Probing the Neutrino Mass Hierarchy in Future Detectors ...ino/Talks/Rajgandhi.pdf · Probing the...

Probing the Neutrino Mass Hierarchy in FutureDetectors using the Atmospheric νµ Survival Rate

Raj Gandhi

Harish-Chandra Research Institute, Allahabad, India

Probing the Neutrino Mass Hierarchy . . . July 07, 2005 BNL R. Gandhi – p.1/34

Outline . . .

Introduction

Importance of the Mass Hierarchy and futureprospects of its detection

Matter effects in Pµe, Pµτ and Pµµ

Results:Detecting the Mass Hierarchy in atmosphericνµ events

Conclusions


Introduction . . .

Goals for Neutrino Physics experiments have becomesharply defined over the last few years, after strongevidence for neutrino oscillations and mass from solar,atmospheric, reactor and accelerator experiments.

About a decade ago, the goals were understanding theorigin of the solar and atmospheric anomalies anddeficits, and whether these were due to oscillations orwere related to our incomplete understanding of thesources.


Introduction . . .

The present goal is to determine, as precisely as wecan, the elements of the leptonic mixing matrix and themasses/mass-squared differences of neutrinos.

Precision allows us to identify or exclude specialvalued mixing angles like θ13 = 0o, θ23 = 45o, andspecial relations between the quark and lepton sectorslike θ12 + θC = 45o, check for unitarity of 3 generations,non-standard interactions, decoherence scenarios.......


Introduction . . .

Note that measurements in the lepton sector areunhindered by hadronic uncertainties which areinherent in the quark sector. This enables clean testsof flavour physics limited only by experimentalprecision.

A multi-pronged effort to acheive these goals isunderway via various operating, planned and proposedexperiments, e.g. long-baseline, reactor, atmospheric,solar, beta-decay, ν-less double beta decay,large-mass water cerenkov detectors


Introduction . . .

(να) = U(νi) with i = 1, 2, 3 and α = e, µ, τ .

The 3 × 3 neutrino mixing matrix U in the MNSparametrization is:

c12c13 s12c13 s13e−iδ

−s12c23 − c12s23s13eiδ c12c23 − s12s23s13e

iδ s23c13

s12s23 − c12c23s13eiδ −c12s23 − s12c23s13e

iδ c23c13

where cij = cos θij , sij = sin θij (θij = mixing anglebetween ith & jth mass states). δ = CP phase.


Introduction . . .

Summary of present knowledge :

➢ tan2 θ12 = 0.39+0.05−0.04 solar,reactor

➢ tan2 θ23 = 1.0+0.3−0.3 atmospheric, K2K

➢ θ13 < 12o@3σ reactor, atmospheric

➢ δm221 = 8.2+0.3

−0.3 × 10−5eV 2 solar,reactor

➢ |δm231| = 2.2+0.6

−0.4 × 10−3eV 2 atmospheric, K2K

➢ mβ < 2.2 eV beta decay

➢ mββ0ν < 0.3 eV ν less double beta decay

➢ Σmi < 1.6 − 0.7 eV Precision Cosmology

➢ δCP is unknown


ν The Mass Hierarchy, its Significance and Detection

So far we only know |∆m2

31| and not its Sign

νe

νµ

m12

ντ

m22

m32

m12

δm31

2 δm21

2

m22

Normal ordering (δm31

2 > 0)

m32

Inverted ordering (δm31

2 < 0)


The Mass Hierarchy . . .

The importance of the mass hierarchy lies in itscapability to discriminate between various types of models for

unification, and thus in its ability to narrow the focus ofthe quest for physics beyond the Standard Model.

A large class of GUTS use the Type I seesawmechanism to unify quarks and leptons. Severalpositive features are lost if in such models the neutrinohierarchy is inverted rather than normal

C. Albright, Phys. Lett. B599, 285 (2004)



An inverted hierarchy on the other hand would generallyrequire m1,m2 to be degenerate, hinting towards anadditonal global symmetry in the lepton sector.

