Introduction. Experimental evidences towards oscillations....

Neutrino Oscillations, an overview

http://lphe.epfl.ch/∼mtran/seminaires/

TRAN Minh-TâmLPHE / IPEP / SB / EPFL

March 13, 2013

✦ Introduction.

✦ Experimental evidences towards oscillations.

✦ Interpretation of the results.✦ What next ?

● Future measurements.

● What Cosmology can tell us.

✦ Conclusions.

March 13, 2013 (1)


TRAN Minh-Tâm

LPHE / IPEP / SB / EPFL

Introduction

Suppose that you are asked :

✦ What are an electron and a positron ?

● spin 1/2 particle, mass about 511 keV

● carry electric charge (quantum number)± 1 unit

✦ A neutron and anti-neutron ?

● spin 1/2 particles, mass around 940 MeV

● distinguishable with Baryon number

✦ The K0 system ?

● give up flavour conservation in weak decays

● K0 and K0

mix and form physical states Ks and KL● physical states =defined masses and lifetimes

Conservation of electric charge and Baryon numbervalid to a high degree of accuracy

March 13, 2013 (2)


TRAN Minh-Tâm


Introduction

What are the neutrinos ? Much less is known about them.✦ December 1930 : W. Pauli in a letter to

Liebe Radioactive Damen und Herren... in Tübingen,to explain apparent violation of (~p, E) conservation in β-decay and spinstatistics for N14 and Li6 nuclei, he postulated a➣ spin 1/2 , neutral and light particle existing inside the nucleus and➣ emitted at the same time as the β particle.

✦ 1932 : Discovery of the neutron (Rutherford).

✦ ν are leptons and are emitted (absorbed) together with a charged lepton :νe emitted with e

− in β− decay and so are the νµ and the ντ :µ− → e− νe νµ τ− → µ− νµ ντ

✦ within Minimal Standard Model, lepton numbers are conserved separatelyand ν’s are massless .But ...

The nature of the neutrinoscan only be unraveled by experiments

March 13, 2013 (3)


TRAN Minh-Tâm


Neutrinos

➣ General introduction

March 13, 2013 (4)


TRAN Minh-Tâm


The Neutrinos : how many are they

There are PLENTY OF NEUTRINOS around us :

• From the sun : on earth, the flux is Φsolar = 6.4× 1010 cm−2 s−1• From interactions and decays of high energy particles in the atmosphere :

Φatm = 105 cm−2 s−1

• Relic neutrinos from the Big Bang : ∼ 330 cm−3 of the 3 speciesat ∼ 1.95 K. Do they contribute to dark matter ? (1991)

However their interaction rate is very low :

✦ for β-decay ν, cross-sections ' 10−43 cm2✦ Send a beam of 1010 neutrinos to the earth, all but 1 ν will emerge.

✦ ⇒ Need massive detectors !

Due to their extremely low interaction rate, little is known about ν.

• WHY should they be massless when the other leptons do have mass ?• If they show a mass difference, even tiny, the three species should mix.

(following transparencies)

• What can the relation of ν physics with cosmology tell us ?Focus on NEUTRINO MIXING in what follows.

March 13, 2013 (5)


TRAN Minh-Tâm


Neutrino Oscillation ✦

At production and detection neutrinos are emitted or absorbed together with acharged lepton ⇒ neutrinos have then a definite flavour α = e , µ , τ .

W

νβ

lβ

detector

W

lα

ναsource

Propagation implies mass eigenstates νi ( i = 1 , 2 , 3) which can be differentfrom flavour eigenstates να. Need a unitary matrix U to connect them.

Flavour might be not conserved during propagation.

να is produced but νβ 6=α might be detected !

ν i W

l α

ν α W ν β

l β

Σi

source detector

Uαi

Uβi

Long

distance

-1

A phase exp(−i m2i L / 2E) develops.

March 13, 2013 (6)


TRAN Minh-Tâm


Neutrino Oscillation ✦ ✦

Neutrino state of flavour | να 〉 is a superposition of the mass eigenstates | νi 〉| να 〉 =

∑∑∑

i

Uαi | νı 〉

⇒ flavour−α fraction of | νi 〉 : | 〈να | νi〉 |2 = | Uαi |2.Consider 2 flavour oscillations, e.g. ( νe , νµ ). In this simple case, U is a rotationmatrix. Suppose ν1 and ν2 have a non zero mass difference.✦ The flavour eigenstate is a combination of mass eigenstates:

(νeνµ

)

= U

(ν1ν2

)

=

(cos θ sinθ− sin θ cos θ

) (ν1ν2

)

✦ Starting with a neutrino emitted as νe at t = 0, it will evolve to a superposition of νe andνµ at time t (phase difference will then develop due to mass difference) :

| ν(t)〉 = cos θ e−iE1t | ν1〉 + sin θe−iE2t | ν2〉| 〈νµ | ν(t)〉 |2 = 4sin2θ cos2 θ sin2

(E1 −E2)t2

= sin2 2θ sin2∆m2

4Et as ν are relativistic.

Probability for oscillation from νe to νµ is then

Posc = sin2 2θ

︸︷︷︸

amplitude

sin2(

1.27 ∆m2 (eV 2) L (km)

E (GeV )

)

~ = c = 1 E / 1.27 ∆m2 ∝ characteristic oscillation length

March 13, 2013 (7)


TRAN Minh-Tâm


Neutrino Oscillations ✦ ✦ ✦

Posc = sin2 2θ sin2

(1.27 ∆m2 L

E

)

We want to extract 2 fundamental quantities:

✦ sin2 2θ , the magnitude of the oscillation,✦ ∆m2 = m21 − m22 , the difference of the

squares of the masses in eV 2.

Sensitivity depends upon 2 experimental param-eters:✦ L, distance from source to detector (in km),✦ E, neutrino energy (in GeV).

• Small ∆m2Have to have sufficient time to develop the

slow oscillation

• Large ∆m2 Rapid oscillationsOscillations average out !

Choose L/E to select sensitivityto a particular range of ∆m2.

0

Distance from neutrino source (L)

P(ν )µ

P(ν )e

Pro

bab

ilit

y

Fixed neutrino energy (E)1

0

0.2

0.4

0.6

0.8

1

Pro

bab

ilit

y

0 200 400 600 800 1000

Distance from source [km]

E = 1 GeV ∆m = 0.001 eV22

Pee

Pee

Peµ

0

0.2

0.4

0.6

0.8

1

Pro

bab

ilit

y

0 200 400 600 800 1000

Distance from source [km]

E = 1 GeV2 2

∆m = 0.1 eV

∆ L = π E /(1.27 ∆ m )2

2si

n 2θ

March 13, 2013 (8)


TRAN Minh-Tâm


Exploration of the (sin2 2θ , ∆m2) plane

P = sin2 2θ sin2(1.27∆m2ij L/E)

2 experimental parameters to search for :sin2 2θ and ∆m2ij

Report the result on the (sin2 2θ , ∆m2)plane.

