NEUTRINOS Luigi Di Lella Physics Dept., University of Pisa, Italy International School Niccolò Cabeo Ferrara, 25‐29 May 2015
Direct measurement of neutrino masses Double β decay Neutrino oscillations in vacuum Solar neutrinos Neutrino oscillations in matter “Atmospheric” neutrinos Long baseline oscillation searches at accelerators
Measurement of the θ13 mixing angle Do additional (“sterile”) neutrinos exist? Future neutrino projects Units h c == 1 == tLE −− 11 ][][][ += mpE 222
Conversion to more “familiar” units: hc = 33.197 MeV × fermi 1 fermi (fm) = 10-13 cm −2 Cross-section: =σ E ][][
To obtain cm2 multiply with: 2 − 2227 hc ×= 103894.0)( cm GeV Neutrinos in the Standard Model
Measurement of the Z-boson with at LEP: only 3 light neutrinos (νe νμ ντ) Hypothesis: mν = 0 two-component neutrino theory: Helicity (spin component parallel to momentum) = – ½ (neutrinos) p p ν: ν: + ½ (antineutrinos) spin spin helicity +½ neutrinos do not exist in Nature helicity –½ antineutrinos
If mν > 0 helicity is not a relativistic invariant (helicity changes sign in a reference frame moving faster than neutrino) neutrinos and antineutrinos with mν > 0 exist in both helicity states Neutrinos : Dirac or Majorana particles? Dirac neutrinos: ν ≠ ν lepton number conservation – + + Examples: neutron decay N → P + e + νe ; pion decay π →μ + νμ Majorana neutrinos: ν ≡ ν leptonic number is NOT CONSERVED – neutron decay N → P + e + νe : νe helicity + ½ + + V – A coupling pion decay π →μ + νμ : νμ helicity − ½ Neutrino masses: direct measurements
Measurement of the electron spectrum from Tritium ( 3H ) β - decay νe 1 3 3 − H1 → He2 + e + νe F(Z,E): Coulomb correction dn 2 2 ∝ e 0 0 )())((),( −−−+ mEEEEmEpEZF ν p: electron momentum dE E: electron kinetic energy For Tritium: E0 = 18.59 keV; τ1/2 = 12 .33 y E0: max. electron energy (“end point”) ] 1 - [keV
dE m = 0
/ ν dn
mν = 35 eV E0
E [keV]
E [keV] EXPERIMENTAL PROBLEMS
VERY LOW EVENT RATE NEAR END-POINT E ≈ E0 ⇒ require intense Tritium sources with large angular aperture Electron residual range <3 x 10−4 g cm−2 ⇒ gaseous Tritium source (or few atomic layers); electrons stop in the first detector. Solenoidal spectrometer with retarding electrostatic potential (V.M. Lobashev, 1985)
TRITIUM SOURCE B0 = 8.6 T parallel to z - axis
z z
U0 : negative electrostatic potential ≈18kV Troitsk experiment: V. N. Aseev et al., Phys. Rev.D 84 (2011) 112003 Tritium gas, source thickness 1017 molecules/cm2 Magnetic spectrometer: length 7 m, diameter 1.5 m
Expected spectrum (mν = 0)
2 2 mν = ‐0.67 ±2.53 eV ; upper limit mν < 2.05 eV (confidence level 95%) Mainz experiment: Ch. Kraus et al., Eur. Phys. J. C40 (2005) 447 (with apparatus very similar to Troitsk experiment) 2 2 mν = ‐0.6 ±2.2 ±2.1 eV ; upper limit mν < 2.3 eV (confidence level 95%) 2 Combined upper limit mν < 2 eV (PDG 2014, p.690) A new experiment in preparation: KATRIN (KArlsruhe TRItium Neutrino experiment) Gaseous Tritium: source thickness 5x1017 molecules /cm2 Solenoidal magnetic spectrometer: length 23.3 m, diameter 9.8 m Energy resolution ≈1eV at E = 18 keV Expected results after 3 years data-taking:
