NEUTRINO OSCILLATIONSLuigi DiLella

Marienburg CastleAugust 2002

1. Short introduction to neutrinos2. Formalism of neutrino oscillations in vacuum 3. Solar neutrinos: Production Results Formalism of neutrino oscillations in matter Future experiments

4. Atmospheric neutrinos5. LSND and KARMEN experiments6. Oscillation searches at accelerators: Long baseline experiments Short baseline experiments7. Long-term future8. Conclusions

Content of these lectures:

Neutrinos in the Standard Model

Measurement of the Z width at LEP: only three light neutrinos (e, , )

Neutrino mass m = “by hand” two-component neutrinos:

helicity (spin component parallel to momentum) = – for neutrinos + for antineutrinos

p

spin

: : p

spin

helicity + neutrinoshelicity – antineutrinos

do not exist

If m > helicity is not a good quantum number(helicity has opposite sign in a reference frame moving faster than the neutrino) massive neutrinos and antineutrinos can exist in both helicity states

Are neutrinos Dirac or Majorana particles?

Dirac neutrinos: lepton number is conserved Examples: neutron decay N P + e– + e

pion decay + + + Majorana neutrinos: (only one four-component spinor field)

lepton number is NOT conserved

Neutrinoless double– decay: a way (the only way?) to distinguish Dirac fromMajorana neutrinos

(A, Z) (A, Z+2) + e– + e–

violates lepton number conservation can only occur for Majorana neutrinosA second-order weak process:

n

n

p

e–

p

e–

two neutronsof the same nucleus

Process needs neutrino helicity flip between emission and absorption(neutron decay emits positive helicity neutrinos, neutrino capture by neutrons requires negative helicity) neutrinoless double– decay can only occur if m(e) > Transition Matrix Element m(e)

The most sensitive search for double- decay: 76Ge32 76Se34 + e– + e– E (e–

) + E (e–) = keV

Heidelberg–Moscow experiment:Five enriched 76Ge crystals (solid–state detectors)Total mass: 19.96 kg , 86% 76Ge (natural Germanium contains only 7.7% 76Ge)Crystals are surrounded by anticoincidence counters and installed in undergroundGran Sasso National Laboratory (Italy)Search for mono–energetic line at 2038 keVNo evidence for neutrinoless double- decay:m(e) < 0.2 eV for Majorana neutrinos

e

Neutrino mass: relevance to cosmologyA prediction of Big Bang cosmology: the Universe is filled with a Fermi gas of neutrinosat temperature T 1.9 K. Density ~60 cm–3 , 60 cm–3 for each neutrino type (e, , )

Critical density of the Universe :32

0

4

2

0 eV/cm 1005.18

3h

G

Hρ

N

c

H: Hubble constant (Universe

present expansion rate)H = h km s– Mpc – < h <GN: Newton constant

Neutrino energy density (normalized to c):

2

2

094

1cm

hc

eV 60 eV 30 2cm = 1 for

Recent evidence from the study of distant Super-Novae:c consists of ~30% matter (visible or invisible) and ~70% “vacuum energy”

Cosmological models prefer non-relativistic dark matter (easier galaxy formation)with 20% of matter density

eV 4 2cmcosmological limit on neutrino masses

Direct measurements of neutrino massese: mc2 < eV (from precise measurements of the electron energy spectrum from 3H decay)

: mc2 < MeV (from a precise measurement of + momentum from + decay at rest)

: mc2 < MeV (from measurements of + 3, 5 or 6 at LEP)

With the exception of e direct measurements of neutrino masses have no sensitivity to reach the cosmologically interesting region

Neutrino interaction with matterW–boson exchange: Charged–Current (CC) interactionsQuasi-elastic scattering

e + n e– + p e + p e+ + n

+ n – + p + p + + n Energy threshold: ~ MeV

+ n – + p + p + + n Energy threshold: ~ GeV

Cross-section for energies >> threshold: QE x – cm

Deep-inelastic scattering (DIS) (scattering on quarks, e.g. + d – + u)

e + N e– + hadrons e + N e+ + hadrons (N: nucleon)

+ N – + hadrons + N + + hadrons

+ N – + hadrons + N + + hadrons

Cross-sections for energies >> threshold: DIS() x – cm (E in GeV)

DIS( )

DIS()

Z–boson exchange: Neutral–Current (NC) interactionsFlavour-independent: the same for all three neutrino types + N + hadrons + N + hadronsCross-sections: NC( ) CC() NC( ) CC( )

Very low cross-sections: mean free path of a GeV x g cm–

equivalent to x km of Iron

Z

e

E () [GeV]

CC()

CC()Suppression of production

by CC interactions

from mass effects

Neutrino – electron scattering

(all three types)

e e –

W

e– e (e only)

Cross-section: = A x – E cm (E in GeV) e: A e : A , : A , : A

Note: cross-section on electrons is much smaller than cross-section on nucleons because GF

2 W2 (W total energy in the centre-of-mass system) and W2 2meE

NEUTRINO OSCILLATIONS

The most promising way to verify if m > 0(Pontecorvo 1958; Maki, Nakagawa, Sakata 1962)

Basic assumption: neutrino mixinge, , are not mass eigenstates but linear superpositionsof mass eigenstates 1, 2, 3 with masses m1, m2, m3, respectively:

i

iiU

ii V

= e, , (“flavour” index)i = 1, 2, 3 (mass index)

Ui: unitary mixing matrix

*)( ii UV

Time evolution of a neutrino state of momentum pcreated as at time t=0

kk

tiEk

i keUet rp)( )0(Note:

22kk mpE phases

tiEke are different if mj mk

appearance of neutrino flavour at t > 0Case of two-neutrino mixing

21 sincos

21 cossin mixing angle

2)(

1)( sincos)( 121 tEEitEi eet rp

For at production (t = 0):

Probability to detect at time t if pure was produced at t = 0

)4

(sin)2(sin)()(2

222

E

tmtt

P

Natural units: 1c

Note: for m << pp

mpmpE

2

222

E

m

E

mm

p

mmEE

222

221

22

21

22

12

m2 m22 – m1

2

Use more familiar units:

)267.1(sin)2(sin)( 222

E

LmL P

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

(in vacuum!)

