Neutrino Mass Bounds from beta decays and Cosmological Observations (LCDM vs Interacting Dark-Energy Model) Yong-Yeon Keum NAOJ, Mitaka Japan KITPC, Beijing China TeVPA08, IHEP at Beijing September 26, 2008

Primordial Neutrinos in Astrophysics The connection between cosmological observations and neutrino physics is one of the interesting and hot topic in astro-particle physics. The connection between cosmological observations and neutrino physics is one of the interesting and hot topic in astro-particle physics. Precision observations of the cosmic microwave background and large scale structure of galaxies can be used to prove neutrino mass with greater precision than current laboratory experiments. Precision observations of the cosmic microwave background and large scale structure of galaxies can be used to prove neutrino mass with greater precision than current laboratory experiments.

Contents: Neutrinoless Double beta Decays and Total Neutrino Mass bounds Neutrinoless Double beta Decays and Total Neutrino Mass bounds Neutrino Mass bound from Large Scale Structures (CMB, Power Spectrum,…..) Neutrino Mass bound from Large Scale Structures (CMB, Power Spectrum,…..) Discussion Discussion Papers: YYK and K. Ichiki, JCAP 0806, 005, 2008; JHEP 0806, 058, 2008; JHEP 0806, 058, 2008; arXiv: arXiv: References: Massive Neutrinos and Cosmology: J. Lesgourgues and S. Pastor, Phys. Rep. 429:307(2006) Fundamentals of Neutrino Physics and Astrophysics: C. Giunti and C.W. Kim, Oxford University Press

Now we enter the era of Precision Neutrino Measurement Science (PMNS era). What do we hope to learn and which information is likely to teach us more about new physics than others. Four most useful items for probing new physics:  Search for neutrinoless double beta decays  Determined the sign of atmospheric mass difference square (neutrino mass hierarchy)  the magnitude of  establish or refute the existence of sterile neutrinos.

Neutrino Mixing Matrix

Neutrinoless Double Beta Decays Part I

Neutrinoless double-beta decay (A,Z)  (A,Z+2) + e+ e - ( D L=2) -- the most senstive process to the total lepton number and small majorana neutrino masses Neutrinoless double-beta decay (A,Z)  (A,Z+2) + e - + e - ( D L=2) -- the most senstive process to the total lepton number and small majorana neutrino masses

0 nbb -decay has not yet been seen experimentally. 0 nbb -decay has not yet been seen experimentally. The best result has been achieved in the Heidelberg- Moscow (HM) 76 Ge experiment: The best result has been achieved in the Heidelberg- Moscow (HM) 76 Ge experiment: T 0 1/2 > 1.9 x years  |m bb | 1.9 x years  |m bb | < 0.55 eV Many future ambitious projects: CAMEO,CUORE,COBRA,EXO,GENIUS,MAJORANA, Many future ambitious projects: CAMEO,CUORE,COBRA,EXO,GENIUS,MAJORANA, MOON,XMASS MOON,XMASS

Neutrioless Double-beta decay vs Neutrino Mass Mass Ordering (for simplicity) Mass Ordering (for simplicity) The rate of 0nbb decay depends on the mag. of the element of the neutrino mass matrix: The rate of 0nbb decay depends on the mag. of the element of the neutrino mass matrix:

Bound of the total neutrino mass Depends on two parameters; Depends on two parameters; (1) the scale of atm. Neutrino Osci, ( D ) (2) the amplitude of solar Neutrino Osci. ( )

Total Nu-Mass vs Mee ( NH vs IH ) Normal Hierarchy Inverse Hierarchy Mee(eV)

Sensitivities 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) (1) Superallowed transition between mirror nuclei with a relatively short half-life time (~12.3 years)  An acceptable number of observed events (2) (2) Atomic structure is less complicated, which leading to a more accurate calculation of atomic effects.

Kurie Function: Mainz and Troitzk experiments: With neutrino mixing:

Summary of Part 1 Tritium beta decay: Mainz and Troitsk Exp Tritium beta decay: Mainz and Troitsk Exp m 1 < 2.2 eV m 1 < 2.2 eV Future Exp. KATRIN: Future Exp. KATRIN: sensitivity m 1 ~ 0.25 eV sensitivity m 1 ~ 0.25 eV If the 0 nbb decay will not observed in future exp. and If the 0 nbb decay will not observed in future exp. and |m bb | < a few eV, |m bb | < a few eV,  Massive neutrinos are either Dirac or Majorana particle, and normal hierarchy  Massive neutrinos are either Dirac or Majorana particle, and normal hierarchy

The observationof the 0 nbb decay with |m bb | > eV will exclude normal hierarchy. The observationof the 0 nbb decay with |m bb | > eV will exclude normal hierarchy. If the 0 nbb decay will be observed and If the 0 nbb decay will be observed and it will be an indication of the inverted hierarchy it will be an indication of the inverted hierarchy Remarks: It is really difficult to confirm the normal hierarchy in neutrinoless double beta decay.

