C. W. Kim KIAS The Johns Hopkins University Neutrino Physics and Cosmology SDSS-KSG Workshop

Fundamental Building Blocks Quarks u c t d s b (3 Colors ) Leptons e μ τ ν ν ν e μτ Neutrinos 1

Bounds on neutrino masses from nuclear and particle physics 2

3 β- decay of H: m 3 ν < 2 eV (95% CL) (β β) – decay : m < (0.3 ~1) eV ν KATRIN ( KArlsruhe TRItium Neutrino Experiment ) can reach down to 0.2 eV. Every thing is scaled up to 23m x 10m Nuclear Physics Uncertainty ~ a factor of 3 Dozens of experiments under way 0ν0ν n + n p + p + e + e ( ν + ν = ν + ν = 0 ) Majorana nature n p + e + ν ( 2010~ 2015?)

Beta decay of 3 H m < 2.3 eV (95% CL) : Mainz m < 2.5 eV (95% CL) : Troiztk Effective mass in beta decay m = Σ U m m < 2.3 eV m 1 can be larger than 2.3 eV. KATRIN ( KArlsruhe TRItium Neutrino Experiment ) can reach down to 0.2 eV. Every thing is scaled up to 23m x 10m β β ejej 2 2 j = m β β νeνe j 0.67 m m + (<0.05) m √ ________________________________ 3

m ( ν ) < 0.17 Mev (95%CL) from π → μ + ν m ( ν ) < 18.2 MeV (95%CL) from τ → 3 π + 2 π + ν μ μ τ + τ “ Will see that Σ m < O (eV) from Cosmology.” k Nuclear /Particle Physics 4

d d m < ( 0.3 ~ 1.0 ) eV Nuclear unct. ~ a factor of 3 u u e-e- e-e- d d u u Majorana Neutrino Neutrinoless double beta decay U and CP phases ββ ej 2 e-e- e-e- u W+W+ W+W+ u νeνe νeνe νeνe νeνe d d * * e e - - 5

6 Neutrino Oscillation Experiments

If ∑ m j < 8 x 10 eV, the inverted hierarchy is ruled out !! There are at least two neutrinos which are heavier than 8 X 10 eV No lower bound for the lightest neutrino !! 7

Neutrinos in Cosmology Second most abundant particles: n = 330/cm ν o 3 8

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Neutrinos in Cosmology Second most abundant particles: n = 330/cm ν o3 Ω Decoupled at t ∼ 1 sec, T ∼ 1 MeV m > 0.6 eV ⇒ Non-relativistic before recombination m < 0.6 eV ⇒ … after recombination ν ν ν o h = ΣmΣm eV j 2 : Ω ν o < Ω M o ⇒ Σ m < 13 eV j Neutrinos, as HDM, influence LSS formation. Gershtein-Zeldovich, Cowsik-McClelland limit (T~0.3eV) 10

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Neutrino mass effects Temperature fluctuation angular power spectrum ( Two point correlation function : C ) Current matter power spectrum : P(k) l 12

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m ν WMAP 14

m ν 15

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WMAP3 alone * m < 0.7 eV (95% CL) * H and m degeneracy ν o Uncertainty of m ⇒ one of the largest systematic errors for estimating cosmological parameters from CMB (If m > 0.3 eV, a small Hubble constant( h< 0.65 ) is more consistent.) ν ( Clean and Robust) ν ν Polarization measurement would not help either. 20 Same limit from WMAP1

Neutrinos as HDM (If HDM dominates, top-down structure formation but, observation → bottom-up.) P(k) ΔP(k) ~ ( 1 eV Σ m j j ) ( Ω M h 2 ) ● HDM suppresses the formation of small-scale structures through “free streaming”. Thus, the observation of LSS can constrain the amount of HDM( neutrinos) 21 suppression

Horizon distance at matter = radiation Enters in matter dominated era Enters in rad- Dominated era Σ m = 1 eV i 23

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Lyman-α forest data Absorption lines in the spectrum of distant quasars due to intermediate H clouds which absorb Lyman-α lines at λ α = A o 24

Lyman-α forest data Absorption lines in the spectrum of distant quasars due to intermediate H clouds which absorb Lyman-α lines at λ α = A o Layers of H Clouds ⇒ forest 25

