NEUTRINO OSCILLATIONSLuigi DiLella

Physics Dept. and INFN, Pisa, Italy

CHIPP PhD Winter School 2011

Formalism of neutrino oscillations in vacuum Solar neutrinos Neutrino oscillations in matter The KAMLAND reactor experiment “Atmospheric” neutrinos The Chooz reactor experiment Long baseline oscillation searches at accelerators

Future projects: measurement of the 13 mixing angle

Puzzling results: LSND and MiniBooNE experiments

Hypothesis: neutrino mixing(Pontecorvo 1958; Maki, Nakagawa, Sakata 1962)

e are not mass eigenstates but linear superpositions

of mass eigenstates 1 2 3 with eigenvalues m1 m2 m3

i

iiU

ii V

e(flavour index) i 1, 2, 3 (mass index )

Ui : unitary mixing matrix

*)( ii UV

Neutrino oscillations in vacuum

Time evolution of a neutrino with momentum p produced in the flavour eigenstate at time t = 0

kk

tiEk

i keUet rp)( )0(Note:

22kk mpE the complex phases

tiEkeare different if mj mk

appearance of new flavour at time t > 0Example for two – neutrino mixing

mixing angle

If at production (t = 0):

2

)(

1

)( sincos)( 121 tEEitEi eet rp

21sincos

21cossin

For m << pp

mpmpE

2

222

E

m

E

mm

p

mmEE

222

221

22

21

22

12

(in vacuum!)

Probability to detect at time t if (0) = :

1c

m2 m22 – m1

2

Using units more familiar to experimentalists:

E

LmL 222 267.1sin)2(sin)( P

Units: m2 [eV2]; L [km]; E [GeV] (or L [m]; E [MeV])

L = ct distance between neutrino source and detector

NOTE: P depends on m (not on m).

If m << m , m m m m

E

tmtt

4sin)2(sin)()(

222

2 P

Definition of oscillation length :

248.2

m

E

Units: [km]; E [GeV]; m2 [eV2] (or [m]; E [MeV])

LL 22 sin)2(sin)(P

Distance between neutrino source and detector

sin2(2)

m m

and/or m > m

Disappearance experiments

Use source, measure flux at distance L from source

PP 1Disappearance probability

The main source of systematic uncertainties: knowledge of the neutrino flux in the absence of oscillations use two detectors if possible

source Near detector:measureflux

Far detector :

measure P

beam

Examples:

Experiments using e from nuclear reactors

(E few MeV: under threshold for or production)

detection at accelerators or in the cosmic radiation

(search for oscillations if Elower than production threshold)

Appearance experiments

Neutrino source: . Detect at distance L from

source Examples:

Detect e + N e- + hadrons in a beam

Detect + N - + hadrons in a beam (Threshold energy 3.5 GeV)

The contamination at source must be precisely known

(typically e/ 1% in beams from high-energy accelerators)

→ a near detector is often very useful

log(m

2 )

sin2(2)0 1

Under the hypothesis of two – neutrino mixing: Observation of an oscillation signal allowed parameter region in the [m , sin()] plane consistent with the observed signal

No evidence for oscillation upper limit P< P exclusion region

Very large m very short oscillation length average over source and detector dimensions:

)2(sin2

1)(sin)2(sin)( 222

LLP

small m long : L<<

LL)sin(

2

222 )2(sin6.1

E

LmP P

(onset of the first oscillation)

248.2

m

E

source Flavour Distance L Energy Min. accessible m2

Sun e ~1.5x108 km 0.2-15 MeV ~1011 eV2

Cosmic rays e e

10 – 13000 km

0.2 – 100 GeV

~104 eV2

Nuclear reactors

e 20m – 250 km <E> ≈ 3 MeV ~106 eV2

Accelerators e e

15m – 730 km20 MeV – 100 GeV

~103 eV2

Searches for neutrino oscillations:experimental parameters

EXPERIMENTAL EVIDENCE / HINTSFOR NEUTRINO OSCILLATIONS

Solar neutrino deficit: e disappearance between Sun and Earth Convincing experimental evidence Confirmation from a nuclear reactor experiment Measurement of the oscillation parameters

“Atmospheric” neutrino deficit: disappearance in the cosmic radiation over distances of the order of the Earth diameter Convincing experimental evidence Confirmation from long baseline accelerator experiments Measurement of the oscillation parameters

LSND experiment at Los Alamos (1996): e excess in a mixed

, e beam To be confirmed – experimental results from the MiniBoone experiment at Fermilab (designed to verify LSND) unclear and confusing

Birth of a star: gravitational contraction of a primordial gas cloud

(mainly H, He) density, temperature increase

in the star core NUCLEAR FUSIONHydrostatic equilibrium between pressure and gravity

Final result from a chain of fusion reactions in the Sun core:

p He + e+ + e

Average energy produced as electromagnetic energy in the Sun core:

Q = (Mp – MHe + me)c – <E(e)> MeV

( e+ + e– )(<E(2e)> MeV)

Solar luminosity: L = x W = x MeV/s

Neutrino emission rate: dN(e)/dt = L/Q x s

Average neutrino flux on Earth: e x cm s

(average Sun Earth distance = x m)

Solar neutrinos

STANDARD SOLAR MODEL (SSM)(developed in 1960 and continuously updated by J.N. Bahcall and collaborators)

Assumptions: hydrostatic equilibrium energy production by nuclear fusion thermal equilibrium (power output = luminosity) energy transport inside the Sun by radiation

Input data: cross-sections for fusion reactions “opacity” (photon mean free path) as a function of distance from the Sun center

Method:

choice of initial parameters evolution to present epoch (t = xyears) compare predicted and measured quantities modify initial parameters if necessary

TODAY’S SUN: Luminosity L = x W Radius R = x m Mass M = x kg

Core temperature Tc = x K

Surface temperature Ts = K

Hydrogen in Sun core = (initially ) Helium in Sun core = . (initially )

as measured at the surface

p – p cycle ( L)

p + p e+ + e + d p + p e+ + e + d OR (): p + e– + p e + dp + d + He3 p + d + He3

He3 + He3 He4 + p + p OR (x): He3 + p He4 + e+ + e

p + p e+ + e + dp + d + He3

He3 + He4 + Be7 p + Be7 + B8 e– + Be7 e + Li7 B8 Be8 + e+ + e

p + Li7 He4 + He4 Be8 He4 + He4

OR ()

CNO cycle (two branches)

p + N15 C12 + He4 p + N15 + O16

p + C12 + N13 p + O16 + F17

N13 C13 + e+ + e F17 O17 + e+ + e

p + C13 + N14 p + O17 N14 + He4

p + N14 + O15

O15 N15 + e+ + e

NOTE #: for both cycles p He + e+ + e

NOTE #: source of today’s solar luminosity: fusion reactions occurringIn the Sun core ~ years ago (the Sun is a “main sequence star,practically stable over ~108 years).

Two reaction cycles

Predicted solar neutrino flux and energy spectrum on Earth (p p cycle)M

ono-

ener

geti

c l i

nes

: cm

-2 s

-1

Con

tin

uou

s sp

ectr

a: c

m-2 s

-1 M

eV -1

Notationspp : p + p e+ + e + d7Be : e– + Be7 e + Li7

pep : p + e– + p e + d8B : B8 Be8 + e+ + e

hep : He3 + p He4 + e+ + e

Predicted radial distribution of e production in the Sun core

SNU (Solar Neutrino Units): the unit tomeasure event rates in radiochemicalexperiments:1 SNU = 1 event s–1 per 1036 target atomsAverage of all measurements:R(Cl 37) = 2.56 0.16 0.16 SNU (stat) (syst)

SSM prediction: 7.6 SNU

The Homestake experiment (1970–1998): first detection of solar neutrinos A radiochemical experiment (R. Davis, University of Pennsylvania)

e + Cl 37 e– + Ar 37 Energy threshold E(e) = 0.814 MeV

Detector: 390 m3 C2Cl4 (perchloroethylene) in a tank installed in the Homestake

gold mine (South Dakota, U.S.A.) under 4100 m water equivalent (m w.e.)(fraction of Cl 37 in natural Chlorine = 24%)Expected production rate of Ar 37 atoms 1.5 per dayExperimental method: every few months extract Ar 37 by N2 flow through tank,

purify, mix with natural Argon, fill a small proportional counter, detect radioactive

decay of Ar 37: e– + Ar 37 e + Cl 37 (half-life 1/2 = 34 d)

(Final state excited Cl 37 atom emits Augier electrons and/or X-rays)Check efficiencies by injecting known quantities of Ar 37 into tankResults over more than 20 years of data taking