Neutrino Mass bound from Large Scale Structures (CMB, Power Spectrum, …..) Part II

Title Dark Energy 73% (Cosmological Constant) Neutrinos Neutrinos 0.1  3% 0.1  3% Dark Matter 23% Ordinary Matter 4% (of this only about 10% luminous) 10% luminous)

The role played by neutrinos: T dec ~ few m e  dominant e-/e+  photons Tg = 2.73 K T v = 1.96 K = 0.17 meV present neutrino number density: Since T v 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 ( r 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 : If r n is carried by free-moving relativistic particles, If r n is carried by free-moving relativistic particles, we can discriminate between massless vs massive,and we 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-relativistic, which controls the length on which neutrinos travel reducing clustering. 1) temperature at which neutrinos cease to be non-relativistic, which controls the length on which neutrinos travel reducing clustering. 2) the function of energy carried by neutrinos, which controls 2) the function of energy carried by neutrinos, which controls how much neutrinos can smooth inhomogeneities. how much neutrinos can smooth inhomogeneities. In standard cosmology: In standard cosmology:

CMB vs N v

Large Scale Structures

Neutrino mass effects After neutrinos decoupled from the thermal bath, they stream freely and their density pert. are damped on scale smaller than their free streaming scale. After neutrinos decoupled from the thermal bath, they stream freely and their density pert. are damped on scale smaller than their free streaming scale. The free streaming effect suppresses the power spectrum on scales smaller than the horizon when the neutrino become non- relativistic. The free streaming effect suppresses the power spectrum on scales smaller than the horizon when the neutrino become non- relativistic.  Pm(k)/Pm(k) = -8 Ω /Ω m  Pm(k)/Pm(k) = -8 Ω /Ω m Analysis of CMB data are not sensitive to neutrino masses if neutrinos behave as massless particles at the epoch of last scattering. Neutrinos become non-relativistic before last scattering when Ω  h^2 > (total nu. Masses > 1.6 eV). Therefore the dependence of the position of the first peak and the height of the first peak has a turning point at Ω h^2 = Analysis of CMB data are not sensitive to neutrino masses if neutrinos behave as massless particles at the epoch of last scattering. Neutrinos become non-relativistic before last scattering when Ω  h^2 > (total nu. Masses > 1.6 eV). Therefore the dependence of the position of the first peak and the height of the first peak has a turning point at Ω h^2 =

Mass Power spectrum vs Neutrino Masses

Power spectrum P m (k,z) = P * (k) T 2 (k,z) Transfer Function: P m (k,z) = P * (k) T 2 (k,z) Transfer Function: T(z,k) :=  (k,z)/[  (k,z=z * )D(z * )] T(z,k) :=  (k,z)/[  (k,z=z * )D(z * )] Primordial matter power spectrum (Ak n ) Primordial matter power spectrum (Ak n ) z * := a time long before the scale of interested have entered z * := a time long before the scale of interested have entered in the horizon in the horizon Large scale: T ~ 1 Large scale: T ~ 1 Small scale : T ~ 0.1 Small scale : T ~ 0.1  P m (k)/P m (k) ~ -8 Ω / Ω m  P m (k)/P m (k) ~ -8 Ω / Ω m = -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/ r It is really difficult to find the origin of dark-energy with non-interacting dark-energy scenarios. Dynamical Dark-Energy Models

Summary of EoS Canada-France-Hawaii Wide Synoptic Survey: Canada-France-Hawaii Wide Synoptic Survey: w o < based on cosmic share data alone w o < based on cosmic share data alone Supernova Lagacy Survey (SNLS): Supernova Lagacy Survey (SNLS): Combined with SDSS measurement of BAO Combined 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 data: 2) Drop prior of flat universe, WMAP+LSS+SNLS data:

Interacting dark energy model Example At low energy, The condition of minimization of V tot determines the physical neutrino mass. n v m v  Scalar potential in vacuum Interacting Neutrino-Dark-Energy Model

Theoretical issue: Adiabatic Instability problem: Afshordi et al Gravitational collapse Gravitational collapse Kaplan, Nelson, Weiner 2004 Kaplan, Nelson, Weiner 2004 Khoury et al Khoury et al Zhao, Xia, X.M Zhang 2006 Zhao, Xia, X.M Zhang 2006 Always positive sound velocity Always positive sound velocity No adiabatic instability No adiabatic instability Brookfield et al, Brookfield et al, YYK and Ichiki, 2007, 2008 YYK and Ichiki, 2007, 2008

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 factor yyk and ichiki, JHEP 0806,

The impact of Scattering term:

Varying Neutrino Mass Mn=0.9 eVMn=0.3 eV With full consideration of Kinetic term V( f )=Vo exp[- lf ]

EoS vs z

Neutrino Masses vs z

Mn=0.9 eV

Mn=0.3eV

Power-spectrum (LSS) Mn=0.9 eVMn=0.3 eV

Constraints from Observations

Neutrino mass Bound: M n < % C.L.

