Sanjib Kumar Agarwalla - Institute of Mathematical Sciences, …ino/Talks/magic.pdf · 2007-06-15 · Sanjib Kumar Agarwalla [email protected] Harish-Chandra Research Institute,

Magic Baseline Beta Beam

Sanjib Kumar [email protected]

Harish-Chandra Research Institute, Allahabad, Indiawork done in collaboration with

S. Choubey, A. Raychaudhuri and A. Samanta

Phys.Lett.B629(2005)33-40

Nucl.Phys.B771(2007)1-27

S. K. Agarwalla MPI-K Heidelberg, Germany 21st May, 07 – p.1/43

PLAN


PLAN

Present Status & Missing Links

“Golden Channel”, Peµ


PLAN



“Eight-fold” degeneracy

“Magic Baseline”


PLAN





CERN based β-beam source

India-Based Neutrino Observatory (INO)


PLAN





CERN based β-beam source

India-Based Neutrino Observatory (INO)

Results

Conclusions


Then and Now

Then (1930): Pauli

I have hit upon a desperate remedy to save the

exchange theorem and the conservation of energy.

Namely, the possibility that there could exist

electrically neutral spin 12 particles of small mass . . . .


Then and Now

Then (1930): Pauli

I have hit upon a desperate remedy to save the

exchange theorem and the conservation of energy.

Namely, the possibility that there could exist

electrically neutral spin 12 particles of small mass . . . .

Now (2004): APS Neutrino Study Group

Much of what we know about neutrinos we have

learned in the last six years. . . . . We have so many

new questions, . . . We are most certain of one thing :

neutrinos will continue to surprise us . . . .


Past and Present

Neutrino physice, a bit player on the physics stage

in yesteryears, has now donned a central role


Past and Present



Spectacular results from a series of experiments

involving solar, atmospheric, reactor and accelerator

neutrinos have firmly established neutrino

oscillations

Research in this area is now poised to move into the

precision regime


Past and Present



Spectacular results from a series of experiments

involving solar, atmospheric, reactor and accelerator

neutrinos have firmly established neutrino

oscillations

Research in this area is now poised to move into the

precision regime

Next generation experiments have been

planned/proposed world-wide to further pin down

the values of the oscillation parameters


Present Status

⇒ ATM + K2K + MINOS :

|∆m231| ≃ 2.5+0.7

−0.5 × 10−3eV2, θ23 ≃ 45.0◦+9.22◦

−9.22◦ (3σ)

⇒ Solar Neutrino Experiments + KamLAND :

∆m221 ≃ 8.0+1.2

−0.8 × 10−5eV2, θ12 ≃ 33.83◦+4.82◦

−3.83◦ (3σ)

(Our convention : ∆m2ij = m2

i – m2j)


Present Status

⇒ ATM + K2K + MINOS :

|∆m231| ≃ 2.5+0.7

−0.5 × 10−3eV2, θ23 ≃ 45.0◦+9.22◦

−9.22◦ (3σ)

⇒ Solar Neutrino Experiments + KamLAND :

∆m221 ≃ 8.0+1.2

−0.8 × 10−5eV2, θ12 ≃ 33.83◦+4.82◦

−3.83◦ (3σ)

(Our convention : ∆m2ij = m2

i – m2j)

⇒ Chooz + Palo Verde :

sin2 2θ13 < 0.17 (3σ)

⇒ Two large mixing angles and the relative

oscillation frequencies open the possibility to

test CP violation in the neutrino sector, if θ13

and δCP are not vanishingly small


Unsolved Issues

The sign of ∆m231 (m2

3 − m21) is not known.

Neutrino mass spectrum can be normal or

inverted hierarchical

∆m2

∆m2

∆m

2

12

3

3

12solar {

} solar

atm

osp

he

ric

ma

ss

νe νµ τν

NORMAL INVERTEDHIERARCHYHIERARCHY


Continued..

Only an upper limit on sin2 2θ13 (< 0.17 at 3σ)

exists

The Dirac CP phase (δCP ) is unconstrained

We will focus on the first two issues. . .