+1.3 –1.1

SolarNeutrinoDeficit

Two experiments: Kamiokande ()Fiducial volume: mHOSuper-Kamiokande ()Fiducial volume: mHOin theKamioka mine (Japan)

Depth m HO eq.

cossun

The signal solar origin is demonstratedby the angular correlation betweenthe directions of the detected electronand the incident neutrino

~15 events / dayIn the peak

“Real time” experiments with water Čerenkov counters

Neutrino – electron elastic scattering: + e– + e–

Detect Čerenkov light emitted by electrons in waterEnergy threshold ~MeV (5 MeV electron residual range in HO cm)

Cross-sections: (e) 6 () 6 ()

W , Z exchange Z exchange only

(all threetypes)

Z

e(e only)

e e

W

e e

Super-Kamiokande detector

Cylinder, height=41.4 m, diam.=39.3 m50 000 tons of pure waterOuter volume (veto) ~2.7 m thickInner volume: ~ 32000 tons (fiducialmass 22500 tons)11200 photomultipliers, diam.= 50 cmLight collection efficiency ~40%

Inner volume while filling

Eve

nts

/day

6 8 10 12 14 Electron kinetic energy (MeV)

SSM prediction

Data

E

Recoil electron kinetic energy distribution frome – e elastic scattering of mono-energetic neutrinos

is almost flat between 0 and 2E/(2 + me/E)

convolute with predicted spectrum to obtainSSM prediction for electron energy distribution

Results from 22400 events (1496 days of data taking) Measured neutrino flux (assuming all e): (e) = (2.35 0.02 0.08) x 106 cm-2 s –1

(stat) (syst)

SSM prediction: (e) = (5.05 ) x 106 cm-2 s –1

Data/SSM = 0.465 0.005 (stat)

+1.01

–0.81+0.093

–0.074(including theoretical error) e DEFICIT

0.465 0.016

2.56

0.23

Comparison of Homestake and Kamioka results with SSM predictions

Homestake and Kamioka results were known since the late 1980’s.However, the solar neutrino deficit was not taken seriously at that time.Why?

The two main solar e sources in the Homestake and water experiments:

He3 + He4 + Be7 e– + Be7 e + Li7 (Homestake)

p + Be7 + B8 B8 Be8 + e+ + e (Homestake, Kamiokande, Super-K)Fusion reactions strongly suppressed by Coulomb repulsion

d

Z1e Z2e

R1

R2

d

Z1Z2e2/d

~R1+R2

Ec

Potential energy:

MeV fm RR

ZZ

137

fm MeV 197

RR

ZZ

RR

ZZE

21

21

21

212

21

221

c

c

c

ee

Ec 1.4 MeV for Z1Z2 = 4, R1+R2 = 4 fm

Average thermal energy in the Sun core <E> = 1.5 kBTc 0.002 MeV (Tc=15.6 MK)kB (Boltzmann constant) = 8.6 x 10-5 eV/deg.K

Nuclear fusion in the Sun core occurs by tunnel effect and depends

strongly on Tc

Nuclear fusion cross-section at very low energies

E)(eE

1E)( 2- S

Tunnel effect:v = relative velocity v

ZZ 221

e

Nuclear physics term difficult to calculatemeasured at energies ~0.1– 0.5 MeVand assumed to be energy independent

Predicted dependence of the e fluxes on Tc:

From e– + Be7 e + Li7: e Tc8

From B8 Be8 + e+ + e : e Tc18

Tc N / = N Tc/Tc

How precisely do we know the temperature T of the Sun core?

Search for e from p + p e+ + e + d (the main component of thesolar neutrino spectrum, constrained by the Sun luminosity) very little theoretical uncertainties

Gallium experiments: radiochemical experiments to search fore + Ga71 e– + Ge71 Energy threshold E(e) > 0.233 MeV reaction sensitive to solar neutrinosfrom p + p e+ + e + d (the dominant component)Three experiments: GALLEX (Gallium Experiment, 1991 – 1997) GNO (Gallium Neutrino Observatory, 1998 – )

SAGE (Soviet-American Gallium Experiment)

In the Gran Sasso National Lab150 km east of RomeDepth 3740 m w.e.

In the Baksan Lab (Russia) underthe Caucasus. Depth 4640 m w.e.

Target: 30.3 tons of Gallium in HCl solution (GALLEX, GNO) 50 tons of metallic Gallium (liquid at 40°C) (SAGE)

Experimental method: every few weeks extract Ge71 in the form of GeCl4 (a highly volatile

substance), convert chemically to gas GeH4, inject gas into a proportional counter, detect

radioactive decay of Ge71: e– + Ge71 e + Ga71 (half-life 1/2 = 11.43 d)(Final state excited Ga71 atom emits X-rays: detect K and L atomic transitions)

Check of detection efficiency: Introduce a known quantity of As71 in the tank (decaying to Ge71: e– + Ge71 e + Ga71) Install an intense radioactive source producing mono-energetic e near the tank:

e– + Cr51 e + V51 (prepared in a nuclear reactor, initial activity 1.5 MCurie equivalent

to 5 times the solar neutrino flux), E(e) = 0.750 MeV, half-life 1/2 = 28 d

SAGE (1990 – 2001) 70.8 SNU

SSM PREDICTION: 128 SNU

Data/SSM = 0.56 0.05

+6.5–6.1+9–7

Ge71 production rate ~1 atom/day

0.4650.016

Concluding evidence for solar neutrino oscillations(Sudbury Neutrino Observatory, Sudbury, Ontario, Canada)

SNO: detector of Čerenkov light produced in tons of ultra-pure heavy water DO

contained in an acrylic sphere (diam. m), surrounded by tons of ultra-pure water HO

Light collection: photomultipler tubes,diam. cm, on a spherical surface of m radius

Depth: m ( m HO eq.) in a Nickel mine

Detection energy threshold: MeV(reduced to 3.5 MeV in a recent analysis)

Reconstruct the event position from the measurement of the photomultipliersignal relative timings

SNO

Solar neutrino detection in the SNO experiment

(ES) Neutrino – electron elastic scattering : + e– + e–

Directional, (e) 6 () 6 () (as in Super-K)

(CC) e + d e– + p + p Electron angular distribution cos(sun) Measurement of the e energy (most of the e energy is transferred

to the electron)(NC) + d + p + n Identical cross-section for all three neutrino flavours ⇒ measurement of the total neutrino flux from B8 Be8 + e+ +

independent of oscillations

13

DETECTION OF + d + p + n Detect neutron capture after “thermalization”

Phase I (November – May ):

n + d H3 + ( E= MeV, = 5x10–4 b ); → Compton electron, ee pair

Phase II (July 2001 – September 2003): add 2 tons of ultra-pure NaCl to D2O

n + Cl 35 Cl 36 +several’s ( <N> ≈ 2.5, E MeV, = 44 b )

Phase III (November 2004 – November 2006: insert in the D2O volume an array of cylindrical proportional counters (diameter 5 cm) filled with He3 n + He3 p + H3 (0.764 MeV mono-energetic signal, = 5330 b)

nH3

p

Neutron detection efficiency in Phase I and II

Efficiency measurement using a Cf neutron source(spontaneous fission, ½ = 2.6 years)Average over a spherical volume of radius R cm (50 cm from the edge of the D2O sphere)

Detection efficiency for neutrons from + d + p + n =

Efficiency without NaCl .

An additional advantage of Phase II with respect to Phase I

n + Cl 35 Cl 36 +several ’ s (on average, N = 2.5)The Čerenkov light is more isotropic with respect to the CC and ES reactions which have only one electron in the final state

To measure the isotropy of the light emitted in each event define anan “isotropy parameter” using the space distribution of photomultiplier hits

Phase IIsolar data

.