L = ct distance betweenneutrino source and detector

NOTE: P depends on m2 and not on m. However, if m1 << m2

(as for charged leptons and quarks), then m2 m 22 m12 m2

2

Define oscillation length :

248.2

m

E

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

)(sin)2(sin)( 22

LL P

Distance from neutrino source

sin2(2)

Larger E, smaller m2Smaller E, larger m2

Disappearance experiments

Use a beam of and measure flux at distance L from source

PP 1Measure

Examples:

Oscillation experiments using e from nuclear reactors

(E few MeV: under threshold for or production)

detection at accelerators or from cosmic rays

(to search for oscillations if Eis under threshold

for production)Main uncertainty: knowledge of the neutrino flux for no oscillation the use of two detectors (if possible) helps

source Near detectormeasures flux

Far detector

measures P

beam

Appearance experiments

Use a beam of and detect at distance L from

source Examples: Detect e + Nucleon e- + hadrons in a beam

Detect + Nucleon - + hadrons in a beam (Energy threshold 3.5 GeV)

NOTEScontamination in beam must be precisely known

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

Most neutrino sources are not mono-energetic but have wide energy spectra. Oscillation probabilities must be averaged over neutrino energy spectrum.

log(m2)

sin2(2)

Under the assumption of two-neutrino mixing: Observation of an oscillation signal allowed region m2 versus sin2(2)

Negative result upper limit to P (P< P) exclusion region

Large m2 short Average over source and detector size:

)2(sin2

1)(sin)2(sin)( 222

LLP

Small m2 long

LL

)sin(

0 1

2

222 )2(sin6.1

E

LmP P

(the start of the first oscillation)

PARAMETERS OF OSCILLATION SEARCH EXPERIMENTS

Neutrino source Flavour Baseline L Energy Minimum m2

Sun e 1.5 x 108 km 0.2 15 MeV 1011 eV2

Cosmic rays

Nuclear reactors

Accelerators

e

e

e

e

e

10 km 13000 km

20 m 250 km

15 m 730 km

0.2 GeV 100 GeV

<E> 3 MeV

20 MeV 100 GeV

104 eV2

101 106 eV2

103 10 eV2

EVIDENCE/HINTS FOR NEUTRINO OSCILLATIONS Solar Neutrino Deficit: e disappearance between Sun and Earth

Atmospheric neutrino problem: deficit of coming from the other side of the Earth

LSND Experiment at Los Alamos: excess of e in a beam consisting mainly

of ,e and

SOLAR NEUTRINOSBirth of a visible star: gravitational contraction of a cloud of

primordial gas (mostly 75% H2, 25% He) increase of

density and temperature in the core ignition of nuclear fusionBalance between gravity and pressure hydrostatic equilibrium Final result from a chain of fusion reactions:

4p He4 + 2e+ + 2e

Average energy produced in the form of electromagnetic radiation:

Q = (4Mp – MHe4 + 2me)c2 – <E(2e)> 26.1 MeV

(from 2e+ + 2e– 4)

(<E(2e)> 0.59 MeV)

Sun luminosity: L = 3.846x1026 W = 2.401x1039 MeV/s

Neutrino emission rate: dN(e)/dt = 2 L/Q 1.84x1038 s –1

Neutrino flux on Earth: e 6.4x1010 cm–2 s –1

(average Sun-Earth distance = 1.496x1011 m)

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

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

Input: cross-sections for fusion processes opacity versus distance from Sun centre

Method:

choose initial parameters evolution to present time (t = 4.6x109 years) compare measured and predicted properties modify initial parameters (if needed)

Present Sun properties: Luminosity L = 3.846x1026 W Radius R = 6.96x108 m Mass M = 1.989x1030 kg

Core temperature Tc = 15.6x106 K

Surface temperature Ts = 5773 K

Hydrogen fraction in core = 34.1% (initially 71%) Helium fraction in core = 63.9% (initially 27.1%)

as measured onsurface today

Two fusion reaction cycles pp cycle (98.5% of L)

p + p e+ + e + d p + p e+ + e + d or (0.4%): p + e– + p e + dp + d + He3 p + d + He3

He3 + He3 He4 + p + p or (2x10-5): He3 + p He4 + e+ + e 85%

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

15%or (0.13%)

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 #1: in all cycles 4p He4 + 2e+ + 2e

NOTE #2: present solar luminosity originates from fusion reactions which occurred ~ 106 years ago. However, the Sun is practically stable over ~ 108 years.

Expected neutrino fluxes on Earth (pp cycle)L

ine

spe c

tra:

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

Radial distributions of neutrino productioninside the Sun, as predicted by the SSM

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

Real-time experiments using water Čerenkov counters to detect solar neutrinos

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

Detect Čerenkov light emitted by recoil electron in water (detection threshold ~5 MeV)

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

W and Z exchange Only Z exchange

Two experiments: Kamiokande (1987 – 94). Useful volume: 680 m3

Super-Kamiokande (1996 – 2001). Useful volume: 22500 m3

installed in the Kamioka mine (Japan) at a depth of 2670 m w.e.

(5MeV electron pathin water 2 cm)

cossun

Verify solar origin of neutrino signalfrom angular correlation betweenrecoil electron and incident neutrinodirections

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

R1R2

d

Z1Z2e2/d

~R1+R2

Ec

Potential energy:

MeV RR

ZZ

137

197

RR

ZZ

RR

ZZE

21

21

21

212

21

221

c

ccee

(R1 + R2 in fm)

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

The real solar neutrino puzzle:There is evidence for B8 in the Sun (with deficit 50%), but no evidence for Be7;yet Be7 is needed to make B8 by the fusion reaction p + Be7 + B8

Possible solutions: At least one experiment is wrong The SSM is totally wrong The e from e– + Be7 e + Li7 are no longer e when they reach the Earth and become invisible e OSCILLATIONS

Data are consistent with: Full e flux from p + p e+ + e + d ~50% of the e flux from B8 Be8 + e+ + e

Very strong (almost complete) suppression of the e flux from e– + Be7 e + Li7

Unambiguous demonstration of solar neutrino oscillations: SNO (the Sudbury Neutrino Observatory in Sudbury, Ontario, Canada)

SNO: a real-time experiment detecting Čerenkov light emitted in 1000 tons of high purity heavy water D2O contained in a 12 m diam. acrylic

sphere, surrounded by 7800 tons of high puritywater H2O

Light collection: 9456 photomultiplier tubes,diam. 20 cm, on a spherical surface with a radiusof 9.5 m

Depth: 2070 m (6010 m w.e.) in a nickel mine

Electron energy detection threshold: 5 MeV

Fiducial volume: reconstructed event vertexwithin 550 cm from the centre

Solar neutrino detection at SNO:

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

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

(CC) e + d e– + p + p Weakly directional: recoil electron angular distribution 1 – (1/3) cos(sun) Good measurement of the e energy spectrum (because the electron takes

most of the e energy)

(NC) + d + p + n Equal cross-sections for all three neutrino types Measure the total solar flux from B8 Be8 + e+ + in the presence of oscillations by comparing the rates of CC and NC events

