a. yu. smirnov

A. Yu. Smirnov

International Centre for Theoretical Physics, Trieste, Italy

ICTP, December 11, 2012

Race for the neutrino mass hierarchy

Neutrino oscillograms of the Earth

Searches for CP violation

PINGU, ORCA and mass hierarchy

E. Akhmedov, S. Razzaque, A. Y. S.arXiv: 1205.7071 v.5

e

2

1

3

mass

m231

m221

Normal mass hierarchy

|Ue3|2

|U3|2 |U3|2

|Ue1|2

|Ue2|2 tan23 = |U3|2 / |U3|2

sin13 = |Ue3|2tan12 = |Ue2|2 / |Ue1|2

m231 = m2

3 - m21

m221 = m2

2 - m21

Mixing parameters

f = UPMNS mass

UPMNS = U23IU13IU12

flavor

Mixing matrix:

1

2

3

e

= UPMNS

0.023

e

2

1

1

2

3

3

MA

SS

32

ij=m2ij /2E

D31 ~ 2D32

Inverted hierarchyNormal hierarchy

Oscillations

31

Cosmolog

y

31

32

31 > 32 31 < 32

makes the e-flavor heavier changes two spectra differently

Fourier analysis

S. Petcov M. Piai

Matter effect

-decay

Quark-lepton

symmetryUnification

Flavor symmetries

Quasi-degenerate- symmetry

Similar to quark spectrum

Supernova neutrinos

Atmosphericneutrinos

Earth matter effects,energy spectra

NOvA

Neutrino beam Fermilab-PINGU

Sterile neutrinos may help?

LBNO

MSW flavor MSW flavor conversion conversion inside the starinside the star

Propagation Propagation in vacuumin vacuum

Oscillations Oscillations inside the Earthinside the Earth

Collective flavor trasformationCollective flavor trasformation

Shock wave effect on conversion

Shock wave effect on conversion

Normal hierarchy Inverted hierarchy

Level crossing scheme

m2 (

eff

ect

ive)

the Earth matter effect in the antineutrino channel only

the Earth matter effect – in the neutrino channel only

Cossible collective effects may affect this picture

and mass hierarchy

P. Lipari ,T. OhlssonM. Chizhov, M. Maris, S .PetcovT. Kajita

and physics of oscillations

core

mantle

flavor-to-flavor transitions

Oscillations inmultilayer medium

- nadir angle

core-crossingtrajectory

-zenith angle

= 33o

- accelerator- atmospheric- cosmic neutrinos

Applications:

innercore

outercore

upper mantle

transition zone

crustlower mantle

(phase transitions in silicate minerals)

liquidsolid

Fe

Si

PREM model A.M. Dziewonski D.L Anderson 1981

Re = 6371 km

exclude

d

M. Maltoni

exclude

d

Lines of equal probability

MSW-resonancepeaks 1-2 frequency

1 - Pee

Parametric peak1-2 frequency

MSW-resonancepeaks 1-3 frequency

Parametric ridges1-3 frequency

exclude

d

B = (sin 2m, 0, cos2m)

2 lm

= (B x P)

Equation of motion (= spin in magnetic field)

= 2t/ lm

Phase of oscillations

Pee = e+e = PZ + 1/2 = cos2Z/2Probability to find e

e

,

BP

x

z

dP dt

y

where ``magnetic field’’ vector:

P = (Re e+ , Im e

+ , e+ e -

1/2)

mantle

mantle

1

2

1 2

core

mantle

mantle

mantle core mantle

1

2

3

4

1

2 3

4

core

mantle

mantle

1

2

3

4 3

2

4

1

E. Kh. Akhmedov, S.Razzaque, A.S.

Oscillations test dispersion relation for neutrinos

10

1

100

0.1

E,

GeV

MINOS

T2K

CNGS

NuFac 28000.005

0.03

0.10

T2KK

IceCube

LENF

IC Deep Core

NOvA

PINGU-1

e

contours of constant oscillation probability in energy- nadir (or zenith) angle plane

HyperK

Pyhasalmi

Energy range: 0.01 – 105 GeV

Baselines: 0 – 13000 kmMatter effects: 3 – 15 g/cm3

Flavor content nue, numu

Lepton number nu - antinu

Discovery of neutrino oscillations

Measurements of 2-3 mixing and mass splitting

Enormous physics potentialwhich is not completely explored and largely unused

Bounds on new physics - sterile neutrinos - non-standards interaction - violation of fundamental symmetries, CPT

which change with energy and zenithangle

E. Kh Akhmedov, M. Maltoni, A.Y.S. JHEP 05, (2007) 077 [hep-ph/0612285] JHEP 06 (2008) 072 [arXiv:0804.1466] PRL 95 (2005) 211801 arXiv:0506064 M Maltoni talks, unpublished

E. Kh Akhmedov, S Razzaque, A.S. arXiv: 1205.7071

A.Y.S. , hep-ph/0610198.