Lyman-α forest spectrum from Q (z= 3.23) 26

Lyman-α forest data Absorption lines in the spectrum of distant quasars due to intermediate H clouds which absorb Lyman-α lines at λ α = A o Layers of H Clouds ⇒ forest Absorption lines ⇒ Study of change of power spectrum of δρ/ρ for small λ But this is very difficult and model dependent ( bias ). ΔP(k)/P(k) ~ -10 Ω / Ω : a factor of 2 suppression for Σm = 1 eV(7% of CDM) ν o M o j 27

WMAP3 * m < 0.7 eV (95% CL) * H and m degeneracy ν O Unknown m ⇒ one of the largest systematic errors for estimating cosmological parameters from CMB * m > 0.3 eV favors smaller Hubble constant. ν ( Clean and Robust ν ν * To improve the limit, need data other than WMAP ! SDSS, 2dFGRS, Lyman-α forest, Gravitational lensing,… But inherent systematic errors need to be understood. Conclusions even with WMAP1 alone) 29

Immediate Questions Dirac or Majorana? Absolute mass scale? How small is  13 ? CP Violation? Mass hierarchy? Is  23 maximal?

Ubiquitous Neutrinos They must have played some important role in the universe!

The Data Evidence for oscillation: “ Indisputable ” –Atmospheric –Solar –Reactor “ strong ” –Accelerator (K2K) And we shouldn ’ t forget: “ unconfirmed ” –Accelerator (LSND) excluded?

Outstanding Questions Mixing matrix elements, in particular θ ? Dirac or Majorana ? CP violation ? Normal or inverted hierarchy ? Relic neutrinos ? Magnetic moment ? Why are neutrino masses so small ? Why is the mixing matrix so different from that of quark sector ? ………… 13 ＊ ＊ ＊ m, m, m ? 123

Radioactive materials ( : H, Ge, … : KeV ) Nuclear Reactors ( ν : MeV ) Accelerators ( ν : MeV ~ 500MeV ) Astrophysics/Cosmology Atmospheric Neutrinos ( ν : 100 MeV ~ 100 GeV ) Solar Neutrinos ( ν : up to 14 MeV ) SN Neutrinos ( ν : 1 MeV ~ 100 MeV ) Relic Neutrinos ( ν : 10 eV ~ 1 MeV ) Galactic Nuclei, Ultra high energy sources, … ( ν : very high energy ) Free sources !!! 3 76 e e,μ,τ μ,e e e,μ,τ -4 e,μ,τ ν e β β decay Nuclear/Particle Physics

Number of Neutrino flavors

N inv ( Z → l l ) = ± This is valid for m < 45 GeV. Nuclear / Particle Physics Γ = N ν Γ ( Z → ν νν ν) = ν inv Γ ν ( Z → ) Γ Γ ν νν ν l ( Z → ) Z boson: SM

Astrophysics/Cosmology BBN More than 3 flavors → larger ρ → larger H → takes less time to reach T = 1 MeV → less n decay → more He Δ Y ≈ ΔN N = 3.24, Δ N ν < 1.44 (95%CL) CMBR N >0 → larger H → enhancement of the first acoustic peak, peaks shifted to larger values ΔN ν = (95 % CL) CMBR + LSS Larger ρ delays time of M-R equality → shifts the peak of a larger wavelength ΔN ν = 1.0 (95%CL) ν ν Δ ν

Neutrinos are mixed Production and detection via Weak eigen States Propagation (Equ. Of motion) via Mass eigen States ν ν ν µ e τ = UUU e1e2e3 UUU µ1µ1µ2µ2µ3µ3 UUU τ1τ1τ2τ2τ3τ3 ν ν ν 2 1 3

Δm = m - m = 8 x (1±0.09) x 10 eV Δm = m - m = 2.4 x (1± SOL -5 ATM ) x 10 eV Solar and Atmospheric Neutrinos

m m m m m m m (eV) Normal Inverted m (eV) 3

SN Neutrinos SN 1987A: unexpected bonanza Kamiokande II (12) IMB (8) Baksan (5) ( LSD: 5 hours earlier) m νe < 5.7 eV (95% CL) : Some well-motivated assumptions m νe < 30 eV : Model Independent S-K, SNO, LVD, KamLAND, AMANDA, MiniBOONE,… are ready !! Galactic SN: ~10 4 events Physics of SN explosion, some neutrino properties We have to wait. No control ! Sensitivity of ~ 3 eV due to intrinsic spread in time of neutrino burst If one sees a signal due to black hole formation, down to ~ 1.8 eV ( mag.mom., life time, charge radius,..)