If no oscillation is observed, determine lim-its according to experimental sensitivity.

In real experiment, E and L have some spread⇒convolution of P with some gaussian distributionaround central value b0 of b = 1.27L/E withknown standard deviation σb :

〈P 〉 = 12

sin2 2θ[1− cos

(2b0∆m

2ij

)exp

(− 2σ2b ∆m2ij

)]

✦ Large ∆m2ij : fast oscillations washed out

⇒ sin2 2θ = 2 〈P 〉✦ Large sin2 2θ : ∆m2ij '

√

〈P 〉/b0√

sin2 2θ

Hints and excluded regions

ν → νµ τ

sin 2θ2

∆m

(

eV )

22

CHORUS

NOMAD

Atmospheric

CDHS

CCFR

E531 ν ↔ νµ τ90%

Conf. limits

March 13, 2013 (9)


TRAN Minh-Tâm


Experimental evidences toward oscillations

Compelling evidences for ν oscillations :

➣ Solar neutrinos

➣ Atmospheric neutrinos

➣ Reactor and accelerator experiments

March 13, 2013 (10)


TRAN Minh-Tâm


Solar neutrinos : principle of the experiments

Measure fluxes of solar neutrinos and compare the results to solarmodels. Each experiment has its own threshold of detection.

Difference between results and model can point to either

➣ deficiency of the model, or

➣ oscillation of the neutrino “en route”.

Interpretation as oscillations has to account for “matter effect” :

✦ Neutral current is the same for all neutrino types and hence doesnot matter,

✦ νe can have charged current scattering that νµ and ντ don’t.

✦ Resonant amplification of ν oscillations can take place andincrease the probability that νe created in the Sun core arrives asνµ (or ντ) on earth.

This is the MSW EFFECT (Mikheyev - Smirnov - Wolfenstein).

March 13, 2013 (11)


TRAN Minh-Tâm


The reactions in the Sun

The main Solar cycle : Hydrogen burning

pp neutrinos pep process

p p → H2 e+ νe p p → H2 e+ νe (99.75%) p e−p → H2 νe (0.25%)

H2 p → He3 γ H2 p → He3 γ H2 p → He3 γHe3 He3 → He4 p p (86%)

Also

p p → H2 e+ νe H2 p → He3 γHe3 He4 → Be7 γ (14%)

Be7 e− → Li7 νe (99.89%) Be7 p → B8 γ (0.11%)Li7 p → He4 He4 B8 → Be8 e+ νe

Be8 → He4 He4Be neutrinos B neutrinos

Combined effect : 4 p→ He4 + 2 e+ + 2 νeEnergy generation : Q = 26.73 MeV

Sun luminosity : L = 3.846 × 1026 W = 2.4 × 1039 MeV/sRate of νe emission : 2L/Q = 1.8 × 1038 s−1Flux on earth : Φ = 6.4 × 1010 cm−2s−1

March 13, 2013 (12)


TRAN Minh-Tâm


The Standard Solar Model (SSM)

The Model : standard theory of stellar evolution pionneered by John Bahcall.

±1.5%±10%

7Be

pp

Chlorine SuperKGallium

0.1 0.50.2 1 52 10 20

pep

hep

8B

1012

1010

108

106

104

102

+20%–16%

±?

±1%

Flu

x a

t 1 A

U (

cm

s M

eV

)

(

for

line : c

m s

)

-2-2

-1-1

-1

Electron Neutrino Energy (MeV)

March 13, 2013 (13)


TRAN Minh-Tâm


Oscillations in matter ✦

Consider only 2 flavours νe and νµ.In vacuum, propagation eigenstates are the mass eigenstates ν1 , ν2 :

Hv | ν1〉 = E1 | ν1〉 and Hv | ν2〉 = E2 | ν2〉. With| νe〉 = cos θv | ν1〉 + sin θv | ν2〉| νµ〉 = − sin θv | ν1〉 + cos θv | ν2〉

In (νe , νµ) basis, Hv is not diagonal : Hv =

(Hvee H

vµe

Heµ Hµµ

)

where Hvee = E1 cos2 θv + E2 sin

2 θv '1

2

(

2E +µ2

2E− ∆m

2

2Ecos 2θv

)

Hvµµ = E1 sin2 θv + E2 cos

2 θv '1

2

(

2E +µ2

2E+

∆m2

2Ecos 2θv

)

Hvµe = Hveµ = − (E2 − E1) sin θv cos θv '

1

2

∆m2

2Esin 2θv

with ✦ µ2 = m21 + m22 ✦ ∆m

2 = m22 − m21Diagonalize Hv and get back propagation eigenstates and mass eigenstates !One can subtract 2E without changing the eigenstates.

March 13, 2013 (14)


TRAN Minh-Tâm


Oscillations in matter ✦ ✦

Look for eigenstates of

Hv =1

2E

(M2ee M

2eµ

M2eµ M2µµ

)

M2ee =1

2

(µ2 − ∆m2 cos 2θv

)M2eµ =

1

2∆m2 sin 2θv M

2µµ =

1

2

(µ2 + ∆m2 cos 2θv

)

In matter in addition to propagation must include coherent ν scattering :

✦ all ν’s have Z exchange

✦ only νe’s have W exchange

Additional potential diagonal in the νe νµ basis :

✦ VZ

(1 00 1

)

same for all ν’s → ignore

✦ VW

(1 00 0

)

only for νe’s

VW =√

2 GF Ne = 7.63× 10−14 ZA ρ [eV]

Mass matrix then becomes(

M2ee + 2 E VW M2eµ

M2eµ M2µµ

)

Z W

e- νe

e-νeνανα

W

e-e-

νe νe

a) b) c)

X X

a) : neutral current of να , α = e, µ, τ

X = p, n, Nucleus, e−

b) : charged current of νec) : charged current of νe.

March 13, 2013 (15)


TRAN Minh-Tâm


Oscillations in matter, the MSW effect

Consider a CONSTANT density medium. Diagonalizing the mass matrix andsetting B = 2 E VW and µ

2 = m21 + m22, one gets

✦ Two mass eigenvalues :

m2 =1

2

(µ2 + B

)± 1

2

√

(∆m2 cos 2θv − B)2 + ∆m4 sin2 2θv

✦ Mixing angle in matter :

tan 2θm =sin 2θv

cos 2θv − B∆m2Maximal mixing (i.e. resonance) occurs when

B = 2 E VW = 2 E × 7.63× 10−14Z

Aρ = ∆m2 cos 2θv

⇒ ρres =∆m2 cos 2θv

1.526× 10−13 ZA

E

Then :

νe = cos θm ν1 + sin θm ν2νµ = − sin θm ν1 + cos θm ν2

March 13, 2013 (16)


TRAN Minh-Tâm


Oscillations in matter, the MSW effect in the Sun

The Sun density varies from 150 g · cm−3(∼ 6× 1025 e−/cm3) in core to ∼ 0 at surface.