Detection of + d + p + n Detect photons ( e+e–) from neutron capture at thermal energies:

First phase (November 1999 – May 2001): n + d H3 + (E = 6.25 MeV)

Second phase (in progress): add high purity NaCl (2 tons) n + Cl 35 Cl 36 +– ray cascade (E 8. 6 MeV)

At a later stage: insert He3 proportional counters in the detector n + He3 p + H3 (mono-energetic signal)

SNO expectationsUse three variables: Signal amplitude (MeV) cos(sun) Event distance from centre (R) (measured from the PM relative times)

cos(sun) (R/Rav)3

(proportional to volume)(Rav = 6 m = radius of the acrylic sphere)

Use and radioactive sources to calibrate the energy scaleUse Cf252 neutron source to measure neutron detection efficiency (14%)Neutron signal does not depend on cos(sun)

From 306.4 days of data taking:

Number of events with kinetic energy Teff > 5 MeV and R < 550 cm: 2928Neutron background: 78 12 events. Background electrons 45 events

+18–12

Use likelihood method and the expected distributions to extract the three signals

Solar neutrino fluxes, as measured separately from the three signals:

CC(e) = 1.76 x 106 cm-2s-1

ES() = 2.39 x 106 cm-2s-1

NC() = 5.09 x 106 cm-2s-1

+0.06 +0.09–0.05 –0.09

+0.24 +0.12–0.23 –0.12

+0.44 +0.46–0.43 –0.43

SSM() = 5.05 x 106 cm-2s-1

+1.01–0.81

Calculated under the assumption thatall incident neutrinos aree

NC() – CC(e) = () = 3.33 0.64 x 106 cm–2 s –1

5.2 standard deviations from zero evidence that solar neutrino flux on

Earth contains sizeable or component (in any combination)

stat. syst. stat. and syst. errors combined

Write ES() as a function of (e) and ():

Note: CC(e) (e)

)(6

1)()( eES

(because ) )(6

1)( eESES

() = (e) + ()

Interpretation of the solar neutrino data using the two-neutrinomixing hypothesisVacuum oscillations e spectrum on Earth (e) = Pee 0(e) (0(e) spectrum at production)

e disappearance probability

L = 1.496 x 1011 m (average Sun – Earth distance with 3.3% yearly variation from eccentricity of Earth orbit) Fit predicted e spectrum to data using , m2 as adjustable parameters

)267.1()sin2(sin1 222ee E

LmP

4x10–10 eV2

10–10

4x10–11

Regions of oscillation parametersconsistent with solar neutrinodata available before the endof the year 2000

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

NEUTRINO OSCILLATIONS IN MATTERNeutrinos propagating through matter undergo refraction.

)0(2

112

Nfp

n

Refraction index:p: neutrino momentumN: density of scattering centresf(0): forward scattering amplitude (at = 0°)

In vacuum:

But energy must be conserved! Add a term V neutrino potential energy in matter

V < 0: attractive potential (n > 1)V > 0: repulsive potential (n < 1)

22 mpE

E

pEmnpE

222)( (for << 1)

Plane wave in matter: = ei(np•r –Et)

VEE

)0(22

NfEE

pV

(L. Wolfenstein, 1978)

Neutrino potential energy in matter

1. Contribution from Z exchange (the same for all three flavours)

Z

e,p,n e,p,n

)θ(NG(e)V(p)V wpFZZ2sin41

2

2

nFZ NG(n)V2

2

GF: Fermi coupling constant

Np (Nn): proton (neutron) density

w: weak mixing angle2. Contribution from W exchange (only for e!)e

e

W+

e

e

ρA

Z.NG[eV]V eFW

14106372

matter density [g/cm3]

NOTE: V() = – V( )

electron density

Example: two-neutrino mixing between e and in a constant

density medium(same results for mixing between e and )

Use flavour basis:

eEvolution equation:

tiH

2x2 matrix

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: m1, m2, are defined in vacuum

Rewrite:

22

22 2

2

1

10

01)(

MM

MEVM

EVEH

e

eWeeZ

diagonal term: no mixing

term responsible for e– mixing

= constant time-independent HDiagonalize non-diagonal term in H to obtain mass eigenvalues and eigenstates

Eigenvaluesin matter 2sin)()2cos(

2

1)(

2

1 2222222 mmM

EA

ZEVW 710526.12 [eV2]

Mixing angle in matter

( in g/cm3, E in MeV)

2cos

2sin2tan

2

2

m

mm

For = m2cos2 res mixing becomesmaximal (m = 45°) even if the mixing anglein vacuum is very small: “MSW resonance”(discovered by Mikheyev and Smirnov in 1985)

Notes: MSW resonance can exist only if < 45° (otherwise cos2 < 0)

For e < 0 no MSW resonance if < 45°

M2

M22

M12

Mass eigenvalues versus

2cos2mres

2sin)()2cos( 22222

2

mm

mm

Oscillation length in matter:

( oscillation length in vacuum)

At = res: 2sin

m

Matter-enhanced solar neutrino oscillations Solar neutrinos are produced in a high-density medium (the Sun core) and travel through variable density = (t) Use formalism of neutrino oscillations in matter: Evolution equation H = i / t H (2 x 2 matrix) depends on time t through(t)

H has no eigenstates

Solve the evolution equation numerically:

solar densityvs. radius

0. 0.2 0.4 0.6 0.8

R/RO

100

10

1

0.1

[g/cm3]

0

1)0(

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

iHt t

(pure e at production)

( = very small time interval)

)()()()()( ttiHtt

ttt

(until neutrino escapes from the Sun)

A simple class of solutions ( “adiabatic solutions”): a1 a1(0), a2 a2 (0) at all t

(if varies slowly over an oscillation length)At exit from the Sun (t=tE):

At production (t=0, in the Sun core): )0(sin)0(cos 20

10 mme

where 1, 2 are the “local” eigenstates of the time-independent Hamiltonian for fixed

Assume (mixing angle in vacuum) < 45°: cos> sinin vacuum

m> 45° at production if > res :

> res ( m2 in eV2, in g/cm3)

It is always possible to write:

2211 )()()( tatat

m < 45° m > 45°

M2

(|a1|2 + |a2|

2 = 1)

)0(0mm [ ; 1(0), 2(0) eigenstates of H for =(0)]

02

01 sin)0(cos)0( mm aa

)()0()()0()( 2211 EEE tatat 1(tE), 2(tE) :mass eigenstates in vacuum

In vacuum(because < 45° in vacuum)