if mν = 0 upper limit mν <0.35eV; if mν > 0, mν statistical error ≈0.08eV pre-spectrometer (similar to the Troitsk experiment) 3 H2 injection
Decay electron transport by Main spectrometer solenoidal magnets + + + νμ Precision measurement of μ momentum from π →μ + νμ decay at rest K. Assamagan et al., Phys. Rev. D53 (1996) 6065 (at the PSI 590 MeV high-intensity cyclotron) + + Kinematics of π → μ + νμ decay at rest: 222 22 μπν −+= 2 + mpmmmm μμπ
Precise energy measurement of photon m = ± 00035.057018.139 MeV emitted in 4f → 3d transition of π π − − 24Mg “mesic atoms”: ΔE = 25.9 keV Precise measurement of μ+ magnetic moment (geħ/2mμ) (from measurement mμ = ± 000005.0658357.105 MeV of muon spin angular precession in magnetic field) p = ± 00011.079200.29 MeV (measured) + independent precise measurement of g μ (from the g – 2 experiments)
2 2 (consistent with m 2 = 0) mν ±−= 022.0001.0 MeV ν
mν < 0.19 MeV (confidence level 90%)
Contributions to ±0.022 MeV2 error: 0.021 MeV2 from m Dominant π uncertainty 0.008 from pμ 0.0003 from mμ + − + − ντ e + e →τ+ τ (ALEPH experiment at LEP) − − − → e νe ντ , μ νμ ντ , π ντ , .... Decays to one charged particle (τ+τ− identification) + + − →ντ π π π 2939 events + + + − − →ντ π π π π π 52 events + + + − − ° →ντ π π π π π π 2 events
= EE Measurement errors h ∑ π = pp rr h ∑ π 22 r 2 −= pEM hhh
kinematic boundaries versus mν mτ = 1776.84 ± 0.17 MeV Event distribution near the kinematic boundaries consistent with mν = 0 R. Barate et al., Europhys. Journal C2 (1998) 395
m(ντ ) <18.2MeV (confidence level 95%) Double β decay with no neutrino emission (ββ0ν) A method (the only one?) to distinguish Dirac from Majorana neutrinos (A, Z) → (A, Z + 2) + e– + e– Violation of lepton number conservation reaction possible only for Majorana neutrinos n p Neutrino helicity flip between emission and absorption e– ν Neutron decay → emission of helicity ½ neutrinos e − V - A p νe + n → p + e requires helicity −½ neutrinos n e– Decay rate: 4 22 two neutrons 0ν GF ×∝Γ phase( × Mspace) 0 mνν in the same nucleus G : Fermi constant Choice of nucleus F M0ν : nuclear matrix element
− (A, Z) → (A, Z + 1) + e + νe Forbidden from energy conservation 2 Q >2mec 76 76 − – A method to search for ββ0ν decay (E. Fiorini, 1967) : Ge32 → Se34 + e + e – – Sum of electron kinetic energies E (e 1) + E (e 2) = 2039 keV (“ Q – value”) GERDA (GERmanium Detector Array) at Gran Sasso: 8 high-purity, enriched Germanium crystals used as solid state detectors ; Total mass: 17. 67kg , 86% 76Ge (natural Germanium contains only ~7.7% 76Ge ) ; Crystal are immersed in 64 m3 liquid Argon, inside 3m thick water shielding equipped with photomultipliers to detect Čerenkov light and reject cosmic rays; Experiment located in the Gran Sasso underground laboratory at a depth equivalent to
3740 m H2O (3740 m w.e.)
Artist’s view of GERDA GERDA : search for a mono-energetic signal at 2038 keV (energy resolution: 1 − 2 ‰)
Results from an exposure of 21.6 kg · y Agostini et al., PRL 111 (2013) 1
No evidence for ββ0ν decay ⇒ lower limit on 76Ge half-life 25 τ1 / 2(ββ0ν) > 2.1 x 10 y (90% C.L.)