Consider :

ADIABATIC case where density varieslittle over an oscillation length. Thencan consider that density is constant.✦ νe produced in high density region

ρ >> ρres ⇒ B (B ∝ ρ) very large⇒ tan 2θm → 0

✦ θm → π/2 : νe is in ν2 state✦ ν2 travels outwards through resonance

region; density varies slowly relative tooscillation length. ν remain in SAMEmass eigenstate ν2

✦ emerges as ν2 in vacuum where θm =θv

✦ ν2 is now a mixture of νe and νµThis is the MIKHEYEV - SMIRNOV -WOLFENSTEIN (MSW) effect.

ν1

ν2

ν1m

ν2m

νe

νµ

1 - 0.5 sin 2θ2

sin θ2

Vacuum - Matter

transition

1.0

0.8

0.6

0.4

0.2

0.0

P ee

E

Pee = |〈νe|ν2〉|2 = sin2 θvMarch 13, 2013 (17)


TRAN Minh-Tâm


The latest solar ν experiment ✦

Earlier experiments used✦ radio-chemical methods

(Chlorine, Gallium) or✦ water Cherenkov

(Kamioka and Super-Kamioka)(see page 13 for the thesholds of the experiments)

All found a deficit of νe w.r. to SSM.This deficit is energy dependent.This is the “solar neutrino problem”which lasted for more than 30 years !

SNO uses heavy water.

In SNO a neutrino νi can have

✦ Neutral current interactions(all 3 να species participate)

✦ Charged current interactions(only νe’s participate)

✦ Elastic scattering on electrons(all 3 να species participate)

The SNO detector1 kT D2O , 7 kT H2O , 9456 PMT’s

2000 m overburden.

March 13, 2013 (18)


TRAN Minh-Tâm


The latest solar ν results ✦ ✦

0 1 2 3 4 5 60

1

2

3

4

5

6

7

8

φµ

τ (106 cm

−2s

−1)

φe (106 cm−2s−1)

SNOφCC

φSSM

SNOφES

SNOφNC

αφ

=

1.76 ± 0.05 ± 0.09

3.4

1±0

.45

+ 0

.48

- 0

.45

✦ With all three flavours :➣ recover the total solar ν flux

above 5 MeV predicted by SSM,➣ show evidence for ν mixing.

Results corroborated by νe disappearanceat KamLAND.

GLOBAL FIT

(a): global fit includes Cl results, Gaflux measurements, SuperKamiokandeH20 and SNO D2O results.

θ2tan θ2tan

)2

(eV

2 m

∆

10-5

10-4

10-1

1

(a)

10-1

1

90% CL

95% CL

99% CL

99.73% CL

(b)

(b): with KamLAND antineutrino re-sults.

∆m2 = 7.1 +1.0−0.3 × 10−5 eV2

θ = 32.5 +1.7−1.6 degrees

March 13, 2013 (19)


TRAN Minh-Tâm



Compelling evidences for ν oscillations :

➣ Solar neutrinos



March 13, 2013 (20)


TRAN Minh-Tâm


Atmospheric neutrinos at Super Kamiokande ✦

Isotropy of ≥ 2 GeV cosmic rays andassuming NO νµ DISAPPEARANCE

SK

downward ν

upward ν

✦ downward ν : L ∼ 15 km✦ upward ν : L ∼ 12500 km

expectΦνµ(up)

Φνµ(down)= 1

findΦνµ(up)

Φνµ(down)' 0.5

The Super-Kamiokande detector

uses Cherenkov light in 50 kT water

Three variables are determined :✦ neutrino flavor : νe or νµ (cf. p. 70)✦ neutrino energy E✦ neutrino direction : gives the path

length.

March 13, 2013 (21)


TRAN Minh-Tâm


Atmospheric neutrinos at Super Kamiokande ✦ ✦

100

200

300

400

100

200

300

400

Saji, NOON2004

500

0

100

200

300

0

40

80

120

-1 -0.5 0 0.5 1

cos θ-1 -0.5 0 0.5 1

cos θ

-1 -0.5 0 0.5 1

cos θ-1 -0.5 0 0.5 1

cos θ-1 -0.5 0 0.5 1

cos θ

-1 -0.5 0 0.5 1

cos θ

Sub-GeV e-like

Multi-GeV e-like

Sub-GeV µ-like

Multi-GeV µ-like

Sub-GeV Multi-R

µ-like

Multi-GeV Multi-R

µ-like

2- flavour oscillations Best fit

Null oscillation

sin 2θ = 1.0

∆m = 2.0 10 eV

2

2 2−3

~12500 km ~500 km ~15 km

µ-like : induced by ν

e-like : induced by νµ

e

ν νµ τ

Well described by νµ → ντ ∆m2 = 2.2 × 10−3 eV2

sin2 2θ = 1.0Gonzalez-G NOON 2004

Confirmed by experiment using accelerator generated νµ (K2K).

March 13, 2013 (22)


TRAN Minh-Tâm


Another confirmation at CNGS

CERN has sent a beam of νµ of around 20 GeV to the laboratory of the Gran Sasso (Italy) 730km away.

After ≈ 3.52 1019 protons on target, OPERA, an experiment using emulsions at NGS lab,observe the first appearance (2010) of a τ lepton created by an charged current interaction of aντ in the dense matter of the emulsion, from a beam of νµ initially.

νµ → ντ during his flight to NGS labντ + nucleus → τ + X (τ track in red)

→ µν νThe number of ντ in the beam is negligible.

March 13, 2013 (23)


TRAN Minh-Tâm


Evidence for oscillation

Super-Kamiokande

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 10 102

103

104

L/E (km/GeV)

Da

ta/P

red

iction (

nu

ll osc.)

Neutrinos do know how far they have travelled !Time does matter to them ! ⇒ They do have masses !

March 13, 2013 (24)


TRAN Minh-Tâm



Other less compelling evidences for ν oscillations :

➣ Solar neutrinos



March 13, 2013 (25)


TRAN Minh-Tâm


Reactor experiments CHOOZ and PALO VERDE

Reactors can explore the sameL/E domain as atmospheric neutrinos.✦ L ∼ 1000 km → 1 km✦ E ∼ 1000 MeV → 1 MeVUse liquid scintillator to detect

νe + p → n + e+

e+ prompt signal and annihilation γn capture in Gadolinum gives8.1 MeV γ cascade

✦ CHOOZ (8.4 GWtherm)good agreement with NO-OSCILLATION expectation.Systematics dominated by under-standing of reactor ν.PLB 466 (1999) 415

✦ PALO VERDE (10.9 GWtherm)NO OSCILLATION SIGNAL either.

10-4

10-3

10-2

10-1

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

sin2(2 θ)

∆m2 (e

V2)

νe

→

νX

90% CL limit

CHOOZ

SK

νµ → νe excluded as source ofatmospheric neutrinos anomaly !

