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NEUTRINO OSCILLATIONS Luigi DiLella Marienburg Castle August 2002. Content of these lectures :. Short introduction to neutrinos Formalism of neutrino oscillations in vacuum Solar neutrinos: Production Results Formalism of neutrino oscillations in matter

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Luigi DiLella

Marienburg Castle

August 2002

Content of these lectures:

  • Short introduction to neutrinos
  • Formalism of neutrino oscillations in vacuum
  • Solar neutrinos:
  • Production
  • Results
  • Formalism of neutrino oscillations in matter
  • Future experiments
  • Atmospheric neutrinos
  • LSND and KARMEN experiments
  • Oscillation searches at accelerators:
  • Long baselineexperiments
  • Short baseline experiments
  • Long-term future
  • Conclusions

Neutrinos in the Standard Model

Measurement of the Z width at LEP: only three light neutrinos (ne, nm, nt)

Neutrino mass mn = 0 “by hand” two-component neutrinos:

helicity (spin component parallel to momentum) = – 1 for neutrinos

+ 1 for antineutrinos







helicity +1 neutrinos

helicity –1 antineutrinos

do not exist

If mn > 0 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: n  n lepton number is conserved

Examples: neutron decay N  P + e– + ne

pion decay p+m+ + nm

Majorana neutrinos: n  n (only one four-component spinor field)

lepton number is NOT conserved


Neutrinoless double–b decay: a way (the only way?) to distinguish Dirac from

Majorana neutrinos

(A, Z)  (A, Z+2) + e– + e–

violates lepton number conservation can only occur for Majorana neutrinos

A second-order weak process:

Process needs neutrino helicity flip between emission and absorption

(neutron decay emits positive helicity neutrinos, neutrino capture by neutrons requires negative helicity)

neutrinolessdouble–b decay can only occur if m(ne) > 0

Transition Matrix Element m(ne)

The most sensitive search for double-b decay:

76Ge32 76Se34 + e– + e– E (e–1) + E (e–2) = 2038 keV








two neutrons

of the same nucleus

Heidelberg–Moscow experiment:

Five enriched76Ge 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 underground

Gran Sasso National Laboratory (Italy)

Search for mono–energetic line at 2038 keV

No evidence for neutrinoless double-b decay:

m(ne) < 0.2 eV for Majorana neutrinos


Neutrino mass: relevance to cosmology

A prediction of Big Bang cosmology: the Universe is filled with a Fermi gas of neutrinos

at temperature T 1.9 K. Density ~60 n cm–3 , 60 n cm–3 for each neutrino type (ne, nm, nt)

Critical density of the Universe :

H0: Hubble constant (Universe

present expansion rate)

H0 = 100 h0 km s–1 Mpc –1(0.6 < h0 <0.8)

GN: Newton constant

Neutrino energy density (normalized to rc):

Wn = 1 for

Recent evidence from the study of distant Super-Novae:

rc consists of ~30% matter (visible or invisible) and ~70% “vacuum energy”

Cosmological models prefer non-relativistic dark matter (easier galaxy formation)

with rn 20% of matter density

cosmological limit on neutrino masses

Direct measurements of neutrino masses

ne: mc2 < 2.5 eV(from precise measurements of the electron energy spectrum from 3H decay)

nm: mc2 < 0.16 MeV (from a precise measurement of m+ momentum from p+ decay at rest)

nt: mc2 < 18.2 MeV(from measurements of t nt + 3, 5 or 6 p at LEP)

With the exception of ne direct measurements of neutrino masses have no sensitivity

to reach the cosmologically interesting region


Neutrino interaction with matter

W–boson exchange: Charged–Current (CC) interactions

Quasi-elastic scattering

ne + n  e– + p ne + p  e+ + n

nm + n  m– + p nm + p  m+ + n Energythreshold: ~112 MeV

nt + n  t – + p nt + p  t+ + n Energythreshold: ~3.46 GeV

Cross-section for energies >> threshold: sQE 0.45 x 10–38 cm2

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

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

nm + N  m– + hadrons nm + N  m+ + hadrons

nt + N  t – + hadrons nt + N  t+ + hadrons

Cross-sections for energies >> threshold: sDIS(n)  0.68E x 10–38 cm2(E in GeV)

sDIS( n )  0.5sDIS(n)

Z–boson exchange: Neutral–Current (NC) interactions

Flavour-independent: the same for all three neutrino types

n + N  n + hadrons n + N  n + hadrons


sNC( n)  0.3sCC(n)

sNC( n )  0.37sCC( n)

Very low cross-sections:

mean free path of a 10 GeV nm 1.7x1013 g cm–2

equivalent to 2.2x107 km of Iron









Suppression of t production

by nt CC interactions

from t mass effects

Neutrino – electron scattering

0 20 40 60 80 100




nee –



E (n) [GeV]

Cross-section: s = A x10–42E cm2 (E in GeV)

ne: A 9.5ne : A 3.4

nm, nt: A 1.6nm, nt : A 1.3

(all three

n types)

(ne only)

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

because s  GF2 W2 (W  total energy in the centre-of-mass system) and W2 2meEn



The most promising way to verify if mn > 0

(Pontecorvo 1958; Maki, Nakagawa, Sakata 1962)

Basic assumption: neutrino mixing

e, , are not mass eigenstates but linear superpositions

of mass eigenstates 1, 2, 3 with masses m1, m2, m3, respectively:

  • = e, ,  (“flavour” index)

i = 1, 2, 3 (mass index)

Uai: unitary mixing matrix


Time evolution of a neutrino state of momentum p

created as  at time t=0


are different if mj mk


appearance of neutrino flavour    at t > 0

Case of two-neutrino mixing

  mixing angle

For  at production (t = 0):


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

Natural units:

m2 m22 – m12

(in vacuum!)

