Probing Neutrino Properties with Astrophysics: Neutrino Masses

Size: px

Start display at page:

Download "Probing Neutrino Properties with Astrophysics: Neutrino Masses"

Melanie Belinda Carter
5 years ago
Views:

1 Probing Neutrino Properties with Astrophysics: Neutrino Masses Yong-Yeon Keum IBS/Seoul National University, Seoul Korea International Workshop on UNICOS May, 2014 Panjab University, Chandigarh, India

2 Dark Energy 68.3% (Cosmological Constant) Title Ordinary Matter 4.4% (of this only about 10% luminous) Dark Matter 26.8% Neutrinos 0.1 2%

3 Contents: Theoretical Aspects of Neutrino Masses and Lepton Mixing Angles: Absolute Neutrino Masses from laboratory tests. ( S. Goswami s talk) Neutrino Masses in cosmology (CMB, Power Spectrum in Large Scale Structures: Lambda CDM vs INuDE- Model Discussions Papers: X.G. He, YYK, and RR Volkas, JHEP 0604 (2006) 039. YYK and K. Ichiki, JCAP 0806, 005, 2008; JHEP 0806, 058, 2008; arxiv:

4 Theoretical Aspects: A Non-vanishing neutrino mass is the first evidence of the incompleteness of the Standard Model[SM]. Questions: How to extend the SM in order to accommodate neutrino masses? Why neutrino masses are so small, compared with the charged fermion masses? Why lepton mixing angles are so different from those of the quark sector?

12 For charged lepton case, it is quite possible that the reason why the observed CKM matrix is nearly identity, is the hierarchical breaking A4 Z3 ~ C3={1,c,a} nothing with the small mixing angles generated by higher order effects after the relatively weak subsequent breaking of the residual C3. In neutrino sector, the flavor breaking pattern is A4 Z2 ={1, r2}

13 The Known unknowns: what are the potential astrophysical consequences? We know two mass^2 differences, but not the absolute scale of v-mass. We know three mixing angles, two large mixing angles and one small mixing angle. We do not know the Dirac/Majorana nature of the mass. We do not know the hierarchy, normal and inverted.

14 We do not know the sizes or roles in nature of three CPviolating phases. We have not explored other MSW crossings or potentials. We do not know whether neutrinos have nonzero electromagnetic moments. We do not know the high-energy limits of v physics. We do not know whether there are additional v species.

15 Neutrino Mixing Matrix iδ νe ν1 cc 2 3 cs 2 3 se 2 ν1 iδ iδ νµ = UV ν2 = cs 1 3 ssce cs 1 3 ssse cs 2 1 V ν2 iδ iδ ν τ ν 3 ss 1 3 scce sc 1 3 scse cc 2 1 ν 3 where iφ1 i( δ+ φ2) V=diag(1, e,e ) δ = Dirac Phase; φ = Majorana Phases 1,2 Pr esent Data with 3 σ ranges of mixing paramters: θ ~9 is small: 0.07 sin 2 θ 0.12 small mixing angle (Daya Bay/RENO/Double Choose) Solar Neutrino Data Large Mixing Angle Sol sin 2 θ s [ev ] ; s= m m Atmospheric Neutrino Data Maximal Mixing Angle Sol. 2 sin 2 θ a [ev ]; a=m m

16 Neutrino Masses: three important laboratory tests Direct kinematic tests: m = Uei mi ; νe ~ 0.8 ν ν ν ν 3 e i= 1

17 Neutrino oscillations: m 2 L 2 sin 2 θ 2 sin 12 ν ν = 12 P µ Neutrinoless double beta decay: e 4 E m ββ ν 3 k=1 2 ek = U mk