252Cf: neutron source (neutron energy: few MeV)16N: – ray source (6.13 MeV) Compton electron, collinear ee pair

Direct measurement of the electron angular resolutionusing the 16N – ray source

Knownsource

position rayMeV

Comptonelectron

T MeV collinear

with incident

Use four independent variables to separate the three reactions

ES CC NC

Teff

Energy distribution(from signal amplitude)

Cossun

Directionality

14

Isotropy parameter

= (R/R0)3

Event radial positionR0 = 600.5 cm

radius of the D2O sphere

( Hatched histograms correspond to Phase II )

cos sun

distribution

Event position:distribution

of distance from center

(R R)

R = 600.5 cmradius of DO sphere

DATA

Energy distribution(from signal amplitude)

Extract all components (ES, CC, NC, background) by maximum likelihood method

Number of events:

CC: ES: NC: Background from external neutrons:

Solar neutrino fluxes, as measured from the three signals:

CC = ( .) x cm s

ES = ( . ) x cm s

NC = ( . ) x cm s

(stat) (syst)

Calculated assuming that all incident neutrinos are e

Note: CC (e)

+–SSM( ) = xcms

The TOTAL solar neutrino flux agrees with SSM predictions (determination of the solar core temperature to ~ 0.5% precision)

Composition of solar neutrino flux on Earth:

~ % e ; ~ % (ratio unkown)

DEFINITIVE EVIDENCE OF SOLAR NEUTRINOOSCILLATIONS

CC

NC

.. differs from by standard deviations

Difference between the measured values of CC and ES

eeCC )(

6

1)()(

)(

)()( ,

e

eES

ES

eES

eeNC

)()()(

SNO phase IIIB. Aharmim et al., Phys. Rev. Lett. 101, 111301 (2008)Insert 40 cylindrical proportional countersfilled with He3 (NCD) vertically in the D2O volume (no salt)36 Tubes filled with 85% He3, 15% CF4; 4 tubes filled with 85% He4, 15% CF4 Pressure 2.5 bar Ultra-pure Nickel tubes, diam. 5.08 cmTube wall thickness 370 m Variable length

Detect neutrons from NC process + d → + p + n from capture by He3 after thermalization

Na24 calibration :Energy distribution

Reduced signal amplitudefor neutron capturesnear the tube wall

n + He3 → p + H3 + 764 KeV mono-energetic signal

(~ 20,000 electron – ion pairs in gas)

detection efficiency ~18% measured using Na24 sources (, 2.754 MeV) inserted in the D2O volume: + d → p + n (neutron detection efficiency from n + d → H3 + ≈ 4.9 %)

NCD energy distribution during Phase III data - taking(November 2004 – november 2006)

Contamination from radioactivityin the Nickel wallsmeasured by the four countersfilled with He4

Number of solar neutrino events:Neutrons: 983 ± 77 (NCD); 267 ± 23 (n + d → H3 + )

Electrons from CC events : 1867 ; electrons from ES events: 171 ± 24

Background neutrons: 185 ± 24 (NCD); 77 ± 12 (n + d → H3 + )

+91-101

CC

NC

.. Measurement of the solar e deficit using an independent methodwith different systematic effects

Hypothesis: two – neutrino mixing

Vacuum oscillations e energy spectrum measured on Earth (e) = Pee 0(e) (0(e) e energy spectrum at production)

Probability to detect e on Earth :

0.33)267.1()sin2(sin1 222ee

E

LmP

L [m]E [MeV]m2 [eV2]

Solar e disappearance: interpretation

Solar neutrino energy in SNO, Super-K experiments E = 5 – 15 MeVVariation of Sun – Earth distance during data taking

(the Earth orbit is an ellipse) L = 5.01 x m( <L> = x m)

Check dependence of Pee on E and L

Electron kinetic energy (MeV)

Dat

a/SS

MSuper-K

SNO: e + d e– + p + p electron energy distribution

SNO: data / SSM prediction

e deficit independent of energy within measurement errors(no spectral distortions)

Spectral distortions

Seasonal modulation

The observed effect is consistent with the expected solid angle variation

Yearly variation of the Sun - Earthdistance: % seasonal modulationof the solar neutrino flux

Expected seasonal variationfrom the variation of solid angle in the absence of oscillations: ~ %

Days from start of data taking

2

0.33)sin2(sin1267.1)sin2(sin1 22222ee

L

E

LmP

L [m]E [MeV]m2 [eV2]

For oscillation lengths << source dimension (~ 0.15 RO ≈ 1 x 108 m); << Earth diameter (~ 1.3 x 107 m)

Pee is independent of E and L :

0.5)2(sin2

11sin2sin1 222

ee

L

P

in disagreement with the experimental result ~ 0.33

Neutrino oscillations in vacuum do not describe

the observed solar e deficit

Neutrino refractive index in matter

)0(2

112

Nfp

n

p: neutrino momentumN: density of scattering centersf(0): scattering amplitude at = 0°

V : attractive potential (n )V : repulsive potential (n )

In vacuum: 22 mpE

E

pEmnpE

222)( ( )

Plane wave in matter: = ei(np•r –E’t)

Energy conservation:

V neutrino potential energy in matterVEE

)0(22

NfEE

pV

(L. Wolfenstein, 1978)

NEUTRINO OSCILLATIONS IN MATTER

Neutrino potential energy in matter

1. Z-boson exchange (the same for the three neutrino types)

Z

e,p,n e,p,n

)θ(NG(e)V(p)V wpFZZ2sin41

2

2

nFZ NG(n)V2

2

GF: Fermi constant

Np (Nn): proton (neutron) density

w: weak mixing angle

NOTE: V() = – V( )

2. W- boson exchange (only for e!)e

e

W+

e

e

ρA

Z.NG[eV]V eFW

14106372

matter density [g/cm]electron density

Example: e – mixing in a constant density medium

(identical results for e – mixing)

In the “flavour” representation:

eEvolutionequation:

tiH

xmatrix

00

01

2

1

10

01)( 22

22

We

eeeZ V

MM

MM

EVEH

(Remember: for M p) E

ME

p

MpMp

22

2222

)2cos(2

1 222 mMee

)2cos(2

1 222 mM

2sin2

1 222 mMM ee

22

21

2 mm 2

12

22 mmm

NOTE: m, m, are defined in vacuum

22

22 2

2

1

10

01)(

MM

MEVM

EVEH

e

eWeeZ

diagonal term:no mixing Term inducing e– mixing

= constant H is time - independentH diagonalization eigenvalues and eigenvectors

Eigenvectorsin matter

2sin)()2cos(2

1)(

2

1 2222222 mmM

EA

ZEVW 710526.12 [eV2] ( in g/cm3, E in MeV)

Mixing angle in matter:

2cos

2sin2tan

2

2

m

mm

= m2cos res maximum mixing(m = °) even if the mixing angle in vacuumis very small: “MSW resonance ”(discovered by Mikheyev and Smirnov in 1985)

M2

m

m

Mass eigenvaluesas a function of

2cos2mres

2sin)()2cos( 22222

2

mm

mm

Oscillation length in matter:

( oscillation length in vacuum)

For = res: 2sin

m

EA

ZEVW 710526.12

NOTE: for e oscillations the MSW resonance exists only if m2cos2 > 0

m2 > 0, cos2 > 0 ( < 45º) or m2 < 0, cos2 < 0 ( > 45º)

DEFINITION (to remove the ambiguity): m2 = m22 – m1

2 > 0

Matter effects in solar neutrino oscillations Solar neutrinos are produced in a high – density medium (the solar core).

0

1)0(

)0()0()0()0()(0

iHt t

(pure e at production)

( = very small time interval)

)()()()()( ttiHtt

ttt

(until the neutrino emerges from the Sun)

Solar density

R/RO

[g/cm3]Oscillations in solar matter

Time evolution: H = i / t H (xmatrix) depends on time via (t)

H has no eigenvectors Numerical solution of the evolution equation:

Variable density along the neutrino path: = (t)

)/(

2cos106.6

2][

26

AZ

m

VMeVE

W

res m2 [eV2]

[g/cm3] > res

Assumption: mixing angle in vacuum ° → cos sincosMixing angle in matter:

2cos

2sin2tan

2

2

m

mm

MeVg/cm10526.12 37 EA

ZEV

W

“Adiabatic solutions” (Negligible variation of matter density over an oscillation length)

)()0()()0()(2211

tvatvat (t) , (t) : “local” mass eigenstates obtained by setting constant = local densityat time t in the evolution Hamiltonian

0

2

0

1sin)0( ;cos)0(

mmaa constant along the whole path inside the Sun

)0(0

mm mixing angle in matter at neutrino production point (in the Sun core)

)0(sincos)0( 45 :)2cos( If2

00

1

02 aθθaθθmmmmres

ee

12at production

( tE ), ( tE ) : mass eigenstates in vacuum

)(sin)(cos)(2

0

1

0

EmEmEttt

)()( 45For 00

m EeEtt

e DEFICIT

m 45° m 45°

M2

2)( Area ti

In vacuum, at exit from Sun (t = tE):

In case of “adiabatic” solutions, at exit from Sun ( t = tE ):

22 in vacuum because e

Day – night modulation (from matter effects on neutrino oscillations

through Earth at night e flux increase at night for some values

of the oscillation parameters )Study e deficit as a function of pathinside Earth (length and density)subdividing the night spectrumin bins of zenith angle (with respect to local vertical axis)

)(5.0 ND

NDADN

SNO: Day and Night spectra(CC events)

Day – night difference

cos(Sun zenith angle)

“Best fit” to SNO data

Best fit:

252 eV 1057.4 m

447.0tan2 72/8.73/2 dofN

NOTE: tan is used instead of sin because sin is symmetric around =°

MSW solutions exist only if °

Confidence levels for two-parameter fits

CL = min

68.27% 2.3090% 4.6195% 5.9999% 9.2199.73% 11.83

)45(2sin)290sin()290sin()45(2sin 0000

Best fit to all solar neutrino experimentsincluding a recent re-analysis of SNO Phase I and II datawith detection threshold reduced to 3.5 MeV B.Aharmim et al., Phys. Rev. C81, 055504 (2010)

Best fit:

mxeV

tan

º

Ndof

+2.132.16

+0.038

0.041

+1.07

1.24

KamLANDConfirmation of solar e oscillations using antineutrinos from nuclear reactors

CPT invariance: Posc( – ) = Posc ( – )

same disappearance probability for e and e Nuclear reactors: strong, isotropic e sources from decay of fission

fragments Energy spectrum (E MeV, <E> MeV) known from experiments.

e production rate : x Pth s Systematic uncertainty on e flux : ± %

Pth: reactor thermal power (GW)

Detection: e + p e+ + n (on the free protons of hydrogen–rich liquid scintillator )

e+ e– 2 prompt signal E = E(e+) + 2me

E= E + 0.782 MeV

“thermalization” from multiple collisions(< t > 180 s), followed by capturen + p d + EMeV)

delayed signal

KamLAND (KAMioka Liquid scintillator Anti-Neutrino Detector)

e source : nuclear reactors in Japan

Expected e flux x cm– s–

(all reactors at full power, no oscillations)

Expected oscillation length

for m = x – eV :

osc km

Total thermal power GW

>% of the e flux from

reactors, < L < kmDistance weighted average:

<L>: km (weight = e flux)

KamLAND: detector

tons liquid scintillator

Transparent nylon balloon

Mineral oil

Acrylic sphere Photomultipliers ()(coverage: 35% of 4)

External anticoincidenceagainst cosmic rays (pure HO )225 photomultipliers m

m

KamLAND: event selectionPrompt signal: E MeV, distance from center m Delayed signal: t s, R m with respect to the prompt signal

KamLAND: final results S. Abe et al., Phys. Rev. Lett. 100, 221803 (2008)

Expected number of events for no oscillation : 2179 ± 89 (syst.)

Background: 276.1 ± 23.5 events

Number of observed events: 1609

Effect of scintillator contaminationfrom radioactivity

KamLAND: e disappearance probability

)267.1(sin)2(sin1 0222

E

Lm

ee P

Best fit

2514.0

13.0

2 eV 10)15.058.7(

m

(sist)(stat)56.0tan 10.0

06.0

10.0

07.0

2

L0 = 180 km

source - detectoraverage distance

Solar – KamLAND fit comparison

Combined best fit : m2 = (7.59 ± 0.21) x 105 eV2

tan2 = 0.457 = 34.06Ndof

+ 0.040

– 0.029

+ 1.16 – 0.84

Best fit to all solar neutrino data + KamLAND

Solar e disappearanceSummary

)(

)(48.2)(

22 eVm

MeVEm

Oscillation length in vacuum

= 5.06 x 104 m for E = 1 MeV; = 5.06 x 105 m for E = 10 MeV.

Oscillation length in matter

09.12sin

m

Adiabatic solutions:

Negligible variation of the solar densityover an oscillation length

11

mdR

d

)/( dRdm

(R: distance from Sun center)

m / dRd

O/ RRThe solar neutrino propagation inside the Sun is described by adiabatic solutions

Mixing angle in matter

2cos

2sin2tan

2

2

m

mm

EA

ZEVW 710526.12 [eV2] ( in g/cm3, E in MeV)

Solar density

R/RO

[g/cm3]

R/RO < 0.15solar e

production regionRO ≈ 6.96x105 km

< Z / A > ≈ 0.77 in the Sun core:34% H (Z/A = 1), 66% nuclei with Z/A = ½(mainly He4)

At the MSW resonanceE ≈ 234 g cm MeV

Solar e detection probability on Earth ( Pee )

Assumption: e – mixing ⇒ Pee = 1 - Pe

At exit from Sun (adiabatic solution):

20

10 )sin()cos( mmE

osc

Lt

E

m

2cos

2cos

2

osc << Earth diameter / variation of Sun-Earth distance

02cos

osc

L

Neutrino propagation to a detector on Earth:

tiEm

tiEm eet 21

20

10 )sin()cos()(

E

mpmpE

2

2

2,12

2,1

2

2,1

2

20

10

21

221 )sin()cos()cos()sin()( tiE

mtiE

me eet P

2

200200

21

22

12 )sin()cos()cos()sin()sin()cos()cos()sin(t

E

mmi

mm

tEEi

mmee

22

0

22

00

2sin)sin()cos(

2cos)sin()cos()cos()sin( t

E

mt

E

mmmm

t

E

mmmmm 2

cos)cos()sin()cos()sin(2)(sin)(cos)(cos)(sin2

00022022

)(sin)(cos)(cos)(sin11 022022mmeee PP

BOREXINOAn experiment at the Gran Sasso National Laboratories

Goal:Detection of elastic scattering process + e → + e (dominated by e)in liquid scintillatorScintillation light >> Čerenkov light→ detection threshold < < 1 MeVScintillator: pseudocumene (PC) + PPO;“buffer liquid”: PC + DMP (no scintillation)

Real – time experiment

Scintillation light is ISOTROPIC → no signal correlation with the Sun directionThe signal solar origin can be verified after few data-taking years by observing the seasonal modulation induced by the excentricity of the Earth orbit around the Sun

After background subtraction:

evidence for monoenergeticsolar neutrinos from reaction

e + Be7 → e + Li7

E(e) ≈ 0.87 MeV Electron energy distribution frome + e → e + e practically flat up to ~0.67 MeV

Results after ~ 200 data-taking days

– radioactive contaminantsin scintillatorSignal shape from -particlesdiffers from electron signal

BOREXINOMeasured spectrum, E > 2 MeV

All events

After removal of cosmic rays(external anticoincidence)

Excluding events at < 1m fromdetector edge

After subtracting background from radioactive contaminants

monoenergetic e

E ≈ 0.87 MeV

Measurement of the solar e deficit as a function of energy

N(measured events)

N(SSM prediction)Pee =

Matter effects NEGLIGIBLEFor E(e) = 0.87 MeV

57.0)2(sin2

11P 2

ee (for = 34º)

2

ee

2

ee

Atmospheric neutrino energies: — GeVVery low event rates: ~ year for a ton detector

Typical uncertainty on the atmospheric neutrino fluxes: ± % (from uncertainties on the primary cosmic ray spectrum, on hadron production, etc.)

Incertainty on the e ratio : ± %

“Atmospheric” neutrinos e

Primary cosmic ray interacting in the atmosphere

DETECTOR

Main sources of atmospheric neutrinos:

, K + ( )

e + e( e) + ()For energies E GeV most pions and muons decay before reaching the Earth:

At higher energies most muonsreach the Earth before decaying:

(increasing with E )

Atmospheric neutrino detection

+ Nucleon + hadrons: presence of a long, minimum – ionizing track

(the muon)

e + n e– + p, e + p e+ + n : presence of an electromagnetic shower

(e interactions with multiple hadron production cannot be easily distinguished from Neutral Current interactions + N → + hadrons )

°

Direct measurement of the electron muon separation by exposing a 1000 ton water Čerenkov detector (a small copy of Super-K) to electron and muon beams from aproton accelerator. Measured probability of wrong identification ~%

R = = (/e)measured

(/e)predicted

Event identification in water Čerenkov detectorsMuon track: dE/dx consistent with ionization minimum; well defined edges of Čerenkov light ring Electromagnetic shower: high dEdx (many secondary electrons); fuzzy edges of Čerenkov light ring (from the shower angular aperture)

Measurement of the e ratio: first hints for a new phenomenonWater Čerenkov detectors: Kamiokande (1988), IMB (1991), Super-K (1998)Conventional calorimeters (iron plates + proportional tubes): Soudan2 (1997)

Atmospheric neutrino events in Super-KDistance between interaction point and inner detector walls meter

(April 96 – July

01)

lepton (e/) energy [GeV]

H2O radiation length ≈ 36 cm → energetic electrons are totally absorbed in ~8 m of water

An additional event sample:Up – going muons from interactions in the rock

Note: down – going muons are mainly decays in the atmosphere traversing the mountain rock and reaching the detector

Uncertainty on neutrinoproduction point ±5 km

Earth

detector

Measurement of the zenith angle distribution

Definition of the zenith angle :Polar axis along the local vertical axis, pointing downwards

Earth atmosphere

Local vertical axis

Down-going : = º

Up-going: = °

Horizontal : = °

L (distance between neutrino production point and detector) depends on zenith angle

cos–1. –0.5 0. 0.5 1.