Note: for m << p

Use more familiar units:

L = ct distance between

neutrino source and detector

Units:Dm2 [eV2]; L [km]; E [GeV] (or L [m]; E [MeV])

NOTE: Pab depends on Dm2 and not on m. However, if m1 << m2

(as for charged leptons and quarks), then Dm2m22m12  m22


Define oscillation length l:

Units:l [km]; E [GeV]; Dm2 [eV2]

(or l [m]; E [MeV])

Larger E, smaller Dm2

Smaller E, larger Dm2


Distance from neutrino source


Disappearance experiments

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



  • Oscillation experiments using ne from nuclear reactors

(En few MeV: under threshold for m or t production)

  • nm detection at accelerators or from cosmic rays

(to search for nmnt oscillations if En is under threshold

for t production)

Main uncertainty: knowledge of the neutrino flux for no oscillation

the use of two detectors (if possible) helps

n beam

Far detector

measures Paa

Near detector

measures n flux

n source


Appearance experiments

Use a beam of na and detect nb (b  a)at distance L from source

  • Examples:
  • Detect ne + Nucleon  e- + hadrons in a nm beam
  • Detect nt + Nucleon  t - + hadrons in a nm beam

(Energy threshold  3.5 GeV)


  • nbcontamination in beam must be precisely known

(ne/nm  1% in nm 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.


Under the assumption of two-neutrino mixing:

  • Observation of an oscillation signal allowed region Dm2 versus sin2(2)
  • Negative result upper limit to Pab (Pab< P) exclusion region

Large Dm2 short l

Average over source and detector size:

Small Dm2 long l:


(the start of the first oscillation)






Neutrino source Flavour Baseline L Energy Minimum Dm2

Sun ne1.5 x 108 km 0.2 15 MeV 10-11 eV2


nm ne

10 km 

13000 km

0.2 GeV 

100 GeV

Cosmic rays

10-4 eV2

20 m 

250 km

Nuclear reactors


<E>  3 MeV

10-1  10-6 eV2


nm ne

15 m 

730 km

20 MeV 

100 GeV


10-3  10 eV2


  • Solar Neutrino Deficit: ne disappearance between Sun and Earth
  • Atmospheric neutrino problem: deficit of nm coming from the other side

of the Earth

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

of nm ,ne and nm



Birth 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 fusion

Balance between gravity and pressure hydrostatic equilibrium

Final result from a chain of fusion reactions:

4p  He4 + 2e+ + 2ne

Average energy produced in the form of electromagnetic radiation:

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

(<E(2ne)>  0.59 MeV)

(from 2e+ + 2e–  4g)

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

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

Neutrino flux on Earth: F(ne) 6.4x1010 cm–2 s –1

(average Sun-Earth distance = 1.496x1011 m)



(developed and continuously updated by J.N. Bahcall since 1960)


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


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


  • 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

RadiusR = 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 on

surface today


Two fusion reaction cycles

pp cycle (98.5% of L)

p + p  e+ + ne + d p + p  e+ + ne + d or (0.4%): p + e– + p ne + d

p + d  g + He3 p + d  g + He3

He3 +He3 He4 + p + p or (2x10-5): He3 + p He4 + e+ + ne


p + p  e+ + ne + d

p + d  g + He3

He3 +He4  g + Be7 p + Be7  g + B8

e– + Be7  ne + Li7 B8  Be8 + e+ + ne

p + Li7  He4 +He4 Be8  He4 +He4


or (0.13%)

CNO cycle (two branches)

p + N15  C12 +He4 p + N15  g+O16

p + C12  g+N13 p + O16  g+F17

N13  C13 + e+ + ne F17  O17 + e+ + ne

p + C13 g+N14 p + O17  N14 +He4

p + N14 g+O15

O15  N15 + e+ + ne

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

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)


pp : p + p  e+ + ne + d

7Be : e– + Be7  ne + Li7

pep : p + e– + p ne + d

8B : B8  Be8 + e+ + ne

hep : He3 + p He4 + e+ + ne

Line spectra: cm-2 s-1

Continuous spectra: cm-2 s-1 MeV -1

Radial distributions of neutrino production

inside the Sun, as predicted by the SSM


The Homestake experiment (1970–1998): first detection of solar neutrinos

A radiochemical experiment (R. Davis, University of Pennsylvania)

ne + Cl 37 e– + Ar 37 Energy threshold E(ne) > 0.814 MeV

Detector: 390 m3C2Cl4 (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 day

Experimental 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 ne + Cl 37(half-life t1/2 = 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 tank

Results over more than 20 years of data taking

SNU (Solar Neutrino Units): the unit to

measure event rates in radiochemical


1 SNU = 1 event s–1 per 1036 target atoms

Average of all measurements:

R(Cl 37) = 2.56  0.16  0.16 SNU

(stat) (syst)

SSM prediction: 7.6 SNU







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

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

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

Cross-sections: s(ne)  6 s(nm)  6 s(nt)

(5MeV electron path

in water  2 cm)

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.

Verify solar origin of neutrino signal

from angular correlation between

recoil electron and incident neutrino




Super-Kamiokande detector

Cylinder, height=41.4 m, diam.=39.3 m

50 000 tons of pure water

Outer volume (veto) ~2.7 m thick

Inner volume: ~ 32000 tons (fiducial

mass 22500 tons)

11200 photomultipliers, diam.= 50 cm

Light collection efficiency ~40%

Inner volume while filling


Recoil electron kinetic energy distribution from

ne– e elastic scattering of mono-energetic neutrinos

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

convolute with predicted spectrum to obtain

SSM prediction for electron energy distribution


SSM prediction



6 8 10 12 14

Electron kinetic energy (MeV)

Results from 22400 events (1496 days of data taking)

Measured neutrino flux (assuming all ne): F(ne) = (2.35  0.02  0.08) x 106 cm-2 s –1

(stat) (syst)

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

Data/SSM = 0.465  0.005







(including theoretical error)


Comparison of Homestake and Kamioka results with SSM predictions

0.465  0.016

2.56  0.23

Homestake and Kamioka results were known since the late 1980’s.