18 Absolute Neutrino Masses in three important laboratory tests Part I

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

22 T 0ν 1/2 where 0v 0v 1/2 0v 01 1 ( AZ, ) e1 1 e2 2 e3 3 0ν 2 2 0v A 01 0 m M ( AZ, ) g G ( E, Z) T ( AZ, ) = half-life time; M =nuclear matrix element G ββ = phase space factor; m = U m + U m + U m ββ = 0nbb-decay has not yet been seen experimentally. Heidelberg-Moscow (HM) 76 Ge experiment: T 0 1/2 > 1.9 x years m bb < 0.55 ev New results from experiments using 136 Xe: T 0 1/2 > 1.9 x years at 90% CL (KamLAND-ZEN:2013) T 0 1/2 > 1.6 x years at 90% C.L. (EXO) (2012) T 0 1/2 > 3.4 x years at 90% CL (Combined, 2013) m bb < 0.25 ev

23 Neutrioless Double-beta decay vs Neutrino Mass Mass Ordering (for simplicity) m < m < m (non-negative m ) The rate of 0nbb decay depends on the mag. of the element of the neutrino mass matrix: ν e ve M = ccm+ csme + sme m i Two possible mass spectra: s = m m, a= m m (normal hierarchy); where a >> s i ee iφ2 2 iφ3 (Case I); s = m m, a= m m (inverted hierarchy) iφ2 2 iφ3 = ccm csme sme 2 1 (Case II); may be determined from the lightest mass m and mass-squared differences

24 Bound of the total neutrino mass Since sin 2 θ ~ 0.1 or s ~ 0.024, ee The limit on Σ for θ = 0 are 2 M + M ± Σ 2 ee ( + for Case I and -- for Case II) Depends on two parameters; 2 2 M + M ± cos 2θ (1) the scale of atm. Neutrino Osci, (D) 2 2 ee ee 3 cos 2 θ 2 (2) the amplitude of solar Neutrino Osci. ( sin 2θ 3 ) 3

25 Total Nu-Mass vs Mee ( NH vs IH ) Normal Hierarchy Inverse Hierarchy Planck Compare with S. Sharma works in poster Mee(eV)

26 Effective Majorana Nu-mass m = ev, m = ev, sin θ = 0.29 [best fit values] sol atm 12 2 sin θ 13 = 0.024

27 Sensitivities of the future exps.

28 Mee vs lightest m Normal Hierarchy Inverse Hierarchy

29 76 Ge 100 Mo

30 Tritium beta decays _ 3-3 H He + e + ν e ( m ve limit) Q β = KeV 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.

31 Kurie Function: Mainz and Troitzk experiments: With neutrino mixing: K(T) = [ (Q -T) (Q T) m e ] 2 2 1/2 β β ν m < 2.3 ev (95% C.L.) ve m < 2.5 ev (95% C.L.) _ 3-3 H He + e + νk ( νe =ΣkUekνk ) Then K(T) = [ (Q -T) Σ U (Q T) m ] β ve ek /2 β k m = Σ U m = c c m + s c m + s m β k ek k m < 2.3 ev (95% C.L.) β k

32 Summary of Part 1 Tritium beta decay: Mainz and Troitsk Exp m 1 < 2.2 ev Future Exp. KATRIN: sensitivity m 1 ~ 0.25 ev If the 0nbb decay will not observed in future exp. and m bb < a few 10-2 ev, Massive neutrinos are either Dirac or Majorana particle, and normal hierarchy

33 The observationof the 0nbb decay with m bb > ev will exclude normal hierarchy. If the 0nbb decay will be observed and 0.42 m m m 2 2 atm ββ atm it will be an indication of the inverted hierarchy Normal Hierarchy : M_nu > 0.03 ev Inverted Hierarchy: M_nu > 0.07 ev Remarks: It is really difficult to confirm the normal hierarchy in neutrinoless double beta decay in future experiments. How can we reach there? Maybe Long baseline /Magic Baseline Exp. with HE v-beam (Goswami s talk) or some Astrophysical Observations.