⇒ upper limit on < mν >
< mν > = 0.2 – 0.4 eV (valid only if νe is a Majorana neutrino)
Range of
+ 14.0 21 2/1 =νββτ ( − 10.0 )×1084.1)2( y keV 2038 136 136 – – Xe54 → Ba54 + e + e E(e1) + E(e2) = 2458 keV
KamLAND‐Zen detector in the Kamioka mine (Japan) at a depth of ~2700 m w.e.
Inner Balloon: 300 kg 136Xe in Liquid Scintillator (contained in 25 mm transparent nylon film) Outer Balloon: 1 kton Liquid Scintillator 1879 photomultiplier tubes (PMT) mounted on a stainless steel tank (SST, diameter 18 m) Event localisation by PMT relative timings Outer Detector: 3.2 kton water Cerenkov counter to reject cosmic ray background KamLAND‐Zen results from an exposure of 89.5 kg∙y 136Xe
Unexpected background from β –decay of metastable 110mAg (τ½ ≈ 250 d, end –point 2.892 MeV) probably contamination of the Inner Balloon from the fallout of the Fukushima 2011 accident (the Inner Balloon was fabricated at 100 km from Fukushima)
No evidence for ββ0ν decay ⇒ lower limit on 136Xe half-life : 25 τ1 / 2(ββ0ν) > 1.9 x 10 y (90% C.L.) EXO experiment Liquid‐Xenon Time Projection Chamber in the Waste Isolation Pilot Plant near Carlsbad, N.M., U.S.A. (an underground site for nuclear waste storage, depth 1585 m w.e.)
measure ionization electrons after drift
avalanche photodiodes measure UV scintillation light
View of one half‐module Liquid Xenon is both ββ source and detector Useful mass 110 kg Xe (enriched to 80.6% in 136Xe) EXO results M. Auger et al., PRL 109 (2012) 032505
Single –Site events ( localized source in the Xe volume )
2458 keV
136 25 Lower limit on Xe half‐life τ½(ββ0ν) > 1.6 x 10 y (90% C.L.) Combine with KamLAND‐Zen lower limit: 25 τ½(ββ0ν) > 3.4 x 10 y (90% C.L.)
< mν> < 0.12 –0.25 eV Time Projection Chambers with ββ0ν candidate isotope deposited on cathode
Measurement of electron tracks
Thin layer deposit of ββ0ν isotope on cathode NEMO3 In the Fréjus Underground Laboratory between France and Italy Depth ~4800 m w.e.
Cylindrical detector with 25 Gauss vertical magnetic field 20 independent sectors equipped with low density gas trackers (mainly He4) + scintillators ββ0ν candidate isotope deposited on thin foils in the middle of each sector Isotope deposit thickness: 30 –60 mg cm‐2
Reaction Q –value (keV) 100Mo → 100Ru 3034 82Se → 82Kr 2995 96Zr → 96Mo 3350 48Ca → 48Ti 4271 150Nd → 150Sm 2802 Magnetic field direction B =25Gauss
NEMO3: details of a sector Vertical wires define 6180 open octagonal drift cells operating in Geiger mode Data ββ2ν prediction Background Results from an exposure of ~7 kg · y Mo100
Lower limits to half-lifes for ββ0ν decay (90% C.L.): 100 24 Mo : τ1 / 2 > 1.1 x 10 y ⇒
Crystal (Ge, TeO2, Al2O3, CaWO4, ...) Deposited energy −3 Cooled to 12 x 10 °K = 12 mK ⇒ heat ⇒ΔT
Example: TeO2 crystal, mass = 0.76 kg Thermal capacity: C = δQ /dT ≈ 1 MeV/ 0.1 mK ( for T → 0 C ~ T3 ) Thermometer: Ge thermistor, R = 100 MΩ, dR/dT ≈ 100 kΩ/μK Deposited energy E = 1 MeV →ΔT = 100 μK →ΔR = 10 MΩ Response time: few milliseconds Energy resolution:
(Al2O3)
210Po α line
TeO2
Counts Mass 0.76 kg Resolution 4 keV a 5.4 MeV