However, the solar neutrino deficit was not taken seriously at that time.



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

He3 +He4  g + Be7 e– + Be7  ne + Li7 (Homestake)

p + Be7  g + B8 B8  Be8 + e+ + ne (Homestake, Kamiokande, Super-K)

Fusion reactions strongly suppressed by Coulomb repulsion






Potential energy:





(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

Nuclear physics term difficult to calculate

measured at energies ~0.1– 0.5 MeV

and assumed to be energy independent

Tunnel effect:

v = relative velocity

Predicted dependence of the ne fluxes on Tc:

From e– + Be7  ne + Li7: F(ne)  Tc8

From B8  Be8 + e+ + ne : F(ne)  Tc18

F  TcN DF/F = N DTc/Tc

How precisely do we know

the temperature T of the Sun core?

Search for ne from p + p  e+ + ne + d (the main component of the

solar neutrino spectrum, constrained by the Sun luminosity)

very little theoretical uncertainties


Gallium experiments: radiochemical experiments to search for

  • ne + Ga71  e– + Ge71
  • Energy threshold E(ne) > 0.233 MeV reaction sensitive to solar neutrinos
  • from p + p  e+ + ne + 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 Lab

150 km east of Rome

Depth 3740 m w.e.

In the Baksan Lab (Russia) under

the 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 ne + Ga71 (half-life t1/2 = 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 ne + Ga71)
  • Install an intense radioactive source producing mono-energetic ne near the tank:

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

to 5 times the solar neutrino flux),E(ne) = 0.750 MeV, half-life t1/2 = 28 d



production rate

~1 atom/day



SAGE (1990 – 2001) 70.8 SNU


Data/SSM = 0.56  0.05





Data are consistent with:

  • Full ne flux from p + p  e+ + ne + d
  • ~50% of the ne flux from B8  Be8 + e+ + ne
  • Very strong (almost complete) suppression

of the ne flux from e– + Be7  ne + Li7

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  g + B8

Possible solutions:

  • At least one experiment is wrong
  • The SSM is totally wrong
  • The ne from e– + Be7  ne + Li7are no longer ne when they reach the Earth and become

invisible ne OSCILLATIONS


Unambiguous demonstration of solar neutrino oscillations: SNO

(the Sudbury Neutrino Observatory in Sudbury, Ontario, Canada)

SNO: a real-time experiment detecting Čerenkov

light emitted in1000 tons of high purity heavy

water D2O contained in a 12 m diam. acrylic

sphere, surrounded by 7800 tons of high purity

water H2O

Light collection: 9456 photomultiplier tubes,

diam. 20 cm, on a spherical surface with a radius

of 9.5 m

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

Electron energy detection threshold: 5 MeV

Fiducial volume: reconstructed event vertex

within 550 cm from the centre


Solar neutrino detection at SNO:

  • (ES) Neutrino – electron elastic scattering: n + e– n + e–

Directional,s(ne)  6 s(nm)  6 s(nt) (as in Super-K)

(CC) ne + d  e–+ p + p

Weakly directional: recoil electron angular distribution  1 – (1/3) cos(qsun)

Good measurement of the ne energy spectrum (because the electron takes

most of the ne energy)

(NC) n + dn + p + n

Equal cross-sections for all three neutrino types

Measure the total solar flux from B8  Be8 + e+ + nin the presence of

oscillations by comparing the rates of CC and NC events

Detection of n + dn + p + n

Detect photons ( e+e–) from neutron capture at thermal energies:

  • First phase (November 1999 – May 2001):

n + d  H3 + g (Eg = 6.25 MeV)

  • Second phase (in progress): add high purity NaCl (2 tons)

n + Cl 35Cl 36 + g – ray cascade (S Eg 8. 6 MeV)

  • At a later stage:

insert He3 proportional counters in the detector

n + He3p + H3 (mono-energetic signal)


SNO expectations

  • Use three variables:
  • Signal amplitude (MeV)
  • cos(qsun)
  • Event distance from centre (R)

(measured from the PM relative times)


(proportional to volume)


(Rav = 6 m = radius of the acrylic sphere)

Use b and g radioactive sources to calibrate the energy scale

Use Cf252 neutron source to measure neutron detection efficiency (14%)

Neutron signal does not depend on cos(qsun)


From 306.4 days of data taking:

Number of events with kinetic energy Teff > 5 MeV and R < 550 cm: 2928

Neutron background: 78  12 events. Background electrons 45 events



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


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

FCC(ne) = 1.76 x 106 cm-2s-1

FES(n) = 2.39 x 106 cm-2s-1

FNC(n) = 5.09 x 106 cm-2s-1

+0.06 +0.09

–0.05 –0.09

Note: FCC(ne) F(ne)

Calculated under the assumption that

all incident neutrinos are ne

+0.24 +0.12

–0.23 –0.12

FSSM(n) = 5.05 x 106 cm-2s-1

+0.44 +0.46

–0.43 –0.43



stat. syst.

stat. and syst. errors


FNC(n) – FCC(ne) = F(nmt) = 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 nm or nt component (in any combination)

Write FES(n) as a function of F(ne) andF(nmt):

(because )

F(n) = F(ne) + F(nmt)


Interpretation of the solar neutrino data using the two-neutrino

mixing hypothesis

Vacuum oscillations

ne spectrum on Earth F(ne) = Pee F0(ne) (F0(ne)spectrum at production)

ne disappearance probability

L = 1.496 x 1011 m (average Sun – Earth distance with 3.3% yearly variation

from eccentricity of Earth orbit)

Fit predicted ne spectrum to data using q, Dm2 as adjustable parameters

L [m]

E [MeV]

Dm2 [eV2]