34 Neutrino Mass bound from Large Scale Structures (CMB, Power Spectrum,..)

35 Neutrino Mass in Cosmology

37 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. The free streaming effect suppresses the power spectrum on scales smaller than the horizon when the neutrino become nonrelativistic. Pm(k)/Pm(k) = -8 Ω ν /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 ν 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 ν h^2 =

38 Mass Power spectrum vs Neutrino Masses

40 Power spectrum P m (k,z) = P * (k) T 2 (k,z) Transfer Function: T(z,k) := δ(k,z)/[δ(k,z=z * )D(z * )] Primordial matter power spectrum (Ak n ) z * := a time long before the scale of interested have entered in the horizon Large scale: T ~ 1 Small scale : T ~ 0.1 P m (k)/p m (k) ~ -8 Ω ν /Ω m = -8 f ν M_nu

41 Numerical Analysis

42 Experimental Obs.(WMAP+PLANCK) n_s: Spectral index tau: optical depth sigma_8: rms fluctuation parameter A_s: the amp. of the primordial scalar power spectrum σ 2 δ M 2 sin( ) cos( ) 2 4 ( )[3 kr = = dk πk P k kr kr ] 8 2 M ( kr)

43 Within Standard Cosmology Model (LCDM)

44 Planck 2013 Results

45 Questions: issues a bit farther from resolution; it is known that the dark energy 4 density ~ m ν is this an accident, or not? What is the upper bound of neutrino masses beyond ΛCDM Model?

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

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

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

51 W_eff Mn=0.9 ev Mn=0.3 ev

52 Neutrino Masses vs z

53 Power-spectrum (LSS) Mn=0.9 ev Mn=0.3 ev

54 Constraints from Observations

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

Cosmological parameters after Planck obs.

56 Cosmological parameters after Planck Good A greement! Good A greement!

58 Summary: Neutrino Mass Bounds in Interacting Neutrino DE Model Without Ly-alpha Forest data (only 2dFGRS + HST + WMAP5) Omega_nu h^2 < ; (inverse power-law potential) < ; (sugra type potential) < ; ( exponential type potential) provides the total neutrino mass bounds M_nu < 0.45 ev (68 % C.L.) < 0.87 ev (95 % C.L.) Including Ly-alpah Forest data Omega_nu h^2 < ; (sugra type potential) corresponds to M_nu < 0.17 ev (68 % C.L.) < 0.43 ev (95 % C.L.) We have weaker bounds in the interacting DE models

59 Nonlinear Effects

60 Future Prospects:

affected by galaxy bias uncertainty Well

accuracy <10%, White & Vale 04) Tiny 1-2%

galaxy, ~30% Needs numerous number (10^8)

61 past z=zs 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 z=zl present z=0

62 Future Prospects from Astrophysical Observations

Summary LCDM model provides M_nu < 0.6-0.7 ev (LSS + CMB +BAO) < 0.23-0.93 ev (Planck + WP + High L +BAO) < 0.2-0.

63 Summary LCDM model provides M_nu < ev (LSS + CMB +BAO) < ev (Planck + WP + High L +BAO) < ev (including Lya data) Interacting Neutrino Dark-Energy Model provides more weaker bounds: M_nu < ev (LSS + CMB ) < ev (including Lya data) Lya-forest data includes the uncertainty from - continuum errors - unidentified metal lines - noise

65 Summary of Methods to Obtain Neutrino Masses Single beta decay Σ ι m i 2 U ei 2 Sensitivity 0.2 ev Double beta decay Neutrino oscillations m ββ = Σ ι m i U ei 2 ε i ε i = Majorana phases δm 2 = m m 2 2 Sensitivity 0.01 ev Observed ~ 10-5 ev 2 Cosmology Ω ν Σ ι m i Observed ~ 0.1 ev Only double beta decay is sensitive to Majorana nature.

67 Thanks For your attention!

68 Backup Slides

NEUTRINO COSMOLOGY. ν e ν µ. ν τ STEEN HANNESTAD UNIVERSITY OF AARHUS PARIS, 27 OCTOBER 2006

NEUTRINO COSMOLOGY. ν e ν µ. ν τ STEEN HANNESTAD UNIVERSITY OF AARHUS PARIS, 27 OCTOBER 2006 NEUTRINO COSMOLOGY ν e ν µ ν τ STEEN HANNESTAD UNIVERSITY OF AARHUS PARIS, 27 OCTOBER 2006 OUTLINE A BRIEF REVIEW OF PRESENT COSMOLOGICAL DATA BOUNDS ON THE NEUTRINO MASS STERILE NEUTRINOS WHAT IS TO COME