March 13, 2013 (26)


TRAN Minh-Tâm


The LSND positive results

✦ Location: LAMPF 800 MeV protonbeam (∼ 1mA) on beam stop.

✦ Detector: 167 tons of liquid scintilla-tor and oil, surrounded by phototubesat 30 m from beam stop.

✦ Experiment ran from 1993 to 1998,(Phys. Rev. D66 (2002) 013001)

Decay at rest :stopped π+ → νµ µ+

↪→ νµ νe e+If νµ → νe oscillation,the detection process is:

νe + p → e+ n followed byn + p → d + γ

Observe excess of νe .

sin 2θ2

22

∆m

(eV

)

LSND

1993 - 97 Data

Blue 90% conf.

Yellow 99%

ν νeµ

Osc. Prob. = (3.3± 0.9± 0.5)× 10−31 eV2 ≥ ∆m2 ≥ 1× 10−1 eV2

March 13, 2013 (27)


TRAN Minh-Tâm


The NOMAD experiment

✦ The observed motion of matter in galax-ies cannot be explained by the LUMINOUSmatter seen.

✦ Points to 10 times more matter (or other ex-otic component) than is actually seen.

✦ This “DARK MATTER” can be made upof non-zero mass RELIC NEUTRINOS.

✦ If relic neutrinos are distributed in haloaround galaxies : need an average mass of∼ 30 eV.

Distance (m)10 (m)

Velo

cit

y (

m/s

)

1.5 x 10 m/s

0

5

20

Newtonian motion

1/√ R

Observed

The NOMAD experiment was pro-posed in this context in 1992.

➣ Explore in the high ∆m2 > 10 eV 2 region➣ Use the CERN wide band νµ beam

〈E〉 ∼ 25 GeV➣ Mean νµ flight path : 620 meters➣ Search for appearance of ντ

via ντ CC interactions

March 13, 2013 (28)


TRAN Minh-Tâm


The NOMAD experiment

NOMAD is a counter experiment whichused :✦ Drift chambers (target and momen-

tum measurements) : 3 tons in a0.4 T magnetic field.

✦ Electromagnetic calorimeter and TRDfor electron ID

✦ Muons chambers

EXCELLENT track reconstructionability.

Use this property to define a SERIE OFCUTS each allowing a certain degree ofseparation to search for the appearance ofa ντ .

NO EVIDENCE for oscillation in allavailable decay modes of the τ .

BUT very nice physics results : di-muon

production, Λ polarization, sin2 θW .

10-1

1

10

102

103

10-4

10-3

10-2

10-1

1

sin2 2θ

∆m

2 (eV

2)

E531

CHARM II

CCFRNOMAD

CHORUS

CDHS

νµ → ν

τ

90% C.L.

1998

➣ Super Kamiokande observed νµ → ντoscillation with ∆m2 ∼ 2× 10−3 eV2

➣ Neutrinos contribute for littleto dark matter

TOO BAD ! WE HAVE LOOKED ATTHE WRONG REGION !

March 13, 2013 (29)


TRAN Minh-Tâm


Interpretation of the results

➣ How many neutrinos ?

➣ The preferred solution

➣ What next ?

March 13, 2013 (30)


TRAN Minh-Tâm


How many neutrinos ?

THREE effects need explanation

✦ LSND ⇒ ∆ m2 ≥ 1× 10− 1 eV2✦ Solar neutrinos ⇒ ∆ m2 ∼ 7× 10− 5 eV2✦ Atmospheric neutrinos ⇒ ∆ m2 ∼ 2.2× 10− 3 eV2

THREE known ν’s cannot accomodate three mass differences

✦ Either ONE observation is WRONG ... or

✦ More ν’s but these do not couple to Z0

otherwise LEP would have counted themMust be STERILE.

LSND is the only observation NOT CORROBORATED by another experiment.

Verification of this experiment is in progress at FermiLab (MiniBoone).

First results from MiniBoone published on April 11th 2007 !

March 13, 2013 (31)


TRAN Minh-Tâm





➣ What next ?

March 13, 2013 (32)


TRAN Minh-Tâm


The preferred solution ✦

IGNORE LSND in what follows ⇒ THREE FAMILY MIXING

νeνµντ

=

U11 U12 U13U21 U22 U23U31 U32 U33

ν1ν2ν3

Writing U as a product of 3 rotations :

U =

1 0 00 c23 s230 −s23 c23

︸︷︷︸

Atmospheric

c13 0 s13 eiδ

0 1 0−s13 e

iδ 0 c13

︸︷︷︸

Cross−mixing

c12 s12 0−s12 c12 0

0 0 1

︸︷︷︸

Solar

(Maki - Nakagawa - Sakata)

✦ s = sine and c = cosine

✦ θ12 : characteristic of SOLAR oscillations,

✦ θ23 : characteristic of ATMOSPHERIC oscillations,

✦ θ13: the missing link. Solar and Atmospheric oscillations decouple if θ13 = 0,

✦ δ : the CP phase. No CPv evidence if θ13 = 0 .

March 13, 2013 (33)


TRAN Minh-Tâm


The preferred solution ✦ ✦

GLOBAL FIT for 3 generation mixing

Best fit 3σ range

∆m212 7.1× 10−5 eV2 [ 5.2 , 9.8 ] 10−5 eV2tan2 θ12 0.42 [0.29 , 0.64]∆m223 2.4× 10−3 eV2 [ 1.4 , 3.4 ] 10−3 eV2tan2 θ23 1.0 [0.49 , 2.2]sin2 θ13 0.006 sin

2 θ13 < 0.054

Gonzalez-Garcia NOON 2004

✦ Maximum mixing of atmospheric neutrinos.

✦ sin2 θ13 small ⇒ solar and atmospheric oscillations almost decoupled.✦ Consequences : Recall : fraction of flavour α in state i is | Uαi |2

● Fraction of νe in ν3 = | U13 |2 = sin2 θ13 is small and will be neglected.● Fraction of νe in ν2 = Psolar(νe → νe) = | sin θ12 |2 = | 〈νe | ν2〉 |2'

1

3(SNO results).

● Fraction of νe in ν1 = 1 −1

3● ν3 composed by 50% νµ and 50% ντ (50% = c

223 = s

223).

● νµ and ντ contents in ν1 and ν2 are in the same ratio ( = s212/c

212).

March 13, 2013 (34)


TRAN Minh-Tâm


The preferred solution ✦ ✦ ✦

ν

ν

1

ν3

2∆msol2

∆matm2

ντ

νµ

νe

Upper limit

from ChoozFrom max. mixing

of atmospheric ν

mν2

P (ν ν ) =

fraction of ν in ν

solar e

e

e

2

From max. mixing

of atmospheric ν

equal prop of ν

and ν in ν and νµ

τ

:

1 2

sin θ213

cos sin22 θ23θ13

cos cos22 θ23θ13

Is the solar pair of ν at the bottom (normal hierarchy) or at the top (invertedhierarchy) of the spectrum ? Depends on sign of ∆m213 ∼ ∆m

223 ∼ ∆m

2atm

March 13, 2013 (35)


TRAN Minh-Tâm





➣ What next ?➣ Check the LSND result

March 13, 2013 (36)


TRAN Minh-Tâm


Checking the LSND results

Need a decisive answer at 5σ !