4x10–10 eV2



Regions of oscillation parameters

consistent with solar neutrino

data available before the end

of the year 2000



(L. Wolfenstein, 1978)

Neutrinos propagating through matter undergo refraction.

p: neutrino momentum

N: density of scattering centres

f(0): forward scattering amplitude

(at  = 0°)

Refraction index:

In vacuum:

Plane wave in matter: = ei(np•r –Et)

(for e << 1)

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)


Neutrino potential energy in matter

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

n n


GF: Fermi coupling constant

Np (Nn): proton (neutron) density

w: weak mixing angle

e,p,n e,p,n

2. Contribution from W exchange (only for ne!)




matter density [g/cm3]

electron density



NOTE: V(n) = – V( n )


Example: two-neutrino mixing between ne and nm in a constant

density medium(same results for mixing between ne and nt)

Use flavour basis:

Evolution equation:

2x2 matrix

(Remember: for M p)

NOTE: m1, m2,  are defined in vacuum



diagonal term: no mixing

term responsible for ne–nm mixing

r = constant time-independent H

Diagonalize non-diagonal term in H to obtain mass eigenvalues and eigenstates


in matter


(r in g/cm3, E in MeV)

Mixing angle in matter

For x = Dm2cos2qxres mixing becomes

maximal (qm = 45°) even if the mixing angle

in vacuum is very small: “MSW resonance”

(discovered by Mikheyev and Smirnov in 1985)

Notes: MSW resonance can exist only if q < 45° (otherwise cos2q < 0)

For nex < 0 no MSW resonance if q < 45°





Mass eigenvalues versus x

Oscillation length in matter:

(l oscillation length in vacuum)

At x = xres:


Matter-enhanced solar neutrino oscillations

Solar neutrinos are produced in a high-density

medium (the Sun core) and travel through

variable density r = r(t)

Use formalism of neutrino oscillations in matter:

Evolution equationHn= i n / t

H (2 x 2 matrix) depends on time t through r(t)

H has no eigenstates

Solve the evolution equation numerically:

solar density

vs. radius








0. 0.2 0.4 0.6 0.8

(pure ne at production)

(d = very small time interval)

(until neutrino escapes from the Sun)


It is always possible to write:

(|a1|2 + |a2|2 = 1)

where n1, n2 are the “local” eigenstates of the time-independent Hamiltonian for fixed r

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

[;n1(0), n2(0) eigenstates of H for r=r(0)]

Assume q (mixing angle in vacuum) < 45°: cosq > sinq in vacuum

qm> 45° at production if x > xres :

x > xres (Dm2 in eV2, r in g/cm3)

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

(if r varies slowly over an oscillation length)

At exit from the Sun (t=tE):


n1(tE), n2(tE) :mass eigenstates in vacuum

In vacuum

(because q < 45° in vacuum)

qm < 45°

qm > 45°



Regions of the (Dm2 , sin22q) plane allowed by the solar neutrino flux

measurements in the Homestake, Super-K and Gallium experiments

Different energy thresholds

different regions

of the (Dm2 , sin22q) plane


The regions common to the three measurements

contain the allowed oscillation parameters


Matter-enhanced solar neutrino oscillations (“MSW solutions”)

(using only data available before the end of the year 2000)

Survival probability

versus neutrino energy



10–5 eV 2



10–3 10–2 10–1

LMA: Large Mixing Angle

SMA: Small Mixing Angle


Additional experimental information

Energy spectrum distortions

Super-K 2002


Electron kinetic energy (MeV)

SNO recoil electron spectrum

from ne + d  e–+ p + p

SNO data/SSM prediction

ne deficit is energy independent within errors (no distortions)


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 from

change of solid angle  6.6%

Days since start of data taking

The observed effect is consistent

with 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 ne flux at night)

Subdivide night spectrum into

bins of Sun zenith angle to study

dependence on path length inside

Earth and density

cos(Sun zenith angle)

SNO Day and Night Energy Spectra

(CC + ES + NC events)

Difference Night – Day


SK data: comparison with oscillations

Sun zenith angle distributions

for different electron energy bins

Electron energy


Vacuum oscillation




  • 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 q, Dm2)  46 degrees of freedom

LMA solution: 2 = 43.5; Dm2 = 6.9x10– 5 eV2; q = 31.7° (BEST FIT)

LOW solution: 2 = 52.5; Dm2 = 7.2x10– 8 eV2; q = 39.1°

D2 = 9; Prob(D2  9) = 1.1% (marginally acceptable)


Dm2 [eV2]

The present interpretation

of all solar neutrino data

using two-neutrino mixing

Note: variable tan2q is preferred

to sin22q because sin22q is symmetric

around q = 45° and MSW solutions

are possible only if q < 45°



Verification of the LMA solution using antineutrinos from nuclear reactors

Nuclear reactors: intense, isotropic sources of ne from b decay of neutron-rich fission fragments

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

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

Uncertainty on the expected ne flux: ±2.7 %


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

thermalization by multiple collisions

(<t> 180 ms), followed by capture

e+ e– 2gn + p  d +g (Eg = 2.2 MeV)

prompt signal delayed signal

E = En – 0.77 MeV

KAMioka Liquid scintillator Anti-Neutrino Detector (KAMLAND)

ne source: several nuclear reactors surrounding the Kamioka site

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

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

Average oscillation length <losc>  110 km for Dm2 = 6.9 x 10–5eV 2 (LMA)

expect large ne deficit with measurable energy modulation


KAMLAND detector

1000 tons liquid scintillator

Transparent balloon

Mineral oil

Acrylic sphere

Photomultipliers (1879)

(coverage: 35% of 4p)

Outer detector (pure H2O)

225 photomultipliers

13 m

18 m


KAMLAND sensitivity to ne oscillations

Fiducial mass: 600 tons

Exclusion regions

if no ne deficit

is observed

1 s regions

after 3 years

Data taking in progress since January 2002 — results expected soon


Borexino experiment (at Gran Sasso National Lab)