E Kh Akhmedov, A Dighe, P. Lipari, A Y. S. , Nucl. Phys. B542 (1999) 3-30 hep-ph/9808270

Uncertainties of

original fluxesFlavor identification

Reconstruction of direction

Energy resolutionLow statistics

Developments

of new detection

methods?

TITAND?Y. Suzuki

High statistics will solve the problems

Integrationaveraging

averaging and smoothing effects reconstruction of neutrino energyand direction

Original fluxes

identification of flavor

different flavors: e and

Detection

neutrinos and antineutrinos

Screening factors (1 - r s23

2 )

Reduces CP-asymmetry

(1 - e

)

(1 – )

PA = |Ae3|2

NeIH - Ne

NH ~ (PA - PA) (1 – ) [r s232 - (1 – e)/(1 -

)]

Flavor suppression(screening factors)

Neutrino - antineutrino factor

unavoidable

CP asymmetry

can be avoided

NIH - N

NH ~ (P- P) (1 – ) - r-1(1 – e) (Pe - Pe)]

Triple suppression

= ()/()

Oscillation physics with Huge atmospheric neutrino detectors

ANTARES

DeepCore

Oscillations at high energies 10 – 100 GeV in agreement with low energy data

no oscillation effect at E > 100 GeV

Ice Cube

Oscillations 2.7

Precision IceCube NextGeneration Upgrade

OscillationResearch withCosmics with the Abyss

PINGU: 18, 20, 25 ? new strings (~1000 DOMs) in DeepCore volume

IceCube : 86 strings (x 60 DOM)100 GeV thresholdGton volume

Existing IceCube stringsExisting DeepCore stringsNew PINGU strings

D. Cowen

Deep Core IC : - 8 more strings (480 DOMs)- 10 GeV threshold- 30 Mton volume

Digital Optical Module

20 new strings (~60 DOMs each) in 30 MTon DeepCore volume

Few GeV threshold in inner 10 Mton volume

Existing IceCube strings

Existing DeepCore strings

New PINGU-I strings

PINGU v2

125 m

Denser array

Energy resolution ~ 3 GeV

normal inverted

neutrino antineutrino

For 2 system

e - e e - e

e - e -

25

neutrinos antineutrinos

NH – solidIH – dashedx = - blue x = e - red

+ n + h

muon track cascade

measurements

E Eh reconstruction

E = E + Eh Eh E

105 events/year

E. Akhmedov, S. Razzaque, A. Y. S.arXiv: 1205.7071

Oscillations test dispersion relation for neutrinos

Quick estimation of significance

Stot ~ s n1/2

Background 5 – 7 %

S = [ ij Sij2 ]

Smearing with Gaussian reconstruction functions characterized by (half) widths

= A E


)

= B (mp / E)1/2

Reconstruction of neutrino energy and angle

Significance S tot = [ ij Sij2 ]1/2

Sij2 = [ Nij

IH - NijNH]2 / ij

2

ij

2 = NijNH + (f Nij

NH) 2

Uncorrelated systematic error

S = [ ij Sij2 ]

Smearing with Gaussian reconstruction functions characterized by (half) widths

= A E


)

= B (mp / E)1/2

Reconstruction of neutrino energy and angle

Significance S tot = [ ij Sij2 ]1/2

Sij2 = [ Nij

IH - NijNH]2 / ij

2

ij

2 = NijNH + (f Nij

NH) 2

Uncorrelated systematic error

Systematics reduces

significance by factor 2

~ 1/E0.5

= 0.2E

~ 0.5/E0.5

~ 1/E0.5

= 2 GeV

~ 0.5/E0.5

S tot = [ ij Sij2 ]1/2

Improvements of reconstruction of the neutrino angle leads to substantial increase of significance

Under CP-transformations:

cCP- transformations: c = i 02

+ applying to the chiral components

UPMNS UPMNS * -

V - V usual medium is C-asymmetricwhich leads to CP asymmetryof interactions

Degeneracy of effects: Matter can imitate CP-violation

Shape does not change the amplitude changes

Large significance at low energies

Determination of the 1-3 mixing has given start of the race for the neutrino mass hierarchyMass hierarchy: important implications for phenomenology and theory

Dedicated new experiments to determine the

hierarchy: LBL accelerator, reactor, INO magnetized

ICAL, also Supernova neutrinos, double beta decay,

cosmology Good chance that multi-megaton scale under ice (water) atmospheric neutrino detectors with low energy threshold (PINGU, ORCA) will be the first.

