Neutrino oscillation physics

Alberto Gago PUCP

CTEQ-FERMILAB School 2012Lima, Perú - PUCP

Outline

• Introduction • Neutrino oscillation in vacuum • Neutrino oscillation in matter • Review of neutrino oscillation data • Conclusions

Historical introduction

Observed Spectrum – Continuosthree body decay

(1930) W. Pauli propose a new particle for saving the incompatibility between the observed electron energy spectrum and the expected.

XeZAZA )1,(),(

Expected Spectrum-Monoenergetic two body decay

eZAZA )1,(),(

1,, ZAMZAMQEe

XeEZAMZAMQE 1,,

Historical introduction

(1956)- F. Reines y C.Cowan detected for the first time a neutrino through the reaction This search was called as poltergeist project.

First reactor neutrino experiment

(1962)-Lederman-Schwartz-Steinberger, discovered in Brookhaven the muon antineutrino through the reaction:

they did not observe: Confirming that e

First neutrino experiment that used

Historical introduction

(2000) In Fermilab the DONUT collaboration observed for the first time events of . They detected four events.

X

SD

Neutrinos

82

2

cmcm

101010

)()(

41

33

eee

e

Z

0082.09840.2 N

Active neutrinos

Neutrinos -SMTherefore in the Standard Model (SM) we have:

Neutrinos are fermions and neutrals

LLL

e

e

Left-handed doublet

Only neutrinos of two kinds have been seen in nature: left-handed –neutrino right-handed- antineutrinos

Neutrino –SM

In the SM the neutrinos are consider massless (ad-hocassumption)

….BUT we know that they have non-zero masses because they can change flavour or oscillate …

Neutrino oscillations -history

).( to analogy

in of idea the time first the for suggested Pontecorvo Bruno

0000 KKKK

)1957(

(1962) Maki, Nakagawa and Sakata proposed the mixing

Neutrino oscillation in vacuum

.

.

.

.2

1

e

Flavour conversion

kk

kU *

,,e seigenstate flavour 3,2,1k seigenstate mass

ikki

The flavour (weak) eigenstates are coherent superposition of the mass eigenstates

Non-diagonal

332211 UUU

Neutrino mixing

• The mixing matrix is appearing in the charged current interaction of the SM :

,,

*

,,

2

2

e kkLLkLkLk

CCSM

e kLLLL

CCSM

WlUWlUg

L

WlWlg

L

analog to the quark mixing case

LkL

LkL

l

l

LkL

LkL

l

l

CKMUL

DLL

lLPMNS UVVVVU

PMNS=Pontecorvo-Maki-Nakagawa-Sakata

D= down quarks U= up quarks

Neutrino oscillation in vacuum the scheme

Detector

Propagation

k

Source

Flavour states Flavour states

v v

Mass eigenstates

*kU

kU

Coherent superposition of themass eigenstates The flavour conversion happens

at long distances!

Neutrino oscillation in vacuum

• Starting point :

• Evolving the mass eigenstates in time and position (Plane wave approximation):

seigenstateflavourseigenstatemass α,βi,k

amplitudeyprobabilitxtA

iiii

ie

iiiii

UxpitEiU

xpitEiUxt

),(

*

,,

*

exp

exp),(

0,0,,

xtUe

kk

i

iiU *

2

*22

exp),(),( iiii

i UxpitEiUxtxtAP

Neutrino oscillation in vacuum

Analyzing:

onscontributi mass neglecting energy neutrino the isLt assumption

E

LE

mpE

LpELpELptE i

ii

iiiiii 2)(

222

222jiij mmm

L

E

miUUUUP ij

jijjii 2exp

2

,

**

We are using L instead of x

Neutrino oscillation in vacuum

L

E

miUUUUUUELP ij

jijjiii

ii 2

expRe2),(2

**22

energy neutrino distance detector - source

:

:

E

L

constant term oscillating term

2

24

22 ij

oscoscij

m

ELL

E

m

Oscillation wavelength

1,,,,

ee

PP

Valid if there is no sterile neutrinos

Neutrino oscillation in vacuum

LE

miL

E

mUUUUUUUUELP

UUUUUU

LE

miUUUUUUELP

ijij

jijjii

jijjii

jijjiii

ii

ij

jijjiii

ii

2sin

2cosRe2Re2),(

Re2

2expRe2),(

22****

**22

2**22

using

LE

mUUUU

LE

mUUUUELP

ij

jijjii

ij

jijjii

2sinIm2

4sinRe4,

2**

22**

Neutrino oscillation in vacuum• For the antineutrino case:

