Neutrino Mass BoundsNeutrino Mass Bounds fromfrom beta decays and beta decays and

Cosmological ObservationsCosmological Observations(LCDM vs Interacting Dark-Energy Model)(LCDM vs Interacting Dark-Energy Model)

Yong-Yeon KeumYong-Yeon KeumNAOJ, Mitaka Japan NAOJ, Mitaka Japan KITPC, Beijing China KITPC, Beijing China

TeVPA08, IHEP at BeijingTeVPA08, IHEP at BeijingSeptember 26, 2008 September 26, 2008

Primordial Neutrinos Primordial Neutrinos in Astrophysicsin Astrophysics

The connection between cosmological The connection between cosmological observations and neutrino physics is one of observations and neutrino physics is one of the interesting and hot topic in astro-particle the interesting and hot topic in astro-particle physics.physics.

Precision observations of the cosmic Precision observations of the cosmic microwave background and large scale microwave background and large scale structure of galaxies can be used to prove structure of galaxies can be used to prove neutrino mass with greater precision than neutrino mass with greater precision than current laboratory experiments. current laboratory experiments.

Contents:Contents: Neutrinoless Double beta Decays and Total Neutrinoless Double beta Decays and Total

Neutrino Mass boundsNeutrino Mass bounds Neutrino Mass bound from Large Scale Neutrino Mass bound from Large Scale

Structures (CMB, Power Spectrum,…..)Structures (CMB, Power Spectrum,…..) DiscussionDiscussion

Papers: YYK and K. Ichiki, JCAP 0806, 005, 2008;Papers: YYK and K. Ichiki, JCAP 0806, 005, 2008; JHEP 0806, 058, 2008;JHEP 0806, 058, 2008; arXiv:0803.3142arXiv:0803.3142References: References: Massive Neutrinos and Cosmology: J. Lesgourgues and S. Massive Neutrinos and Cosmology: J. Lesgourgues and S.

Pastor, Phys. Rep. 429:307(2006)Pastor, Phys. Rep. 429:307(2006)Fundamentals of Neutrino Physics and Astrophysics: C. Giunti Fundamentals of Neutrino Physics and Astrophysics: C. Giunti

and C.W. Kim, Oxford University Pressand C.W. Kim, Oxford University Press

Now we enter the era of Precision Neutrino Now we enter the era of Precision Neutrino Measurement Science (PMNS era).Measurement Science (PMNS era).

What do we hope to learn and which information is likely to What do we hope to learn and which information is likely to teach us more about new physics than others.teach us more about new physics than others.

Four most useful items for probing new physics:Four most useful items for probing new physics:

1.1. Search for neutrinoless double beta decaysSearch for neutrinoless double beta decays

2.2. Determined the sign of atmospheric mass Determined the sign of atmospheric mass difference square (neutrino mass hieradifference square (neutrino mass hierarrchy)chy)

3.3. the magnitude of the magnitude of

4.4. establish or refute the existence of sterile establish or refute the existence of sterile neutrinos. neutrinos.

13

Neutrino Mixing MatrixNeutrino Mixing Matrix

1 2

e 1 2 3 2 3 2 1

2 1 3 2 1 3 1 3 2 1 3 2 1 2

3 1 3 2 1 3 1 3 2 1 3 2 1 3

i i( + )

1,2

V=diag(1, e ,e )

Dirac Phase; Majo

i

i i

i i

c c c s s e

UV c s s s c e c s s s s e c s V

s s s c c e s c s c s e c c

where

rana Phases

22 2

23

Pr esent Data with 3 ranges of mixing paramters:

is small: sin 2 0.1 @ 95% C.L. (Chooz reactor exp.)

Solar Neutrino Data Large Mixing Angle Sol.