ΔT depends only on E and not on particle type (quenching factor = 1) Energy [keV] 1st phase of the CUORE experiment at Gran Sasso (“CUORICINO”) 3 3 44 TeO2 crystals 5 x 5 x 5 cm + 18 crystals 3 x 3 x 6 cm (mass 40.7 kg) 130 130 − − Te52 → Xe54 + e + e
E(e1) + E(e2) = 2530.3 ± 2.0 keV Results from an exposure of 11.83 kg ∙ y of 130Te C. Arnaboldi et al., Phys. Rev. C78 (2008) 035502
2530.3 keV
Origin of the 2505.68 keV peak: energy sum of the two photons (1173.21 + 1332.47 keV) emitted in 60Co β – decay: 60Co → 60Ni* → 60Ni + γ + γ Origin of the 60Co contamination: cosmic rays interacting in the detector copper structure before transportation to Gran Sasso No evidence for ββ0ν decay: 130 24 τ1/2( Te) > 3.0 x 10 y ⇒ < mν > < 0.19 –0.68 eV Neutrino masses: cosmological constraints Big-Bang cosmology: the Universe is filled with neutrinos and antineutrinos “relic neutrinos” (so far undetected) Today: N ν +ν ≈ 360)( -3 = ×106.3cm m -38
Each relic ν or ν in the Universe forms a Fermi gas with Tν ≈ 1.9ºK.
−4 −4 Average energy
3 −4 ρν ≈120∑ mν eV/cm for mν ×>> 107.1 eV ν Recent measurements of the Cosmic Microwave Background (Planck ESA satellite) Galaxy clustering (“Galaxy Power Spectrum”) Hubble constant provide the constraints (R. de Putter, E.V. Linder, A. Mishra, Phys. Rev. D89 (2014) 103502
∑ mν < 19.0 eV ν = 3Nfor ν m N or ∑ mν < 26.0 eV ; ν ±= 25.059.3N (fitting both ∑ ν and ν ) ν ν Neutrino interactions W± boson exchange: Charged Current(CC) interactions Quasi-elastic (QE) scattering – + νe + n → e + p νe + p → e + n – + νμ + n →μ + p νμ + p →μ + n Threshold energy: ~112 MeV – + ντ + n →τ + p ντ + p →τ + n Threshold energy: ~3.46 GeV –38 2 Cross-section at energies >> threshold: σQE ≈ 0.45 x 10 cm – Deep-inelastic scattering (DIS) (neutrino - quark scattering : e.g., νμ + d →μ + u) – + νe + N → e + hadrons νe + N → e + hadrons (N: nucleon) – + νμ + N →μ + hadrons νμ + N →μ + hadrons – + ντ + N →τ + hadrons ντ + N →τ + hadrons –38 2 Cross-section at energies >> threshold: σDIS(ν) ≈0.68Ε x 10 cm (E in GeV)
σDIS( ν ) ≈0.5σDIS(ν) Z boson exchange: Neutral Current (NC) interactions Flavour independent: the same for the three neutrino flavours ν + N →ν+ hadrons ν + N →ν+ hadrons Cross-sections: Very small cross-sections: ν mean free path σ ( ν) ≈0.3σ (ν) μ NC CC at 10 GeV ≈ 1.7 x 1013 g cm–2 σ ( ν ) ≈0.37σ ( ν) NC CC equivalent to 2.2 x 107 km Iron 0.8 σCC(ντ)
σCC(νμ) 0.6
τ production from ντ CC interactions : large suppression with respect to
νμ CC interactions from τ mass effects 0.4
Neutrino – electron elastic scattering – 0.2 ν , ν νe e νe νe Z W W− e– e– 0.0 e – 0 20 40 60 80 100 e νe ( ν only) (all three (νe only) e E (ν) [GeV] ν flavours) Cross-section: σ = A x 10–42 E cm2 (E in GeV)
νe: A ≈ 9.5 νe : A ≈ 3.4 νμ, ντ: A ≈ 1.6 νμ, ντ : A ≈ 1.3 2 2 NOTE: σ(ν – electron) << σ(ν – Nucleon) because σ ∝ GF W 2 2 W ≈2meEν for ν – electron; W ≈2mNEν for ν –Nucleon (W ≡ total centre-of-mass energy) Neutrino oscillations in vacuum Hypothesis: neutrino mixing (Pontecorvo 1958; Maki, Nakagawa, Sakata 1962)
νe νμ ντ are not mass eigenstates but linear superpositions of mass eigenstates ν1 ν2 ν3 with eigenvalues m1 m2 m3