MiniBooNE experiment at FermiLab.

769 Tons of Liquid Sc.

6 m radius tankInner sphere : 1220 PMTʼs

Outer shell : 269 PMTʼs

✦ Low energy (1 - 2 GeV) νµ beam✦ Low νe contamination ' 0.3 %✦ Detector distance : 500 m.✦ Look for excess of νe from νµ → νe

oscillations.

RESULTS published on April 11 2007!

Blue is LSND

90% Conf.

Yellow 99%

BNL 776

CCFR

MiniBooNE

KARMEN

NOMAD

(Preliminary)

ν ↔ νe µ

sin 2θ2

22

∆m

(

eV

)

110-1

10-2

10-310

-4

10-3

10-2

10-1

1

10

102

103

Chooz

Bugey III

Numbers are expected excess of νe in1 year of running if LSND is correct.

March 13, 2013 (37)


TRAN Minh-Tâm


Checking the LSND results

Excess only at low energy.Shape not consistent with 2ν oscillations.

LSND was a νµ → νe appearanceexperiment !

MiniBooNE νµ → νeappears to confirm LSND results(September 2010)

(3+1) oscillation ?All (3+N) models predict large νµdisappearance.

http://www-boone.fnal.gov/index.html

March 13, 2013 (38)


TRAN Minh-Tâm


What next ?

THE NEXT STEPS :

➣ In pursuit of θ13

➣ Determination of δ and the mass hierarchy

➣ Determination of the absolute scale

March 13, 2013 (39)


TRAN Minh-Tâm


What next ? Determination of θ13 ✦

CP violation and our ability to determine the sign of ∆mdepend on sinθ13 ⇒ measure it a.s.a.p.

ν

ν

1

ν3

2∆msol

2

∆matm

2mν

2

sin θ213

✦ sinθ13 is the small νe piece of ν3.✦ ν3 is at one end of ∆m

2atm.

TEMPORARY approximation

∆m212 = m22 −m21 is small and ≈ 0

⇒ ∆m223 = ∆m213 = ∆m2

νµ → ντ

Pµτ = 4(s23c23c213)

2 sin2(

1.27L ∆m2

E

)

cos θ13 ≈ 1 ⇒ νµ → ντ does nothave much sensitivity to θ13

νµ → νe

Pµe = 4(s23c13s13)2 sin2

(1.27L ∆m2

E

)

sin θ13 very sensitive to θ13 !

Need an experiment with

✦ L/E sensitive to ∆m2atm, ✦ involvement of νe.

March 13, 2013 (40)


TRAN Minh-Tâm


What next ? Determination of θ13 ✦ ✦

Select energy and distance to be at sin2(

1.27 ∆223 LE

)

maximum.

L/E ≈ 400 − 500 km/GeVTwo possibilities

Reactor experiments :νe disappearanceL ' 1.5 kmProposals for experiments at✦ Kashiwazaki (24.3 GW),✦ Double-CHOOZ (8.5 GW),✦ Daya Bay (6 × 2.9 GW).Use far and near detector to reduce sys-tematics to ≤ 1% and sensitivity tosin2 2θ expected to be 7 to 10 times betterthan CHOOZ (sin2 2θ13 < 0.1).

Accelerator experiments :νe appearance from a νµ beamL > several hundreds of km

✦ Use low energy, narrow band beams

at sin2(

1.27∆223

L

E

)

maximum.

✦ Advantage :➣ NO charged current of νµ ,➣ less high energy neutral currentinteractions.

✦ νe appearance will then be maxi-mum.

✦ Detectors optimized for νe detec-tion.

March 13, 2013 (41)


TRAN Minh-Tâm


What next ? Determination of θ13 in reactor experiment: Daya Bay

6 Nuclear Power plants of 2.9 GW thermGuang Dong province, near Hong Kong3 Near detectors and 3 Far detectorsgrouped in 3 locations (2 near, 1 far)Far detectors positioned close to oscilla-tion maximumDetection : νe + p → e+ + n in Gddoped liquid scintillator.

Measured over expected (no oscillation) signal.Reactor and survey data are used to computeflux-weighted baselines.

Results

Deduce :

sin2 2θ13 = 0.092 ± 0.016 ± 0.005

arXiv:1203.1669v1 [hep-ex] 8 March 2012

March 13, 2013 (42)


TRAN Minh-Tâm


What next ? Determination of θ13 in accelerator experiments ✦

➣ OFF-AXIS SUPER BEAMS

〈Eν〉 L L/E[GeV] [km] [km/GeV]

T2K 0.7 295 421NOνA 2.0 810 405

J-PARK to SK (T2K) :new hadron facilty at Tokai,0.77 MW source of 50 GeV protons.νµ beam line to Kamioka (295 km).ν’s energy < 1 GeV (2o off axis).νe contamination of < 0.5%.Expect to start data taking in 2009.Sensitivity to θ13 10 times past CHOOZlimits in 5 years.

NuMi Off axis (NOνA) : earth surfacedetector at Ash River (Minnesota); use“OFF AXIS” ν’s from FermiLab (∼ 810km baseline, ∼ 12 km off axis).Narrow band νµ’s of a few GeV,low (0.5%) νe contamination,pulsed beam ⇒ timing to reject back-ground.Factor x10 more sensitivity in νµ → νethan MINOSConstruction completed in January 2014

March 13, 2013 (43)


TRAN Minh-Tâm


What next ? Determination of θ13 in accelerator experiments ✦ ✦

✦ T2K will use H2O-Cherenkov detectoras quasi-elastic interactions favouredat E ≤ 1 GeV.

● start with present 50 kT Super-K,● upgrade to 1 MT Hyper-K,

mainly for proton decay.

✦ NOνA will use liquid scintillator en-cased in Ti-loaded PVC cells; read-outwith APD (30 kTons).The detector isoptimized to reject π0 from electronsat Eν > 1 GeV.

✦ Matter effect will be more importantfor NOνA (30%) than for T2K (10%).

✦ A single experiment will NOT be ableto separate matter effect from CP vio-lation terms (see following transaprencies).

Experiments at Gran Sasso will NOThave the adequate sensitivity.