Study of the elastic scattering reaction

n + e¯n + e¯

Recoil electron detection threshold = 0.25 MeV

sensitivity to from e– + Be7  ne + Li7

(En = 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


( 3s )

Expected background: ~ 15 events/day

Start data taking: mid 2003




Primary cosmic ray

interacts in upper atmosphere



The main sourcesof atmospheric neutrinos:

p, K   m  + nm( nm)

 e  + ne( ne) + nm(nm)

At energies E < 2 GeV most parent particles

decay before reaching the Earth

At higher energies, most muons

reach the Earth before decaying:

(increasing with E)

Energy range of atmospheric neutrinos: 0.1 — 100 GeV

Very 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 nm/ne ratio: only ±5% (because of partial cancellations)


Detection of atmospheric neutrinos

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

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

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

for atmospheric ne only quasi-elastic interactions can be studied)

Particle identification in a water Čerenkov counter

muon 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 nm/ne ratio: first hints for a new phenomenon

Water Čerenkov counters: Kamiokande (1988), IMB (1991), Super-K (1998)

Conventional calorimeter (iron plates + proportional tubes): Soudan2 (1997)




R = = 0.65 ± 0.08


Atmospheric neutrino data from Super-K

Distance between event vertex and inner detector wall 1 metre

(April 96 – July 01)

PC events are all assumed to be m-like

Lepton (e/m) energy [GeV]


Classification of Super-K events



= 0.638± 0.016 ± 0.05





= 0.658± 0.078


An additional event sample:

Upward-going muons produced by nm interactions in the rock

Note: downward going muons are dominated by high-energy cosmic ray muons

traversing the mountain and reaching the detector


Measurement of zenith angle distribution

Definition of zenith angle q:

Polar axis along the local vertical axis, directed downwards

Earth atmosphere

Down-going: q = 0º


Up-going: q = 180°

Horizontal: q = 90°

Baseline L (distance between

neutrino production point and

detector) depends on zenith angle


local vertical axis





L varies between ~10 and ~12800 km as q varies

between 0º and 180º search for oscillations

with variable baseline

Strong angular correlation between incident neutrino

and outgoing electron/muon for E > 1 GeV:


L [Km]

a  25° for E = 1 GeV;

a  0 as E increases



±5 km uncertainty

on n production point

–1. –0.5 0. 0.5 1.



Super-K zenith angle distributions

No oscillation (c2 = 456.5 / 172 degrees of freedom)

nm– ntoscillation best fit: Dm2 = 2.5x10–3 eV2, sin22q = 1.0

c2 = 163.2 / 170 degrees of freedom


Super-K zenith angle distributions:

  • evidence for nm disappearance over distances of ~1000 — 10000 km
  • Oscillation cannot be nm– ne:
  • 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 nm/ne 2 at production

a nm – ntoscillation is the most plausible solution

(nt + N  t + X requires E(nt) > 3.5 GeV and t  m decay fraction  18% only)


Combined region (90% CL):

Dm2=(1.3 – 3.9) x 10–3 eV2

sin22q > 0.92


CHOOZ: a long baseline ne disappearance experiment

sensitive to Dm2 > 7 x 10–4 eV2

Two reactors at the Chooz EDF power plant(total thermal power 8.5 GW)

L = 998, 1114 m


5 tons of Gadolinium-loaded

liquid scintillator

(neutron capture in Gd g’s

with total energy 8.1 MeV)

17 tons unloaded scintillator

(to contain the g–rays)

90 ton liquid scintillator

(for cosmic ray rejection)

Detector installed in an

underground site

under 300 m w.e.

Data taking: 1997-98

(Experiment completed in 1998)


Event rate with reactors at full power: 25 / day

Background rate (reactors off): 1.2 / day

Positron energy spectrum

(prompt signal from ne + p  n + e+)

and comparison with expected spectrum

without oscillation

Measured spectrum

Expected spectrum (no oscillation)

Ratio (integrated over energy spectrum)

= 1.010 ± 0.028 ± 0.027

no evidence for ne disappearance

Positron energy


CHOOZ experiment

Excluded region for

ne–nx oscillations




nm–nt oscillation


Distinguishing nm–nt from nm –ns oscillations

  • (ns: “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 m–like ring (event sample enriched

inneutral-current events n + N n + hadrons)

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

(nm and nt have the same neutral-current interaction)

nm –ns oscillation: up – down asymmetry similar to that of m–like events

  • Matter effects when neutrinos traverse the Earth

Potential energy in matter: V(nm) = V(nt) = VZ, V(ns) = 0

nm–nt oscillation: no matter effects

nm –ns oscillation:

neutron density

density [g/cm3]

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

Matter-effects are important when VZEn Dm2 (En  20 GeV for r  5 g/cm3)

Study high-energy m-like events


Fit Super-K data with nm– ns oscillations

No oscillation

nm–ns oscillation

(nm–nt oscillations:

c2min=163.2/170 dof)


Try nm– n’oscillation with n’ = cosxnt + sinxns

pure nt

sin2x < 0.19 (90% confidence)


LSND and KARMEN experiments: search for nm–ne oscillations

Conceptual design



800 Mev





+ beam dump



Neutrino sources

Decay At Rest (DAR) ~75%

DAR 100%

nm e+ne



nm m+

Decay In Flight

(DIF) ~5%

800 MeV

(kin. energy)




m– p  nm n

nuclear absorption


DIF few %


nm m–

DAR 10%

The only

source of



nm e–ne



 10–3


Parameters of the LSND and KARMEN experiments


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 mA 200 mA

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 n source 29 m 17 m

Angle q between proton 11° 90°

and n direction

Data taking period 1993 – 98 1997 – 2001

Protons on target 4.6 x 1023 1.5 x 1023

Neutrino energy spectra from p+ m+nmdecay at rest




ne detection: the “classical” way

ne + p  e+ + n

delayed signal from npgd (Eg = 2.2 MeV)