ν α = ∑ U α ν ii α = e, μ, τ (flavour index) i i = 1, 2, 3 (mass index )
Uαi : unitary mixing matrix
ν i = ∑ Vi ν αα α * = UV ααii )( Time evolution of a neutrino with momentum p produced in the flavour eigenstate να at time t = 0
i ⋅rp − k tiE Note: ν )0( = ν ν )( = ∑ α k eUet ν k α k − tiE 2 2 the complex phases e k k += mpE k are different if mj ≠ mk
appearance of new flavour νβ ≠να at time t > 0 Example for two – neutrino mixing ν = cos θ ν + sin θ ν α 1 2 θ ≡ mixing angle
ν β sin 1 +−= cos νθνθ2
If ν=να at production (t = 0):
rp −⋅ 1tEi )( −− 12 )( tEEi ν )( = et {cosθ ν1 + e sinθ ν 2 } m2 For m << p 22 pmpE +≈+= (in vacuum!) 2 p 2 − mm 2 2 − mm 2 Δm2 EE ≈− 2 1 ≈ 2 1 ≡ 12 2 p E 22 E
Probability to detect νβ at time t if ν(0) = να:
2 = c =1 2 ⎛ Δ tm ⎞ h P = ννtt = 2 θ sin)2(sin)()( 2 ⎜ ⎟ αβ β ⎜ 4E ⎟ 2 2 2 ⎝ ⎠ Δm ≡ m2 –m1 Using units more familiar to experimentalists: L L = ct distance between 2 2 ⎛ 2 ⎞ neutrino source Pαβ L = θ ⎜ 267.1sin)2(sin)( Δm ⎟ ⎝ E ⎠ and detector Units: Δm2 [eV2]; L [km]; E [GeV] (or L [m]; E [MeV])
2 NOTE: Pαβ depends on Δm (not on m). Definition of oscillation length λ: E Units: λ [km]; E [GeV]; Δm2 [eV2] =λ 48.2 Δm2 (or λ [m]; E [MeV])
2 2 ⎛ L ⎞ Pαβ L = sin)2(sin)( ⎜πθ⎟ ⎝ λ ⎠
2 2 Ε1, Δm 1 Ε2, Δm 2 sin2(2θ)
Distance between neutrino source and detector 2 2 Ε1 < Ε2 and/or Δm 1 > Δm 2 Disappearance experiments
Use να source, measure να flux at distance L from source
Disappearance probability Pαα =1− ∑Pαβ ≠αβ Examples:
Experiments using νe from nuclear reactors (Eν ≈ few MeV: under threshold for μ or τ production)
νμ detection at accelerators or in the cosmic radiation (search for νμ ⇒ντ oscillations if Eν lower than τ production threshold)
The main source of systematic uncertainties: knowledge of the neutrino flux in the absence of oscillations use two detectors if possible
ν beam Near detector: Far detector : ν source measure ν flux measure Pαα Appearance experiments Neutrino source: να . Detect νβ (β ≠ α) at distance L from source
Examples:
- Detect νe + N → e + hadrons in a νμ beam
- Detect ντ + N →τ + hadrons in a νμ beam (Threshold energy≈ 3.5 GeV)
The νβ contamination at source must be precisely known (typically νe/νμ ≈ 1% in νμ beams from high-energy accelerators) → a near detector is often very useful neutrino mixing thehypothesisoftwo– Under P
(onset of thefirstoscillation) αβ No evidenceforoscillation upperlimit small Observation ofanoscillation signal in the
→ Very large P αβ =λ average oversourceanddetector dimensions: L Δ [ m Δ 48.2 = m 2 → 2 Δ Δ , sin m 2 E long m 2 () 2 → Δ≈< 2 ( 2θ mP λ very shortoscillationlength )] 2 : L<< plane consistentwiththeobserved signal
2 2
πθ λ L λ )(sin)2(sin)( 2 →
≈ θ 1 2 )2(sin6.1
⎝ ⎜ ⎛ π 2
E allowedparameterregion L
λ ⎠ ⎟ ⎞ θ )sin( 2 )2(sin
≈ P π
αβ λ LL < P λ : exclusion region log(Δm2) 01 sin 2 (2 θ ) Searches for neutrino oscillations: experimental parameters
ν source Flavour Distance L Energy Min. accessible Δm2
8 −11 2 Sun νe ~1.5x10 km 0.2-15 MeV ~10 eV
ν ν 10 – 13000 0.2 – 100 Cosmic rays μ μ ~10−4 eV2 νe νe km GeV Nuclear ν 20m – 250 km