90% C.L. SENSITIVITY ON θ13

MINOS with

25, 16 and 7.4 x 10 p.o.t20

CHOOZ

∆m

(e

V )

23

22

NoνA

K. Nishikawa Lepton-Photon 2003

NOνA sin2 2θ13 sensitivity : ' 1× 10−2T2K sin2 2θ13 sensitivity : ' 6× 10−3

March 13, 2013 (44)


TRAN Minh-Tâm


The T2K experiment ✦

Aim : discovery of νµ → νe in an “appearance” experiment

✦ Determine θ13, last unknown mixing angle

Pµe ≈ 4(s23c13s13)2 sin2(

1.27L ∆m2

E

)

sin2 2θ13 < 0.15 at 90 % C.L. (Chooz and MINOS)

✦ Open a possibility to measure CP violation in lepton sector.CPV term in Pµe ∝ s12s13s23sin δ

• T2K design principle :

• Super-Kamiokande (SK) as far neutrino detector

March 13, 2013 (45)


TRAN Minh-Tâm


The T2K experiment ✦ ✦

Super-Kamiokande (SK) as far neutrino detector✦ Excellent performance for single particle event

● νe + n → e + p is the CCQE T2K νe signal

● this kind of event dominates at sub GeV energy

✦ ⇒ reduce high energy tail to reduce background⇒ need high intensity⇒ Use “off-axis” ν beam (see backup slides)

March 13, 2013 (46)


TRAN Minh-Tâm


The T2K experiment ✦ ✦ ✦

Charged Current Quasi-elastic (CCQE) interactions dominateat sub GeV

CCQE : νe(µ) + n → e(µ) + p(T2K signal)

ν interactions at “high energy” causebackground events in T2K, for example :

NC 1π0 is one of the background to theT2K signal.

➣ reduce high energy ν by usingoff axis ν beam(see back-up slide)

ν ν

ν

ν

µ

ππppp

e

CCQE CC1π NC1π

March 13, 2013 (47)


TRAN Minh-Tâm


νe selection

νe selection criteria

✦ signal = single electron eventoscillated νe interaction CCQE :νe + n→ e + p

✦ background● intinsic νe in beam (µ, K decays)● π0 from Neutral current interaction

Selection cuts

1. T2K beam timing and fully containedevent

2. In fiducial volume (no activity outside)3. Single electron4. Visible electron energy > 100 MeV5. No delayed electron (use timing)6. Reconstructed mass < 105 MeV/c2

(reject NC π0)7. Reconstructed energy < 1250 MeV

∆T0 = TGPS@SK − TGPS@JPARC − TOF (∼985µs)

Erec =mnEe −m2e/2− (m2n −m2p)/2

mn − Ee + pe cos θeRejects intrinsic beam background at high en-ergy

March 13, 2013 (48)


TRAN Minh-Tâm


Expected number of events at SK

NexpSK = Rµ,DataND ×

MMCSK

Rµ,MCND

Rµ,DataND : Near detector νµ event rateMMC

SK

Rµ,MCND: Far/Near ratio from MC

Near detector event rate :

Measure the number of inclusive νµ CC events in Near Detector per p.o.t.

Near Detector data consistent with

✦ MC based on NA61 results on νe,µ production

✦ νe,µ interaction simulation

Far/Near ratio : depends on

(flux) × (osc. probability) × (cross-section) × (efficiency) × (detector mass)Can predict the number of events for sin2 2θ13 = 0 for 1.43 × 1020 p.o.t.

N expSK tot. = 1.5 events

Beam νe bkg : 0.8 NC bkg : 0.6 Oscillated νµ → νe (solar term) : 0.11st term : estimation from beam contamination by νe, 2

nd term : calculated from formula

of top page with MMCSK NC, bkg , 3rd term : from solar oscillation.

March 13, 2013 (49)


TRAN Minh-Tâm


T2K Results

Reconstructed ν energyObserved number of events : 6Expected 1.5 ± 0.3 with sin2 2θ13 = 0If sin2 2θ13 = 0, the probability to ob-serve 6 (or more) events is0.007 (≡ 2.5σ)

• 0.03 < sin2 2θ13 < 0.28(normal hierarchy)• 0.04 < sin2 2θ13 < 0.24(inverted hierarchy)

Assuming sin2 2θ23 = 1, δCP = 0

and ∆m223

= 2.4 × 10−3 eV2.

March 13, 2013 (50)


TRAN Minh-Tâm


What next ?

THE NEXT STEPS :

➣ Determination of θ13



March 13, 2013 (51)


TRAN Minh-Tâm


P (νµ → νe) in vacuum

FULL expression

With ∆m212 = m22 −m21 small and ∆m223 ∼ ∆m213 = m23 −m21

Pvac(νµ(νµ)→ νe(νe)) = sin2 2θ13 s223 sin2(

1.27L ∆m213E

)

−12

s212 sin2 2θ13 s

223

(1.27L ∆m212

E

)

sin

(1.27L ∆m213

E

)

+2 Jr cos δ

(1.27L ∆m212

E

)

sin

(1.27L ∆m213

E

)

∓4 Jr sin δ(

1.27L ∆m212E

)

sin2(

1.27L ∆m213E

)

with Jr = c12s12c213s13c23s23, + sign for ν oscillations, − for ν’s.

Under simultaneous transformations δ → π − δ and ∆m213 → −∆m213 ,

all terms are invariant, except the second one which is small.

➣ Probability almost degenerated for two values of δ unless oneknows a priori the sign of ∆m213 (mass hierarchy).

March 13, 2013 (52)


TRAN Minh-Tâm


P (νµ → νe) in matter ✦

Back to 2 flavours oscillation for sake of clarity.

In matter P (νµ → νe) should be enhanced, i.e.more νe detected compared to vacuum case.

ν1

ν2

ν1m

ν2m

νe

νµ

Start with a ν2 states and evolve this ν2 throughearth crust to the detector.(This is the “regeneration” effect searched for insolar ν experiments)

For νe the matter effect (page 15) leads to anamplitude of elastic scattering with matter whichhas the opposite sign compared to νe’s : the po-tential term VW goes ±

√2 GF Ne (− for νe).

This results in less P (νµ → νe).

In matter, the first term in the expressionp. 52 will be approximately mutiplied by

(

1 ± 2 EER

)

and the third and fourth terms by(

1 ± EER

)

The second term is small.

The + sign is for ν and − is for ν.

With ER =∆m213

2√

2 GF ρe, the degeneracy

is lifted as Pmatter is not invariant underflipping the sign of ∆m213.

Conclusion : Measure P (νµ → νe) andP (νµ → νe) in matter (earth crust).

March 13, 2013 (53)


TRAN Minh-Tâm


minhtamtranRectangle

minhtamtranLégendesee page 16

P (νµ → νe) in matter ✦ ✦

P (νµ → νe) and P (νµ → νe) evolution in bi-probability space:

0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6

(%) (%)

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6<

P(ν

)> (

%)

< Eν>=1.5GeV < E

ν>=0.5GeV

CP + matter, ∆m > 013

2

CP + matter, ∆m < 013

2

CP, ∆m > 013

2

CP, ∆m < 013

2

δ = 0

δ = π/2δ = πδ = 3π/2

L = 700 km L = 295 km

0.6 1 .0 1.4 1 .8 2.2 2 .60.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

Note smallness of the probability values and possible false CP violating effects !!