KARMEN has Gd-loaded paper between

adjacent cells  enhanced neutron capture,

SEg = 8.1 MeV

prompt signal

KARMEN beam time structure

Repetition rate 50 Hz

Expect nm ne oscillation signal

within ~10 ms after beam pulse

LSND beam time structure

Repetition rate 120 Hz

0 600 ms

no correlation between event time

and beam pulse

time [ms]


LSND final results: evidence for nm– ne oscillations

Positrons with 20 < E < 200 MeV correlated in space and time with 2.2 MeV g-ray

from neutron capture:

N(beam-on events) – N(beam-off events) = 117. 9 ± 22.4 events

Background from DAR n = 29.5 ± 3.9

Background from DIF ne = 10.5 ± 4.6

ne signal = 87. 9 ± 22.4 ± 6.0 events

(stat.) (syst.)

Posc( nm– ne) = (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

n-induced background = 16.9 ± 2.3

ne signal = 32.2 ± 9.4 events


KARMEN final results

Events 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 = 15

Expected backgrounds: Cosmic rays: 3.9 ± 0.2

Random coincidences between two ne e– events: 5.1 ± 0.2

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

Intrinsic ne contamination: 2.0 ± 0. 2

Total background: 15.8 ± 0. 5 events

no evidence for nm– ne oscillations

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

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

Consistency between KARMEN and LSND

is only possible for a restricted region

of oscillation parameters because the baseline L

is different for the two experiments:

L = 29 m (LSND);

L = 17 m (KARMEN)

LSND allowed region and

KARMEN exclusion region


LSND evidence for nm– ne oscillations: a very serious problem

  • Define: Dmik2 = mk2 –mi2 (i,k = 1, 2, 3)
  • Dm122 +Dm232 +Dm312 = 0
  • Evidence for neutrino oscillations:
  • Solar neutrinos: Dm122  6.9 x 10–5 eV2
  • Atmospheric neutrinos: Dm232  2.5 x 10–3 eV2
  • LSND: |Dm312| = 0.2 — 2 eV2

| Dm122 +Dm232 +Dm312 | = 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 nm – ne appearance search;
  • then search for nm – ne search;
  • if a positive signal is found, build a second detector at different L

50 m



450 m



8 GeV proton




focuses p+ in an

almost parallel beam

n flux

(arbitrary units)

Neutrino beam flux


En [GeV]


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


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

~500K nmC m–X events, ~70K nC nX events

Background to the nm–ne oscillation signal:

1500 neC  e– X events (from beam contamination)

500 mis-identified m–

500 mis-identified p°

+ 1000 neC  e– X events

if the LSND result is correct

Note: the electron energy distributions

from nm – ne oscillations and from

the ne contamination in the beam

are different because the nm

and contamination ne have

different energy spectra

MiniBooNE exclusion region after

two years of data taking

if no oscillation signal is observed

LSND allowed


90% C.L.

99% C.L.

Start data taking: June 2002



Long baseline experiments at accelerators

Purpose: to provide definitive demonstration that the atmospheric nm deficit

is due to neutrino oscillations using accelerator-made nm .

Super-K L/E distribution does not show

oscillatory behaviour expected from

oscillations because of poor resolution

on the L/E variable at large L/E values




Maximum L  12800 km to study the region

L/E > 104 km need events with E < 1 GeV for which

the angular correlation between the incident neutrino and

the outgoing muon is weak poor L/E resolution

L / E [km/GeV]

Planned measurements at long baseline accelerator experiments:

  • Distortions of the nm energy spectrum at large distance (measurement of Dm2 and sin22q);
  • Ratio of neutral current to charged current events (to distinguish nm– ntoscillations

from oscillations to a “sterile” neutrino ns);

  • nt appearance at large distance in a beam containing no nt at production.

Long baseline accelerator experiments

(in progress or in preparation)

Project Baseline L<En>Status

K2K (KEK to KAMIOKA) 250 km1.3 GeVData taking since June 99 MINOS (Fermilab to Soudan) 735 kmfew GeVStart data taking: 2005

CERN to Gran Sasso 732 km17 GeVStart data taking: 2006

  • Threshold energy for nt + N t– + X: En > 3.5 GeV
  • Typical event rate ~1 nm m– event / year per ton of detector mass

need detectors with masses of several kilotons

  • nm beam angular divergence:

beam line



nm from p+m+nm decay

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



12 GeV



L=250 km

Neutrino beam


95% nm

4% nm

1% ne

K2K Front Detector: neutrino flux

monitor and measurement of nm

interactions without oscillations

1 Kton Water Čerenkov detector:

Similar to Super-K;

fiducial mass 25 tons

Scintillating Fibre Water Detector


Detect multi-track events;

fiducial mass 6 tons

Muon chambers:

Measure m range from p decay;

mass 700 tons; nm beam monitor


beam spill duration

1Rm: 1–ring m-like events


Expected Posc(nm–nm) versus En at L = 250 km for Dm2 = 3x10–3 eV2, sin22q = 1

Posc = 0

Expected shape of the nm spectrum

in Super-K with and without nm disappearance

En [GeV]

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)

1Rm events:Observed: 29 events




Measurement of the nm energy distribution in Super-K

using 1Rm events (assumed to be quasi-elastic events nm + n m– + p)




(precisely known)


Recoil proton

(not detected because under

Čerenkov threshold)

Expected shape

(no oscillation)

Expected shape

for nm disappearance

Dm2 = 3x10–3 eV2

sin22q = 1 (Best fit)

Assume target neutron at rest and apply

two-body quasi–elastic kinematics to extract

incident nm energy:

(M  nucleon mass)

Measured En distribution shows distortion

consistent with oscillation with Dm2 = 3x10–3 eV2,

sin22q = 1, as suggested by atmospheric neutrino data

Probability for no oscillation 0.7% (combining event

deficit and distortion of spectral shape)

En [GeV]


MINOS experiment

Neutrino beam from Fermilab

to Soudan (an inactive iron mine

in Minnesota): L = 730 km


Fermilab Main Injector (MI)

120 GeV proton sinchrotron

High intensity (0.4 MW):

4x1013 protons per cycle

Repetition rate: 1.9 s

4x1020 protons on target / y

Hadron 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 by

June 2003

Now 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 nm m–events

Low energy beam, exposure of 10 kton x year

Histogram: no nm disappearance

Data points: oscillation with sin22q = 0.9

Dm2 is measured from position of minimum in the ratio versus E plot;

sin22q is measured from its depth.