Final result from a chain of fusion reactions in the Sun core:
4 + 4p → He + 2e + 2νe Average energy produced as electromagnetic energy in the Sun core:
4 2 Q = (4Mp –MHe + 2me)c –
26 39 Solar luminosity: L = 3.846x10 W = 2.401x10 MeV/s
38 −1 Neutrino emission rate: dN(νe)/dt = 2 L/Q ≈1.84x10 s 10 −2 −1 Average neutrino flux on Earth: Φ(νe) ≈ 6.4x10 cm s (average Sun − Earth distance = 1.496x1011 m) STANDARD SOLAR MODEL (SSM) (developed in 1960 and continuously updated by J.N. Bahcall and collaborators) Assumptions: hydrostatic equilibrium energy production by nuclear fusion thermal equilibrium (power output = luminosity) energy transport inside the Sun by radiation Input data: cross-sections for fusion reactions “opacity” (photon mean free path) as a function of distance from the Sun center Method: choice of initial parameters evolution to present epoch (t = 4.6x109 years) compare predicted and measured quantities modify initial parameters if necessary 26 TODAY’S SUN: Luminosity L = 3.846x10 W 8 Radius R = 6.96x10 m 30 Mass M = 1.989x10 kg 6 Core temperature Tc = 15.6x10 K Surface temperature Ts = 5773 K Hydrogen in Sun core = 34.1% (initially 71%) as measured Helium in Sun core = 63. 9% (initially 27.1%) at the surface Two reaction cycles
p – p cycle (0.985 L) + + – p + p → e + νe + d p + p → e + νe + d OR (0.4%): p + e + p → νe + d 85% p + d →γ+ He3 p + d →γ+ He3 3 3 4 −5 3 4 + He + He → He + p + p OR (∼2x10 ): He + p → He + e + νe
+ p + p → e + νe + d p + d →γ+ He3 He3 +He4 →γ+ Be7 p + Be7 →γ+ B8 15% – 7 7 8 8 + e + Be → νe + Li OR (0.13%) B → Be + e + νe p + Li7 → He4 +He4 Be8 → He4 +He4
CNO cycle (two branches) p + N15 → C12 +He4 p + N15 →γ+O16 p + C12 →γ+N13 p + O16 →γ+F17 13 13 + 17 17 + N → C + e + νe F → O + e + νe p + C13 →γ+N14 p + O17 → N14 +He4 p + N14 →γ+O15 15 15 + O → N + e + νe 4 + NOTE #1: for both cycles 4p → He + 2e + 2νe NOTE #2: source of today’s solar luminosity: fusion reactions occurring in the Sun core ~ 106 years ago (the Sun is a “main sequence” star, practically stable over ~108 years). Predicted solar neutrino flux and energy spectrum on Earth (p − p cycle)
1
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1 M Notations
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s
1 - +
2
s - pp : p + p → e + νe + d
2
- m 7 – 7 7 c Be : e + Be → ν + Li
m e
:
c
s –
: e pep : p + e + p → νe + d
a
n
r i 8 8 8 +
t l
B : B → Be + e + ν c e
c
e i 3 4 + t p hep : He + p → He + e + ν
e s e
g
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u
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o
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Predicted radial distribution of νe production in the Sun core History of the first solar neutrino experiment
1946: Proposal (B. Pontecorvo) to detect neutrinos produced by nuclear reactors using the reaction 37 37 neutrino + Cl17 Æ Ar18 + e⁻ (the Chalk River internal report PD –205 describing the proposal is declared “classified document” by the U.S.A. Atomic Energy Commission for fear that the method may be used by unfriendly countries to measure the power of U.S.A. nuclear reactors)