NOνA will aim at sin2 2θ13 = 0.01 (present limit/10) and will have a modestsensitivity in the determination of the mass hierarchy.

March 13, 2013 (54)


TRAN Minh-Tâm


minhtamtranZone de texte Will start taking data with partial detector in May 2013

Future plans ✦

In the USA

✦ Cancellation of BTeV✦ End of Babar operation < 2010

➣ Changes in prospect for NOνA➣ Strong support for NOνA (> 2010)

Proton Driver ⇒ 6.5×1020 protons/yrtogether with large off-axis detector

➣ Determine whether spectrum isnormal or inverted

➣ Observe CP violationfor sin2 2θ13 > 0.02

➣ Separate CP violation frommatter effect together with T2K

Superconducting Proton LinacThe CERN-Fréjus Project

Classical accelerator νµ beam.⇒ Intrinsic νe component results in abackground✦ Power : 4 MW Energy : up to 5 GeV✦ Target : liquid Hg jet✦ Detector : new lab in Fréjus, 130 km

March 13, 2013 (55)


TRAN Minh-Tâm


Future plans ✦ ✦

β beams

✦ Accelerate protons in SPL and impingeon appropriate source

✦ Ions produced by n from spalation✦ Accelerate radioactive ions decaying

via β+ (Ne18) or β− (He6) in PS andSPS

✦ Bunch resulting ions to avoid atmo-spheric ν’s

✦ Store ions in decay rings✦ No νµ or νµ contamination✦ Lorentz boost ⇒ νe νe focussed

forward in a narrow beam✦ Look for appearance of νµ or νµ using

CC interactions : µ− or µ+ produced✦ Use Eurisol (NP facility using radioac-

tive ions) at CERN✦ Detector : same as for SPL (Fréjus)

New idea : use Electron captureto get monoenergetic ν’s.

J. Bernabeu et C. Espinoza hep-ph/0605132

(A, Z) + e− → (A, Z − 1) + νefor instance Dy150 t1/2 = 7.2 mnDy ions not fully stripped⇒ differentapproach of acceleration + storage.

March 13, 2013 (56)


TRAN Minh-Tâm


Future plans ✦ ✦ ✦

Neutrino FactoriesBeautifully nice idea

Store µ in ring with long straight sectionsPosition ν detectors in line with straightsections and observe ν from µ decays.✦ Stored muons have a single sign, e.g.

µ+ → e+ νµ νe✦ νµ interactions give µ

+

✦ νe → νµ oscillations give µ−

i.e. wrong sign muon✦ Need a magnetic detector

to measure the muon charge.Need :✵ Large acceptance solenoid to

collect pions✵ Momentum cooling of muons as they

have broad spectra in longitudinaland transverse momenta.

Simplified Neutrino Factory

✦ Proton accelerator 5 to 15 GeV1016 p/s

✦ Pion production target : baseline isMercury

✦ Pion to muon decay and beam cool-ing : baseline is 50 m1.2× 1014 µ/s = 1.2× 1021 µ/yr

✦ Muon accelerator : no decision yet✦ Muon to neutrino decay ring : choice

is site dependent 9× 1020 µ/yr

Neutrino sent to detectors far away.

March 13, 2013 (57)


TRAN Minh-Tâm


Future plans ✦ ✦ ✦ ✦

Comparison of beta-beam and ν factory

Beta-beam advantages✦ Synergy with Eurisol and existing PS

and SPS if at CERN✦ Clean νe and νe beams✦ No need for an analyzing magnet (look

for muons only)✦ Negligible matter effects (low energy).

Beta-beam disadvantages✦ Low energy :

● Cross sections not so well known● Atmospheric neutrinos background

(atmospheric neutrino cannot be prevented

as no timing possible in the decay of ra-

dioactive ion)

✦ Need of SPL.

Advantages of a Neutrino factory✦ Presence of both νµ and νe in beam

allows measurement of cross sectionin near detector

✦ Higher energies : better measuredcross sections

✦ Atmospheric neutrino backgroundcan be mastered.

Disadvantages of a Neutrino factory✦ Technically more challenging✦ High energy : matter effect must be

well understood✦ Need for a magnetic detector to sep-

arate signal from background.

March 13, 2013 (58)


TRAN Minh-Tâm


What next ?

THE NEXT STEPS :

➣ Determination of θ13



March 13, 2013 (59)


TRAN Minh-Tâm


Setting the absolute mass scale ✦

KATRIN : end point of Tritium β decay spectrum ⇒ detect mass down tomi ≥ 0.2 eV/c2.∆m2LSND ' 10−1 eV2/c4 ⇒ this νi can be within range of KATRIN if this νicouples to νe. Due to start in 2012. (see www-ik.fzk.de/tritium/ )

If mν 6= 0 the max. possible energy car-ried by the electron will be reduced.

✦ The β electrons are guided adiabatically

✦ ~B field transforms them into a parallel beam.

✦ Electrostatic potential U selects Eβ > qU

March 13, 2013 (60)


TRAN Minh-Tâm


minhtamtranLégendeLes électrons doivent remonter le champ E: seuls ceux qui ont une vitesse suffisante peuvent continuer et être détectés, les autres sont réfléchis.

Setting the absolute mass scale ✦ ✦

Absolute neutrino mass from Super Nova SN 1987A

About 20 neutrino interactions seen mostly in Kamiokande

Time of arrival distribution gives limit on ν mass

But : uncertainty in emission time distribution.

March 13, 2013 (61)


TRAN Minh-Tâm


Setting the absolute mass scale ✦ ✦ ✦

A CONNECTION WITH COSMOLOGY

✦ Recent CMB data from WMAP allows to set∑

i

mi ≈ 1 eV/c2

(J. Lesgourges and S. Pastor, Phys. Rept. 429 (2006) 307 ).⇒ upper limits within reach!

✦ One ν has mass of at least√

∆m223 =√

2.1× 10−3 ' 0.05 eV/c2.✦ For 3 ν : 0.05 eV/c2

︸︷︷︸√∆m2

23

< Mass of heaviest νi < 0.7 eV/c2

︸︷︷︸

COSMOLOGY

✦ Structures evolve since the Big Bang : they get bigger

✦ If neutrinos have mass, because they stream freely, they will not be trapped ina gravitation well.

✦ This means that they will not contribute their mass to the gravitationalattraction forming clusters.

✦ They will start to do so as they become non relativistic

✦ The larger their mass, the earlier they become non relativistic as Universecools ⇒ in this case, they affect small clusters.

March 13, 2013 (62)


TRAN Minh-Tâm


minhtamtranLégendeThey cool down and get trapped

Another issue

ANOTHER ISSUE :

➣ Dirac or Majorana ?

The next major question the

community wants an answer on

March 13, 2013 (63)


TRAN Minh-Tâm


Dirac ν versus Majorana ν

Neutrino having mass means :

✦ There exists a right-handed partner νright or

✦ The ν are their own antiparticle (Majorana) : ν is the right-handed partner.

