Neutrino Physics

Neutrino mass and mixing

No neutrinoless double beta decay

K. Nishikawa＠ XXXIV International Meeting

on Fundamental PhysicsApril 3-7,2006

Neutrinos are Everywhere

• Big Bang:– They are still left over: ~300 neutrinos per cm3

• Natural sources– Sun : 1012 of neutrinos /sec /cm2 – Atmosphere : 103 high energy neutrinos /sec/m2

– Reactor : 1020 　 neutrinos/GWth

• Weak:– Need to stack up lead shield up to three light-years to stop t

hem• Light

– Twelve orders of magnitudes below Mt or weak scale10

– 1930 Pauli’s neutrino hypothesis– 1934 Fermi theory of weak interaction – 1956 Neutrino observation by Reines and Cowan

• Neutrinos are left handed　 　 　 　 　 　 　　　　　　　 puzzle and parity

– 1957 Parity violation by Wu et.al. Helicity of neutrino measured by M.Goldhaber et.al.– 1958 V-A (Sudarshan & Marshak, Feynman & Gell-Mann) Current-current formulat

ion

• Intermediate Vector Boson (W) hypothesis– 1960 Two neutrino hypothesis (Lee, Yang)– 1968 Solar neutrino problem （ Ray Davis)

• Electro-weak unification– 1967 Weinberg, Salam, Glashow– ‘t Hooft’s proof– 1973 Discovery of Weak Neutral Current (Gargamelle) – 1983 Observation of Z,W

Brief history

Conclusion of this series of talks

Experimental evidences for the following summary

• Two mass eigen-states have m2 ~8x10-5 eV2

• Define 　　such that m　　m

• Solar 　 MSW in neutrino (not anti-neutrino)

　　　　　　is the largest component in e

• Third mass eigen-sate () is separated by m2 ~ ±3x10-3 eV2

• Small e component in 　　consists of 　　almost 50;50)　　　　　　which is larger in 　　　

• neutrino mass and charged lepton mass ordering

• same or inverted

8

atm.3x10-3eV2

Issues about neutrinos for coming years?

• What is Neutrino? 　　 Tiny mass (~x 10-10 ) of q,l±

– Majorana : Majorana and Dirac masses co-exist• See Saw m ～ m2/M (M~coupling unification scale)• neutrino = antineutrino L= 2 units

– Dirac : ~ quarks, charged leptons• very very weakly coupled RH

• Different patterns of mixings in quarks and in leptons– Masses and interactions (transitions among elementary parti

cles)– Particle and anti-particle distinction, especially in pure lepto

nic process

• Baryon- Anti-Baryon asymmetry in Universe ?

Neutrino-less

NeutrinoOscillation

Contents-1

• Experimental achievements

1. What are neutrinos?

2. Their interactions?

3. Imaging type water Cherenkov detector (Super-Kamiokande)

Helicity of neutrino (V-A)

Parity

sprspp

ttrrP

)(,

,:

direction of spin = direction of advancement of right handed screw

direction of motion direction of motion

LH RH

P

Maximum parity violation means a possibility where only one of those state exist in nature

Only left handed component exists

Neutrinos must be Massless

• All neutrinos left-handed massless

• If they have mass, can’t go at speed of light.

• Now neutrino right-handed??

contradiction can’t be massive

Anti-Neutrinos are Right-handed

• CPT theorem in quantum field theory

– C: interchange particles & anti-particles

– P: parity (r → -r)

– T: time-reversal (t → -t)

• State obtained by CPT from L must exist: C

R

• Lorenz transformed state

　　　　　　R (Lorenz)

CR

CR = R ?

Standard Model

Finite mass of neutrinos imply the Standard Model is incomplete!

• Not just incomplete but probably a lot more profound

– New kind of field (Majorana : CR=R)

– Very small RH interaction (Cannot produced by interaction)

Number of neutrino species

Intermediate Vector Boson and decay

• Feinberg’s argument (1958)• V-A current-current formulation suggest W± analog to

• Pontecorvo (1959) Schwartz (1960) idea of high energy neutrino beam

　　e ?