22 e

)()( EeE tt

e DEFICIT

)/(

2cos106.6

2][

26

AZ

m

VMeVE

W

res

Regions of the (m2 , sin22 plane allowed by the solar neutrino fluxmeasurements in the Homestake, Super-K and Gallium experiments

Different energy thresholds different regions

of the (m2 , sin22 plane

The regions common to the three measurementscontain the allowed oscillation parameters

Super-K

Matter-enhanced solar neutrino oscillations (“MSW solutions”)(using only data available before the end of the year 2000)

LMA

SMA

LOW

10–3 10–2 10–1

sin22

10–5 eV 2

Survival probabilityversus neutrino energy

LMA: Large Mixing AngleSMA: Small Mixing Angle

Additional experimental informationEnergy spectrum distortions

Electron kinetic energy (MeV)

Dat

a/SS

MSuper-K 2002

e deficit is energy independent within errors (no distortions)

SNO recoil electron spectrumfrom e + d e– + p + p

SNO data/SSM prediction

Seasonal variation of measured neutrino flux in Super-K

Yearly variation of the Sun-Earth distance: 3.3% seasonal variation of the solar neutrino flux for some vacuum oscillation solutions

Note: expected seasonal variation fromchange of solid angle 6.6%

Days since start of data taking

The observed effect is consistentwith the variation of solid angle alone

Day-night effects (expected for some MSW solutions from matter-enhanced

oscillations when neutrinos traverse the Earth at night increase of e flux at

night)Subdivide night spectrum intobins of Sun zenith angle to study dependence on path length insideEarth and density

cos(Sun zenith angle)

)(5.0 ND

NDADN

SNO Day and Night Energy Spectra(CC + ES + NC events)

Difference Night – Day

SK data: comparison with oscillations

Electron energy distribution

Sun zenith angle distributionsfor different electron energy binsVacuum oscillation

SMA

LMA

LOW

Vacuum oscillation and SMA solution disagree with electron energy distribution LMA and LOW solutions describe reasonably well the zenith angle distributions No dependence on zenith angle within errors

Global fits to all existing solar neutrino data

48 data points, two free parameters (mixing angle , m2) 46 degrees of freedom

LMA solution: 2 = 43.5; m2 = 6.9x10– 5 eV2; = 31.7° (BEST FIT)

LOW solution: 2 = 52.5; m2 = 7.2x10– 8 eV2; = 39.1°

2 = 9; Prob(2 9) = 1.1% (marginally acceptable)

tan2

m2 [

eV2 ]

Note: variable tan2 is preferredto sin22 because sin22 is symmetricaround = 45° and MSW solutions are possible only if < 45°

LMA

The present interpretationof all solar neutrino datausing two-neutrino mixing

Verification of the LMA solution using antineutrinos from nuclear reactors

Nuclear reactors: intense, isotropic sources of e from decay of neutron-rich

fission fragments

e production rate: 1.9x1020 Pth s–1 (Pth [GW]: reactor thermal power)

Broad energy spectrum extending to 10 MeV, <E> 3 MeV

Uncertainty on the expectede flux: ±2.7 %

Detection:

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

thermalization by multiple collisions (<t> 180 s), followed by capture

e+ e– 2 n + p d + EMeV) prompt signal delayed signal

E = E – 0.77 MeV

KAMioka Liquid scintillator Anti-Neutrino Detector (KAMLAND)

e source: several nuclear reactors surrounding the Kamioka site

Total power 70 GW — average distance 175 35 km (long baseline)

Expected e flux (no oscillations) 1.3 x 106 cm–2 s–1 ~550 events/year

Average oscillation length <osc> 110 km for m2 = 6.9 x 10–5 eV 2 (LMA)

expect large e deficit with measurable energy modulation

KAMLAND detector

1000 tons liquid scintillator

Transparent balloon

Mineral oil

Acrylic sphere

Photomultipliers (1879)(coverage: 35% of 4)

Outer detector (pure H2O)225 photomultipliers

13 m18 m

KAMLAND sensitivity to e oscillations

Fiducial mass: 600 tons

1 regionsafter 3 years

Data taking in progress since January 2002 — results expected soon

Exclusion regions if no e deficit

is observed

Borexino experiment (at Gran Sasso National Lab)Study of the elastic scattering reaction + e¯ + e¯

Recoil electron detection threshold = 0.25 MeV sensitivity to from e– + Be7 e + Li7

(E = 0.861 MeV)

300 tons of ultra-pure liquid scintillator isotropic light emission no directionality

Expected event rate ( electron energy 0.25 — 0.8 MeV):

No oscillations: 55 events/day

LMA: 35 events/day ( 3 )

Expected background: ~ 15 events/day

Start data taking: mid 2003

+5–3

“ATMOSPHERIC” NEUTRINOS e

The main sources of atmospheric neutrinos:

, K + ( )

e + e( e) + ()At energies E < 2 GeV most parent particlesdecay before reaching the Earth

2

eeAt higher energies, most muons reach the Earth before decaying:

(increasing with E)

2

ee

Energy range of atmospheric neutrinos: 0.1 — 100 GeVVery low event rate: ~100 /year for a detector mass of 1000 tons

Uncertainties on calculations of atmospheric neutrino fluxes: typically ± 30% (from composition of primary spectrum, secondary hadron distributions, etc.)

Uncertainty on the /e ratio: only ±5% (because of partial cancellations)

Primary cosmic rayinteracts in upper atmosphere

Detection of atmospheric neutrinos

+ Nucleon + hadrons: presence of a long, minimum ionizing track (the )

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

(e interactions with multiple hadron production is difficult to separate from neutral current events

for atmospheric e only quasi-elastic interactions can be studied)Particle identification in a water Čerenkov countermuon track: dE/dx consistent with minimum ionization sharp edges of Čerenkov light ring

electron shower: high dE/dx “fuzzy” edges of Čerenkov light ring (from shower angular spread)

Measure electron/muon separation by exposing a 1000 ton water Čerenkov counter(a small Super-K detector) to electron and muon beams from accelerators.Probability of wrong identification ~2%

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

(/e)measured

(/e)predicted

42°

R = = 0.65 ± 0.08

Atmospheric neutrino data from Super-KDistance between event vertex and inner detector wall metre

(April 96 – July

01)

Lepton (e/) energy [GeV]

PC events are all assumed to be -like

Classification of Super-K events

(/e)Data

(/e)MC

= 0.638 ± 0.016 ± 0.05 (/e)Data

(/e)MC

= 0.658 ± 0.078+0.030–0.028

An additional event sample:Upward-going muons produced by interactions in the rock

Note: downward going muons are dominated by high-energy cosmic ray muons traversing the mountain and reaching the detector

Earth

detector

Measurement of zenith angle distribution

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

Earth atmosphere

local vertical axis

Down-going: = 0º

Up-going: = 180°

Horizontal: = 90°

Baseline L (distance betweenneutrino production point anddetector) depends on zenith angle

cos–1. –0.5 0. 0.5 1.

