Resolving Neutrino Mass Hierarchy and CP Degeneracy Using Two Identical Detectors

with Different BaselinesHiroshi Nunokawa

(Pontificia Universidade Catolica do Rio de Janeiro)

@Nufact05 WG1 June 22, 2005

Based on the work with M. Ishitsuka, T. Kajita and H. Minakata, hep-ph/0504026

Outline

• Introduction

• Basic Idea of 2 Detectors with Different Baselines

• Results of Our Analysis

• Summary

IntroductionCurrent Knowleadge about ν Mixing parameters

@ 90 % C.L.

+7.3 × 10−5

eV2

< ∆m221

< +9.0 × 10−5

eV2

0.25 < sin2θ12 < 0.37

1.5 × 10−3

eV2

< |∆m232| < 3.4 × 10

−3eV

2

0.36 < sin2θ23 ≤ 0.64

0 ≤ sin2θ13 < 0.04

Unknowns• How small is θ13 ?

• Is Mass Hierarchy Normal or Inverted ?

• What is the value of CP phase δ ?

However, it is well known that so called parameter degeneracy makes these determinations difficult

(1) θ23 octant degeneracy (Fogli and Lisi, 1996) (2) Intrinsic θ13-δ degeneracy (Burguet-Castell et al, 2001)

(3) sign of Δm13 degeneracy (Minakata, HN, 2001) 2

8 fold degeneracy (Barger et al, 2002)

Proposed Experiments

• T2K (Phase I + Phase II)

• NOvA

• BNL VLBL

• SPL-Frejus

• β Beam

• Reactor

It is GOOD to consider some alternative

We propose to determine both Mass Hierarchy and CP phase at the same time

• by using two Identical detectors with Different baselines

• in such a way that both detectors receive the neutrino beam with the same energy spectrum w/o oscillation

• by running both νµ→νe and νµ→νe modes

For alternative methods using only neutrino mode

See S. Palomarse-Ruiz’s (hep-ph/0504015) talkSee N. Okamura’s (hep-ph/0504061) talk

Clean Measurement of Specturm Modulation by Oscillation Effect

--

As a concrete example, we condisder JPARC as a source and 1 detector at Kamioka (L=295km) and other at Korea (L=1050km)

→cancellation of systematic errors

→reduction of BG uncertainties

→4 degenerate solutions

Degeneracy can be lifted at diffent L

4 non-degenerate points

0 2 4 6 80

2

4

6

8

10

P(!µ!

e) [%

]

Norm. sin22"

13=0.08

Norm. sin22"

13=0.0745

Inv. sin22"

13=0.0808

Inv. sin22"

13=0.0746

Kamioka (L=295 km)

0 2 4 6 8 10

Korea (L=1050 km)

P(!µ!

e) [%]

normal

inverted

overlap

E = 0.65 GeV

mass hierarchy undetermined

E=0.65 GeV

Comparing Probabilities at Different Baselines

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

8

P(!µ!

e)

[%]

E = 0.5 GeV (Normal)

E = 0.6 GeV (Normal)

E = 0.7 GeV (Normal)

E = 0.8 GeV (Normal)

E = 0.5 GeV (Inverted)

E = 0.6 GeV (Inverted)

E = 0.7 GeV (Inverted)

E = 0.8 GeV (Inverted)

Kamioka (L=295 km)

0 1 2 3 4 5 6 7 8

Korea (L=1050 km)

P(!µ!

e) [%]

Despite that events # is smaller at Korea, energy depedendence is much stronger !

0

1

2

3

4

5

6

P(!µ

!e)

[%]

True sol. ("/4, 0.02)

Same sign sol. (2.4, 0.022)

Mixed sign sol.1 (2.64, 0.019)

Mixed sign sol.2 (0.244, 0.022)

Kamioka

0.4 0.6 0.8 1.00

1

2

3

4

5

P(!µ

!e)

[%]

Korea

0.4 0.6 0.8 1

Neutrino Energy (GeV)

Korea (w/o matter)

0.4 0.6 0.8 1 1.2

(#, sin22$

13)

Energy Spectrum Information is Crucial

WIN05, June 6-11 Hisakazu Minakata

Yes, we are the neighbours

!"#$%&'()*&+",-."("&$/&"01

How can we get the same energy spectrum at 2 detectors with different baselines?

Kamioka JPARC

It is possible to get the same Off-Axis Angle both at Kamioka and Korea

By Choosing the same Off-Axis Angle at Kamioka and Korea

Taken from Hagiwara et al (hep-ph/0504061)

We assume OA 2.5° Beam with 4 MW Powerand 2 HK (Mt) class detectors

Hyper-Kamiokande

48m

54

m

250m

Fiducial mass = 0.27!2

=0.54 Mton

What will happen if we construct one of the 2 detectors in Korea?We propose to place one of them at somewhere in Korea

Expected Event # Dist.

4+4 yrs of ν+ν2 × 0.27 Mt FV

2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.5 1 1.5

Kamioka !µ

0

100

200

300

400

500

600

700

800

900

1000

0 0.5 1 1.5

Kamioka !–

µ

0

20

40

60

80

100

120

140

160

180

200

0 0.5 1 1.5

Korea !µ

Reconstructed E! (GeV)

Num

ber

of e

ve

nts

/bin

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5

Korea !–

µ

χ2 =4∑

k=1

(5∑

i=1

(N(e)obs

i − N(e)expi

)2

σ2i

)+

3∑j=1

(εj

σ̃j

)2

N(e)expi = NBG

i · (1 +2∑

j=1

fij · εj) + N signal

i · (1 + fi3 · ε3)

1

Definiton of χ

νν × kamioka

korea = 4 combinations ( ) ( )

5 energy binsSystematic Errors

5 % BG (Overall)5 % BG (Energy Dep.)