Dirac neutrinos ν 6= νν has negative helicityν has positive helicity.

ν with positive helicity Do notν with negative helicity exist.Lepton number is conservedπ+ → µ+νµ then

νµ + Nucl. → µ− + hadronsπ− → µ− νµ then

νµ + Nucl. → µ+ + hadrons

Majorana neutrinos ν ≡ νTwo opposite helicity states of the sameparticle ν, interacting differently withmatter.

Lepton number is not conservedπ+ → µ+←−ν µ then←−ν µ + Nucl. → µ− + hadronsπ− → µ−−→ν µ then−→ν µ + Nucl. → µ+ + hadrons

Thought experiment : Reverse the helicity and study interaction !π+ → µ+←−ν µ Reverse helicity and obtain −→ν µ

Dirac : this −→ν µ does not interact Majorana : −→ν µ + Nucl. → µ+ + hadrons

March 13, 2013 (64)


TRAN Minh-Tâm


Neutrinoless double-β decay

(A,Z) → (A,Z + 2) + e− + e−

Lepton number NOT conserved ⇒ Not possible for Dirac ν.

n p

n p

e-

e-

Dirac :

Majorana :

n p e ν

n p e ν, ν has mostly positive helicity

Dirac :

Majorana : ν n e p ,

ν must have negative helicity

ν n e p

0ν2β only possible if Majorana ν produced with negative helicity.Probability for this is ∝ m2ν/E2Observation of 0ν2β decay : evidence for Majorana ν with mν > 0.

If mν = 0, no way to distinguish between Dirac and Majorana ν.

March 13, 2013 (65)


TRAN Minh-Tâm


Limits on Neutrinoless double-β decay

Rate(2β0ν) = Phase space factor × (Matrix element)2 × 〈mee〉2

Recall :

νeνµντ

=

Ue1 Ue2 Ue3Uµ1 Uµ2 Uµ3Uτ1 Uτ2 Uτ3

ν1ν2ν3

〈mee〉 = |Ue1|2 m1 + |Ue2|

2 m2 + |Ue3|2 m3

✦ Normal hierarchy : m3 > m1,2but Ue,3 is small, so large mass multi-plied by very small U ⇒ small mee

✦ Inverted hierarchy : m1,2 > m3larger Uei multiplied by large m1,2⇒ large mee

✦ Degenerated : all 3 masses are ap-prox. the same ⇒ No difference be-tween normal and inverted

March 13, 2013 (66)


TRAN Minh-Tâm


➣ CONCLUSIONS

Neutrinos do change flavour

and, therefore, have mass !

March 13, 2013 (67)


TRAN Minh-Tâm


Conclusions : Neutrinos do change flavor !

✦ We know two mass differences but not the absolute scale.

✦ We know two mixing angles :• solar and reactor data → θ12 • atmospheric ν data → θ23.

✦ θ13, the missing link, is still to be determined.

✦ δ, the CP phase, and the mass hierarchy are still to bedetermined.

✦ We know now that there are 3 ν species (MiniBoone 2007).

✦ Main effort to determine sin θ13 in the near future ( → 2013, 2014).✦ Many mid and long term ideas : NuMI ON and Off-axis, J-PARK

to SK, Reactor experiments, large off-axis detector with protondriver, neutrino factory, β beams...

✦ We do not know if neutrinos are Dirac or Majorana

(⇒ wait for 0ν2β) , nor their mass generation mechanism (whichmight be very different from the quark sector one).

March 13, 2013 (68)


TRAN Minh-Tâm


➣ BACKUP SLIDES

March 13, 2013 (69)


TRAN Minh-Tâm


Backup : Four neutrino mass spectra

With four neutrinos, one can have the following mass2 spectra :

solar

∆m2

atm.∆m2

solar∆m2

atm.∆m2

LSND∆m2

LSND∆m2(m

ass)2

2 + 2 spectrum 3 + 1 spectrum

In the “2 + 2” scenario, the two “solar” and “atmospheric” pairs are separatedby the large ∆m2LSND ' 1 eV2 .Recent analyses conclude that this scenario is incompatible with data.


In the “3 + 1” scenario, essentially all the sterile flavour can be placed in thethe isolated neutrino and its mass eigenstate driven by LSND result.

3 + 1 still marginal at 99% CL with ∆m2LSND < 4.3 eV2


Primordial Nucleosynthesis excludes active-sterile oscillations (astro-ph/0108341).

March 13, 2013 (70)


TRAN Minh-Tâm


Backup : Particle ID in SK water Cherenkov (2 GeV)

Courtesy Mark Messier

March 13, 2013 (71)


TRAN Minh-Tâm


Backup : Why do we favour an off-axis experiment ?

ν’s are produced from π → µ ν decays Eν =0.43Eπ

1 + γπ θ2

0 10 20 30 40

14

12

10

8

6

4

2

0 E (GeV)π

E (

GeV

)ν

0 mrad

5 mrad

10 mrad

15 mrad

20 mrad

✦ On axis ν’s energy is proportionnal to pion energy

✦ Off axis ν’s energy is almost INDEPENDENT of Eπ⇒ know at which energy to expect νe CC from νµ → νe oscillations.

✦ Low (< 1%) νe contamination.

March 13, 2013 (72)


TRAN Minh-Tâm


Backup : Thought experiment

Thought experiment : Reverse the helicity and study interaction !π+ → µ+←−ν µ Reverse helicity and obtain −→ν µ

Dirac : −→ν µ does not interact Majorana : −→ν µ + Nucl. → µ+ + hadrons

To reverse the helicity, need βπ (lab) > βν (π rest frame)

βπ (lab) >p?

√

p? 2 + m2ν' 1

2

(1

2+

m2νm2π

)− 12

⇒ pπ (lab) > 103 TeV for mν = 0.5 eV/c2

March 13, 2013 (74)


TRAN Minh-Tâm


Backup : Normal and inverted hierarchy

νeνµντ

=

Ue1 Ue2 Ue3Uµ1 Uµ2 Uµ3Uτ1 Uτ2 Uτ3

ν1ν2ν3

(U) =

c12 c13 s12 c13 s13 e−iδ

−s12 c23 − c12 s23 s13 e−iδ c12 c23 − s12 s23 s13 e−iδ s23 c13s12 c23 − c12 c23 s13 e−iδ −c12 s23 − s12 c23 s13 e−iδ c23 c13

ν

ν

1

ν 3

2 ∆m

122

∆m = 7.1 x 10 eV122

∆m2

∆m 232

∆m = 2.4 x 10 eV 232

ν

ν

1

ν3

2

m ν

2

sin θ 2 13

12

232

∆m

2

2

-3

-5

Normal Hierarchy Inverted Hierarchy

March 13, 2013 (75)


TRAN Minh-Tâm


Introduction. Experimental evidences towards oscillations....

Documents

Transcript of Introduction. Experimental evidences towards oscillations....