*UUUi

ii

LE

mUUUU

LE

mUUUUELP

ij

jijjii

ij

jijjii

2sinIm2

4sinRe4,

2**

22**

This is the only difference…we will return to this later

Two neutrino oscillation

cossin

sincos)(U

21

21

cossin

sincos

e

LEm

LEm

LEm

iLEm

LEm

i

LEm

iUUUU

ULE

miUP

ee

ii

ii

ee

4sin2sin

2cos12sin

21

2sin

2cos1sincos

2expcossinsincos

2exp

2exp

22122

2212

2221

22122

2221

2221

2*21

*1

222

*

,

Two neutrino oscillation

IIn the two neutrino framework we have:

yprobabilit transition

yprobabilit survival

phase noscillatioamplitude noscillatio

LEm

ELP

LEm

ELP

e

ee

4sin2sin,

4sin2sin1,

22122

22122

ELPELP

ELPELP

,,

,,

Two neutrino oscillation • Introducing units to L and E

)(

)(27.1)(

)(27.1

4

221

221

221 km

GeVeV

ormMeV

eV 22

LEm

LEm

LEm

kmeV

GeVm

eVMeV

22 )()(

47.2)(

)(47.2

4221

221

221 m

EmE

mE

Losc

Oscillation regimes

oscLL

LE

mL

Em

44

221

221

• Oscillation starting

• Ideal case

• Fast oscillations

114

221

oscLL

LEm

21

~)1(4

221

oscLL

LEm

114

221

oscLL

LEm

04

00

02

221

1212221

E

Lm

mmmmm or

sen2

No oscillation

Oscillation regimes

Short distance

Ideal distance

Long distance

2sin21 2

'2

'22212

2

2'

2

2'

27.1

2

dEe

dEeE

Lm

P

E

E

e EE

EE

sinsin2

Fixed E

Sensitivity plot

c

a

b

Not sensitivity

sensitivity

L

LL

L

L

PL

Em

PL

Em

E

LmP

E

LmP

P

27.1log2log2

1)(log

27.12

127.12

27.12

22

1

2221

221

2

221

221

sin

sinsinc)

sinsinb)

sina)

2

22

2

LP lower probability limit for having a positive signal in a detector

ysensitivit maximum b @

2~27.1 2

EL

m

Exclusion plot

allowed

excluded

LPupper limit of the oscillation probabilityPPL

⟨L/E = 18km/GeV ⟩

Positive signal

⟨L/E = 1km/GeV ⟩

0.05 < P < 0.150.001< P < 0.005

The mixing matrix

1

)1(2 22

2

*

UUUU

NNNNN

NU

iiiUU

NN

condition the satisfies and unitary is matrix ng mixi the

parameters 2 has matrix complex general A

from

rows different between ityorthogonalrow eachof length unitarity

phases complexangles rotation

has matrix mixing unitary

phases complexangles rotation

2

)1(2

)1(

2

)1(

2

)1(2

NN

NN

NNNNN

phases complex )(

angles rotation )(

:scheme 3 In

62

133

32

133

-

The mixing matrix

L

L

Li

i

iTYPECKM

i

i

LLL

LkLk

e

e

e

eUe

e

lU

e

100

00

00

100

00

002

1

321

* : within tionrepresenta 33 matrix unitary a written

rephasing by absorbed be can and nosantineutri neutrinos neutrinos Dirac are IF *

invariant are lagrangian theof terms Other

and

: rephasing by absorbed be can and , phases The *

phase) complex 1 & angles rotation

21

)(,

'

3(

s

elel

UU

Li

LLi

elL

e

CKM

l

The mixing matrix

• If neutrinos are equal than antineutrinos

condition Majorana noantineutrineutrino

TC C

2

12

phases physical

2

2

angles mixing

Neutrinos Majorana Neutrinos Dirac :scheme 3 the In

3)1()2)(1(

3)1(

3)1(

NNNN

NNNN

Charge conjugation operator

fixed are phases neutrino the since absorbed be not can and 21

CiCiii vevevevevv 2if instance, For zero be to has

3-mass scheme

21

22

m

m

23m

21

22

m

m

23m

Normal Hierarchy Inverted Hierarchy

22 eVeV 5221

3231 1010 mm

2m

M

D

D

i

i

U

i

i

M

e

e

cs

sc

ces

esc

cs

scU

100

00

00

100

0

0

0

010

0

0

0

001

2

1

1212

1212

1313

1313

2323

2323

The mixing matrix in 3 scheme

03 withii

iDMDM eUDUU

Dirac CP phase

Majorana phases

…Tomorrow we will see the current measurements of these angles done by the experiments