Relic Neutrinos Neutrinos decoupled (relativistic at the time) 1.3 MeV for ν e 1.5 MeV for ν µ, τ T = ( ) x eV For m ~ O ( eV), they are non-relativistic, in fact since z ~ 10 3 ( m / eV) Neutrino number density: n + n = n = (111.9 ± 0.1) / cm 3 ρ = ∑ m ( n + n ) ~ ν ° ν ° ν ° 3 11 γ ° ν ° j j νjνj ° νjνj ° at T = Simply from Ω h 2 < Ω h , we have ∑ m < 13 eV. j j ~ ν ° M ° ~ ν ν How to detect them is one of the most challenging tasks in 21st century. Gershtein-Zeldovich Cowsik-McClelland

Neutrinos as HDM ● As long as HDM is relativistic, HDM perturbations within the horizon are erased by “ Free – Streaming”. ● Free-streaming stops when HDM becomes non-relativistic at Z n-r. → If HDM dominates, top-down structure formation but, observation → bottom-up. → limit on Σ m j j P(k) ΔP(k) ~ ( 1 eV Σ m j j ) ( Ω M h 2 ) ● _

CMBR Relic neutrinos with mass of O (eV) are HDM (relativistic at decoupling). Due to free streaming, LSS formation is top-down, which is not the case. Free streaming HDM suppresses power spectrum at small wave lengths. Global fits of CMBR, SDSS Galaxies, SN Ia, Cluster Abundance, Weak Lensing, and Lyman Alpha Forest data give ∑ m < 0.4 ~ 1.0 eV Weak Gravitational Lensing, yet to be improved Lyman- Alpha Experiment, very difficult. If we find ∑ m < 8 x eV, the mass hierarchy can be resolved to be NORMAL! j j Better than β β, β, …... j j *

Limits on sin θ 13 Mixing matrix elements

< 0.22 (3 sigma)

Mixing Matrix : Nuclear/Particle Physics 3 √ √ sin θ 13 e i δ U ≈ θ θ θ ≈ ≈< oo o Bi-large mixing with U =0, θ = θ, θ = θ = π/6 e3 ATM 2312 SOL √2 1 1 √ 2 √ 3 1 √ 2 2 √2 1 √ 2 √ 3 1 2

Magnetic Moment : e-e- νeνe νeνe e-e- γ (ν)(ν)µ, μ

Nuclear/ Particle Physics νeνe (ν ) + e-e- νeνe e-e- e dσdσ dE ~ S.M. + α2α2 m2m2 µ2(ν )µ2(ν ) E µ (ν e ) ( 1 ~ 2) µ B < ~ µ (νµ )(νµ ) µ B < ~ ….. μ μ Reactor Expt. : Accelerator Expt :

Astrophysics / Cosmology Stellar Cooling, BBN → Giants in Globular Cluster → SN 1987A → Solar Neutrinos → µ (ν )(ν ) < ~ µ B µ (ν e ) < ~ ( ~ ) µ B µ (ν ) < ~ µ B µ (νe )(νe ) < ~ (1 ~ 3) µ B (Model Dependent) e

Neutrino Properties from C. W. Kim KIAS The Johns Hopkins Astrophysics/Cosmology

Neutrino Mass from C. W. Kim KIAS The Johns Hopkins Cosmology

m, m, m < O (eV) Two neutrinos are heavier than 8 x 10 eV. No lower mass bound exists for the lightest neutrino. If Σ m < 8 x 10 eV, the inverted hierarchy is ruled out. θ < 13, θ = 35, θ = 45 Current cosmological data ⇒ Σ m ≤ O (eV) Lyman alpha forest, weak gravitational lensing, sharper image of CMBR, more SDSS data : Must be improved To find mixings from Astro/Cosmology, the nature of sources must be much better known. 1 2 Summary -3 j o 12 o 23 o j ~ ~ ~ ~ 3..

Neutrinos as HDM ● As long as HDM is relativistic, HDM perturbations within the horizon are erased by “ Free – Streaming”. ● Free-streaming stops when HDM becomes non-relativistic at Z n-r. → If HDM dominates, top-down structure formation but, observation → bottom-up. → limit on Σ m j j P(k) ΔP(k) ~ ( 1 eV Σ m j j ) ( Ω M h 2 ) ● _