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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.