0.70 sin 2 0.94

-5 -5 2 2 2

2 1

21

-3 -3 2

7.1 10 s 8.9 10 [eV ] ; s=

Atmospheric Neutrino Data Maximal Mixing Angle Sol.

sin 2 0.87

1.4 10 | a| 3.3 10 [eV

m m

2 23 1]; a=m m

NeutrinolessNeutrinoless Double Beta Decays Double Beta Decays

Part IPart I

Neutrinoless double-beta Neutrinoless double-beta decaydecay

(A,Z) (A,Z) (A,Z+2) + e (A,Z+2) + e- + e+ e- - ( (L=2)L=2)

-- -- the most senstive process to the total lepton number the most senstive process to the total lepton number

and small majorana neutrino masses and small majorana neutrino masses

22 0 2 0A 01 00

1/ 2

0 01/ 2

001

2 2 2e1 1 e2 2 e3 3

1 ( , ) g ( , )

( , )

( , ) half-life time; =nuclear matrix element

= phase space factor;

= U U U

v

v v

v

m M A Z G E ZT A Z

where

T A Z M

G

m m m m

00-decay has not yet been seen experimentally.-decay has not yet been seen experimentally. The best result has been achieved in the The best result has been achieved in the

Heidelberg-Moscow (HM) Heidelberg-Moscow (HM) 76 76Ge experiment:Ge experiment:

TT001/2 1/2 > 1.9 x 10> 1.9 x 1025 25 years years |m |m| < 0.55 eV| < 0.55 eV

Many future ambitious projects: Many future ambitious projects: CAMEO,CUORE,COBRA,EXO,GENIUS,MAJORANA,CAMEO,CUORE,COBRA,EXO,GENIUS,MAJORANA,

MOON,XMASSMOON,XMASS

Neutrioless Double-beta decay Neutrioless Double-beta decay vs Neutrino Mass vs Neutrino Mass

Mass Ordering (for simplicity)Mass Ordering (for simplicity)

The rate of The rate of decay depends on the mag. decay depends on the mag. of the element of the neutrino mass of the element of the neutrino mass matrix:matrix:

e ev

32

32

2 2 2 2 22 3 1 2 3 2 2 3

2 2 2 2 22 3 3 2 3 2 2 1

| | (Case I);

| | (Case II);

may be determined from the lightest mass m and mass-squared differences

iiee

ii

i

M c c m c s m e s m e

c c m c s m e s m e

m

1 2 3 i

2 2 2 22 1 3 2

2 2 2 23 2 2 1

m < m < m (non-negative m )

Two possible mass spectra: s , a= (normal hierarchy);

s , a= (inverted hierarchy)

where a >>

m m m m

m m m m

s

Bound of the total neutrino massBound of the total neutrino mass

Depends on two parameters;Depends on two parameters;

(1)(1) the scale of atm. Neutrino Osci, the scale of atm. Neutrino Osci, (())(2)(2) the amplitude of solar Neutrino Oscithe amplitude of solar Neutrino Osci. . ( (

) )

2 22 2

2

2 2ee 32

ee3

Since sin 2 0.1 or s 0.026,

The limit on for 0 are

2 M cos 22 M

| cos 2 |

( for Case I and -- for Case II)

eeee

MM

23sin 2

Total Nu-Mass vs Mee ( NH vs IH )Total Nu-Mass vs Mee ( NH vs IH )

Normal Hierarchy Inverse Hierarchy

Mee(eV)

Sensitivities of the future expsSensitivities of the future exps. .

Mee vs lightest m

Normal Hierarchy

Inverse Hierarchy

Bilenky at al. 2004

Tritium beta decays

Most sensitive to the electron neutrino mass Since tritium beta-decay has one of the smallest Q-values

among all known beta decays:(1) Superallowed transition between mirror nuclei with a

relatively short half-life time (~12.3 years) An acceptable number of observed events

(2) Atomic structure is less complicated, which leading to a more accurate calculation of atomic effects.