It would also favour theories utilising the Type II seesaw

mechanism with additional Higgs triplets.

The type of hierarchy impacts the effectiveness ofleptogenesis in most theoretical models.


The Mass Hierarchy . . . Future Measurements

Superbeam, Megaton Water Cerenkov and NeutrinoFactory Experiments will attempt to measure the signof ∆31 in the future :

➢ T2K superbeam, 295 km,< Eν >= 0.76 GeV, viaνµ → νe

➢ NOνA superbeam, 812 km,< Eν >= 2.22 GeV, viaνµ → νe

➢ HK, UNO Megaton Water Cerenkov, viaatmospheric νµ → νe

➢ Nu Factories substantial improvement in bounds


The Mass Hierarchy . . . Future Measurements

Superbeam, Megaton Water Cerenkov and NeutrinoFactory Experiments will attempt to measure the signof ∆31 in the future :➢ T2K superbeam, 295 km,< Eν >= 0.76 GeV, viaνµ → νe

➢ NOνA superbeam, 812 km,< Eν >= 2.22 GeV, viaνµ → νe

➢ HK, UNO Megaton Water Cerenkov, viaatmospheric νµ → νe

➢ Nu Factories substantial improvement in bounds



Detection of the hierarchy via the νµ → νe channel, atnot-so-long baselines, is hampered by aδCP − sign(∆31) degeneracy which reduces sensitivity.Additionally, in “off-resonance” sitiuations, there is aθ13 − sign(∆31) that must be taken into account.

Overcoming this in superbeam experiments wouldrequire using either multiple oscillation channels, 2 baselines,

different energies, the magic baseline, 2 off-axis locations or acombination of these stategies.Minakata et al, Beavis et al, Donini et al, Barger et al, Huber et al, Burguet-Castell et al,

O. Mena Requejo et al.....

These degeneracies are absent in methods whichutilise the muon survival probability.



Detection of the hierarchy via the νµ → νe channel, atnot-so-long baselines, is hampered by aδCP − sign(∆31) degeneracy which reduces sensitivity.Additionally, in “off-resonance” sitiuations, there is aθ13 − sign(∆31) that must be taken into account.

Overcoming this in superbeam experiments wouldrequire using either multiple oscillation channels, 2 baselines,

different energies, the magic baseline, 2 off-axis locations or acombination of these stategies.Minakata et al, Beavis et al, Donini et al, Barger et al, Huber et al, Burguet-Castell et al,

O. Mena Requejo et al.....

These degeneracies are absent in methods whichutilise the muon survival probability.Probing the Neutrino Mass Hierarchy . . . July 07, 2005 BNL R. Gandhi – p.12/34

Matter effects in Pµe

Vacuum 1-MSD limit (∆m221 = 0 ) :

Pµe = sin2 θ23 sin2(2θ13) sin2 [∆31L/E]

In matter,Pm

νµ→νe= sin2 θ23 sin2(2θm

13) sin2 [∆m31L/E]

where

sin2 2θm13 =

sin2 2θ13

( Aδm2

31

− cos 2θ13)2 + sin2 2θ13

and ∆m31 = ∆31

√

( Aδm2

31

− cos 2θ13)2 + sin2 2θ13



We note that: Pmµe is maximized not just at resonance

but when the combination sin2(2θm13) sin2 [∆m

31L/E] ismaximal, i.ei.e. when E = Eres = Em

peak.

For Earth baselines, this translates to:

[ρL]maxµe =

(2p + 1)π × 5.18 × 103

tan 2θ13km gm/cc

Note sensitivity to θ13.

The L where these (p = 0) maxima occur are 7600 kmfor sin22θ13 = 0.2, 10200 km for sin22θ13 = 0.1 and11200 km for sin22θ13 = 0.05.Co-relations and degeneracies play an important role and reducesensitivity when Pm

µe is used to determine the hierarchy






peak.