L [

Km

]

104

103

102

10

±5 km uncertaintyon production point

L varies between ~10 and ~12800 km as variesbetween 0º and 180º search for oscillationswith variable baselineStrong angular correlation between incident neutrinoand outgoing electron/muon for E > 1 GeV:

e/

25° for E = 1 GeV;as E increases

Super-K zenith angle distributions

No oscillation (2 = 456.5 / 172 degrees of freedom)

– oscillation best fit: m2 = 2.5x10–3 eV2, sin22 = 1.0

2 = 163.2 / 170 degrees of freedom

Super-K zenith angle distributions:

evidence for disappearance over distances of ~1000 — 10000 km

Oscillation cannot be – e:

Excluded by reactor experiment CHOOZ (see later) Zenith angle distribution for e-like events would show opposite sign up-down asymmetry (more upward-going e-like events) because /e 2 at production

a – oscillation is the most plausible solution + N + X requires E() > 3.5 GeV and decay fraction 18% only)

Combined region (90% CL):

m2=(1.3 – 3.9) x 10–3 eV2

sin22 > 0.92

Super-K

CHOOZ: a long baseline e disappearance experiment

sensitive to m2 > 7 x 10–4 eV2

Two reactors at the Chooz EDF power plant (total thermal power 8.5 GW)L = 998, 1114 m

Detector:5 tons of Gadolinium-loadedliquid scintillator(neutron capture in Gd ’swith total energy 8.1 MeV)17 tons unloaded scintillator(to contain the –rays)90 ton liquid scintillator(for cosmic ray rejection)

Detector installed in anunderground siteunder 300 m w.e.

Data taking: 1997-98(Experiment completed in 1998)

Event rate with reactors at full power: 25 / dayBackground rate (reactors off): 1.2 / day

Positron energy spectrum

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

and comparison with expected spectrumwithout oscillation

Measured spectrum

Expected spectrum (no oscillation)

Ratio (integrated over energy spectrum)

=

no evidence for e disappearancePositron energy

m2

[eV2]

Excluded region fore – x oscillations

CHOOZ experiment

Super-K –oscillation

Distinguishing – from – s oscillations

(s: “sterile” neutrino, a hypothetical neutrino with no coupling to W and Z

no interaction with matter)Two methods: Select a sample of multi-ring events with no –like ring (event sample enriched in neutral-current events + N + hadrons)

– oscillation: no up – down asymmetry in the zenith angle distribution

( and have the same neutral-current interaction)

– s oscillation: up – down asymmetry similar to that of –like events

Matter effects when neutrinos traverse the Earth

Potential energy in matter: V() = V() = VZ, V(s) = 0

– oscillation: no matter effects

– s oscillation:

GeV

eV

A

ZANGV nFZ

25108.3

2

2

neutron densitydensity [g/cm3]

(VZ < 0 for neutrinos, VZ > 0 for anti-neutrinos)

Matter-effects are important when VZE m2 (E 20 GeV for 5 g/cm3) Study high-energy -like events

Fit Super-K data with – s oscillations

No oscillation

–s oscillation

(– oscillations:

2min=163.2/170 dof)

Try – ’ oscillation with ’ = cos + sin s

sin< 0.19 (90% confidence)

pure

LSND and KARMEN experiments: search for – e oscillations

Conceptual design

800 Mevprotons

target+ beam dump

±

shielding

Detector

Anti-coincidence counter

Neutrino sources

800 MeV (kin. energy) proton-nucleus collision

70–90% +

~20%

nuclear absorption

Decay At Rest (DAR) ~75%

Decay In Flight (DIF) ~5%

+

DAR 100% e+ e

30–10% – DIF few %–

capture90%– p n

DAR 10%

e– e

The onlysource of

ee

e

10–3

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

LSND final results: evidence for – e oscillations

Positrons with 20 < E < 200 MeV correlated in space and time with 2.2 MeV -rayfrom neutron capture:N(beam-on events) – N(beam-off events) = 117. 9 ± 22.4 events Background from DAR = 29.5 ± 3.9

Background from DIF e = 10.5 ± 4.6

e signal = 87. 9

± 22.4 ± 6.0 events (stat.) (syst.)

Posc( – e) = (0.264 ± 0.067 ± 0.045) x 10-2

Tighter event selection (less background)Positrons with 20 < E < 60 MeV N(beam-on) – N(beam-off) = 49.1 ± 9.4 events-induced background = 16.9 ± 2.3

e signal = 32.2 ± 9.4 events

KARMEN final resultsEvents selection criteria: space and time correlation between prompt and delayed signal; time correlation between prompt signal and beam pulse; 16 < E(e+) < 50 MeV

Number of selected events = 15Expected backgrounds: Cosmic rays: 3.9 ± 0.2 Random coincidences between two e e– events: 5.1 ± 0.2

Random coincidences between e e– and uncorrelated : 4.8 ± 0. 3

Intrinsic e contamination: 2.0 ± 0. 2

Total background: 15.8 ± 0. 5 events

no evidence for – e oscillations

Posc( – e) < 0.085 x 10-2 (90% confidence)

LSND value: (0.264 ± 0.067 ± 0.045) x 10-2

Consistency between KARMEN and LSNDis only possible for a restricted regionof oscillation parameters because the baseline Lis different for the two experiments:L = 29 m (LSND);L = 17 m (KARMEN)

LSND allowed region andKARMEN exclusion region

LSND evidence for – e oscillations: a very serious problem

Define: mik2 = mk

2 – mi2 (i,k = 1, 2, 3)

m122 + m23

2 + m312 = 0

Evidence for neutrino oscillations:

Solar neutrinos: m122 6.9 x 10–5 eV2

Atmospheric neutrinos: m232 2.5 x 10–3 eV2

LSND: |m312| = 0.2 — 2 eV2

| m122 + m23

2 + m312 | = 0.2 — 2 eV2

If all three results are correct, at least one additional neutrino is needed.