MINOS: distinguishing between nm–nt and nm–ns oscillations

Compare ratio NC/CC defined as

Rate of muonless events

Rate of m– events

in Far and Near Detector.

nm– nt oscillations:

nt is under threshold for t production

no charged current events;

same neutral current events as nm

nm– ns oscillations:

ns does not interact with matter

no charged current events;

no neutral current events

MINOS excluded region for nm–nt oscillations

if (NC/CC) is found to be the same within errors

in the Near and Far Detector

10 kton x year

Beam energy:





CNGS (CERN Neutrinos to Gran Sasso)

Search for nt appearance at L = 732 km

Expected number of nt + N t– + X events (Nt):

Normalization constant:

contains detector mass,

running time, efficiencies,



for t– production

nm flux

nm–nt oscillation probability Pmt:

Good approximation for: L = 732 km, E > 3.5 GeV, Dm2 < 4x10–3 eV2


  • L = 732 km is too short to reach the first nm–nt oscillation maximum
  • Nt depends on (Dm2) 2 very low event rates at low values of Dm2


  • Beam optimization does not depend on Dm2 value

400 GeV proton beam from


Neutrino beam

layout at CERN


Neutrino beam energy

spectra and interaction

rates at Gran Sasso

Primary protons:

400 GeV;

4x2.3x1013 / SPS cycle

SPS cycle: 26.4 s

Running efficiency 75%

Running time 200 days/year

Protons 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 nt appearance at Gran Sasso

Two detectors (OPERA, ICARUS)

No near detector

Gran Sasso National Laboratory and the two neutrino detectors


OPERA experiment: t – detection through the observation of one-prong decays

Typical t mean decay length 1 mm need very good space resolution

Use photographic emulsion (space resolution ~1 mm)

Plastic base

50 mm thick emulsion films

“Brick”: 56 emulsion films

separated by 1 mm thick Pb plates

packed under vacuum

Internal brick structure

Bricks are arranged into “walls” of 52 x 64 bricks

Walls are arranged into “supermodules”: 31 walls / supermodule

Two supermodules, each followed by a magnetic spectrometer

206 336 bricks, total mass 1800 tons

Track 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 and

automatic scanning and measurement using computer-controlled microscopes


OPERA supermodule

Magnetic spectrometer:

magnetized iron dipole

12 Fe plates

5 cm thick

equipped with

trackers (RPC)


OPERA: backgrounds and sensitivity

5 year run

1800 ton target mass

2.25x1020 protons on target

Exclusion regions

nm–nt oscillation signal

3 years

5 years


ICARUS: a novel detector based on

a liquid Argon Time Projection Chamber


Detect primary ionization in Argon

3-dimensional event reconstruction

with space resolution ~1 mm

Excellent calorimetric energy resolution

for hadronic and electromagnetic


UV scintillation light emitted in Argon

is collected by PM tubes to provide

a t=0 signal

Cryostat length along z: 19.6 m

Charge-collecting electrodes

Electrodes at

negative high


Drift field: 1 kV/cm

Drift 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





Muon decay

at rest

Electromagnetic shower

Hadron interaction


T3000 ICARUS Detector (proposed, operational by Summer 2006)

~70 m

  • 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

ICARUS T3000: search for nt appearance in the t – nte–ne decay channel

  • Main background source: ne + N  e–+ X(from the <1% necontamination in the beam)
  • Use kinematic criteria to separate signal from background:
  • Beam ne have harder spectrum than nm signal has lower visible energy
  • Signal has two invisible neutrinos in the final state larger missing transverse


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
  • r = pTe / (pTe + pThad + pTmiss)

For each event define two likelihoods:

  • Likelihood to be a signal event LS(Evis ,pTmiss,r)
  • Likelihood to be a background event LB(Evis ,pTmiss,r)

Define l = LS/LB

Expected signal event rates and background

Dm2=1.6x10–3 eV2 Dm2=2.5x10–3 eV2 Dm2=3.0x10–3 eV2Dm2=4.0x10–3 eV2 Background

3.7 9.0 13.0 23.00.7

t e signal

for 2.25x1020 protons on target (5 years of data taking)

Same sensitivity as OPERA


Short baseline searches for nm– nt oscillations

CHORUS and NOMAD experiments at CERN (approved in 1992 to verify the hypothesis

that nt 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 emulsion

Magnetic spectrometers and calorimeters: to measure secondary particle momentum

and energy


NOMAD detector



Momentum resolution: Dp/p = ±3.5% for p < 10 GeV/c

Electromagnetic Calorimeter resolution:

(E in GeV)


Three typical NOMAD events

nm + N m– + hadrons

m– track

ne + N  e– + hadrons



signal amplitude

ne + N  e+ + hadrons


CHORUS:t – detection through the observation of one-prong decays

Neutrino event vertex reconstruction with sub-mm resolution

Scan secondary tracks for decay “kink” near the event vertex

1m events (candidates for t –m– decay)

Expected for sin22q=1 and Dm2> 50 eV2: 5014 events

Expected background: 0.1


0m events (candidates for t – h– decay)

Expected for sin22q=1 and Dm2> 50 eV2: 2004 events

Expected background: 1.1


NOMAD:t – detection using kinematic criteria

t – e– candidates

Expected for sin22q=1 and Dm2> 50 eV2: 2826 events

Expected background: 0.61


t – h– candidates

Expected for sin22q=1 and Dm2> 50 eV2: 5343 events

Expected background: 0.76


t –  (h– h– h+) candidates

Expected for sin22q=1 and Dm2> 50 eV2: 675 events

Expected background: 0.32


No evidence

for nm– nt oscillations



exclusion regions

for nm– nt oscillation

Dm2 [eV2]

CHORUS result:

two different statistical methods

T. Junk

Feldman & Cousins

Combined result uses the

Feldman & Cousins method


the most sensitive oscillation

search experiments done so far.