[ρL]maxµe =

(2p + 1)π × 5.18 × 103

tan 2θ13km gm/cc


The L where these (p = 0) maxima occur are 7600 kmfor sin22θ13 = 0.2, 10200 km for sin22θ13 = 0.1 and11200 km for sin22θ13 = 0.05.

Co-relations and degeneracies play an important role and reducesensitivity when Pm

µe is used to determine the hierarchy






peak.


[ρL]maxµe =

(2p + 1)π × 5.18 × 103

tan 2θ13km gm/cc


The L where these (p = 0) maxima occur are 7600 kmfor sin22θ13 = 0.2, 10200 km for sin22θ13 = 0.1 and11200 km for sin22θ13 = 0.05.Co-relations and degeneracies play an important role and reducesensitivity when Pm

µe is used to determine the hierarchyProbing the Neutrino Mass Hierarchy . . . July 07, 2005 BNL R. Gandhi – p.14/34

Matter effects in Pµτ and Pµµ

Vacuum 1-MSD limit (∆m2

21= 0 ) :

Pµe = sin2 θ23 sin2(2θ13) sin2 [1.27∆m231L/E]

Pµτ = cos4 θ13 sin2(2θ23) sin2 [1.27∆m231L/E]

➳Pµµ = 1 − Pµe − Pµτ


Matter effect on P (νµ → ντ )

The 1-MSD vacuum expression is:

Pvνµ→ντ

= cos2 θ13 sin2 2θ23 sin2(∆31)

− cos2 θ23Pvacνµ→νe

The 1-MSD analytic expression in matter is:

Pmνµ→ντ

= cos2 θm13 sin2 2θ23 sin2[(∆31 + A + ∆m

31)/2]

+ sin2 θm13 sin2 2θ23 sin2[(∆31 + A − ∆m

31)/2]

− cos2 θ23Pmatνµ→νe

➺Probing the Neutrino Mass Hierarchy . . . July 07, 2005 BNL R. Gandhi – p.16/34

Maximizing the matter effect in Pµτ

E = Eres = Evpeak leads to:

∆Pµτ ' cos4[sin 2θ13(2p + 1)π/4] − 1

(with sin2 2θ23 = 1, cos2 θ13, cos 2θ13 ' 1).

The maximum matter effect condition for L is:

[ρL]maxµτ = (2p + 1)π × 5.18 × 103 × cos 2θ13 km gm/cc

The maximum matter effect occurs for L = 9700 km forp=1 & sin2 2θ13 = 0.1 (9300 km, 9900 km for 0.2, 0.05).


Summary of Conditions for Large Matter effects . . .

Thus, conditions for maximizing the matter effects at verylong baselines are:

[ρL]maxµe = (2p+1)π5.18×103

tan 2θ13

Km gm/cc.

[ρL]maxµτ = (2p + 1)π5.18 × 103 cos 2θ13 Km gm/cc.

[ρL]maxµµ = pπ × 104 cos 2θ13 Km gm/cc.


Plot of Probabilities . . .

5 10 15

0.20.40.60.8

15 10 15

0.20.40.60.81

0.20.40.60.8

1

0.20.40.60.81

∆m2

31 > 0

Vacuum

∆m2

31 < 0

5 10 15

E (GeV)

00.20.40.60.8

1

5 10 15

E (GeV)

00.20.40.60.81

Pµe

Pµτ

Pµµ

(b) 7000 Km(a) 9700 Km

R. Gandhi et al., Phys. Rev. Lett. 94, 051801 (2005); hep-ph/0411252


Plot of Probabilities . . .

5 10 15

0

0.2

0.4

0.6

0.8

1

Vacuum∆31 > 0∆31 < 0

5 10 15

0

0.2

0.4

0.6

0.8

1

5 10 15

E (GeV)

0

0.2

0.4

0.6

0.8P(ν

µ→ν µ)

5 10 150

0.2

0.4

0.6

0.88000 km 10000 km

6000 km 7000 km

R. Gandhi et al., Phys. Rev. Lett. 94, 051801 (2005); hep-ph/0411252


Survival Probability : θ13 sensitivity . . .

