Recent status of ν
oscillation study
and its future
Osamu Yasuda
Tokyo Metropolitan University
12-25-2005 at rironkon05

Contents
1. ν oscillation
2. Future long baseline experiments(3. High energy astrophysical ν)
4. CP phases in ν oscillation
5. Summary1. ν oscillation(i) 2 flavor oscillations in vacuum

mass eigenstates

E j ≡ p 2 + m2j

flavor eigenstates
mixing matrix in vacuum

(ii) 2 flavor oscillations in matter (MSW effect)

If Ne=const.
even if θ in vacuum is~small θ in matter could
be large (MSW effect)If Ne varies adiabatically ( e.g., in solar ν)

average over rapid oscillations

(iii) 3 flavor ν oscillation

KamLAND(reactor)

ν →νe

νe → νe

Large Mixing
Angle solution
θ12 ≅ π/6∆m221 = 8 × 10 −5 eV 2e

ν →ν +νμ → νμμμmaximal mixing
θ 23 ≅ π/4| ∆m232 |= 2.5 × 10 −3 eV 2

νe → νe(reactor)

small mixing

sin2 2θ13 < 0.15

mixing matrix of 3 flavor ν oscillationn Bothhierarchies
are allowedNν=3 : νatm+νsolar+νreactor
Mixing matrix321n θ13 :only upperbound is known

2
13normalhierarchy

invertedhierarchyn δ :undetermined∆m232 > 0∆m232 < 0U
 e1 Ue2 Ue3   c12
U = UUU≅  − s12 / 2µ1µ2µ3  
UUU   s12 / 2
τ2
τ3  τ1

s12c12 / 2− c12 / 2

ε 1/ 2 1/ 2 

Mixing angles & mass squared differencesθ12 ≅ π/6, θ 23 ≅ π/4| θ13 |≅| ε |≤ 0.15 /2∆m221 = 8 × 10 −5 eV 2| ∆m232 |= 2.5 × 10 −3 eV 2

(iv) Scenario other than 3 flavor ν oscillation

So far the only promising scenario to explain
LSND in terms of ν is (3+2)-scenario with 2kind of sterile neutrinos.
Until LSND is confirmed by MiniBOONE, sterile
neutrino scenarios don’t seem to havestrong motivations. →In most of the talk,Nν=3 is assumed.

5LSND’
4LSND
321atmsolar

(v) Theoreticalprediction for θ13
All kinds of values of θ13
are predicted by theory,and it doesn’t look likeilluminating.
→ Theory is not yet
developed enough to saysomething from mass &mixing of quarks &leptons.

hep-ex/0402041

2. Future LBL (Long BaseLine experiments)U e1 Ue2 Ue3   c12UU≅  − s12 / 2
U = Uµ1µ2µ3  UUU   s12 / 2
τ2
τ3 
 τ1

s12
c12 / 2− c12 / 2ε 1/ 2 
1/ 2 n θ13 :only upper bound is knownn δ :undeterminedn Bothhierarchies
are allowed

32121

3

normalhierarchy

invertedhierarchy∆m232 > 0∆m232 < 0

Next task is to measure θ13 , sign(∆∆m231)
and δ.
Most realistic way to measure θ13 ,sign(∆∆m231) and δ is long base line
experiments by accelerators or reactors.
→Matter effect contributes in LBL in
most cases

Measurement of θ13 and sign of ∆m231
to leading
order in∆m221/ | ∆m232 |For large L, difference between P(νμ →νe ) and P(νμ → νe )due to matter effect becomes significant

Measurement of δ

sin2 2θ13 < 0.15

All the contributions of δ appear with the factor of sinθ13→ Unless there is enhancement due to matter effect,effects of CP phase δ are expected to be small, or may
be ignored in the zero-th approximation
1
U = 000c23− s230  c130s23  01
c23  − s13eiδ 0s13e-iδ  c12 s12 − s12 c120
c13  000

0
1 

Particle physicists are interested in CP violation, so nomatter how small θ13 may be we make efforts to measure

δ → Attitude by astrophysicists may be different

Theoretical argument on measurement of δJarlskog factor

Practical measurement of δMeasureP(ν → ν )μeandP(νμ → νe )and thenEnhancement of CP violating term
It isilluminating
to consider
T-violatingterm inmatter withconstantdensity

cf. Complete treatment of oscillation
probability in matter with constant density

Kimura, Takamura,
Yokomakura ‘02

Example: Enhancement of T-violation after passing
through the EarthOY (Ustron’99)

sin2 2θ12 = 0.006 ,∆m221 = 5 × 10 −6 eV 2

Future LBL
To perform precise measurements of θ13 and δ,
one has to have a lot of numbers of events toimprove statistical errors.
→We need high intensity beam
Candidates for high intensity beam in the future:

π + → μ + + νμT2K phase I (0.75MW) , II (4MW)● (conventional) superbeam● neutrino factoryµ in a storage ring
● beta beam

RI in a storage ringμ + → e + + νe + νμn → p + e − + νe

Expected sensitivity to sin22 θ13 ofongoing and near future experiments
Guglielmi, Mezzetto, Migliozzi , Terranova, hep-ph/0508034
@FNAL
@CERN

reactor@France@JAERI

Planned reactor experiments to measure sin22 θ13 : Double CHOOZ(FR), KASKA (JP), Braidwood (US), Daya Bay (CN), Angra (BR), RENO(KR), …

Parameter degeneracy()()

Even if we know P νμ →νe and P νμ →νe in a long
baseline accelerator experiments with approximately
monoenergetic neutrino beam, precise determination of θ13,sign(Δm231) and δ is difficult because of the 8-foldparameter degeneracy.