_3 -

ve3 He + e + ( m limit)

Q 18.574 KeVeH

Kurie Function:

Mainz and Troitzk experiments:

With neutrino mixing:

2 2 1/2K(T) = [ (Q -T) (Q ) ] eT m

m 2.3 eV (95% C.L.)

m 2.5 eV (95% C.L.)ve

ve

_3 -

k e

2 2 2 1/2ek

2 2 2 2 2 2 2 2 2 2 2k 12 13 1 12 13 2 13 3

3 He + e + ( )

Then K(T) = [ (Q -T) |U | (Q ) ]

m = | | + s + s

m 2.3 eV (95% C.L.)

k ek k

k k

ek k

H U

T m

U m c c m c m m

Summary of Part 1Summary of Part 1 Tritium beta decay: Mainz and Troitsk ExpTritium beta decay: Mainz and Troitsk Exp

mm11 < 2.2 eV < 2.2 eV Future Exp. KATRIN: Future Exp. KATRIN:

sensitivity msensitivity m11 ~ 0.25 eV ~ 0.25 eV

If the 0If the 0 decay will not observed in future exp. decay will not observed in future exp. andand

|m|m| < a few 10| < a few 10-2 -2 eV , eV ,

Massive neutrinos are either Dirac or Majorana Massive neutrinos are either Dirac or Majorana particle, and normal hierarchyparticle, and normal hierarchy

The observationof the 0The observationof the 0 decay with |m decay with |m| > 4.5 10| > 4.5 10-2 -2 eV eV will exclude normal hierarchy.will exclude normal hierarchy.

If the 0If the 0 decay will be observed and decay will be observed and

it will be an indication of the inverted hierarchyit will be an indication of the inverted hierarchy

Remarks: It is really difficult to confirm Remarks: It is really difficult to confirm the normal hierarchy in neutrinoless the normal hierarchy in neutrinoless double beta decay.double beta decay.

2 20.42 atm atmm m m

Neutrino Mass bound from Neutrino Mass bound from Large Scale Structures Large Scale Structures

(CMB, Power Spectrum,(CMB, Power Spectrum,……..)..)Part IIPart II

TitleTitleDark Energy 73%Dark Energy 73%(Cosmological Constant)(Cosmological Constant)

NeutrinosNeutrinos 0.10.13%3%

Dark MatterDark Matter23%23%

Ordinary Matter 4%Ordinary Matter 4%(of this only about(of this only about 10% luminous)10% luminous)

The role played by neutrinos:

Tdec ~ few me dominant e-/e+ photons T = 2.73 K Tv = 1.96 K = 0.17 meV

present neutrino number density:

Since Tv is smaller than the neutrino mass scale, CMB neutrinos are today mostly non-relativisitic:

Present data: H=100 h km/s Mpc with h=0.7

The total energy density in relativistic particles: T~0.3eV;

with Nv = 3 (small corrections from the approximation Nv=3.04)

Measurements of CMB anisotropies allow to reconstruct Nv in two different ways:

a) from the total energy density in relativisitic particles (rad) significantly contributes to the measurable expansion rate around recombination b) the energy density in freely moving relativistic ptls (like neutrinos and unlike photons) can be reconstructed, they smooth out inhomogeneities (p= the fraction of freely moving neutrinos)

We remark that these cosmological data cannot measure the relative weight of each neutrino flavor, and cannot discriminate neutrinos from other speculative free-moving relativistic particles.

Neutrino free-stream :Neutrino free-stream : If If is carried by free-moving relativistic particles, is carried by free-moving relativistic particles, we can discriminate between massless vs massive ,andwe can discriminate between massless vs massive ,and between free vs interacting neutrinos.between free vs interacting neutrinos.

Neutrino masses determine two-different things:Neutrino masses determine two-different things:

1) temperature at which neutrinos cease to be non-1) temperature at which neutrinos cease to be non-relativistic, which controls the length on which neutrinos relativistic, which controls the length on which neutrinos travel reducing clustering.travel reducing clustering.

2) the function of energy carried by neutrinos, which 2) the function of energy carried by neutrinos, which controlscontrols

how much neutrinos can smooth inhomogeneities.how much neutrinos can smooth inhomogeneities.