Detection of ντCC in DONUT All tracks in the Scanning region

(4179 tracks)

Reject passing

through tracks

(420 tracks remained)

Reject Low momentum tracks

(114 tracks remained)

Vertex detection :

Neutrino interaction and decay of short lived particles

　

Interaction Point

Decay Point of

DONUT FNAL E872 Beam dump beam

neutrino

Status 　 : 406 　 neutrino interaction analyzed. 7 　　 CCevent detected On-going 　： Component analysis of the prompt neutrino beam νe ： νμ ： ντ 　

The Number of Neutrinoscollider experiments

• most precise measurements come from Z e + e

• invisible partial width, inv, determined by subtracting measured visible partial widths (Z decays to quarks and charged leptons) from the Z width • invisible width assumed to be due to N

• Standard Model value ( l)SM = 1.991 0.001 (using ratio reduces model dependence)

SM

l

l

invN

N = 2.984 0.008

Neutrinos How they interact

Charged current interaction

2

2

82 W

F

M

gG

•Coupling constant(GF) is universal for all particles•Left-handed particles form weak isospin-doublets •All right-handed particles have no charged current interaction (even if they exist in nature) iso-singlets • Interaction is mediated by W intermediate vector boson

eR R R

(R　　R　　R) uR cR tR

dR sR bR

t3=1/2

t3=-1/2

W22

gGF =

eL L L uL cL tL

eL L L dL sL bL

Transformation between pair of particles, differ by unit charge

mixing exist (CKM)

l+e → e+l

l

eW

l

e

s

msG

d

d lF

CM

22

2

2 )(

)2(

isotropic in cms

~10-41 ・ E cm2

E　th~10GeV for

Em

E

e2ｌ： Forward peak　small

22 NN mEms

FFs

msG

d

d NF

CM

22

2

2 )(

)2(

~10-38・ E　cm2

GF : Fermi coupling constant

Ems e2

2

225

8

21017.1~

WF M

gGeVG

l + n → l(-) + p

l + p → l(+) +n

g

g

Complication by free, almost free nucleonsform factors, Nuclear effect(Pauli blocking) H2O D2O CH

Quasi-elastic scattering cross-sections

• Two form factors

•MV fixed by e.m. (CVC)

•Axial V form factor

magenta Old MCred new MC

Cross-section ()

10-3

8 cm

2

/E　cm2/GeV)

1 10 100 GeV

n

pW 2

2V,A

2VA

M

q1

1f,f

Data on charged current processes

• Not well known

• Especially 2~3 GeV

• must be determined internally

Neutral current interaction

eR R R (R　　R　　R) uR cR tR dR sR bR

eL L L eL L L uL cL tL dL sL bL

Iso-doublet gL Iso-singlet gR

eL L　L -1/2 + sin2W eR R　R sin2W

eL L　L +1/2 eR R　R 0

uL cL tL 1/2 - 2/3sin2W uR cR tR -2/3sin2W

dL sL bL -1/2 +1/3 sin2W dR sR bR 1/3sin2W

g=T3 - sin2W·Q

l

e(N)

Zl

e(N)

gL,R

gL,R

Neutrino mass and oscillation

Neutrino oscillation

• Inteferometry (i.e., Michaelson-Morley)

– Coherent source

– Interference (i.e., large mixing angles)

– Need long baseline for small m2

• Neutrino mass must be non-zero, if oscillation occurs

21

21

cossin

sincos

cossin

sincos

2

1

ipLm

ctipm

ctipmpm

differencephase

2/

)(2/

)()(

2

2

221

222

The Hamiltonian

• The Hamiltonian of a freely-propagating massive neutrino

• But in quantum mechanics, mass is a matrix in general. 22 case:

　　H 　

p 2 m2 p m2

2p

M2 m2

11 m212

m221 m2

22

　

　　

　

　　

M2 1 m12 1

M2 2 m22 2

　

,t 1 cos e im12t /2 p 2 sin e im2

2t /2 p

Two-Neutrino Oscillation

• When produced (e.g., ++), neutrino is of a particular type

• At time t

• No longer 100% , partly !

• “Survival probability” for after t

　　P , t

21 sin2 2 sin2 1.27

m2c4

eV2GeV

c　p

ct

km

　

　　

　

　　

　

e im12t /2 p,t

　

e im22t /2 p|

　

,t 1 cos e im12t /2 p 2 sin e im2

2t /2 p

Three Flavor Mixing in Lepton Sector

3

2

1CPMMNSVU

e

100

0

0

0

010

0

0

0

001

U 1212

1212

1313

1313

2323

2323PMNS cs

sc

ces

esc

cs

sci

i

e

Weak eigenstates m1

m2

m3

mass eigenstates

100

0e0

00e

V 2

1

i

i

CPM

12, 23, 13

+ 　　(+2 Majorana phase)

m122, m23

2, m132

cij = cosij, sij=sinij

Matter effect MSW effect

• Neutrinos propagate in matter receive a refractive effect due to their interaction (extra energy V, the energy E, momentum k’) with matter

VmkE 22'

The refractive index n is defined by )exp( iEtxkni

E2=k2+m2 the dispersion relation in vacuum and k’=nk

n=1-EV/k2

eWF

eWFe

nGV

nGV

)sin221(2:

)sin221(2:

2,

2

ne electron density

MSW effect (II)

nFpWFne

e nGnGV 212)sin22

1(2: 2

,,

,,

eWFe

eWFee

nGVNC

nGVNCCC

)sin221(2:)(

)sin221(2:)(

2,

2

n=1-n ~7.6 x 10-19 (100g cm-3)(E/10MeV)-1 for e small for

velocity changes == effective mass changes in matter(100g/cc at the center of Sun)

Active neutrinos by interaction with p,n

Can distinguish ‘active’ and ‘sterile’ neutrinos

- for anti-neutrino

effective mass in matter

cossin

sincos,

2

1 UHUHdt

di

x

e

x

e

eFeeeF NGVee

GL 2,])1(][)1([

255

n

ne

V

VVU

m

mU

EE

EH

0

0

0

0

2

1

0

0 1

22

21

222222

21

2

22

2222

21

)2sin()2cos()(2

1

2cos2sin

2sin2cos

2

1

10

01)(

2

12

mAmAmmm

mAm

mmAAmmEH

2cos2222 2mENGAENGA eFreseF

22222 )2sin()2cos( mAmm matter

Schrodinger eq.

Hamiltonian

Effective mass difference of e and in matter by Ve

Mass difference and mixing angle in matter

2sin2cos2

2sin2sin

22

2

22

m

EVe

m

22222 )2sin()2cos( mAmm matter

ENGA eF22

Ne= 6x1025 /cc = 6 x 10-14 /fm3 for 100g/ccGF~10-5 GeV-2 (0.2GeV·fm)3 =8 x 10-8 GeV fm3

A =10-2 E (GeV) eV2

A change sign for anti-neutrinos

22222 )2sin()2cos( mAmm matter

2sinmm 2resmatter

2

)10~(10~2cos 242 MeVEeVmA In(sin2

In(m2)

centere

F NEG

m

2cos

222

2cos22

222mENGA

ENGA

eFres

eF

m2

m1

Also Day Night!

MSW in the Solar neutrinos

‘MSW’ for sterile

00

0

0

0

2

1

0

0 1

22

21 nV

Um

mU

EE

EH

cossin

sincos,

2

1,,,, UHUHdt

di

s

e

sterile

e

2cos22 2mENGAENGA nFresnF

22222 )2sin()2cos( mAmm matter

nnFpWFne

e nnGnGV

22212)sin22

1(2: 2

,,

,,

Large m2 →(E >10 GeV in earth) m2~A

matter effect in the earth for sterile neutrinos

PC, Evis>5GeV<Eν> ～ 25GeVup/down ratio

up through going μ<Eν>～ 100GeVvertical/horizontal ratio

νμ ー ντ

νμ ー νs

νμ ー νs

νμ ー ντ

m2

22

2n

2

m2

2sinGeV20E

2sin2cosm

EV2

2sin2sin

s

s

Z

n

n

Detectors for Neutrino Oscillation Experiments

• Massive

• Neutrino oscillation is the oscillation between different flavors

– e, μ, τidentification by charged current interactions

– target and sensor must be combined

• Only Flux(E) x (E) will be measured

– E L must be known event-by event to get m2

– Two distances if possible

)GeV(E

)km(L)eV(m27.1sin2sin)(P

)E()(P)E(FN

2222

obs

Particle identification

• -ID

– minimum ionizing particle with long range R500g/cm2/GeV

• e-ID

– showering particle, large 　(TRD), E/p1(with magnet)

• -ID

• short decay length

• isolated hadronic activity (charm)

• →e　→　→　hadrons

Super Kamikande

Inside Super-K

Kamiokande

４０ｍ

４１．４ｍ

Super-Kamiokande (1996)1996-50000ton water11146 50cm PMT (40% photo coverage)1000m undergroundMin det. energy ~ 5 MeVInner and outer

Principle of the technique

• Cherenkov radiation: electromagnetic radiation in a medium with refractive index n if n>1 (=v/c)– cosc = 1/n,

– where N is the number of emitted Cherenkov photons with wavelength , dx is the particle’s path length, and =1/137

– Cherenkov photons are detected with a large number of photomultiplier tubes (PMT)

• For Super-K, C = 42deg ( = 1), good at simple geom.• N(photo e.) ~ 6 / Mev e- : about 1/1000 of scintillator• Attenuation length can be attained upto ~100m• P(threshold)~1.2 GeV/c for protons

dN 2sin2c

dxd　 2=

c

Cherenkov light

Charged particle

Electron-like and muon-like eventse-like -like

e

Particle ID (e & )　 (in single ring events)

• An experiment with test beams confirmed the particle ID capability (PL B374(1996)238)

K2K 98% beamnear detector

e

e

Atm. data

Excellent for low multiplicity Low energy

Particle ID in multi ring events (0 selection)

π0←