Outstanding Problems in Neutrino Physics ( Future Direction in Neutrino Physics ) C. W. Kim KIAS, Johns Hopkins

Outstanding Questions m , m , m ? Mixing matrix elements, in particular θ ? Dirac or Majorana ? CP violation ? Normal or inverted hierarchy ? How to detect relic neutrinos ? …… Why are neutrino masses so small ? Why is the mixing matrix so different from that of quark sector ? ………… 1 2 3 ＊ 13 ＊ ＊

0.22 (3 sigma)

Bounds on masses

Δm = 8 x (1±0.09) x 10 eV Δm = 2.4 x (1± ) x 10 eV 2 -5 2 2 2 -3 SOL 0.21 ) x 10 eV ATM 0.26

Normal Inverted m m 3 2 m m 2 1 m 1 m 3 m (eV) m (eV) 3 1

If ∑ m j < 8 x 10 eV, the inverted hierarchy is ruled out !! -3 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 . -3 No lower bound for the lightest neutrino !!

Limits on sin θ 13

Limits on = sin θ U e3 13 Recall: Jarlskog Rephasing Invariant J ~ sin θ sin δ 13 CP - Reactor ν disappearance expt. (CHOOZ,Palo Verde) e 2 2 2 2 sin θ = 4 U ( 1 - U )= sin (2 θ ) e3 e3 13 ⇒ 2 -2 U < 5 X 10 ( 3 σ ) or e3 o U < 0.22 ( 3 σ ) or θ < 13 e3 13 Global fit: K2K : Absence of ν ν ( limits on 4 U U ) S-K ATM : Constraint on Δ m SOL ν, KamLAND : Survival prob. of ν depends on U 2 2 μ e μe e3 2 31 2 e e3

U ≈ θ θ θ ≈ 45 < 13 ≈ 35 Mixing Matrix √ 3 1 sin θ13 e 2 2 1 √ 1 3 o o o θ θ θ ≈ 45 < 13 ≈ 35 12 23 13 Bi-large mixing with U =0, θ = θ , θ = θ = π/6 e3 23 ATM 12 SOL

Future LBL Experiments Beam Detector Channels L (km) E (GeV) Start * NuMI MINOS ν 730 3.5 2005 ν μ e,μ CNGS OPERA,ICARUS ν ν 732 18 2007 μ e,τ ν T2K(OA) S-K 295 0.7 2009 ν μ e,μ NOvA Low –Z Calori. ν ν ~ 800 2 >2010 μ e,μ ~ (OA) .... * * Beta beams from He Ne 130(Frejus) >2015 6 , 16 T2KK Cosmic neut. Neutrino Telescopes

Allowed regions MINOS The results of the four different extrapolation methods are in excellent agreement with each other.

CP Violation Conditions for CP violation No two neutrinos are degenerate in mass No mixing angle is equal to 0 or Physical phase is different from 0 or   2 det C≠0, where C = - i [Ml Ml+, Mν Mν+] mass matrix ν ↔ ν β ≠ ν ↔ ν β α α Complex mixing matrix (3generations)

CP Violation : Jarlskog Invariant Formulars in Vacuum

T2KK (Subject of this workshop) expt T2KK (Subject of this workshop) Matter effects: sensitive to sin ( Δm L / 2 E) sin θ 2 kj 13 Sign of Δm , sin θ and sin δ can be observed U > 0.08 : twin HK, Japan and Korea Ishitsuka, Kajita, Minakata, Nunokawa U > 0.13 : 100Kton in Korea Hagiwara, Okamura, Senda RENO, Double CHOOZ,.. : U if U > 0.08 2 cp 31 13 if e3 e3 e3 e3

LBL Reactor Experiments (Other than RENO) Double-CHOOZ (프랑스) Braidwood (U.S.) KASKA (Japan) Daya Bay (China) Near Detectors Far Detector

√ Beta decay of 3H KATRIN ( KArlsruhe TRItium Neutrino Experiment ) m < 2.3 eV (95% CL) : Mainz m < 2.5 eV (95% CL) : Troiztk β β Effective mass in beta decay 2 m = Σ U m ej 2 = m νe j β j ________________________________ √ 2 2 2 m < 2.3 eV m1 can be larger than 2.3 eV. 0.67 m + 0.33 m + (<0.05) m β 1 2 3 KATRIN ( KArlsruhe TRItium Neutrino Experiment ) can reach down to 0.2 eV. Every thing is scaled up to 23m x 10m

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

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: ~104 events Physics of SN explosion, some neutrino properties ( mag.mom., life time, charge radius,..) 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

Relic Neutrinos Neutrinos decoupled (relativistic at the time) 1.3 MeV for νe ~ at T = 1.5 MeV for νµ , τ T = ( 1.676 + 0.001) x 10-4 eV For m ~ O ( eV), they are non-relativistic, in fact since z ~ 103 ( m / eV) ° ν ν ν Neutrino number density: n + n = n = (111.9 ± 0.1) / cm3 ρ = ∑ m ( n + n ) 3 ° ° ° ν ν γ 11 ° ° ° Gershtein-Zeldovich Cowsik-McClelland ν νj j νj j Simply from Ω h2 < Ω h2 0.14 , we have ∑ m < 13 eV. ° ° ~ ν ~ M νj j How to detect them is one of the most challenging tasks in 21st century.

● As long as HDM is relativistic, HDM perturbations within the horizon 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 Zn-r . → If HDM dominates, top-down structure formation but, observation → bottom-up. Σ m j j → limit on Σ m j j ΔP(k) _ 0.1 ● ~ ( ) ( ) P(k) 1 eV ΩM h2

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 Better than β β, β , …... j j Weak Gravitational Lensing, yet to be improved Lyman- Alpha Experiment, very difficult. If we find ∑ m < 8 x 10-2 eV, the mass hierarchy can be resolved to be NORMAL! j j

⇒ 0 ≤ θ ≤ π / 4 covers 0 ≤ sin (2θ) ≤ 1 [ sin ( 2 θ ) , Δm ] Plot ⇒ 0 ≤ θ ≤ π / 4 covers 0 ≤ sin (2θ) ≤ 1 2 ( Light side ) Same for θ and π / 2 - θ Good enough for oscillations in vacuum What about π / 4 ≤ θ ≤ π / 2 ? ( Dark side ) 2 This can be covered if Δm < 0 is allowed. Use 0 ≤ θ ≤ π with a fixed sign for Δm . 2 2 2 ( Use either sin θ or tan θ ) ↘ Good for log scale

Summary 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 : U < 0.22 If U < 0.08 , it is difficult to measure θ and CP violation. Current cosmological data ⇒ Σ m ≤ O (eV) Lyman alpha forest, weak gravitational lensing, sharper image of CMBR ~ 1 2 3 -3 -3 ~ j o o o ~ ~ 13 12 23 e3 e3 13 j

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