  
For	
  20GW	
  5kton	
  5yrs	
  exposure,	
  
	
  	
  	
  50km	
  	
  Baseline	
  Length	
  is	
  opImal	
  
	
  	
  	
  2-­‐3%	
  	
  sta:s:cal	
  error	
  
	
  	
  	
  	
  	
  	
  	
  1%	
  	
  systema:c	
  error	
  
	
  	
  	
  0.5%	
  	
  accuracy	
  is	
  achieved	
  for	
  Neutrino	
  parameters	
  	
  	
  	
  
of	
  Energy	
  Resolu:on	
  is	
  required	
  
Expected	
  Sensi)vity	
  
10
-7
10-6
10-5
10
-4
10
-3
0.01
0.1
1
0 1 2 3 4 5 6 7 8 9 10 11
1-P
1
2
3
4
5
×1
×4
×9
×1
×4
×9
×16
×25
No Fluctuation
Fluctuation
(a, b) = (2, 0.5)
(3, 0.75)
( 2)min
Sta)s)cal	
  Fluctua)on	
  
is	
  considered.	
  
	
  	
  	
  	
  	
  	
  	
  	
  20GW	
  5kton	
  5yrs	
  	
  n n
We	
  can	
  expect	
  	
  	
  
for	
  
15yrs	
  run	
  |	
  a	
  =	
  2%	
  
50yrs	
  run	
  |	
  a	
  =	
  3%	
  
3

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2013.02.15 poster @ Toyama

  • 1. Introduc)on                                                                  is  observed     Reactor  Experiments  (Medium  Baseline)   will  determine  the  Neutrino  Mass  Hierarchy  .   We  study  the  sensi:vity     of  such  future  Experiments.   sin2 2 13 0.1 RENO   DayaBay  
  • 2. Neutrino  Mass  Hierarchy     m1   m2   m3   Normal  Hierarchy  (NH)   m3   m1   m2   Inverted  Hierarchy  (IH)   m2 21 | m2 31| 2.3 10 3 eV2 7.5 10 5 eV2 m2 21 | m2 31| Which  Hierarcy  is  realized  in  Nature?   m
  • 3. Oscilla)on   Mass  Hierarchy  difference   e e How  to  dis)nguish  MH  ?  (theory)   ± sin2 12 2 sin2 2 13 sin(2 21) sin(2| 31|) Pee = 1 cos4 13 sin2 2 12 sin2 ( 21) sin2 2 13 sin2 (| 31|) sin2 12 sin2 2 13 sin2 ( 21) cos(2| 31|)
  • 4. Reactor  neutrino  experiment   e + p e+ + n e  Flux  @  Reactor    @  Detector  ee = Baseline  (L  km)   Pee How  to  dis)nguish  MH  ?  (experiment)   Reactor   Detector  
  • 5. We  esImate  the  sensi)vity     to  dis)nguish  the  MH  difference.   Method                    analysis    2
  • 6.    Baseline  Length   MH  difference  disappears  aJer  shiJ  in                              @  L  =  30km.   | m2 31| | m2 31|+ | m2 31|+| m2 31| | m2 31| L  =  30km   L  =  50km   What  affects  the  sensi)vity  ?   MH  difference  remains  aJer  shiJ  in                                @  L  =  50km.  | m2 31| Short  Baseline  (  L  <  50km  )  is  less  sensi)ve    
  • 7. Energy  Distribu)on  @  Detector   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 L  =  30km   L  =  40km   L  =  50km   L  =  60km   e
  • 8.        Energy  Resolu)on     b: systematic error part a: statistical error part w/o  Resolu)on   a  =  6%   | m2 31|+ ShiJ  in  | m2 31| a  =  6%   E E = a E 2 + b2 E = 0 What  affects  the  sensi)vity  ?          Energy  Resolu)on  affects  significantly.  
  • 9. Sensi)vity  for  Mass  Hierarchy   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 20GW  5kton  5yrs   opImal  Baseline   L  ~  50km   a  <  3%   is  required  for                                                                                            .    ( 2 )min 9 Results  1-­‐a          Sta:s:cal  part  of  Energy  ResoluIon       E E = a E 2 + b2
  • 10. 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 b   opImal  L   b  <  1%   is  required  for                                                                                            .    ( 2 )min 9 20GW  5kton  5yrs   Sensi)vity  for  Mass  Hierarchy   Results  1-­‐b          Systema:c  part  of  Energy  ResoluIon       E E = a E 2 + b2
  • 11. Parameter  measurement   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 m 2 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 eV 2 Results  2   FiZed  parameter  values  are  not  so  sensi:ve  to  the  Energy  Resolu:on   ~  0.5%  accuracy  can  be  achieved  for    sin2 2 12, m2 21, m2 31
  • 12.    Summary   We  have  studied  the  sensi:vity  of     Medium  Baseline  Reactor  Experiments     for  MH  determina:on.   For  20GW  5kton  5yrs  exposure,        50km    Baseline  Length  is  opImal        2-­‐3%    sta:s:cal  error                1%    systema:c  error        0.5%    accuracy  is  achieved  for  Neutrino  parameters         of  Energy  Resolu:on  is  required  
  • 13. Expected  Sensi)vity   10 -7 10-6 10-5 10 -4 10 -3 0.01 0.1 1 0 1 2 3 4 5 6 7 8 9 10 11 1-P 1 2 3 4 5 ×1 ×4 ×9 ×1 ×4 ×9 ×16 ×25 No Fluctuation Fluctuation (a, b) = (2, 0.5) (3, 0.75) ( 2)min Sta)s)cal  Fluctua)on   is  considered.                  20GW  5kton  5yrs    n n We  can  expect       for   15yrs  run  |  a  =  2%   50yrs  run  |  a  =  3%   3