Intensive study of capacity of these

detectors is under way

m231hierarchy

versus

23

Grid of magic lines and CP domains

AS = 0

- true (experimental) value of phasef - fit value

P = P() - P(f)

P = 0

(along the magic lines)

( + ) = - ( + f) + 2 k

(E, L) = - ( + f)/2 + k

= Pint() - Pint(f)

AA = 0

int. phase condition

depends on

Interference term:

P = 2 s23 c23 |AS| |AA| [ cos( + ) - cos ( + f)]

For e channel:

AS = 0

Pint = 0

= /2 + k

AA = 0

interference phase does not depends on

For channel

- The survival probabilities is CP-even functions of - no CP-violation- dependences on phases factorize

Pint ~ 2s23c23|AS||AA|cos cos

Dependence on disappears

Form the phase line grid

V. Barger, D. Marfatia, K WhisnantP. Huber, W. Winter, A.S.

form magic grid

e e

fU23I

I = diag (1, 1, ei )

e

e

~

Propagation basis

~

~

~

~

projection projectionpropagation

A(e ) = cos23Ae2ei + sin23Ae3

Ae3

Ae2

CP-violation and 2-3 mixingare excluded from dynamicsof propagation

CP appears in projection only

For instance:

For E > 0.1 GeV

A22 A33 A23

AS = 0

Pint = 0

= /2 + k

AA = 0


For channel




Form the phase line grid


form magic grid

Ae2 = 0

Pint = 0

- solar magic lines

( + ) = /2 + 2 k

(E, L) = - + /2 + k

Ae3 = 0

- interference phase condition

depends on

Pint = 2s23c23|Ae2||Ae3|cos( + )

P(e ) = c232|Ae2|2 + s23

2|Ae3|2 + 2s23c23|Ae2||Ae3|cos( + )

Explicitly

= arg (Ae2 Ae3*)

Dependence on disappears, interference term is zero if


- atmospheric magic lines

Grids do not change with

Int. phaseline (blue) moves with -change

P

P = P() - P(f) = const

White: atmosphericBlack: solar

e

- mass hierarchy

- deviation of 2-3 mixing

from maximal one

- CP violationProbe of nature of neutrino mass (soft-hard);

Neutrino images

of the Earth

Atmospheric vs.

LBL

- sterile neutrinos- tests of fundamental symmetries- non-standard interactions

Neutrino fluxes averaged over all directions

M. Honda et al astro-ph/0611418

Flavor ratiosCharge asymmetries

1.33

1.00

39

Radiography of the Earth core and mantle

M. C. Gonzalez-GarciaF. Halzen, M. Maltoni, H. TanakaarXiv:0711.0745 [hep-ph]

Zhenith angle distribution of events in IceCube for different energy thresholds for PREM model

Ratio of zenith angle distribution of expected events for PREM model and for homogeneous Earth matter distribution (stat. error)

71

Measuring oscillograms with atmospheric neutrinos

E > 2 - 3 GeV

with sensitivity to the resonance region

Huge Atmospheric Neutrino Detector

Better angular and energy resolution

Spacing of PMT ?

V = 5 - 10 MGt

Should we reconsider a possibility to use atmospheric neutrinos?

develop new techniques to detect atmospheric neutrinos with low threshold in huge volumes?

0.5 GeV

a). Resonance in the mantle

b). Resonance in the core

c). Parametric ridge A

d). Parametric ridge B

e). Parametric ridge C

f). Saddle point

a). b).

c).

e).

d).

f).

Y. Suzuki

- Proton decay searches- Supernova neutrinos- Solar neutrinos

Totally Immersible Tank Assaying Nucleon Decay

TITAND-II: 2 modules: 4.4 Mt (200 SK)

Under sea deeper than 100 m

Cost of 1 module 420 M $

Modular structure

Y. Suzuki

Totally Immersible Tank Assaying Nucleon Decay

Module: - 4 units, one unit: tank 85m X 85 m X 105 m - mass of module 3 Mt, fiducial volume 2.2 Mt - photosensors 20% coverage ( 179200 50 cm PMT)

TITAND-II: 2 modules: 4.4 Mt (200 SK)

Contours of constant oscillation probability in energy- nadir (or zenith) angle plane

P. Lipari ,T. OhlssonM. Chizhov, M. Maris, S .PetcovT. Kajita

e

Michele Maltoni

1 - Pee

exclude

d

Fig. 4

Oscillations in matter with nearly constant density (mantle)