To be consistent with LEP results (only three neutrinos), any additional neutrino, if it exists, must be “sterile” (no coupling to W and Z bosons no interaction with matter)

LSND result needs confirmation

MiniBooNE (Booster Neutrino Experiment at Fermilab)Goal: to definitively confirm (or disprove) the LSND signal start with – e appearance search;

then search for – e search;

if a positive signal is found, build a second detector at different L

Fermilab8 GeV proton synchrotron

Beryllium target

50 mdecayregion

450 mearth

focuses+ in analmost parallel beam

fl

ux

(arb

itra

ry u

nit

s)E [GeV]

Neutrino beam fluxcalculations

MiniBooNE detector 12 m diameter spherical tank 807 tons mineral oil used as Čerenkov radiator fiducial mass 445 tons optically isolated inner region with 1280 20 cm diam. PM tubes external anticoincidence region with 240 PM tubes

Particle identification:based on different behaviour of electrons,muons, pions and pattern of Čerenkov light rings

sin22

LSND allowedregion: 90% C.L. 99% C.L.

MiniBooNE expectations for two years of data taking (1021 protons on target)

~500K C –X events, ~70K C X events

Background to the – e oscillation signal:

1500 eC e– X events (from beam contamination)

500 mis-identified –

500 mis-identified°

+ 1000 eC e– X events

if the LSND result is correct

Note: the electron energy distributions

from – e oscillations and from

the e contamination in the beam

are different because the and contamination e have

different energy spectra

MiniBooNE exclusion region aftertwo years of data taking

if no oscillation signal is observed

Start data taking: June 2002

Long baseline experiments at acceleratorsPurpose: to provide definitive demonstration that the atmospheric deficit

is due to neutrino oscillations using accelerator-made .

Distortions of the energy spectrum at large distance (measurement of m2 and sin22);

Ratio of neutral current to charged current events (to distinguish – oscillations

from oscillations to a “sterile” neutrino s); appearance at large distance in a beam containing no at production.

Super-K L/E distribution does not showoscillatory behaviour expected from oscillations because of poor resolutionon the L/E variable at large L/E values

L / E [km/GeV]

Dat

a

Pre

dic

tion

Ideally:

E

Lm222 27.1sin)2(sin1

Prediction

Data

Maximum L 12800 km to study the regionL/E > 104 km need events with E < 1 GeV for whichthe angular correlation between the incident neutrino andthe outgoing muon is weak poor L/E resolution

Planned measurements at long baseline accelerator experiments:

Long baseline accelerator experiments(in progress or in preparation)

Project Baseline L <E> Status

K2K (KEK to KAMIOKA) 250 km 1.3 GeV Data taking since June 99

MINOS (Fermilab to Soudan) 735 km few GeV Start data taking: 2005

CERN to Gran Sasso 732 km 17 GeV Start data taking: 2006

Threshold energy for + N – + X: E > 3.5 GeV

Typical event rate ~1 – event / year per ton of detector mass

need detectors with masses of several kilotons beam angular divergence:

+

beam line

from + + decay GeV 10at mrad 3][

03.0

GeVE

GeV

p

p

L

T

Beam transverse size: 100 m – 1 km at L > 100 km no problems to hit the far detector

but neutrino flux decreases as L–2 at large L

K2K

12 GeVproton

synchrotron

K2K Front Detector: neutrino fluxmonitor and measurement of interactions without oscillations1 Kton Water Čerenkov detector:Similar to Super-K;fiducial mass 25 tonsScintillating Fibre Water Detector(SciFi):Detect multi-track events;fiducial mass 6 tonsMuon chambers:Measure range from decay;mass 700 tons; beam monitor

Neutrino beamcomposition:95% 4% 1% e

L=250 km

1R: 1–ring -like eventsbeam spill duration

E[GeV]

Expected Posc(–) versus E at L = 250 km

for m2 = 3x10–3 eV2, sin22 = 1

Expected shape of the spectrum

in Super-K with and without disappearance

Beam–associated events in Super-K

June 1999 – July 2001 (4.8x1019 protons on target)

FCFV events, Evis > 30 MeV: Expected (Posc = 0): 80.1 events Observed: 56 events (probability of a statistical fluctuation ~3% if Posc = 0)

Nov 1999 – July 2001 (stable beam conditions)

1Revents:Observed: 29 events

+6.2–5.4

Posc = 0

Measurement of the energy distribution in Super-K

using 1R events (assumed to be quasi-elastic events + n – + p)

–

Recoil proton(not detected because under Čerenkov threshold)

Incident direction(precisely known)

Assume target neutron at rest and apply two-body quasi–elastic kinematics to extract incident energy:

cos

5.0 2

pEM

mMEE

(M nucleon mass)

E [GeV]

Expected shape(no oscillation)

Expected shapefor disappearancem2 = 3x10–3 eV2

sin22 = 1 (Best fit)

Measured E distribution shows distortion

consistent with oscillation with m2 = 3x10–3 eV2, sin22 = 1, as suggested by atmospheric neutrino data

Probability for no oscillation 0.7% (combining eventdeficit and distortion of spectral shape)

MINOS experimentNeutrino beam from Fermilabto Soudan (an inactive iron minein Minnesota): L = 730 km

Accelerator:Fermilab Main Injector (MI)120 GeV proton sinchrotronHigh intensity (0.4 MW):4x1013 protons per cycleRepetition rate: 1.9 s4x1020 protons on target / yHadron decay pipe: 700 m

MINOS Far Detector

8 m octagonal steel tracking calorimeter Magnetized steel plates 2.54 cm thick 4 cm wide scintillator strips between plates 2 modules, each 15 m long 5400 ton total mass (fiducial mass 3300 tons) 484 planes of scintillator strips (26000 m2) Steel plates are magnetized: toroidal field, B = 1.5 T

Far Detector is half-built, to be completed byJune 2003Now recording cosmic ray events

MINOS Near Detector 3.8x4.8 m “octagonal” steel tracking calorimeter Same basic construction as Far Detector 282 magnetized steel plates 980 ton total mass (fiducial mass 100 tons) installed 250 m downstream of the end of the decay pipe

First protons on target scheduled for December 2004

MINOS: Expected energy distributions for – events

Low energy beam, exposure of 10 kton x year

Histogram: no disappearance

Data points: oscillation with sin22 = 0.9

m2 is measured from position of minimum in the ratio versus E plot;sin22 is measured from its depth.

MINOS: distinguishing between – and – s oscillations

Compare ratio NC/CC defined as

Rate of muonless events

Rate of – events

in Far and Near Detector.

