1. Neutrino Mass Bounds from Onbb Decays and Large Scale Structures
Yong-Yeon Keum
National Taiwan University
Dec. 4-7, 2007
OMEG07, Hokkaido Univ., Japan
Collaborations with K. Ichiki and T. kajino

2. Primordial Neutrinos in Astrophysics
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.

3. Contents:
Neutrinoless Double beta Decays and Total Neutrino Mass bounds
Neutrino Mass bound from Large Scale Structures (CMB, Power Spectrum,…..)
Discussion

4. Nature of Neutrinos:
Dirac Particles:
- anti-Particle is different from Particle;
- L is conserved.
Majorana Particles:
- anti-Particle = Particle;
processes.
The nature of neutrinos is directly related to the fundamental symmetries of elementary particle interactions.
The relative smallness of nu-masses can naturally be explained
by at a high scale:(Seesaw-Mechanism: Gell-Mann, Ramond, Slansky;
Yanagida[1979], Mohapatra,Senjanovic[1980])
In this case, the massive neutrinos are Majorana particles
nu-oscillations cannot distinguish between Dirac and Majorana particles:
only processes can answer this question and the most sensitive one is (bb)on decay.

5. What we know right Now: neutrinos have mass (NuOsc-exp.)
the rough magnitude of the leptonic mixing angles (two large and one relatively small angles)
the masses of all three neutrino species are very small compared with charged fermions

6. What we don’t know: Are neutrinos their own anti-particles ?
( Dirac vs Majorana particles )
What is the absolute mass of neutrinos and their mass ordering, i.e.
(normal, inverted or quasi-degenerate ?)
Is there CP violation in the leptonic sector ?

7. Neutrino Mixing and Oscillation
If neutrinos are massive, it is possible that the weak eigenstates
are not the same as the mass eigenstates:
PMNS (Pontecorvo-Maki-Nakagawa-Sakata) matrix ( )

8. Neutrino Mixing Matrix

9. Neutrinoless Double Beta Decays
Part I

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

11. 0nbb-decay has not yet been seen experimentally.
The best result has been achieved in the Heidelberg-Moscow (HM) 76Ge experiment:
T01/2 > 1.9 x 1025 years  |mbb| < 0.55 eV
Many future ambitious projects: CAMEO,CUORE,COBRA,EXO,GENIUS,MAJORANA,
MOON,XMASS

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

13. Sum of Neutrino masses
Since the solar mass-squared difference is very small, it can be ignored; setting
For the sum of neutrino masses :

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

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

16. Effective Majorana Nu-mass

17. Mee vs lightest m
Normal Hierarchy
Inverse Hierarchy

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

19. Neutrino free-stream :
If rn is carried by free-moving relativistic particles,
we can discriminate between massless vs massive ,and
between free vs interacting neutrinos.
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.
2) the function of energy carried by neutrinos, which controls
how much neutrinos can smooth inhomogeneities.
In Standard cosmology:

20. CMB vs Nv

22. Within Standard Cosmology Model (LCDM)

24. Equation of State (EoS)
W = p/r
It is really difficult to find the origin of dark-energy with non-interacting dark-energy scenarios.

25. Interacting dark energy model
Interacting Neutrino-Dark-Energy Model
Interacting dark energy model
Example
At low energy,
The condition of minimization of Vtot determines
the physical neutrino mass.
nv mv
Scalar potential
in vacuum

26. Background Equations:
K. Ichiki and YYK:2007
Background Equations:
Perturbation Equations:
We consider the linear perturbation in the synchronous
Gauge and the linear elements:

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

29. W_eff
Mn=0.9 eV
Mn=0.3 eV

30. Mn=0.9 eV

31. Mn=0.3eV

32. Power-spectrum (LSS)
Mn=0.9 eV
Mn=0.3 eV

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

34. Discussions
Neutrinoless double beta decays can provides very important properties of neutrinos: Dirac or majorana particles; neutino mass information;
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.
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.
This could allow us to discriminate between normal and inverted neutrino mass hierarchy.

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

37. Thanks
For
your attention!

38. Backup Slides

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

40. Max and Min values of m For a given value of Mee;
The minimum value of m with
The maximum value of m with

41. Sensitivities of the future exps.

42. 76Ge
100Mo

43. present neutrino number density:
The role played by neutrinos:
Tdec ~ few me  dominant e-/e+  photons
Tg = 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
Neutrino masses have a minor effect(not yet observed),
so that it is convenient, in first approximation, to consider neutrinos as massless.

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