L [

Km

]

104

103

102

10

= º — º L = ~ — ~ km Search for oscillations with variable distance L Strong angular correlation between incidente neutrinoand produced electron/muon for E GeV:

e/

° at E = GeV;for increasing E

Zenith angle distribution in Super-K

No oscillation (2 = / degrees of freedom)

– oscillation (best fit): m2 = x eV, sin =

2 = / degrees of freedom

Zenith angle distributions in the Super-K experiment:

Evidence for disappearance over ~ — km distance

Not a – e oscillation:

e disappearance from oscillations with m2 > 103 eV2 excluded by the

CHOOZ experiment (discussed later) For – e oscillation expect a zenith angle distribution for “e-like” events

with opposite asymmetry (excess of up-going “e-like” events) because e at production

+ N + X requires E() > 3.5 GeV; fraction of decays 18%

Super-K

Region of oscillation parameters(confidence level 90%):

x –m x – eV

sin

The most plausible interpretation: – oscillation

Two nuclear reactors at theCHOOZ (EDF) power plantTotal thermal power GWL = , m

Detector: ton Gadolinium-enrichedliquid scintillatorn + Gd raysTotal energy 8.1 MeV

ton liquid scintillator without Gd ( ray containment)

ton liquid scintillator(cosmic ray veto)

Underground site:depth m HO eq.(negligible matter effects)Data – taking : Experiment completed in

Search for e disappearance over ~ km distance

Sensitivity to m x eV

CHOOZ

positron energy

Event rate at max. power : dayBackground (reactors OFF): / day

Positron energy spectrum

(prompt signal from e + p n + e+)

Comparison with predicted spectrumfor no oscillation

Measured spectrum

Predicted spectrum (no oscillation)

Energy – integrated ratio

=

no evidence for e disappearance

CHOOZ Experiment

e – ( e – ) oscillation:

excluded region

Summary Solar e oscillation: m x eV

Atmospheric oscillation: m x eV

e oscillation with m x eV

not observed: <

m

[eV]

Super-K –oscillation

Motivations: Conclusive demonstration that the atmosferic deficit is due to

neutrino oscillations using beams from proton accelerators

(directional beams with known energy spectra):

- Distortions of the energy distribution → measurement of m2 , sin22;

- appearance at long distance from source in a beam with no at

production.

Measurement of the Neutral Current event rate to distinguish

–from –s oscillations (s : a possible “sterile”

neutrino) ;

Search for – e oscillations driven by the m2 value associated

with the atmospheric neutrino deficit.

Searches for long baseline oscillationsusing neutrino beams from accelerators

Focusing of positively or negatively charged hadrons to produce analmost parallel beam with wide momentum distribution using “magnetichorns” (invented at CERN in 1963 by S. Van der Meer)The horns are followed by a long decay tunnel under vacuum

Wide band neutrino beams from accelerators

Axially symmetric conductors Pulsed current Cylindrically symmetric magnetic field perpendicular to the hadrons produced in the target

Changing the direction of the current pulseselects opposite charge hadron beams

→→

“On – axis” neutrinos (emitted at decay angles = 0º with respect to the hadron beam) have a wide momentum distribution.

“Off –axis” beams have narrower energy distributions but lower fluxes

beam axis

off – axis beam

+ parallel beam

energy at fixed :

)cos1(

*

EE

E*: energy in the + rest frame (0.03 GeV) = E /m

v /c

(from Lorentz transformation)

E() GeV

p (GeV/c)

→ decay

energyversus momentum

for different angles

For > 0neutrino beams are enrichedin monoenergetic neutrinos

but flux is reduced by a factor ~4

Monoenergetic neutrinos:

first oscillation maximum at L = osc /

Project Distance L < E > beam type Status

K2K 250 km 1.3 GeV on – axis completed

MINOS 735 km few GeV on – axis data – taking

CNGS 732 km 17 GeV on – axis data – taking

T2K 295 km ~0.6 GeV off – axis few events

NOA 810 km ~1.6 GeV off – axis under construction

+

Energy threshold for + N – + X: E GeV

Event rate ~1 – event year for one ton detector mass

need detector masses of several kiloton. Angular divergence of the beam from pion decay :

Beam axis

from + + decay GeV 10at mrad 3][

03.0

GeVE

GeV

p

p

L

T

Neutrino beam lateral dimensions: 100 m – 1 km for L 100 km no problem to hit the far detector

The neutrino flux decreases as L– at large distance L

K2K

12 GeVproton

synchrotronNeutrino beam:% % % e

L= km

Neardetector

Near detector: measurement of flux and interaction ratein the absence of oscillation1 kton water Čerenkov counter: similar to Super-K; fiducial mass 25 tonMuon chambers: measurement of muon energy spectrum from → decay

Data - taking: from June to February (x protons on target)

Events fully contained in the Super-K detector, Evis MeV:

predicted (Posc = 0): events

observed: events

Best fit

No oscillation

Quasi-elastic scattering kinematics assuming target neutron at rest energy determination:

Best fit:m = x – eV

sin = in agreement with atmospheric results)

Probability of no oscillation x (equivalent to 4 standard deviations)

Contained events with only one muon:Measurement of the energy spectrum in Super-K from the events

assuming quasi-elastic scattering + n – + p

Incident direction(precisely known)

– (energy measured by residual range in H2O)

Outgoing proton(undetected because under Čerenkov threshold)

(M nucleon mass)

cos

5.02

pEM

mMEE

MINOS experimentNeutrino beam from Fermilab to Soudan (an old iron mine in Minnesota): L = km

Accelerator:Fermilab Main Injector (MI)120 GeV proton synchrotronHigh beam intensity ( MW):

x protons per cycle (1.9 s)x protons / yearDecay tunnel : m

NUMI beam (“Neutrinos from Main Injector”)

The neutrino beam average energy can be changedby varying the target – magnetic horn distanceand the horn current

Aerial viewof the Fermilab accelerators

MINOS: Far detector

Octagonal tracking calorimeter diameter m Iron plates cm thick Plastic scintillator 4 cm wide strips between adjacent iron plates modules, each m long total mass tons, fiducial mass tons. scintillator planes ( m) Magnetized iron plates: toroidal field, B = T

MINOS: Near detector “Octagonal” tracking calorimeter , x m Construction similar to far detector magnetized iron plates Total mass tons, fiducial mass tons Installed m downstream of the decay tunnel end

Start – up of data – taking:

MINOS: far detector

MINOS results (June 2008)P. Adamson et al., Phys. Rev. Letters 101, 131802 (2008)

3.36 x1020 protons on target (May 2005 → July 2007)

Two neutrino beams: low energy (<E> ≈5 GeV); high energy (<E> ≈13 GeV)

+ N → – + X events Low energy beam : 730 events;High energy beam: 848 eventi

beam typical composition: 93% , 6% , 1.2% e , 0.1% e

Best fit :

m2 = ( 2.43 ± 0.13 ) x 10–3 eV2

sin2(2) > 0.95

(confidence level 68%)

Data

Prediction ( Posc = 0 )

Good approximation for : L = 732 km, E > 3.5 GeV, m < x– eV2

CNGS (CERN Neutrinos to Gran Sasso)

Search for appearance at L = km

22222222 ))(2(sin27.1)27.1(sin)2(sin

E

Lm

E

LmP

– oscillation probability (P):

max

5.3

22222 )(

)())(2(sin61.1E

GeV

dEE

EELmN

Disadvantages:L = km: distance – oscillation length

N depends on (m) very low event rate at small m2 values

Advantages: Beam optimization independent of m2

flux

Normalization:depends on detector mass ,running time, detectionefficiency , etc.

dEEEEANE

GeV

)()()(max

5.3

P

– production cross-section

Predicted number of + N – + X (N) events:

CC()

CC()

+ N – + X :

suppression factor with respect to

+ N – + X

from mass effects

E () [GeV]

Proton beam ( GeV) from the CERN SPS

Pulsed magnetic lenses

CNGS:neutrino beam

production

Beam energy spectraand interaction ratesat Gran Sasso

Primary protons: GeV;xx / SPS cycle SPS cycle: s Running efficiency %Data-taking days/yearProtons on target: x / year

FluxesFluxes

Interactionrates

Search for appearance at Gran SassoOPERA experimentNo near detector (negligible production at the proton target)

OPERA experiment: detect – by observing its decays to one charged particle(~%)Mean decay path mm need very high space resolution Photographic emulsion: space resolution ~ m