● intrinsic (δ, θ13)degeneracy● Δm231⇔-Δm231 degeneracy● θ23⇔π/2-θ23 degeneracy

To solve parameter degeneracy, combine the following:(A) LBL measurement at | Δm 231 | L/4E = π/2→ hyperbola shrinks to a straight line(B) reactor measurement of θ13 νe → νe→ depends only on θ13(C) LBL measurement of νμ →νe (or νe →νμ )with different L/E(D) measurement of νe →ντ
3.5

4

2.5

32
1.5

2

00(A)+(B)0.05
sin2 2θ130.1

JPARC ν+ν
correct
wrong

2
1.5

11(A)+(D)

2.5

1/s22321/s23

1/s223

invertednormalfake
3
true

0.02(A)+(C)

0.04

0.06

0.08

sin2 2θ130.1

10.02

0.04

0.06

0.08

sin2 2θ130.10.12

June 2005 ～ Sept. 2006

http://www.hep.ph.ic.ac.uk/iss/● Evaluate the physics case for the facility● Study options for the accelerator complex

and neutrino detection systems

Error (or sensitivity) of the CP phase δ of far future
experiments

T2HK = Tokai toHyperKamiokande

Huber-Lindner-Winter '05

Physics which could be done for a ν factory● Check of unitarity (as at a B factory)● Study of new physics

 exotic interactions

 mass varying neutrino scenario
Yukawa couplings
λνλNiMeff=nNNucleon number density
i2mφ
 existence of sterile neutrinos
scenarios with or w/o LSND

Futureproblems

Flux of high energy cosmic νfrom Active Galactic Nuclei
or Gamma Ray Burstetc.

10510

410

310

2

S/N ratio is
expected to belarge due to little
background ofatmospheric ν

102-2-1

E j(E) eV cm sec sr-1

3. High energy
astrophysical ν

1-1

10-210-3

10-4109101112131415161718192021222324

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10Neutrino Energy (eV)25

n Precise normalization of flux is not known The ratio of different flavors is important
quantity to observen Initial flux:
Just like in νatm , thesource of ν is π decay
F0 (ν ) : F0 (ν ) : F0 (ν )eµτ

π + → μ + + νμe + + νe + νμπ − → μ − + νμe − + ν e + νμ

≅ 1: 2 : 0n Observed flux on Earth:
Due to ν oscillations|θθ13|<<1, |π/4-θθ23 |<<1

F(ν ) : F(ν ) : F(ν )eµτ

≅ 1: 1: 1In standard Nν=3, when L→∞→∞oscillation probability in vacuum
2Pαβ = ∑ Uαj Uβjj222cs0 2  1212

22U≅  s12/2 c12/2 1/2 αj s2 /2 c 2 /2 1/2 12 12

LearnedPakvasa‘95

F(ν e ) = F0 (ν e )(Pee + 2Pμe ) = F0 (ν e )(1- Pτe + Pμe ) = 1F(νµ ) = F0 (ν e )(Peμ + 2Pμμ ) = F0 (ν e )(1- Pτμ + Pμμ ) = 1F(ν τ ) = F0 (ν e )(Peτ + 2Pμτ) = F0 (ν e )(1- Pττ + Pμτ) = 1F(να ) = F0 (ν e )Peα + F0 (νμ )Pμα = F0 (ν e )(Peα + 2Pμα )Peα + 2Pμα = (Peα + Pμα ) + Pμα = 1- Pτα + Pμα = 1

CHOOZ+νatm: |θ
θ13|<<1νatm: |π/4 -θθ23 |<<1
Deviation from 1:1:1 is smalle

AtharJezabek-OY‘00eNν=3no oscµ• Fτ

FµFe

τµτ

A few scenarios to predict deviation from1:1:1 have been proposed Standard flux + ν decay

α:1:1 (α=1.4~6)

Beacom-Bell-HooperPakvasa-Weiler ‘03

 Standard flux + pseudo-Dirac ν Beacom -Bell-

α:1:1 (α=2/3~14/9)

Hooper-LearnedPakvasa-Weiler‘04

 Electromagnetic energy losses of π & µ

α:1:1 (α=1/1.8~1)

Kashti-Waxman ‘05

4. CP phases in ν oscillations
Derivation of propagation of ν oscillations
Grimus-Scharnagl, ‘93
Dirac eq.  (Tani-Foldy like transf.)  positive energy
part  Schroedinger type eq. to order m2/p2
For simplicity Majorana case isdiscussed here

µαβ: magnetictransitions

β,β, γ (Majorana CP phases) don’t appear in the eq.
cf. neutrinoless double β decayCP phases β’,, γ’γ from the charged lepton sector remain
if off-diagonal part of µ or0

In this case analysis of 6x6 matrix is reduced
to that of 3x3:

λ3 = diag(1, −1,0), λ8 = diag(1,1, −2)

If the effect of magnetic transitions µ or the offdiagonal part ofdue to new physics, then the effectof these CP phase may be important and should betaken into account5. Summary● CP phase δ is always accompanied by asmall factor sinθ13 so unless it is enhanced bymatter effect, it may be neglected in theleading order.

● There are CP phases from the charged lepton
sector and in principle they appear in νoscillations if off-diagonal elements ofmagnetic transition or matter term are nonzero. Again unless these terms are large, theCP phases may be ignored.