Parametric enhancement of oscillations

Mantle – core - mantle

Interference

constant density + corrections

Peaks due to resonance enhancement of oscillations

Low energies: adiabatic approximation

Parametric resonance parametric peaks

Smallness of 13 and m21

2/m322

in the first approximation: overlap of two 2–patternsdue to 1-2 and 1-3 mixings

interference

of modesCP-interference

interference(sub-leading effect)

Two layer transitions vacuum-matter(atmosphere-Earth)

of oscillograms

1. One MSW peak in the mantle domain

2. Three parametric peaks (ridges) in the core domain

3. MSW peak in the core domain

1-3 mixing:

1-2 mixing:

1. Three MSW peaks in the mantle domain

2. One (or 2) parametric peak (ridges) in the core domain

1D 2D - structures regular behavior

solar magic linesatmospheric magic linesrelative phase lines

Regions of different sign of P

Interconnectionof lines due to level crossing

factorization is not valid

Normal hierarchy Inverted hierarchy

Level crossing schemem23

2 (Atm) = m232 (effective)

m2 (

eff

ect

ive)

74

Earth matter effects

Flavor evolution of neutrino statesis highly adiabatic

Strong suppression of the neutronization peak: e 3

NH

Adiabaticity is broken in shock front if the relative width of the front:

R/R < 10-4 10 km

Shock wave effect

if larger – no shock wave effect:probe of the width of front

Normal mass hierarchy:

in the antineutrino channel only

Inverted mass hierarchy: in the neutrino channel only

If the earth matter effect is observed for antineutrinosNH is established!

Permutation of the electron and non-electron neutrino spectra

Searching for sterile neutrinos

Reduces the depth of oscillationsinterference

P(e ) = s232|Ae3|2

Modifiesphase

= arg (A22 A33*)

E Kh Akhmedov, S Razzaque,A. Y.S.

Reduces the average probability

P( ) = 1 – ½ sin2 223 - s23

4|Ae3|2 + ½ sin2 223 (1 - |Ae3|2) cos

P( ) = ½ sin2 223 - s23

2 c232|Ae3|2 - ½ sin2 223 (1 - |Ae3|2) cos

for hierarchy determination

½

½

neglecting 1-2 mass splitting

e

2nd and 3rd parametric peaks

MSWresonance in core

MSW resonance in mantle

AS = 0

Pint = 0

= /2 + k

AA = 0


For channel




Form the phase line grid32

AS = 0

- true (experimental) value of phasef - fit value

P = P() - P(f)

P = 0

(along the magic lines)

( + ) = - ( + f) + 2 k

(E, L) = - ( + f)/2 + k

= Pint() - Pint(f)

AA = 0

int. phase condition

depends on

Interference term:

P = 2 s23 c23 |AS| |AA| [ cos( + ) - cos ( + f)]

For e channel:

(- 0.7 – 0.8)

(- 0.9 - 0.8)

(- 1. - 0.9)

50 Mt yr

Blue – normalRed – inverted1 error

For different zenith angle bins

O. Mena, I Mocioiu, S. Razzaque, arXiv:0803.3044

IceCubeDeep core

- Effective area – too big- Relation between neutrino and muon energies

e

2

1

MA

SS 1

2

3

3

MA

SS

m223m2

32

m221

m221

Inverted mass hierarchyNormal mass hierarchy

?

~ Tri-bimaximal mixing

1-3 mixing

bi-maximal?

tri-maximal

FLAVOR FLAVOR

m232 = 2.4 x 10-3 eV2

m221 = 7 x 10-5 eV2

- symmetry?

Neutrinos (resonance channels):

Pee = |Ue3|2

No earth matter effect

Antineutrinos (no resonances):

Pee = PE1e = |U1e|

2

without Earth matter effect:

the Earth matter effect in the antineutrino channel only

Disappearance of neutronization peak

~ complete permutation of spectra Partial permutation of spectra:mixed soft spectrum

p = 1 - |Ue1|2

p = 1 - |Ue3|2

~1/3

Neutrinos (L resonance ):

= |U2e|2

without Earth matter effect

Pee = |Ue3|2

No Earth matter effect

Antineutrinos (H - resonance):

Pee = PE2e

the Earth matter effect – in the neutrino channel only

~ Complete permutation of spectra

p = 1 - |Ue2|2

Partial suppression of neutronization peak

~ 2/3

Partial permutation: mixed hard spectra

p = 1 - |Ue3|2

Experiment Parameters Effect Construction Result Cost

No collective effects

a. yu. smirnov

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