“Brick”: 56 1mm thick Pb plates interleaved with 57 emulsion films

and tightly packedBrick internal structure

200 m plastic base

50 m emulsion layers

Each brick is followed by a Changeable Sheet ( two emulsion films replaced quite often to reduce the scanning load) “Bricks” arranged into “walls” : one “wall” = 2850 bricks “Walls” arranged into two “super-modules” → ~150,000 bricks ≈ 1.25 ktons in total Each super-module is followed by a magnetic spectrometer Planes of orthogonal scintillating strips are inserted between walls to provide the trigger and to identify the brick where the neutrino interacted.Immediate removal of the brick and Changeable Sheet, emulsion development and automatic measurement using computer – controlled microscopes

OPERA super-module

Magnetic spectrometer: magnetized iron dipole

12 5 cm thickFe plateswith RPC trackers

20 m

10 mMuon

Spectrometer

HIGH PRECISION TRACKERS6 drift-tube layers/spectrometerspatial resolution < 0.5 mm

Veto

Drifttubes

RPC

10 m

Target

INNER TRACKERS• 990-ton dipole magnets (B= 1.55 T) instrumented with 22 RPC planes• 3050 m2, ~1.3 cm resolution

TARGET TRACKERS• 2x31 scintillator strips walls • 256+256 X-Y strips/wall• WLS fiber readout• 64-channel PMTs• 63488 channels• 0.8 cm resololution, 99% • rate 20 Hz/pixel @1 p.e.

BMSBrick Manipulator System

The OPERA detector

Target

BRICK WALLS 2850 bricks/wall • 53 walls •150000 bricks ~ 1.25 kton

Electronic Detectors are needed for:

Triggering, Timing

Neutrino interactions Location

Calorimetry

Muon I.D. and Spectrometry

Expectations for 5 data – taking years with 4.5x1019 protons on target / year

decay channel

B.R. (%) Signal m2 = 2.5 x 10-3 eV2

Background

17.7 2.9 0.17

e 17.8 3.5 0.17

h 49.5 3.1 0.24

3h 15.0 0.9 0.17

All BR*eff

=10.6%10.4 0.75

OPERA: signal and backgrounds

Main backgrounds: Production of charged “charmed” hadrons decaying to only one charged particle in events with unidentified primary lepton (negative muon, electron);

Primary large angle elastic scattering near the neutrino interaction point;

Charged hadron interacting close to the neutrino interaction point, with one or three outgoing charged particles and unidentified primary lepton.

The signal rate depends on (m2) 2

2008 run 2009 run

total 1.782x1019 pot 3.522x1019 pot

On-time events 10122 21428

candidate in the target 1698 3693

OPERA after two years of data - taking (2008 – 09)

Events with neutrino interaction vertex identified in a brick: 218 with no primary ; 1163 with identified primary .

Neutral “charmed” hadron decay to four charged particles;Decay vertex - primary vertex distance 313.1 m

The first OPERA event consistent with production N. Agafonova et al., Phys. Letters B 691 (2010) 138

Event interpretation: + N → + hadrons

º

2

Event projectionsorthogonal to the

neutrino beam direction

Number of → → events

expected in the analysedevent sample:0.54 ± 0.13

Expected background(“charm” events with

unidentified primary , NC events with

Interacting hadron):

0.018 ± 0.007

ICARUS detector (proposed by C. Rubbia in 1977)

600 ton liquid Argon in two adjacent containers

Container dimensions 3.6 x 3.9 x 19.9 m3

Time Projection Chamber (TPC): electrons from primary ionization drift in the liquid and are collected by read-out wires → 3-dimensional event reconstruction Number of primary ionization electrons from a charged particle at minimum ionization ~ 6000 / mm of track length Electron drift without recombination over lengths of ~1.8 m require ultra-pure Argon (concentration of electro-negative impurities <10-10) Drift velocity ~ 1.5 mm/s for electric fields ~ 0.5 kV/cm

Liquid Argon density 1.4 g/cm3

Radiation length 14 cm

DETECTOR FILLED AT MID MAY 2010

PRESENTLY TAKING DATAAT THE GRAN SASSO

NATIONAL LABORATORIES

ICARUSUV scintillation light from liquid Argonis collected by photomultiplier tubeslocated behind the read-out wires The scintillation signal is necessary to localize the event along the drift direction

ICARUS PHYSICS PROGRAMMESearch for → oscillations:

appearance by detecting → e decays

Event topology similar to e interactions (~1% in the CNGS beam)but with missing transverse momentum from undetected

Liquid Argon total mass (600 tons) probably not large enough (~1 event for 5 data – taking years), but useful to demonstrate the detector potential for future, very high mass neutrino detectors

ICARUS tracks recorded during the first detector tests in 2001

Electron shower

Interactinghadron

Cosmic muon with rays (hard-scattered electrons)

Assumption: only three neutrinos ⇒ two independent mvalues

Experimental information presently available:

Solar neutrino experiments + KAMLAND ∙ m

– m = (7.59 ± 0.21) x –eV (m2 > m1 by definition)

∙ Large mixing angle: º± º

Atmospheric neutrino experiments+ K2K + MINOS ( disappearance)

∙ |m – m

| || = (±) x eV (MINOS)

∙ Large mixing angle: ≈º (consistent with maximum mixing)

CHOOZ experiment: no evidence for e disappearance associated with

Future projects

Precise measurement of the neutrino mixing matrix Search for CP violation in neutrino oscillations

Neutrino masses: normal or inverted hierarchy?

normal hierarchy inverted hierarchy

23 > 0 23 < 0

Three – neutrino oscillations are described by three angles (, , )+ a phase angle inducing violation of CP – symmetry

3

2

1

231313122323121323122312

231323131223122313121223

1312131312

ccesscscesccss

scesssccesscsc

essccc

ii

ii

i

cik cosik; sik sinik

3

2

1

1212

1212

1313

1313

2323

2323

100

0

0

00

010

001

0

010

0

00

010

001

0

0

001

cs

sc

ecs

sc

ecs

scii

e

If s13 = 0 all matrix elements containing the phase vanish

Unitarity condition:

*i

iii

ii UUVU

inverse matrix V = U1

Impact of the CHOOZ experiment on the mixing matrix

e disappearance probability:22

)()(1 LLee

P

Evolution of a neutrino produced as e at distance L from source:

LiE

e

LiE

e

LiE

eeUeUeUL 321

332211)(

LEEie

LEEiee

LiE eUUeUUUUeL )(33

)(2211

13121)(

Remember: for E >> m E

mmEE ki

ki 2

22

Ignoring the overall phase exp(–iE1L) :

LE

i

e

LE

i

ee eUUeUUUUL 233

22211

1312

)(

LEEie

LEEiee

LiE eUUeUUUUeL )(33

)(2211

13121)(

LE

i

e

LE

i

ee eUUeUUUUL 233

22211

1312

)(

In the CHOOZ experiment <E> ≈ 3 MeV , L ≈ 1000 m

1(m)(MeV)

)(eV534.2

2

21212

LE

LE

oscillation effects associated with 12 are negligible

03.013

12

Define:

CHOOZ limit: Pee < 0.11 for |13| ≈ 2.5 x 103 eV2 (90% conf. level)

°

Series expansion of three – flavour e (and e) disappearance probability(E.K. Akhmedov et al., JHEP 04 (2004) 078):

E

LLL

ee 13

2

13

2

12

2222

267.1sinsin42sin1)()(1 P

3

2

1

00

00

00

2/12/34cos2/34sin

2/12/34cos2/34sin

034sin34cos

e

< 0.2 CHOOZ

limit

Three – neutrino mixing matrix consistent with all measured oscillation parameters:

Solar e oscillations

assuming Ue3 = sin13 = 0

(consistent with the limit from the CHOOZ experiment)

e disappearance probability :22

)()(1 LLee

P

LE

i

ee eUUUUL 22211

12

)(

LE

i

ee eUUUUL 22211

12

)(

Solar e oscillate to and with equal probabilities

LiEe

LiEe eUeUL 21

2211)(

)()( LL 23 = 45º → sin(23 ) = cos(23 )

Violation of CP symmetry in three – neutrino mixing

CP violation : Posc( – ) Posc( – )

CPT invariance: Posc( – ) = Posc( – ) (, = e, , )

Posc( – ) = Posc( – ) (CPT invariance)

CP violation in neutrino oscillations can only be detected in appearance experiments

CP violation in – e oscillations:Define: )( ; )( oscosc ee PPPP ee

Vacuum oscillations:

CP – violating terms (note the sign of )