In standard cosmology:In standard cosmology:

CMB vs NCMB vs Nvv

Large Scale StructuresLarge Scale Structures

Neutrino mass effects Neutrino mass effects

After neutrinos decoupled from the thermal bath, they stream After neutrinos decoupled from the thermal bath, they stream freely and their density pert. are damped on scale smaller than freely and their density pert. are damped on scale smaller than their free streaming scale. their free streaming scale.

The free streaming effect suppresses the power spectrum on The free streaming effect suppresses the power spectrum on scales smaller than the horizon when the neutrino become non-scales smaller than the horizon when the neutrino become non-relativistic.relativistic.

Pm(k)/Pm(k) = -8 Pm(k)/Pm(k) = -8 ΩΩ / /ΩΩmm

Analysis of CMB data are not sensitive to neutrino masses if Analysis of CMB data are not sensitive to neutrino masses if neutrinos behave as massless particles at the epoch of last neutrinos behave as massless particles at the epoch of last scattering. Neutrinos become non-relativistic before last scattering. Neutrinos become non-relativistic before last scattering when scattering when ΩΩh^2 > 0.017 (total nu. Masses > 1.6 eV). h^2 > 0.017 (total nu. Masses > 1.6 eV). Therefore the dependence of the position of the first peak and the Therefore the dependence of the position of the first peak and the height of the first peak has a turning point at height of the first peak has a turning point at ΩΩ h^2 = 0.017. h^2 = 0.017.

Mass Power spectrum vs Neutrino Masses

Power spectrumPower spectrum

PPmm(k,z) = P(k,z) = P**(k) (k) TT22(k,z) Transfer Function:(k,z) Transfer Function:

T(z,k) := T(z,k) := (k,z)/[(k,z)/[(k,z=z(k,z=z**)D(z)D(z**)])]

Primordial matter power spectrum (AkPrimordial matter power spectrum (Aknn))

zz**:= a time long before the scale of interested have entered := a time long before the scale of interested have entered

in the horizon in the horizon

Large scale: T ~ 1Large scale: T ~ 1

Small scale : T ~ 0.1Small scale : T ~ 0.1

PPmm(k)/P(k)/Pmm(k) ~ -8 (k) ~ -8 ΩΩ//ΩΩmm

= -8 f= -8 f

M_nu

Numerical Analysis

Cosmological parameters Omega_c : fraction of the dark-matter density Omega_b: fraction of the baryon matter

density Theta: the (approx) sound horizon to the

angular diameter distance tau: optical depth n_s : scale spectral index Ln[10^10 As] : primordial superhorizon power in the curvature perturbation on 0.05 Mpc^-1 scale

Within Standard Cosmology Model (LCDM)

Equation of State (EoS)

W = p/

It is really difficult to find the origin of dark-energy It is really difficult to find the origin of dark-energy with non-interacting dark-energy scenarios.with non-interacting dark-energy scenarios.

Dynamical Dark-Energy Models

Summary of EoS Summary of EoS

Canada-France-Hawaii Wide Synoptic Survey:Canada-France-Hawaii Wide Synoptic Survey:

wwoo < - 0.8 based on cosmic share data alone < - 0.8 based on cosmic share data alone Supernova Lagacy Survey (SNLS):Supernova Lagacy Survey (SNLS):

Combined with SDSS measurement of BAOCombined with SDSS measurement of BAO

WMAP3 data:WMAP3 data:

1) assume flat universe with SNLS data: 1) assume flat universe with SNLS data:

2) Drop prior of flat universe, WMAP+LSS+SNLS 2) Drop prior of flat universe, WMAP+LSS+SNLS data:data:

1.023 0.090 0.054w

0.070.090.97w

0.128 0.0160.079 0.013 and 0.0241.062 kw

Interacting dark energy modelInteracting dark energy model

Example At low energy,

The condition of minimization of Vtot determines the physical neutrino mass.

nv mvScalar potential

in vacuum

Interacting Neutrino-Dark-Energy Model

Theoretical issue: Theoretical issue: Adiabatic Instability problem: Adiabatic Instability problem:

Afshordi et al. 2005Afshordi et al. 2005

Gravitational collapseGravitational collapse

Kaplan, Nelson, Weiner 2004Kaplan, Nelson, Weiner 2004 Khoury et al. 2004Khoury et al. 2004 Zhao, Xia, X.M Zhang 2006Zhao, Xia, X.M Zhang 2006

Always positive sound velocity Always positive sound velocity No adiabatic instabilityNo adiabatic instability

Brookfield et al,. 2006Brookfield et al,. 2006 YYK and Ichiki, 2007, 2008YYK and Ichiki, 2007, 2008

2 2 2/

H (Chameleon DE models)

eff eff

eff

m d V d

m

< H (Slow-rolling Condition)effm

Background Equations:Background Equations:

We consider the linear perturbation in the synchronous Gauge and the linear elements:

Perturbation Equations:

K. Ichiki and YYK:2007

Energy Density vs scale factorEnergy Density vs scale factoryyk and ichiki, JHEP 0806,085 2008yyk and ichiki, JHEP 0806,085 2008

The impact of Scattering term:The impact of Scattering term:

Varying Neutrino MassVarying Neutrino Mass

eV eV

With full consideration of Kinetic term

V( )=Vo exp[- ]

EoS vs zEoS vs z

Neutrino Masses vs zNeutrino Masses vs z

eV

eV

Power-spectrum (LSS)Power-spectrum (LSS)

eV eV

Constraints from Constraints from ObservationsObservations

Neutrino mass Bound: M < 0.87 eV @ 95 % C.L.

Neutrino Mass BoundsNeutrino Mass BoundsWithout Ly-alpha Forest data (only 2dFGRS + HST + WMAP3)Without Ly-alpha Forest data (only 2dFGRS + HST + WMAP3) Omega_nu h^2 < 0.0044 ; 0.0095 (inverse power-law potential)Omega_nu h^2 < 0.0044 ; 0.0095 (inverse power-law potential) < 0.0048 ; 0.0090 (sugra type potential)< 0.0048 ; 0.0090 (sugra type potential) < 0.0048 ; 0.0084 ( exponential type potential)< 0.0048 ; 0.0084 ( exponential type potential)

provides the total neutrino mass boundsprovides the total neutrino mass bounds

M_nu < 0.45 eV (68 % C.L.)M_nu < 0.45 eV (68 % C.L.)

< 0.87 eV (95 % C.L.)< 0.87 eV (95 % C.L.)

Including Ly-alpah Forest dataIncluding Ly-alpah Forest data

Omega_nu h^2 < 0.0018; 0.0046 (sugra type potential)Omega_nu h^2 < 0.0018; 0.0046 (sugra type potential)

corresponds tocorresponds to

M_nu < 0.17 eV (68 % C.L.)M_nu < 0.17 eV (68 % C.L.)

< 0.43 eV (95 % C.L.)< 0.43 eV (95 % C.L.)

We have weaker bounds in the interacting DE modelsWe have weaker bounds in the interacting DE models

Cosmological constraints with Lya dataCosmological constraints with Lya data

Questions :Questions :

How can we test mass-varying neutrino model in How can we test mass-varying neutrino model in Exp. ?Exp. ?

--- by the detection of the neutrino mass variation in --- by the detection of the neutrino mass variation in space via neutrino oscillations. space via neutrino oscillations.

Barger et al., M. Cirelli et al., 2005Barger et al., M. Cirelli et al., 2005

--- by the measurement of the time delay of the --- by the measurement of the time delay of the neutrino emitted from the short gamma ray bursts. neutrino emitted from the short gamma ray bursts.

X.M. Zhang et al.X.M. Zhang et al.

How much this model can be constrainted from, How much this model can be constrainted from, BBN, CMB, Matter power spectrum observations ?BBN, CMB, Matter power spectrum observations ?