5 % Signal Efficiency

-

-

signalBG

sin 2θ13=0.1, δ = π/22

Kamioka 0.54Mton detector, ! 2yr + !– 6yr 4MW beams

10-2

10-1

(a)

normal

10-2

10-1

0 2 4 6

(b)

inverted

"

sin

22#

13

(c)

normal

0 2 4 6

(d)

inverted

Examples of Degenerate Solutions (w. only HK@Kamioka)

true sol.

fake sol.

fake sol. true sol.fake sol.

fake sol.

Only HK@Kamioka can not Resolv All the Degeneray

fiducial mass

Kamioka 0.27Mton + Korea 0.27Mton detectors, ! 4yr + !– 4yr 4MW beams

10-2

10-1

(a)

normal

10-2

10-1

0 2 4 6

(b)

inverted

"

sin

22#

13

(c)

normal

0 2 4 6

(d)

inverted

Twin HK at Kamioka and Korea: T2KK

true sol.

true sol.

fake sol.

fake sol.

Twin HKs can determine Mass Hierarchy if θ13 is not so small!

keep

ing

the

sum

= 0

.54

Mt

Regions of Sensitivities for Mass Hierarchy

10-2

10-1

0 1 2 3 4 5 6

normal

Kamioka 0.54 Mton

Kamioka 0.27 Mton + Korea 0.27 Mton

Kamioka 0.16 Mton + Korea 0.38 Mton

Kamioka 0.05 Mton + Korea 0.49 Mton

Korea 0.54 Mton

10-2

10-1

0 1 2 3 4 5 6

inverted

!

s

in22"

13

|χ (true hierachy) -χ (wrong hierachy)| > 4 (9) for 2(3) σ CL

Mass Hierarchy can beDetermined in the region

above these curves

2

2

Choice of the same detector size is BEST!

min

min

keeping sum of total FV = 0.54 Mt

10-2

10-1

0 1 2 3 4 5 6

normal

10-2

10-1

0 1 2 3 4 5 6

inverted

!

s

in22"

13

Sensitivity to CP violation

|χ (true value of δ) -χ (δ ≠0 or π)| > 4 (9) for 2(3) σ CL

CP violation can beEstablished in the region

above these curves

GOOD sensitivities also to CP violation!

2

2min

min

Optimizing Running Time

10-2

10-1

0 1 2 3 4 5 6

normal

! 4yr + !– 4yr, 4MW beams

! 2yr + !– 6yr, 4MW beams

! 8yr, 4MW beam

10-2

10-1

0 1 2 3 4 5 6

inverted

"

s

in22#

13

10-2

10-1

0 1 2 3 4 5 6

normal

10-2

10-1

0 1 2 3 4 5 6

inverted

!

s

in22"

13

Mass Hierarchy CP Violation

4+4 yrs runs of ν + ν seems to be Optimal -

Stability Check of Our Results Against

10-2

10-1

normal (a)

10-2

10-1

0 1 2 3 4 5 6

inverted

!

s

in22"

13

5% systematic uncertainties

2% systematic uncertainties

10% systematic uncertainties

normal (b)

0 1 2 3 4 5 6

inverted

!

#Korea

= 2.8 g/cm3

#Korea

= 2.5 g/cm3

#Korea

= 3.1 g/cm3

normal (c)

0 1 2 3 4 5 6

inverted

!

sin2"

23 = 0.50

sin2"

23 = 0.45

sin2"

23 = 0.55

1

Change of Systematic errors

Change of mater density

Deviation of θ23 from maximal

Our Results are Stable

Sensitivity to mass hierarchy

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

10-2

10-1

sin22!13

Fra

ctio

n o

f "

Sensitivity to CP violation

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

10-2

10-1

sin22!13

Fra

ctio

n o

f "

Kamioka 0.27Mton + Korea 0.27Mton detectors

# 4yr + #– 4yr, 4MW beams

normal mass hierarchy

inverted mass hierarchy

Kamioka 0.54Mton detector

# 2yr + #– 6yr, 4MW beams

normal mass hierarchy

inverted mass hierarchy

1

Sensitivity: T2KK vs T2K-II (Orignal)

thin 2σthik 3σ

Sensitivity to mass hierarchy:T2K-II vs. (Kam+Korea) vs. No!a

!"#$%&'(",

!"#)&'*"

+*,'--

*"

Sensitivity to CP:T2K-II vs. (Kam+Korea) vs. No!a

!"#$%&'(",

!"#)&'*"

("

!"#$%&'(!,

!"#)&'*!

95% CL dashed: w/

solid: w/o proton D

Mena-Palomares-Ruiz-Pascoli;

L=200 and 810 km

Both 1st osci. max

Sensitivity to mass hierarchy:T2K-II vs. (Kam+Korea) vs. super-No"a

#

Summary• We propose to determine mass hierarchy and CP

phase at the same time by using Two Identical Detectors with Different Baselines

• As a concrete example, we consider JPARC Phase II 4MW Beam Power and 0.27 Mt Detector at Kamioka and other 0.27 Mt one at Korea

• 4 + 4 yrs runs of ν+ν modes, it is possible to determine mass hierachy for sin 2θ13 > 0.03 (0.055) at 2 (3) σ CL for any value of δ

• At the same time, good sensitivity to CP violation

- 2