A = (sin23 sin213 )2

B = (cos23 sin212 )2

C = cos13 sin212 sin213 sin223

)27.1sin()27.1sin()27.1cos()27.1(sin)27.1(sin 122323122

232

E

L

E

L

E

LC

E

LB

E

LAe P

)27.1sin()27.1sin()27.1 cos()27.1(sin)27.1(sin 122323122

232

E

L

E

L

E

LC

E

LB

E

LAe P

CP violation in – e oscillations

can only be measured if

AND the experiment is simultaneously sensitive

to and

The most urgent problem: to measure precisely

need new oscillation experiments

(e disappearance / – e appearance )

more sensitive to than the CHOOZ experiment

e disappearance experiments in preparation

(with near detector to measure directly the e flux)

. DOUBLE CHOOZ (with near detector identical to far detector) Start–up of data – taking : end 2011

. Daya Bay (on the East coast of China, 55 km North-East of Hong Kong) Two nuclear power plants 1100 m apart: Daya Bay (two reactors, 2 x 2.9 GW) Ling Ao (two reactors, 2 x 2.9 GW + 2 under construction) Total thermal power 17.4 GW after 2011 8 identical liquid scintillator detectors (similar to CHOOZ) in 8 different sites (4 near the reactors, 4 at ~2 km distance) Start–up of data – taking: 2012

1. RENO: two identical underground detectors consisting of 15 ton Gd – doped liquid scintillator (similar to CHOOZ) at the Yonggwang power plant (South-Korea); 6 reactors, total thermal power 16 GW

Start–up of data – taking : 2011Expected sensitivity after 3 years: sin2213 < 0.02 (CHOOZ limit : sin2213 < 0.15)

High – sensitivity searches for – e oscillations: detector distance L ½ require low energy neutrino beams ( – GeV) for the existing detectors

KK: neutrino flux too low despite the very large detector mass (Super-K)

CNGS: physics programme optimized for appearance

(beam energy production threshold, too high for – e oscillations) ,

no near detector to measure the intrinsic e contamination in the beam)

MINOS: preliminary results (April 2010) Distance L = 735 km: the neutrino beam traverses the Earth crust (< > ≈ 3 g/cm3, Z/A ≈ ½ ) matter effects cannot be neglected

13

2

13

13

2

13

13 2cos

2sin2tan

m

mmatter

)(eV 10526.12 24 EA

ZEVW

( in g/cm3, E in GeV)223

21

22

22

23

21

23

213 )()( mmmmmmmm

Matter effects depend on the sign of m223

At the first peak of the – e oscillation:

E ≈ 1.4 GeV ; ≈ 3.3 x 10-4 eV2 ; m213cos213 ≈ ± 2.4 x 10-3 eV2

– e oscillations : Series expansions for three-flavor neutrino oscillation probabilities

in matterE.K. Akhmedov et al., JHEP 04 (2004) 078

2

2

132

232

)1(

)1(sin2sinsin)(

A

Ae

P

sin

1

)1sin(sinsin2sin2sinsin2

231213

A

A

A

A

cos

1

)1sin(sincos2sin2sinsin2 231213

A

A

A

A

13

4

13

)/(10526.12

EAZEV

A W 03.013

12

E

L13267.1

(g/cm3) ; E (GeV) ; L (km) ; ik (eV2)

Note the weak dependence on the CP-violating phase coming from terms to first order in 12 ( ≈ ±0.03)

MINOS: search for – e oscillationsPreliminary results (April 2010)

7x1020 protons on target (May 2005 – August 2009)

Typical neutrino event configurations(from simulations)

Experimental method: Select e → electron events from event topology (no muon, presence of an electromagnetic shower consistent with an electron) Measure backgrounds in the near detector (no oscillation) Predict backgrounds for the far detector Compare far detector data with predictions

N. of events

MINOSFar detector predictionsfor no – e oscillation

Expected number of events for no – e oscillation: 49.1 ± 7.0 (stat.) ± 2.7 (sist.)

Observed: 54

No evidence for – e oscillation

e → electron selected events:Energy distributionin the far detector

Excluded regions in the plane , sin2213 for |23| = 2.43 x 103 eV2

(23 = 45º)

Limits (C.L. 90%) for = 0 :

23 > 0 (normal hierarchy): sin2213 < 0.12 ; 13 < 10.1º 23 < 0 (inverted hierarchy): sin2213 < 0.20 ; 13 < 13.3º

High sensitivity – e oscillation searches (Posc sin)

J-PARC (Japan Proton Accelerator Research Complex): 50 GeV high intensity proton

synchrotron at JAERI (Tokai) in operation since 2009 T2K (Tokai to Kamioka): experiment to measure using a 2.5º off-axis neutrino beam

of ~0.6 GeV aimed at the Super-K detector (L = km) T2K includes a near detector

NOA: esperiment approved in 2008 to use the Fermilab NUMI beam at a distance of 810 km . The detector is located on the surface, 12 km from the beam axis (14.8 mr off – axis). Neutrino beam energy ~1.6 GeV

Detector: 15,000 ton liquid scintillator in plastic rectangular tubes 15.5 m long, section 3.9cm x 6cm

Search for →e oscillations in the T2K experiment: expectations (from simulations)

Energy distribution of e → e events8.3 x 1021 protons on target at 30 GeV(5 years of data – taking)

Sensitivity : limit obtained ifN(e events) = N(background)

(23 = 45º)

)2(sin2

1)(sin)2(sin)2(sin 13

223

213

22 e

NOTE: → e oscillation probability proportional to

January – June 2010 run:3.3 x1019 protons on target22 fully contained eventsobserved in the Super-K detector

Measurement of CP violation (phase angle in the mixing matrix)

First – order approximation for – e and – e oscillation probabilities:

2

2

13

2

23

2

)1(

)1(sin2sinsin

A

A

e

e

P

sin

1

)1sin(sinsin2sin2sinsin2

231213

A

A

A

A

cos

1

)1sin(sincos2sin2sinsin2 231213

A

A

A

A

13

4

13

)/(10526.12

EAZEV

A W

03.013

12

E

L13267.1

(g/cm3) ; E (GeV) ; L (km) ; ik (eV2)

Matter effects:Opposite signs for ,

Two possible methods:

Data – taking with and beams;

Data – taking with beams only, measurement of the – e oscillation probability at the first and second oscillation maximum ( ≈ /2, 3/2).

Experiment L (km) 1st maximum 2nd maximum

T2K 295 km 0.58 GeV 0.19 GeV

NOA 810 km 1.6 GeV 0.53 GeV

Neutrino energy at the 1st and 2nd – e oscillation maximum

For T2K E at 2nd maximum is too low to separate electrons from muons need longer baseline distances

PROPOSAL FOR AN ICARUS-LIKE LIQUID ARGON DETECTOR WITH A 100 KTON MASS IN THE OKINOSHIMA ISLANDS OR IN KOREA

J-PARC

Proposal for a new water Čerenkov detector with 500 kton massfor the new underground laboratory under construction at Homestake (U.S.A.) .

Neutrino beam from the 28 GeV proton synchrotron (AGS)at the Brookhaven National Laboratory (L.I., N.Y., U.S.A.)

L = 2540 kmM.V. Diwan, et al., Phys. Rev. D 68 (2003) 012002

Expectations (from simulations)for 1022 protons on target (~ 4 data – taking years)

The new Homestake underground laboratory (“DUSEL”) is expected to be operational in 2018

Muon storage ring with long straight sections pointing to neutrino detectors

at large distance. N(): / year

Components of a Neutrino Factory: High – intensity proton accelerator (up to 1 protons/s, energy few GeV) ; High – aperture solenoidal magnetic channel following the proton target to capture ± and ± from ± decay; Muon “cooling” to reduce the muon beam angular spread and momentum interval; Two or more muon accelerators in series; A muon magnetic storage ring with long straight sections.