– oscillations:

is under threshold for production

no charged current events; same neutral current events as

– s oscillations:

s does not interact with matter

no charged current events; no neutral current events

MINOS excluded region for – oscillations if (NC/CC) is found to be the same within errors in the Near and Far Detector

NearFar CC

NC

CC

NC

NearFar CC

NC

CC

NC

10 kton x year

Beam energy:

Low

Medium

High

CNGS (CERN Neutrinos to Gran Sasso)

Search for appearance at L = 732 km

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

dEEEEANE

GeV

)()()(max

5.3

PNormalization constant:contains detector mass,running time, efficiencies,etc.

flux cross-section for – production

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

E

Lm

E

LmP

– oscillation probability P:

Good approximation for: L = 732 km, E > 3.5 GeV, m2 < 4x10–3 eV2

max

5.3

22222 )(

)())(2(sin61.1E

GeV

dEE

EELmN

Disadvantages:L = 732 km is too short to reach the first – oscillation maximum

N depends on (m2) 2 very low event rates at low values of m2

Advantages: Beam optimization does not depend on m2 value

Neutrino beamlayout at CERN

400 GeV proton beam fromthe CERN SPS

Neutrino beam energyspectra and interactionrates at Gran Sasso

Primary protons:400 GeV;4x2.3x1013 / SPS cycleSPS cycle: 26.4 s Running efficiency 75%Running time 200 days/yearProtons on target: 4.5 x 1019 / year (sharing SPS with other users)

With SPS in dedicated mode (no other user) expect 7.6 x 1019 protons on target / year

Search for appearance at Gran SassoTwo detectors (OPERA, ICARUS)No near detector

Gran Sasso National Laboratory and the two neutrino detectors

OPERA experiment: – detection through the observation of one-prong decaysTypical mean decay length 1 mm need very good space resolutionUse photographic emulsion (space resolution ~1 m)

“Brick”: 56 emulsion filmsseparated by 1 mm thick Pb plates

packed under vacuumInternal brick structure

Plastic base

50 m thick emulsion films

Bricks are arranged into “walls” of 52 x 64 bricksWalls are arranged into “supermodules”: 31 walls / supermoduleTwo supermodules, each followed by a magnetic spectrometer206 336 bricks, total mass 1800 tonsTrack detectors (orthogonal planes of scintillator strips) are inserted among brick walls to provide trigger and to identify the brick where the neutrino interaction occurred. The brick is immediately removed for emulsion development andautomatic scanning and measurement using computer-controlled microscopes

OPERA supermodule

Magnetic spectrometer: magnetized iron dipole

12 Fe plates5 cm thickequipped withtrackers (RPC)

OPERA: backgrounds and sensitivity

– oscillation signalExclusion regions

3 years

5 years

5 year run1800 ton target mass2.25x1020 protons on target

ICARUS: a novel detector based ona liquid Argon Time Projection Chamber(TPC)Detect primary ionization in Argon3-dimensional event reconstructionwith space resolution ~1 mmExcellent calorimetric energy resolutionfor hadronic and electromagneticshowersUV scintillation light emitted in Argonis collected by PM tubes to providea t=0 signal

Cryostat length along z: 19.6 m

Electrodes atnegative highvoltage

Charge-collecting electrodes

Drift field: 1 kV/cmDrift times > 3 ms

Measurement of coordinates:

x, z: charge-collecting electrodes (wires planes) y: drift time

A 600 Ton module (T600) is operational;installation at Gran Sasso starts in 2003

Some events detected by T600

Hadron interaction

Muon decayat rest

Electromagnetic shower

Cosmicmuonwith -rays

T3000 ICARUS Detector (proposed, operational by Summer 2006)

3000 tons, 2350 tons of active Argon target

Physics topics to be addressed by ICARUS T3000 Solar neutrinos Atmospheric neutrinos Supernova neutrinos CNGS beam neutrinos Proton decay

~70 m

ICARUS T3000: search for appearance in the – e– e decay channel

Main background source: e + N e– + X (from the <1% e contamination in the beam)

Use kinematic criteria to separate signal from background: Beam e have harder spectrum than signal has lower visible energy Signal has two invisible neutrinos in the final state larger missing transverse momentum

Expected distributions for 2.25 x 1020 protons on target (5 years of data taking)

Final signal selection is based on 3-dimensional likelihood using three variables with different distributions for signal and background: visible energy Evis

missing transverse momentum pTmiss

= pTe / (pT

e + pThad + pT

miss)

For each event define two likelihoods: Likelihood to be a signal event LS(Evis , pT

miss, )

Likelihood to be a background event LB(Evis , pTmiss, )

Define = LS/LB

Expected signal event rates and background

m2=1.6x10–3 eV2 m2=2.5x10–3 eV2 m2=3.0x10–3 eV2 m2=4.0x10–3 eV2 Background

3.7 9.0 13.0 23.0 0.7

for 2.25x1020 protons on target (5 years of data taking)Same sensitivity as OPERA

e signal

Short baseline searches for – oscillationsCHORUS and NOMAD experiments at CERN (approved in 1992 to verify the hypothesisthat was an important component of dark matter with a mass few eV)

The SPS Neutrino Beam from 1992 to 1998

Target: 800 kg of fully sensitive emulsion Fibre tracker: high resolution tracker to localize neutrino event in emulsionMagnetic spectrometers and calorimeters: to measure secondary particle momentum and energy

NOMAD detector electron/hadron

separation

Momentum resolution: p/p = ±3.5% for p < 10 GeV/cElectromagnetic Calorimeter resolution:

%1%2.3

EEE (E in GeV)

Three typical NOMAD events

+ N – + hadrons

e + N e– + hadrons

e + N e+ + hadrons

– track

Electromagneticcalorimeter

signal amplitude

CHORUS: – detection through the observation of one-prong decaysNeutrino event vertex reconstruction with sub-m resolutionScan secondary tracks for decay “kink” near the event vertex

1 events (candidates for – – decay)Expected for sin22=1 and m2> 50 eV2: 5014 events Expected background: 0.1 Observed: 0

0 events (candidates for – h– decay)Expected for sin22=1 and m2> 50 eV2: 2004 events Expected background: 1.1 Observed: 0

NOMAD: – detection using kinematic criteria

– e– candidatesExpected for sin22=1 and m2> 50 eV2: 2826 events Expected background: 0.61 Observed: 0

– h– candidatesExpected for sin22=1 and m2> 50 eV2: 5343 events Expected background: 0.76 Observed: 1

– (h– h– h+) candidatesExpected for sin22=1 and m2> 50 eV2: 675 events Expected background: 0.32 Observed: 0

No evidence

for – oscillations

sin22

m2 [

eV2 ]

Final CHORUS & NOMADexclusion regions

for – oscillation

CHORUS result:two different statistical methods T. Junk Feldman & Cousins

Combined result uses theFeldman & Cousins method

CHORUS, NOMAD: the most sensitive oscillationsearch experiments done so far.However, the m2 value driving – oscillations (m2 2.5x10–3 eV2)

is much lower than anticipated in 1992

LONG–TERM FUTURE Precise measurement of the neutrino mixing matrix Detect CP violating effects in neutrino oscillationsAssumptions: LSND result will NOT be confirmed only three neutrinos m1 < m2 < m3 ; two independent m2 values

m22 – m1

2 12 = (0. 3 — 2)x10–4 eV2 (oscillations of solar neutrinos)

m32 – m2

2 23 = (1.3 — 3.9)x10–3 eV2 (oscillations of atmospheric neutrinos)