Ichiki and YYK, 2008Ichiki and YYK, 2008

Cosmological weak lensingCosmological weak lensing

present

z=zs

z=zl

z=0

past

Large-scale structure

Arises from total matter clusteringArises from total matter clustering Note affected by galaxy bias Note affected by galaxy bias

uncertainty uncertainty Well modeled based on simulations Well modeled based on simulations

(current accuracy <10%, White & Vale (current accuracy <10%, White & Vale 04) 04)

Tiny 1-2% level effectTiny 1-2% level effect Intrinsic ellipticity per galaxy, ~30%Intrinsic ellipticity per galaxy, ~30% Needs numerous number (10^8) of Needs numerous number (10^8) of

galaxies for the precise measurementgalaxies for the precise measurement

Future Prospects from Astrophysical Observations

Conclusions:Conclusions: Neutrinoless double beta decays can provides very important Neutrinoless double beta decays can provides very important

properties of neutrinos: Dirac or majorana particles; neutino mass properties of neutrinos: Dirac or majorana particles; neutino mass information;information;

mass-hierarchy pattern. mass-hierarchy pattern. In conclusion, results of precision analysis of CMB and LSS data don’t In conclusion, results of precision analysis of CMB and LSS data don’t

follow only from data, follow only from data, but also can rely on theoretical assumptions.but also can rely on theoretical assumptions.

Prospects:Prospects: Future measurements of gravitational lensing of CMB light and/or of Future measurements of gravitational lensing of CMB light and/or of

photon generated by far galaxies should allow to direct measure the photon generated by far galaxies should allow to direct measure the total density with great accuracy. In this way, total density with great accuracy. In this way, it might be possible to it might be possible to see the cosmological effects of neutrino masses, and measure them see the cosmological effects of neutrino masses, and measure them with an error a few times smaller than the atmospheric mass scalewith an error a few times smaller than the atmospheric mass scale..

This could allow us to discriminate between normal and inverted This could allow us to discriminate between normal and inverted neutrino mass hierarchy.neutrino mass hierarchy.

Summary of Methods to Obtain Neutrino Masses

Single beta decay

mi2 |Uei|2 Sensitivity

0.2 eV

Double beta decay

m = |mi |Uei|2 i| i = Majorana phases

Sensitivity 0.01 eV

Neutrino oscillations

m2 = m12 - m2

2 Observed ~ 10-5 eV2

Cosmology mi Observed ~ 0.1 eV

Only double beta decay is sensitive to Majorana nature.

Thanks Thanks For For your your attention!attention!

Backup SlidesBackup Slides

Uncertainties from Nuclear Matix Uncertainties from Nuclear Matix ElementElement

Higher order terms of nucleon current suppresses the Higher order terms of nucleon current suppresses the nuclear element by about 30 % for all nucleinuclear element by about 30 % for all nuclei

The estimated uncertainty of MThe estimated uncertainty of Moodue to gdue to gA A is around 20 is around 20 % ( in general g% ( in general gA A =1.25, but g=1.25, but gA A =1 in quenched value)=1 in quenched value)

The evaluation of the Nuclear Matrix element MThe evaluation of the Nuclear Matrix element Moois a is a complex task complex task

Two established method : Shell Model vs Quasiparticle Two established method : Shell Model vs Quasiparticle Random Phase Approximation (QRPA)Random Phase Approximation (QRPA)

02

( , )( , ) ( , ) ( , )

oo oFGT T

A

M A ZM A Z M A Z M A Z

g

Limitation of Shell ModelLimitation of Shell Model Cannot allow to take into account the b-strength Cannot allow to take into account the b-strength

from the region of the Gamow-Teller resonance, from the region of the Gamow-Teller resonance, which might play an important role.which might play an important role.

Need to introduce effective operators, a Need to introduce effective operators, a procedure which is not well under control yet.procedure which is not well under control yet.

Limitation of QRPALimitation of QRPA The question is how accurate is it ?The question is how accurate is it ?

the predictive power of QRPA approach is the predictive power of QRPA approach is limited, because of the large variation of the limited, because of the large variation of the relevant bb matrix elements.relevant bb matrix elements.

Neutrino Oscillations

Weak Lensing Tomography- MethodWeak Lensing Tomography- Method