:Notation ijijijij sc sincos

Majorana phases and neutrino oscillations

2

*

2

*

2

*2

),(

Di

xpitEi

i

Di

iDi

xpitEi

i

iDi

Mi

xpitEi

i

Mi

UeU

eUeeUUeUxtA

ii

i

ii

i

ii

Only the dirac phase is observable in neutrino oscillation

CP violation

,, 3,2,1

*1

,, 3,2,1

*

2

2

e kLkLkkLLkCP

CClCP

e kkLLkLkLk

CCl

WlUWlUg

ULU

WlUWlUg

L

UUCP * needs

CP violation

• What does CP mean in neutrino oscillation ?:

PPCP

RR

P

LL

C

LL

violated)isandifCPPP

UU ii

(

*

CP violation

L

E

mUUUUPPP ij

jijjii 2

sinIm4,2

**

Jarlskog invariant CPjjii JUUUU **Im

Independent of the mixing matrix parameterization =rephasing invariant

ji

ji

,,)(

,,)(

andin nspermutatio anticyclicandin nspermutatio cyclic

CP violation

sen sencossencossencos 2323121213132CPJ

CP violation phase All the mixing angles have to be

non-zero to have CP violated.

013

CPS

CP

CP

LE

mL

E

mL

E

mJ

LE

mL

E

mL

E

mJP

44416

2224

231

223

212

231

223

212

),(

sinsinsin

sinsinsin

In particular we just found out that

CP violation

• It is interesting to note that :

• Checking for CPT

conserved is CPT

PPCPT

LL

T

LL

P

RR

C

RR

,, ODDTCP PPPPPP

ODDTCP PP

Useful approximations

• In the three neutrino framework we have:

• Case 1 : sensitive to the large scale :

• Case 2: sensitive to the small scale

2231

2212

21231

232 10~

mm

mmm with

neglect we 221

2221

232 10)1(~

4)1(~

4mL

Em

LEm

out averaged are related terms

2232

221 10)1(

1~

4)1(~

4

L

E

mL

E

m

221

231

232 mmm

Useful approximations

• Case 1: sensitive to the large scale

LE

mUU

LE

mUUUUUU

LE

mUUUUL

E

mUUUUP

Smmm

eff

CP

4sin4

4sinRe4

4sinRe

4sinRe4

)0(0

2312

2sin

2

3

2

3

2312*

22*

113*

3

2312*

223*

3

2312*

113*

3

221

232

231

2

and

Similar structure to the two generation formula

Useful approximations

• Case 1: sensitive to the large scale

LEm

cscsP

LE

msP

LEm

cP

LEm

P

u

e

ee

441

42

42

421

2312

13223

213

223

231

13223

231

23413

231

13

2

22

22

22

sen-1

sensen

sensen

sensen

Explicit formulas

Useful approximations• Case 2: sensitive to the small scale

LE

m

UU

UUUU

LE

mUUUU

UUUULE

mUUP

eff

4sin411

4sin4121

2

1

2

14

4sin41

2212

2sin

22

1

2

2

2

1

2

222

3

4

3

22122

1

2

2

2

3

2

3

2

1

2

3

2

2

2

3

22122

1

2

2

2

Similar structure for the two generation formula

averaged out

21

4sin

232312

L

E

m

Useful approximations• Case 2: sensitive to the small scale

2413

413

3

221

12413

413

3

421

eeee

ee

PcsP

LE

mcsP

22 sensen

ApproximationFull Probability

scale231m

scale221m

Useful approximations• We can get a better approximation for the oscillation formula when we

expand this in small parameters up to second order. We are in the case of sensitivity of the large scale. • These small parameters are :

23121313

213

212

213

2122

122

2132

1322

23

2sin2sin2sin~

4sin

44cos~

4sin2sin

4sin2sin

cJ

LEm

Em

LEm

J

LEm

LEm

sPee

c

223

E

Lm

m

m

2,

221

231

221

13

,

leading term –P2 approximation

Now it is appearing and 2

12m