5 10 15E (GeV)

0.0

0.2

0.4

0.6

0.8

1.0

Pµµ

0.000.050.100.20

sin2 2θ

13

7000 Km

R. Gandhi et al., hep-ph/0411252

5 10 15E (GeV)

0.0

0.2

0.4

0.6

0.8

1.0

Pµµ

0.000.050.100.20

sin2 2θ

13

9700 Km


Results for an Iron Calorimeter type detector


Results : Iron Calorimeter, 1000 kt-yr . . .

6000 7000 8000 9000

L(Km)

0

5

10

15

20

Nµ- ,

Nµ+

Nµ-m

= 204

Nµ-v = 261

Nµ+m

= 103

Nµ+v = 105

L = 6000 to 9700 Km, E = 5 to 10 GeV

sin2 2θ13 = 0.1

∆31 = 0.002 eV2


2.7 2.8 2.9 3 3.1 3.2

Log10L/E [Km/GeV]

0

5

10

15

20

25

Nµ- ,

Nµ+

Nµ-m

= 204

Nµ-v = 261

Nµ+m

= 103

Nµ+v = 105

L = 6000 to 9700 Km, E = 5 to 10 GeV

sin2 2θ13 = 0.1

∆31 = 0.002 eV2



8000 8500 9000 9500 10000 10500

L(Km)

8

10

12

14

Nµ-

Nµ-v(0.10) = 175

Nµ-m

(0.05) = 179

Nµ-m

(0.10) = 192

Nµ-m

(0.20) = 223

L = 8000 to 10700 Km, E = 4 to 8 GeV

∆31 = 0.002 eV2


3 3.1 3.2 3.3 3.4

Log10L/E [Km/GeV]

0

5

10

15

20

Nµ-

Nµ-v(0.10) = 175

Nµ-m

(0.05) = 179

Nµ-m

(0.10) = 192

Nµ-m

(0.20) = 223

L = 8000 to 10700 Km, E = 4 to 8 GeV

∆31 = 0.002 eV2



7000 8000 9000

L(Km)

0.3

0.4

0.5

0.6

0.7

0.8

Up/

Dow

n

mat, ∆31 = +0.002 eV2

mat, ∆31 = -0.002 eV2

vac, ∆31 = +0.002 eV2

L = 6000 to 9700 Km, E = 5 to 10 GeV

sin2 2θ13 = 0.1


7000 8000 9000 10000

L (Km)

2

2.5

3

3.5

Nµ- /

Nµ+

matter, ∆31 = +0.002 eV2

vacuum, ∆31 = +0.002 eV2

matter, ∆31 = -0.002 eV2

L = 6000 to 10700 Km, E = 4 to 8 GeV

sin2 2θ13 = 0.1


Fe Calorimeter, 1000kt-yr, ∆χ2 and σ sensitivity . . .

Choice of the optimal ranges for µ− events for 1000 kiloton-yr:Range 1 : E = 5 - 10 GeV and L = 6000 - 9700 Km (4 selected bins)

sin2 2θ13 Nvac Nmat(∆m2

31> 0) ∆χ2 sensitivity

0.05 260 227 5.35 1.14σ

0.1 261 204 19.76 3.44σ

0.2 263 163 86.40 8.6σ

Range 2 : E = 4 - 8 GeV and L = 8000 - 10700 Km(Log10(L/E)=3.21-3.44)



0.05 23.3 42.6 8.7 2.94σ

0.1 23.3 62.7 24.79 4.97σ

0.2 24.5 104.5 61.24 7.82σ


Results for a Megaton water cerenkov detector


Megaton Water Cerenkov, 1.8 Mt-yr exposure . . .