Golden Channel (Peµ)

The appearance probability (νe → νµ) in matter, upto second

order in the small parameters α ≡ ∆m2

21/∆m2

31and sin 2θ13,

Peµ ≃ sin2 2θ13 sin2 θ23

sin2[(1 − A)∆]

(1 − A)2

+ α sin 2θ13 ξ sin δCP sin(∆)sin(A∆)

A

sin[(1 − A)∆]

(1 − A)

+ α sin 2θ13 ξ cos δCP cos(∆)sin(A∆)

A

sin[(1 − A)∆]

(1 − A)

+ α2 cos2 θ23 sin2 2θ12

sin2(A∆)

A2;

where ∆ ≡ ∆m2

31L/(4E), ξ ≡ cos θ13 sin 2θ21 sin 2θ23,

and A ≡ ±(2√

2GF neE)/∆m2

31

Cervera et al., hep-ph/0002108

Freund, Huber, Lindner, hep-ph/0105071


Eight-fold Degeneracy

(θ13, δCP ) intrinsic degeneracy

Burguet-Castell, Gavela, Gomez-Cadenas, Hernandez, Mena,

hep-ph/0103258

(sgn(∆m231), δCP ) degeneracy

Minakata, Nunokawa, hep-ph/0108085

(θ23, π/2 − θ23) degeneracy

Fogli, Lisi, hep-ph/9604415

Severely deteriorates the sensitivity


Problem & Solution

Degeneracies create “Clone” Solutions

Barger, Marfatia, Whisnant, hep-ph/0112119


Problem & Solution

Degeneracies create “Clone” Solutions

Barger, Marfatia, Whisnant, hep-ph/0112119

Kill the “Clones” at the “Magic” Baseline

Huber, Winter, hep-ph/0301257

Smirnov, hep-ph/0610198


Magic Baseline


Magic Baseline

If one chooses : sin(A∆) = 0

The δCP dependence disappears from Peµ

Golden channel enables a clean determination of

θ13 and sgn(∆m231)


Magic Baseline

If one chooses : sin(A∆) = 0

The δCP dependence disappears from Peµ

Golden channel enables a clean determination of

θ13 and sgn(∆m231)

First non-trivial solution:√

2GF neL = 2π (indep of E)

Isoscalar medium of constant density ρ :

Lmagic[km] ≈ 32725/ρ[gm/cm3]

According to PREM, the “Magic Baseline”

Lmagic = 7690 km


Best-fit values

|∆m231| = 2.5 × 10−3 eV2

sin2 2θ23 = 1.0

∆m221 = 8.0 × 10−5 eV2

sin2 θ12 = 0.31

δCP = 0

Chosen benchmark values of oscillation parameters,

except sin2 2θ13

Exact 3-flav osc. prob using PERM profile


Transition Probability Peµ

1 3 5 7 9 11Energy (GeV)

0

0.25

0.5

P eµ

NHIH

0.00

0.25

0.50

P eµ

L=1000 km L=4000 km

L=10000 kmL=7500 km

1 3 5 7 9 11Energy (GeV)

Agarwalla, Choubey, Raychaudhuri, hep-ph/0610333

Normal .vs. Inverted hierarchy sin2 2θ13 = 0.1


Transition Probability Peµ

1 3 5 7 9 11Energy (GeV)

0

0.25

0.5

P eµ

sin22θ13=0.1

sin22θ13=0.05

0.00

0.25

0.50

P eµ

L=1000 km L=4000 km

L=10000 kmL=7500 km

1 3 5 7 9 11Energy (GeV)


Two different values of sin2 2θ13 Normal hierarchy


What is Beta Beam?