Neutrino Mass Bounds Without Ly-alpha Forest data (only 2dFGRS + HST + WMAP3) Omega_nu h^2 < ; (inverse power-law potential) Omega_nu h^2 < ; (inverse power-law potential) < ; (sugra type potential) < ; (sugra type potential) < ; ( exponential type potential) < ; ( exponential type potential) provides the total neutrino mass bounds provides 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 data Omega_nu h^2 < ; (sugra type potential) Omega_nu h^2 < ; (sugra type potential) corresponds to corresponds 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 models

Cosmological constraints with Lya data

Questions : How can we test mass-varying neutrino model in Exp. ? How can we test mass-varying neutrino model in Exp. ? --- by the detection of the neutrino mass variation in space via neutrino oscillations. --- by the detection of the neutrino mass variation in space via neutrino oscillations. Barger et al., M. Cirelli et al., 2005 Barger et al., M. Cirelli et al., by the measurement of the time delay of the neutrino emitted from the short gamma ray bursts. --- by the measurement of the time delay of the 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, BBN, CMB, Matter power spectrum observations ? How much this model can be constrainted from, BBN, CMB, Matter power spectrum observations ? Ichiki and YYK, 2008 Ichiki and YYK, 2008

Cosmological weak lensing Cosmological weak lensing present z=zs z=zl z= 0 past Large-scale structure Arises from total matter clustering Arises from total matter clustering Note affected by galaxy bias uncertainty Note affected by galaxy bias uncertainty Well modeled based on simulations (current accuracy <10%, White & Vale 04) Well modeled based on simulations (current accuracy <10%, White & Vale 04) Tiny 1-2% level effect Tiny 1-2% level effect Intrinsic ellipticity per galaxy, ~30% Intrinsic ellipticity per galaxy, ~30% Needs numerous number (10^8) of galaxies for the precise measurement Needs numerous number (10^8) of galaxies for the precise measurement

Future Prospects from Astrophysical Observations

Conclusions: Neutrinoless double beta decays can provides very important properties of neutrinos: Dirac or majorana particles; neutino mass information; Neutrinoless double beta decays can provides very important properties of neutrinos: Dirac or majorana particles; neutino mass information; mass-hierarchy pattern. mass-hierarchy pattern. In conclusion, results of precision analysis of CMB and LSS data don’t follow only from data, but also can rely on theoretical assumptions. In conclusion, results of precision analysis of CMB and LSS data don’t follow only from data, but also can rely on theoretical assumptions. Prospects: Prospects: Future measurements of gravitational lensing of CMB light and/or of photon generated by far galaxies should allow to direct measure the total density with great accuracy. In this way, it might be possible to see the cosmological effects of neutrino masses, and measure them with an error a few times smaller than the atmospheric mass scale. Future measurements of gravitational lensing of CMB light and/or of photon generated by far galaxies should allow to direct measure the total density with great accuracy. In this way, it might be possible to see the cosmological effects of neutrino masses, and measure them with an error a few times smaller than the atmospheric mass scale.  This could allow us to discriminate between normal and inverted neutrino mass hierarchy.

Summary of Methods to Obtain Neutrino Masses Single beta decay   m i 2 |U ei | 2 Sensitivity 0.2 eV Double beta decay m  = |    m i |U ei | 2  i |  i = Majorana phases Sensitivity 0.01 eV Neutrino oscillations  m 2 = m m 2 2 Observed ~ eV 2 Cosmology     m i Observed ~ 0.1 eV Only double beta decay is sensitive to Majorana nature.

Thanks Thanks For For your attention!

Backup Slides

Uncertainties from Nuclear Matix Element Higher order terms of nucleon current suppresses the nuclear element by about 30 % for all nuclei Higher order terms of nucleon current suppresses the nuclear element by about 30 % for all nuclei The estimated uncertainty of M o n due to g A is around 20 % ( in general g A =1.25, but g A =1 in quenched value) The estimated uncertainty of M o n due to g A is around 20 % ( in general g A =1.25, but g A =1 in quenched value) The evaluation of the Nuclear Matrix element M o n is a complex task The evaluation of the Nuclear Matrix element M o n is a complex task Two established method : Shell Model vs Quasiparticle Random Phase Approximation (QRPA) Two established method : Shell Model vs Quasiparticle Random Phase Approximation (QRPA)

Limitation of Shell Model Cannot allow to take into account the b-strength from the region of the Gamow-Teller resonance, which might play an important role. Cannot allow to take into account the b-strength from the region of the Gamow-Teller resonance, which might play an important role. Need to introduce effective operators, a procedure which is not well under control yet. Need to introduce effective operators, a procedure which is not well under control yet.

Limitation of QRPA The question is how accurate is it ? The question is how accurate is it ?  the predictive power of QRPA approach is limited, because of the large variation of the relevant bb matrix elements.  the predictive power of QRPA approach is limited, because of the large variation of the relevant bb matrix elements.

Neutrino Oscillations

Weak Lensing Tomography- Method