0 0.02 0.04 0.06 0.08

sin2 θ13

0

20

40

60

80

100

χ2 [mat

ter (

∆ 31 >

0) -

vac

uum

]

0.5

0.6

L = 6000 to 9700 km, E = 5 to 10 GeV

HK, 1.8 Mt yr

sin2 θ

23

∆31

= 0.002 eV2

3σ

In Preparation

0 0.02 0.04 0.06 0.08

sin2 θ13

0

10

20

30

40

50

60

70

80

90

100∆χ

2 [mat

ter (

δm31

2 > 0

) - v

acuu

m]

L = 6000 to 9000 km, E = 7 to 12 GeV

HK, 1.8 Mt yr sin2 θ

23 = 0.5

δm31

2 = 0.003 eV

2

3σ


Megaton Water Cerenkov, 1.8 Mt-yr exposure . . .

0 0.02 0.04 0.06 0.08

sin2 θ13

0

20

40

60

80

100

χ2 [mat

ter (

∆ 31 >

0) -

vac

uum

]

0.5

0.6

Log10

L/E = 3.215 - 3.322 km/GeV

HK, 1.8 Mt yr

sin2 θ

23

∆31

= 0.002 eV2

3σ

In Preparation


Megaton Water Cerenkov, 1.8 Mt-yr, ∆χ2 and σ sensitivity . . .

Choice of the optimal ranges for µ−+µ+ events for 1.8 megaton-yr:Range 1 : E = 5 - 10 GeV and L = 6000 - 9700 Km



0.05 731.8 664.4 6.86 2.62σ

0.1 735.3 616.0 23.09 4.8 σ

0.2 743.0 530.1 85.50 9.25σ

Range 2 : E = 4 - 8 GeV and L = 8000 - 10700 KmLog10(L/E) = 3.215 − 3.322Km/GeV



0.05 40.9 73.5 14.38 3.79σ

0.1 42.9 107.2 38.45 6.2 σ

0.2 48.7 178.3 94.22 9.71σ


To Sum Up . . .

Precision measurements ofneutrino mass differences andmixing angles are the dominant focus of experimentalactivity in neutrino physics for the next 15-20 years

The mass hierarchy is a powerful discriminator betweenvarious classes of unification theories and itsdetermination is a key goal for the future.

Future superbeam experiments using the νµ → νe

channel for hierarchy determination will find it difficult toacheive the required sensitivities due to degeneraciesIt is worthwhile to explore the νµ → νµ channel for thispurpose since it is largely free of degeneracies.


To Sum Up . . .

Precision measurements ofneutrino mass differences andmixing angles are the dominant focus of experimentalactivity in neutrino physics for the next 15-20 yearsThe mass hierarchy is a powerful discriminator betweenvarious classes of unification theories and itsdetermination is a key goal for the future.




To Sum Up . . .



channel for hierarchy determination will find it difficult toacheive the required sensitivities due to degeneracies

It is worthwhile to explore the νµ → νµ channel for thispurpose since it is largely free of degeneracies.


To Sum Up . . .





To Sum Up . . .

Large matter effects are not only confined to Pµe butalso arise in Pµτ at GeV energies at very long Earthbaselines. Both must be properly considered whenevaluating the event-rates for experiments measuringmuon survival.The effects discussed above are significantly sensitiveto θ13 and Sign of ∆m2

31, determination of which areoutstanding problems of neutrino physics.We have tried to show that there is a good possibilitythat one can determine the Sign of ∆m2

31 usingatmospheric neutrinos in a large mass iron calorimeterwith charge id as well as using a Megaton waterCerenkov detector


Matter effect in νµ → ντ

♠ Click here for Pµτ ;

3 The animation shows the matter effects building up in Pµτ for L = 6000 to 10500 km.3 Maximum matter effects seen at 9700 km.3 The term wise break up of probability is also depicted in the animation.

➺

To Summary page


Matter effect in νµ → νµ

♠ Click here for Pµµ ;

3 The animation shows the matter effects building up in Pµτ for L = 6000 to 10500 km.3 Maximum matter effects seen at 9700 km.3 The term wise break up of probability is also depicted in the animation.

➳


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