A pure, intense, collimated beam of νe or νe,

essentially background free

P. Zucchelli, Phys. Lett. B 532 (2002) 166

Beta decay of completely ionized, radioactive ions

circulating in a storage ring. No contamination of

other types of neutrinos


Some positive features

Known energy spectrum

High intensity and low systematic errors

High Lorentz boost of the parent ions ⇒ better

collimation and higher energy of beam


Some positive features

Known energy spectrum

High intensity and low systematic errors

High Lorentz boost of the parent ions ⇒ better

collimation and higher energy of beam

Can be produced with existing CERN facilities

or planned upgrades

It can be operated simultaneously in the νe as

well as νe mode. The boost factors are fixed by

the e/m ratio of the respective ions


Beta Beam : Ion sources

Ion τ (s) E0 (MeV) f Decay fraction Beam

18

10Ne 2.41 3.92 820.37 92.1% νe

6

2He 1.17 4.02 934.53 100% νe

8

5B 1.11 14.43 600684.26 100% νe

8

3Li 1.20 13.47 425355.16 100% νe

Comparison of different source ions

Low-γ design, useful decays in case of anti-neutrinos

can be 2.9 × 1018/year and for neutrinos

1.1 × 1018/year

Larger total end-point energy, E0 is preferred


Schematic Lay-out

Proposed β-beam complex at CERN


Comparison with Nufact

Ultimate choice depends on future R&D


INO

The India-based NeutrinoObservatory

The INO/ICAL will be the world’sfirst magnetized large mass iron

calorimeter with interleaved GlassRPC detectors

Funding considerations in final stage


Location of INO

http://www.imsc.res.in/∼ino/


ICAL Design

Spokesperson: Prof. N.K. Mondal, TIFR


INO : 2nd Phase

3.4−4.0

2.6−2.9

12.71−13.1

9.9 − 12.15

4.4−5.6

(11300)FERMI LAB

(7145)CERN

PUSHEP Rammam

JHF(4828)

CERN(6871)

FERMI LAB(10480)

(6556)JHF

Artificial Source

Beta Beam ?

Neutrino Factory ?

Lmagic = 7690 km


INO

A magnetized Iron calorimeter (ICAL) detector

with excellent efficiency of charge identification

(∼ 95%) and good energy determination

Preferred location is Singara (PUSHEP) in the

Nilgiris (near Bangalore), 7152 km from CERN

A (50+50) Kton Iron detector

Oscillation signal is the muon track

(νe → νµ channel)


Detector assumptions

Total Mass 50 kton

Energy threshold 1.5 GeV

Detection Efficiency (ǫ) 60%

Charge Identification Efficiency (fID) 95%

Detector characteristics used in the simulations

We assume a Gaussian energy resolution function

with σ = 0.15E


β-beam flux at INO-ICAL

350

250

500

Flu

xy

r−

11

05

−2

mM

eV

−1

() ν

e 8B

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10 12 14

Energy (GeV)

350

500

250

νe

Flu

xy

r−

11

05

−2

mM

eV

−1

()

8Li

0

1

2

3

4

5

6

7

0 2 4 6 8 10 12 14

Energy (GeV)


Boosted on-axis spectrum of νe and νe

at the far detector assuming no oscillation


CERN - INO Long Baseline

LCERN−INO = 7152 km

The longer baseline captures a matter-induced

contribution to the neutrino parameters,

essential for probing the sign of ∆m231


CERN - INO Long Baseline

LCERN−INO = 7152 km

The longer baseline captures a matter-induced

contribution to the neutrino parameters,

essential for probing the sign of ∆m231

The CERN - INO baseline, close to the ‘Magic’

value, ensures essentially no dependence of the

final results on δCP . This ‘Magic’ value is

independent of E

This permits a clean measurement of θ13

avoiding the degeneracy issues which plague

other baselines


Resonance in matter effect

The very long CERN - INO baseline provides an

excellent avenue to pin-down matter induced

contributions

In particular, a resonance occurs at

Eres ≡ |∆m2

31| cos 2θ13

2√

2GF Ne

= 6.1 GeV

with |∆m231| = 2.5 × 10−3 eV2, sin2 2θ13 = 0.1 and

ρav = 4.13 gm/cc (PREM) for the baseline of 7152 km


Event Rates in INO-ICAL

sin2θ132

500 & NH500 & IH350 & NH350 & IH250 & NH250 & IH

8B Neutrino Beam

CERN − INO

0

50

100

150

200

250

0.001 0.01 0.1 0.5

Ev

en

ts i

n 5

ye

ars

sin2θ132

500 & IH500 & NH350 & IH350 & NH250 & IH250 & NH

8Li Anti−neutrino beam

CERN − INO

0

50

100

150

200

250

300

350

0.001 0.01 0.1 0.5

Ev

en

ts i

n 5

ye

ars


Event rates sharply depend on mass ordering and θ13


Event Rates (contd..)

sin2θ132

CERN − INO 8B Neutrino Beam

γ = 500 (NH)