However, the Dm2 value driving

nm–nt oscillations (Dm2 2.5x10–3 eV2)

is much lower than anticipated in 1992




  • Precise measurement of the neutrino mixing matrix
  • Detect CP violating effects in neutrino oscillations

Assumptions: LSND result will NOT be confirmed only three neutrinos

m1 < m2 < m3 ; two independent Dm2 values

m22 – m12D12 = (0. 3 — 2)x10–4 eV2(oscillations of solar neutrinos)

m32 – m22D23 = (1.3 — 3.9)x10–3 eV2(oscillations of atmospheric neutrinos)

Oscillations among three neutrinos are described by three angles (q12, q13, q23)

and one CP-violating phase (d):

  • (cik cosqik; sik sinqik )
  • Present experimental information:
  • Solar neutrinos: ne disappearance driven by D12, large mixing (27° < q12 < 39°)
  • Atmospheric neutrinos: nm disappearance driven by D23, large mixing (37° < q23 < 53°)
  • CHOOZ nuclear reactor experiment: no evidence for ne disappearance driven by D23

Constraints from the CHOOZ experiment for three–neutrino mixing

Formalism can be simplified because D12 << D23 (D32/D12 10)

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

comparable to L

neglect oscillation terms driven by D12 ( set L/l12 = 0 in all formulae)

ne disappearance probability in the CHOOZ experiment:

(identical to two-neutrino mixing)

CHOOZ limit: sin22q13 < 0.12 at D23 2.5x10–3 eV2q13 < 10°

CP violation for three–neutrino mixing

CP violation: Posc(na– nb) Posc( na– nb )

CPT invariance: Posc(na– nb) =Posc( nb– na )(a, b = e, m, t neutrino flavour index)

Posc(na– na) =Posc( na– na ) 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 beams

  • at 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: 1021 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 p± from the target and m± from p± 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 m+ pure nm and ne beams

Stored m– pure nm and ne beams

Fluxes and energy spectra precisely calculable from m decay kinematics

Search for ne – nm oscillations:

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

need magnetic detector


A possible scheme for a Neutrino Factory

long 20 cm aperture

superconductive solenoid

B = 10 T

Intense R&D program

on Neutrino Factories

in progress, but no proposal yet.


Muon cooling

In the transverse plane: successive stages of acceleration and ionization loss

beam line

Acceleration increases only

the longitudinal momentum

component  reduce

angle to beam line




RF cavity



reduces pm

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 x0.25 GeV)

through a 10 m diameter

detector at L = 732 km;

m+ with Em = 10, 20, 50 GeV


CP violation in ne–nm oscillations

Definition: Pem Posc(ne– nm) ; Pem Posc(ne– nm)

A = (sinq23 sin2q13 )2

B = (cosq23 sin2q12 )2

C = cosq13 sin2q12 sin2q13 sin2q23

CP violating terms (note sign of phase d)

CP violation in neutrino oscillations is measurable only if q13 0

AND the experiment is sensitive to BOTHD12 and D23

A ne oscillation experiment with much higher sensitivity than CHOOZ

is needed to measure q13

Disappearance experiments at nuclear reactors are systematically limited

by the uncertainty on the ne flux (± 2.7%)

need a nm – ne appearance experiment with very high sensitivity (Poscsin22q13)


A high sensitivity nm – ne oscillation experiment requires a detector located near the first oscillation maximum of D23. Existing experiments need a low energy neutrino beam.

K2K: neutrino flux too low despite large detector mass (Super-K)

CNGS: program optimized for nt appearance (beam energy above threshold for

t production, too high for a nm – ne oscillation search), no near detector to measure

the intrinsic ne contamination in beam

MINOS: expect marginal improvement with respect to CHOOZ


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 sin2q13 with high

sensitivity by aiming a neutrino beam

at Super-K (L = 270 km)




Measurement of CP violation with a Neutrino Factory

  • Problem #1: sensitivity decreases rapidly with decreasing q13
  • No sensitivity to phase d for q13 < 1°

Problem #2: Optimal L to measure d is several 1000 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 2.5x1020m+ decays

in the straight section of a 50 GeV Neutrino Factory:

L [km] nmNm+XneNe–X nNnX

730 8.8x106 1.5x1078x106

3500 3x105 6x105 3x105

7000 3x104 1. 3x105 5x104



  • 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 nm– ne oscillation [presumably, if sterile neutrinos

exist, there is more than one (one for each family?)]

  • Assume no sterile neutrino exists (wrong LSND result) and m1 << m2 << m3:

then m22 D12 and m32 D23m2 = ( 0.5–1.4)x10–2eV; m3 = 0.04–0.06 eV

unless neutrinos are mass degenerate (m >> Dm), 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 nm

(q23 45°), while the largest quark mixing angle is 13° (the Cabibbo angle)

  • Present data suggest: ne consists mainly of n1 and n2, with little (zero?) n3;

nm and ntare ~50% n3 and the remainder is the state

orthogonal to ne

  • How big is the n3 component of ne? Sensitive measurements of q13 must receive

very high priority. The long term future of neutrino physics depends on

the magnitude of q13

  • 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.