+ storage pure , e beams;

– storage pure , e beams;

Neutrino fluxes and energy distributions precisely predicted from decay kinematics

Search for e – oscillations: detection of “wrong sign” muons (electric

charge

opposite to charge of stored muons) MAGNETIC DETECTOR

A NEW CONCEPT:NEUTRINO FACTORY

A possible scheme of Neutrino Factory Superconducting solenoid

20 cm aperture B = 10 T

An alternative Neutrino Factory design

Reducing the muon beam momentum spread:Accelerating cavity with modulated electric field:weak field for early, fast muons;high field for late, slow muons

Predicted fluxes (neutrinos / (year x GeV)

Detector diameter m Distance L = km;

+ , E = GeV

Muon coolingIn the transverse plane: successive stages of acceleration / deceleration by ionization

beam axisInitial muonmomentum

(p)LiH

thicknessreduces p

acceleratingcavity

Acceleration increasesthe momentum longitudinal component the angular

divergence decreases

Measurement of CP violation at a Neutrino Factory

The sensitivity to the phase angle decreases rapidly with → no measureable effect for °

Optimum distance to measure the phase angle : L km: The neutrino beam traverses the Earth crust → matter effects of opposite sign for neutrinos and antineutrinos → apparent violation of CP symmetry

Matter effects and direct CP violation have different E and L dependences

require two detectors at different distances and study CP violation

as a function of the neutrino energy ENumber of events / year expected in a kton detector

for x + decays in the straight section of a 50 GeV Neutrino Factory

L (km) N→+X eN→eX N→X

730 8.8 x 106 1.5 x 107 8 x 106

3500 3 x 105 6 x 105 3 x 105

7000 3 x 104 1.3 x 105 5 x 104

“Beta” beamsAn alternative idea for a Neutrino Factory (P. Zucchelli, 2001)

Produce intense beams of radioactive isotopes undergoing decay Acceleration and injection into a storage ring with long straight sections

He Li + e+ e : <E( e )> = MeV ; = s

Ne F + e + e : <E( e )> = MeV; = s

Conceptual machine schemes studied so far:1. Acceleration: = (He), = (Ne). L = km (CERN – Tunnel Frejus)2. Acceleration: = (He), = (Ne). L = km (CERN – Gran Sasso)3. Acceleration: = (He), = (Ne). L = km (CERN – ?)

1 2 3

Typical event rate: – / yearfor a 1000 ton

detector

CONCLUSIONS ON THREE – NEUTRINO MIXING

Neutrinos mix and have non – zero masses; We do not know the neutrino mass absolute scale because oscillations provide information on m2, and not m2

(The present direct limit on the e mass from H3 – decay is m < 2 eV)

The most urgent problem in the study of neutrino oscillations is to measure 13 with much higher sensitivity than CHOOZ and MINOS ;

Only if 13 > 1º there is hope of observing CP violation in neutrino mixing;

R&D is in progress on new ideas to produce more intense, higher purity neutrino beams (Neutrino Factories, Beta Beams) .

However, there are hints from the LSND experiment at Los Alamos in the1990s, and more recently from the MiniBooNE experiment at Fermilab,that there may be (at least) one more light neutrino:

LSND observes a signal from – e oscillations with m2 ≈ 0.2 – 2 eV2;

MiniBooNE has a similar signal in – e oscillations , but not in – e .

The statistical significance is about 3 standard deviations in both experiments.

These puzzling results need confirmation from two-detector experiments.

LSND and KARMEN experiments: search for – e oscillations

Proton beam800 MeV

kin. energy

target+ beam dump

±

Detector

Veto counter

Experimental method

shielding

e+ e

The only

e

source

– p n

e– ee

e

10–3

Neutrino sources

Proton-nucleuscollisions

Kinetic energy800 MeV

70–90% +

~20%

Nuclear absorption

Decay At Rest (DAR) ~75%

Decay In Flight (DIF) ~5%

+DAR 100%

30–10% – DIF few %–

capture90%

DAR 10%

Parameters of the LSND and KARMEN experiments

LSND KARMEN Accelerator Los Alamos Neutron Neutron Spallation Facility Science Centre ISIS ar R.A.L. (U.K.)

Proton kin. energy 800 MeV 800 MeV Proton current 1000 A 200 A Detector Single cylindrical tank filled with liquid scintillator 512 independent cells Collect both scintillating filled with liquid scintillator and Čerenkov light

Detector mass 167 tons 56 tons Event localisation PMT timing cell size Distance from source 29 m 17 m Angle between proton 11° 90° and direction

Data taking period 1993 – 98 1997 – 2001

Protons on target 4.6 x 1023 1.5 x 1023

MeV

Neutrino energy spectra from + + decay at rest

e+ e

e detection: the “classical” way

e + p e+ + n

prompt signal

delayed signal from np d (E = 2.2

MeV)KARMEN has Gd-loaded paper betweenadjacent cells enhanced neutron capture,E = 8.1 MeV

time [s]

KARMEN beam time structureRepetition rate 50 Hz

Expect e oscillation signal

within ~10 s after beam pulse

LSND beam time structureRepetition rate 120 Hz

0 600 sno correlation between event timeand beam pulse

Consistency of KARMEN and LSND resultsin a limited region of the oscillation parametersbecause of the different detector distance L:L = 29 m (LSND);L = 17 m (KARMEN)

LSND: evidence for – e oscillations

Positrons with 20 < E < 60 MeV N(beam-on) – N(beam-off) = 49.1 ± 9.4 eventsNeutrino background = 16. 9 ± 2.3

e signal = 32.2 ± 9.4 events

Posc = (0.264 ± 0.067 ± 0.045) x 10–2

KARMEN: no evidence for – e oscillations

Positrons with 16 < E < 50 MeV : 15 events

Total background: 15.8 ± 0.5 events

Posc < 0.085 x 10–2 (conf. level 90%)

The LSND – e oscillation signal with m2 ≈ 0.2 – 2 eV2 requiresthe existence of a 4th neutrino:

0)()()( 23

21

22

23

21

22 mmmmmm

m22-m1

2 ≈ 7.6 x 10–5 eV2; |m32-m2

2| ≈ 2.4 x 10–3 eV2

→ |m12-m3

2| = |m32-m2

2|±(m22-m1

2) << 0.2 – 2 eV2

Measurement of the Z – boson width at LEP: number of neutrinos N = 2.984 ± 0.008

⇒ the 4th neutrino does not couple to W or Z ⇒ no interaction with matter:“sterile neutrino” – the mixing matrix dimensions are at least 4 x 4

se ,,, k

kkU

4

1

2

14

211

24

1 2exp)exp()(

tE

iUUUUtiEUUP k

kkeke

kkkeke )( 2

12

1 mmkk

For the LSND experiment oscillation effects associated with 12 and 23 are negligible:

E

LUUt

EiUUUUP e

kekeke 41

22

44

23

1

4144 267.1sin4

2exp)( ])[ ];[( MeVEmL

4

144 0

ke UU from unitarity

8 GeV protonsynchrotron

Berylliumtarget

fl

ux

(arb

itra

ry u

nit

s)

E [GeV]

MiniBooNE at Fermilab An experiment to verify the LSND oscillation signal

Predictedfluxes L ≈ 500 m

similar to LSND experiment

NO NEAR DETECTOR

LE

MiniBooNE detector

Spherical tank, diameter 12 m, filled with 807 ton mineral oil Collect both Čerenkov light (directional) and scintillation light. Fiducial mass 445 tons Optically isolated inner region (1280 photomultiplier tubes, diam. 20 cm) External shell used for anticoincidence (240 photomultiplier tubes)

Particle identificationbased on the different behaviour of electrons,muons, pions and on the Čerenkov light ringconfiguration

MiniBooNE: search for – e oscillations6.46 x 1020 protons on target

A.A.Aguilar-Arevalo et al., Phys. Rev. Lett. 102, 101802 (2009)

Event excess with 0.2 < E < 0.475 GeV: 128.8 ± 43.4 events

The MiniBooNE detector does not distinguish electrons from photons

e energy distribution

for events consistent with e + n → e + p

e energy distribution after background subtraction.

Comparison with three different – e oscillations.

Best fit to – e oscillation for 0.2 GeV < E < 2 GeV:

sin22 = 0.0017 ; m2 = 3.14 eV2

Parameters excluded by KARMEN

MiniBooNE – e results inconsistent with the oscillation parameters describing the LSND signal; Excess of events at low E unexplained

MiniBooNE: search for – e oscillations5.66 x 1020 protons on target

A.A.Aguilar-Arevalo et al., arXiv:1007.1150v3

e energy distributionfor events consistentwith e + p → e+ + n

Excess of eventsconsistentwith LSND

oscillation signal

Best fitassuming

two – neutrinomixing

– e oscillation probability

versus L / E :LSND – MiniBooNE comparison

The MiniBooNE antineutrino result(if confirmed) implies: the existence of a 4th sterile neutrino; violation of CP symmetry in the neutrino mixing matrix

(because the probabilities for – e

and – e oscillations are different)

This result must be confirmed by an experiment which includes a near detector

MINOS: search for – s oscillations as a possible mechanism

for disappearance in the far detector:

measurement of the Neutral Current (NC) event rate

+ N → + hadrons

NC events: no muon track events contained in a limited number of

consecutive detector planes (include e + N → e– + hadron events)

– oscillations:

NC event rate unchanged

(identical cross-section for the

three neutrino types)

– s oscillations:

s does not interact with matter

deficit of NC events Measured energy distributionconsistent with no deficit no evidence of s

Results from a fit including a fraction f(s) of sterile :

f(s) = 0.28 ± 0.28 ; f(s) < 0.68 (confidence level 90%)