PREM profile

− 5 %

+ 5 %

0

50

100

150

200

250

0.001 0.01 0.1 0.5

Ev

en

ts i

n 5

yea

rs


Sensitivity to matter profile


Iso-event curves

100007152

732

4000

8B & NHγ 350=

sin2θ2

13

(deg

ree)

CP

δInputs

sin22

13

CPδ = 0

0.043=θ

10(−2

)

0

50

100

150

200

250

300

350

400

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0

400010000

732

Inputs

sin22

13

CPδ = 0

0.043=θ8Li & IH

γ = 350

(deg

ree)

CP

δ

sin2θ2

13

7152

10( )−2

0

50

100

150

200

250

300

350

400

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5


At CERN-INO distance, the effect of δCP

on the measurement of θ13 is less


The χ2 function

Assume Poissonian distribution and define

χ2({ω}) = minξk

[

2

(

N th − Nex − Nex lnN th

Nex

)

+∑

k

ξ2k

]

{ω}: oscillation parameters, {ξk}: “pulls”, where k

runs over systematic uncertainties

N th({ω}, {ξk}) = N th({ω})[

1 +K∑

k=1

πkξk

]

+ O(ξ2k)

Minimize χ2 with respect to the pulls {ξk} and

finally marginalize over oscillation parameters by

minimizing χ2total = χ2 + χ2

prior


The systematic errors

2% flux normalization error

10% error in the interaction cross section

Detector systematic uncertainty of 2%

No systematic error related to the shape of the

energy spectrum. We work with the energy

integrated total rates


Sensitivity to sin2 2θ13

γ

−3

−2

−1

−4

5 years (3 σ )

(90%)

( %)

(3 σ )10 years

905 years

10 years

Neutrino

CERN − INO

sin

22

θ 13

10

10

10

10

250 300 350 400 450 500γ

−4

−3

−2

−1

5 years (3σ)

(3σ)10 years

5 years

10 years

( )90%

( )90%

Anti−neutrino

sin

2θ 1

32

CERN − INO

10

10

10

10

250 300 350 400 450 500


sin2 2θ13 limit below which experiment is insensitive

For νe (νe) true hierarchy is assumed normal (inverted)

Marginalization over |∆m2

31|, sin2 2θ23 and δCP


Upper limit on sin2 2θ13

At 3σ, sin2 2θ13 < 8.4 × 10−4(1.6 × 10−3) with 80%

detection efficiency and 10(5) years data in the

neutrino mode assuming normal hierarchy as true

with γ = 500

At 3σ, sin2 2θ13 < 1.1 × 10−3(2.1 × 10−3) with 60%

detection efficiency and 10(5) years data in the

neutrino mode assuming normal hierarchy as true

with γ = 500


sin2 2θ13 precision (5 yrs)

= 500γ

= 250γ = 350γ = 500γ

= 250γ

sin 22 θ13sin 2

2 θ13

3σ90 %

− 5

− 3

− 2

− 1

− 4

− 4 − 3 − 2 − 1 − 4 − 3 − 2 − 1 − 4 − 3 − 2 − 1

= 350γ

5 years

CERN − INO

Neutrino

true )( true )( true )(

sin

22

θ 13

sin 22 θ13

10

10

10

10

20 30 40 50 60

70 80 90 100

10 10 10 10 10 10 10 10 10 10 1010

Precis

ion

(%

)

10


Upper panels show the band of “measured” values ofsin2 2θ13 and

lower ones depict the corresponding precisionS. K. Agarwalla MPI-K Heidelberg, Germany 21st May, 07 – p.36/43

sin2 2θ13 precision (10 yrs)= 500γ

= 500γ

sin 22 θ13 sin 2

2 θ13sin 22 θ13

− 5

− 3

− 2

− 1

− 4

− 4 − 3 − 2 − 1 − 4 − 3 − 2 − 1 − 4 − 3 − 2 − 1

= 250γ

= 250γ = 350γ

= 350γ

3σ90 %

10 years

CERN − INO

Neutrino

true )( true )( true )(

sin

22

θ 13

10

10

10

10

20 30 40 50 60

70 80 90 100

10 10 10 10 10 10 10 10 10 10 1010

Precis

ion

(%

)

10


Upper panels show the band of “measured” values ofsin2 2θ13 and

lower ones depict the corresponding precisionS. K. Agarwalla MPI-K Heidelberg, Germany 21st May, 07 – p.37/43