Oscillations among three neutrinos are described by three angles (12, 13, 23)

and one CP-violating phase ():

3

2

1

231313122323121323122312

231323131223122313121223

1312131312

ccsscescsccess

scssseccsscesc

ssccc

ii

ii

e

(cik cosik; sik sinik )

Present experimental information:

1. Solar neutrinos: e disappearance driven by 12, large mixing (27° < 12 < 39°)

2. Atmospheric neutrinos: disappearance driven by 23, large mixing (37° < 23 < 53°)

3. CHOOZ nuclear reactor experiment: no evidence for e disappearance driven by 23

Constraints from the CHOOZ experiment for three–neutrino mixing Formalism can be simplified because 12 << 23 (32/12 10)

Oscillation lengths in the CHOOZ experiment (<E> 3 MeV, L 1000 m):

LE

m 3600054.212

12 50%)( m 300054.223

23

E

comparable to L

neglect oscillation terms driven by 12 ( set L/12 = 0 in all formulae)

e disappearance probability in the CHOOZ experiment:

)27.1(sin2sin1)( 23

2

13

2

EL

eeosc P (identical to two-neutrino mixing)

CHOOZ limit: sin2213 < at 23 .x10–3 eV2 13 < °

CP violation for three–neutrino mixingCP violation: Posc( – ) Posc( – )

CPT invariance: Posc( – ) = Posc( – ) (, = e, , neutrino flavour index)

Posc( – ) = Posc( – ) because of CPT invariance

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

Measuring CP violation effects in neutrino oscillations requires neutrino beamsat least 100 times more intense than existing ones.

NEUTRINO FACTORY: a muon storage ring with long straight sections

pointing to neutrino detectors at large distance. Stored muons: per year

Components of a Neutrino Factory: A very high intensity proton accelerator. Beam intensity up to 1015 protons/s, energy few GeV ; A large aperture magnetic channel located immediately after the proton target to capture± from the target and ± from ± decay; Muon “cooling” to reduce the muon beam angular and momentum spread; Two or more muon accelerators in series; A muon storage ring with long straight sections.

Stored + pure and e beams

Stored – pure and e beams

Fluxes and energy spectra precisely calculable from decay kinematics

Search fore – oscillations:

Detection of “wrong sign” muons (charge sign opposite to stored muons) need magnetic detector

A possible scheme for a Neutrino Factorylong 20 cm aperture

superconductive solenoidB = 10 T

Intense R&D programon Neutrino Factoriesin progress, but no proposal yet.

Muon coolingIn the transverse plane: successive stages of acceleration and ionization loss

beam lineinitialmuon

momentumLiH

absorberreduces p

RF cavity

Acceleration increases onlythe longitudinal momentum

component reduce angle to beam line

In the longitudinal plane:Use RF cavity with time–modulated amplitude:Small amplitude for early (fast) muons;Large amplitude for late (slow) muons

Expected neutrino fluxes (particles / (year x GeV)

through a 10 m diameterdetector at L = km;

+ with E = GeV

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

232

E

L

E

L

E

LC

E

LB

E

LAe P

CP violation in e – oscillationsDefinition: Pe Posc(e – ) ; Pe Posc(e – )

CP violating terms (note sign of phase )

A = (sin23 sin213 )2

B = (cos23 sin212 )2

C = cos13 sin212 sin213 sin223

CP violation in neutrino oscillations is measurable only if 13 0

AND the experiment is sensitive to BOTH 12 and 23

A e oscillation experiment with much higher sensitivity than CHOOZ

is needed to measure 13

Disappearance experiments at nuclear reactors are systematically limitedby the uncertainty on the e flux (± 2.7%)

need a – e appearance experiment with very high sensitivity (Posc sin2213)

A high sensitivity – e oscillation experiment requires a detector located near the first

oscillation maximum of 23. Existing experiments need a low energy neutrino beam.

K2K: neutrino flux too low despite large detector mass (Super-K)CNGS: program optimized for appearance (beam energy above threshold for

production, too high for a – e oscillation search), no near detector to measure

the intrinsic e contamination in beam

MINOS: expect marginal improvement with respect to CHOOZ

CHOOZ

MINOS

Future facilities (before building a full Neutrino Factory) JHF: a high intensity 50 GeV proton synchrotron in Japan scheduled to start in 2006. Can measure sin213 with high

sensitivity by aiming a neutrino beam at Super-K (L = 270 km)

sin213

Measurement of CP violation with a Neutrino Factory

Problem #1: sensitivity decreases rapidly with decreasing No sensitivity to phase for < °

Problem #2: Optimal L to measure is several km neutrino beam traverses the Earth° Matter effects have opposite sign for neutrino and antineutrino apparent CP violation

Solution to problem #2: Matter effects and true CP violation in the mixing matrix

have different E and L dependence take data with

two detectors at different distances and study effect as a

function of E

Expected number of events per year in a 40 kton detector for 2.5x1020 + decays

in the straight section of a 50 GeV Neutrino Factory:

L [km] N+X eNe–X NX

730 8.8x106 1.5x107 8x106

3500 3x105 6x105 3x105

7000 3x104 1. 3x105 5x104

CONCLUSIONS Convincing evidence for neutrino oscillations from solar and atmospheric neutrino experiments evidence for neutrino mixing (not yet included in the Standard Model) Do sterile neutrinos exist? Wait for MiniBooNE results to confirm or disprove the LSND evidence for – e oscillation [presumably, if sterile neutrinos exist, there is more than one (one for each family?)] Assume no sterile neutrino exists (wrong LSND result) and m << m << m:

then m and m

m2 = ( – )x–eV; m3 = – eV unless neutrinos are mass degenerate (m >> m), they are only a small component of dark matter in the Universe Mixing angles are found to be much larger in the neutrino sector than in

the quark sector. Data are consistent with maximal mixing for atmospheric (°), while the largest quark mixing angle is ° (the Cabibbo angle)

Present data suggest: e consists mainly of and , with little (zero?) ;

and are ~% and the remainder is the state

orthogonal to e

How big is the component of e? Sensitive measurements of must receive very high priority. The long term future of neutrino physics depends on

the magnitude of Neutrino Factories appear to be the only way to study CP violation in the neutrino sector. Are they feasible? Are they affordable? Need more R&D to answer.