Sensitivity to Sgn(∆m231)

−2

−3

γ

3σ( )5 years

3σ( )10 years

%)5 years (90

)%10 years (90

−1

Neutrinosin

2θ

2

13

CERN − INO

(tru

e)

10

10

250 300 350 400 450 500 10

γ

−3

−2

−15 years (3 σ )

(90 )

(3 σ )

%)

10 years

5 years (90

10 years %

Anti−neutrino

sin

2θ 1

32

(tru

e)

CERN − INO

10

10

10

250 300 350 400 450 500


Min value ofsin2 2θ13(true) as a function ofγ to rule out wrong

hierarchy. True hierarchy is normal (inverted) forνe (νe).

Marginalized over|∆m2

31|, sin2 2θ23, δCP andsin2 2θ13


Sensitivity to mass ordering

Minimum value of sin2 2θ13 → 8.5 × 10−3(9.8 × 10−3)

for which one can rule out inverted hierarchy at

3σ C.L. with 10(5) years of neutrino run assuming

normal hierarchy as true hierarchy with γ = 500

and 80% detection efficiency

Minimum value of sin2 2θ13 → 8.7 × 10−3(1.0 × 10−2)

for which one can rule out inverted hierarchy at

3σ C.L. with 10(5) years of neutrino run assuming

normal hierarchy as true hierarchy with γ = 500

and 60% detection efficiency


How much time we need?

−1

−2

−3

sin

2θ

2

13

(years)

γ = 350 )%(90

γ = 500 )%(90

γ = 500 3σ( )

γ = 250 )%(90

γ = 250

γ = 350

3σ( )

3σ( )

Neutrino

CERN − INO

(tru

e)

1

0 1 2 3 4 5 6 7 8 9 10

10

10

10

Time

−1

−2

−3

sin

2θ

2

13

(years)

γ = 500 )%(90

γ = 250 )%(90

γ = 250

γ = 350

3σ( )

3σ( )γ = 350 )%(90

γ = 500 3σ( )

Anti−neutrino

CERN − INO

(tru

e)

0 1 2 3 4 5 6 7 8 9 10

1

10

10

10

Time


Just 9 months run in theνe mode to rule out the wrong invertedhi-

erarchy at the3σ C.L. with γ = 500 and60% detection efficiency

if sin2 2θ13(true)= 5 × 10−2 and the normal hierarchy is true


Impact of δCP on hierarchy

(deg

ree)

CP

δ

sin2θ2

13

90% 90% 3σ3σ

Thin lines : 10 years Thick lines : 5 years

γ 350=

ν

(true) )10(−2

CERN − INO

0

50

100

150

200

250

300

350

400

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

3σ 3σ90%

90%

5 years Thick lines : Thin lines : 10 years

γ 350=

ν

sin2θ2

13 (true) 10(−2

)

CERN − INO

(deg

ree)

CP

δ

0

50

100

150

200

250

300

350

400

0.6 0.8 1.0 1.2 1.4 1.6


The loss in hierarchy sensitivity due to the uncertainty inδCP is

very marginal. Best sensitivity to hierarchy comes forδCP ≃ 125

(300) in theν (ν) mode


Conclusions

Ical@INO → 50 Kt magnetized iron calorimeter

CERN-INO baseline (7152 Km) - tantalizingly

close to the magic baseline and hence will be

free of the clone solutions


Conclusions





At this baseline we can get near-resonant matter

effect for E ≈ 6 GeV ⇒ possible with 85B and 8

3Li

Near-resonant matter effect gives largest

possible Peµ ⇒ enough statistics


Conclusions





At this baseline we can get near-resonant matter

effect for E ≈ 6 GeV ⇒ possible with 85B and 8

3Li

Near-resonant matter effect gives largest

possible Peµ ⇒ enough statistics

The CERN-INO Beta-Beam experiment is

expected to give sensitivity to θ13 and Sgn(∆m231)

better than all other rival proposals, apart from

a high performance neutrino factory


Wait for Magic

!! Thank You !!


Documents

Sanjib Kumar Agarwalla - Institute of Mathematical Sciences, …ino/Talks/magic.pdf · 2007-06-15 · Sanjib Kumar Agarwalla [email protected] Harish-Chandra Research Institute,