Proposed “radiochemical” method: 3 Install a large volume tank (few m ) filled with C2Cl4 (a cleaning liquid) near a nuclear reactor; Every 3 –4 weeks, bring the liquid to boiling point and collect vapours 37 (which should contain Ar18 atoms) to fill proportional counters; 37 37 Measure the electron capture reaction eˉ + Ar18 Æ Cl17 + neutrino 37 (τ½ ≈ 35 d) by detecting X‐rays or Augier electrons emitted by the Cl17 excited atom (from the missing 1s electron) in returning to ground state. 1954: Raymond Davis installs a tank filled with 3 800 liters C2Cl4 near one of the Savannah River reactors but finds no evidence 37 for A18 after a few weeks exposure.
1958: Negative result confirmed by a second experiment with 11 400 liters C2Cl4 . This result demonstrated that neutrinos from nuclear reactors (produced by βˉ decay of fission fragments) do not produce electrons 37 when they collide with Cl17 nuclei. The most plausible interpretation: nuclear reactors do not produce neutrinos, but antineutrinos: − 37 37 − )1ZA,()ZA,( e ν+++→ ; 17 ArCl 18 +→+ν e NOTE: if neutrinos are Majorana particles, because of the V –A coupling neutrinos from reactors have helicity +½ , 37 37 − while ν + Cl17 → Ar18 + e requires neutrinos with helicity −½
1949: Luis Alvarez proposes to use Pontecorvo’s method to detect solar neutrinos (LBL internal report, unpublished) The Homestake experiment (1970–1998) (R. Davis, University of Pennsylvania) 37 – 37 νe + Cl → e + Ar Energy threshold E(νe) = 0.814 MeV 3 Detector: 390 m C2Cl4 in a tank installed in the Homestake gold mine (South Dakota, U.S.A.) at a depth of 4100 m w.e. (fraction of Cl 37 in natural Chlorine = 24%) Expected production rate of Ar 37 atoms ≈ 1.5 per day
37 Experimental method: every few months extract Ar by N2 flow through tank, purify, mix with natural Argon, fill a small proportional counter, detect radioactive 37 – 37 37 decay of Ar : e + Ar →νe + Cl (half-life τ1/2 = 35 d) 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 experiments: 1 SNU = 1 event s–1 per 1036 target atoms Average of all measurements: R(Cl 37) = 2.56 ± 0.16 ± 0.16 SNU Solar (stat) (syst) +1.3 Neutrino SSM prediction: 7.6 –1.1 SNU deficit “Real time” experiments with water Čerenkov counters Neutrino – electron elastic scattering: ν + e– →ν+ e– Detect Čerenkov light emitted by electrons in water (directional emission !)
Energy threshold ~5 MeV (5 MeV electron residual range in H2O ≈2cm) ν − νe e Cross-sections: σ(νe) ≈ 6 σ(νμ) ≈ 6 σ(ντ) Z W − e − W , Z exchange Z exchange only (all three ν types) e νe (νe only)
Two experiments: Kamiokande (1987 − 94) 3 Fiducial volume: 680 m H2O ~15 events / day Super-Kamiokande (1996 − ) In the peak 3 Fiducial volume: 22500 m H2O in theKamioka mine (Japan) Depth 2670 m w.e.
The signal solar origin is demonstrated by the angular correlation between the directions of the detected electron and the incident neutrino
cosθsun 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 –1 s ν -2 E DEFICIT cm e 6 ν 10 0.08) x (stat) (syst) 0.02 ± ± –1 s ) = (2.35 -2 e ν ( cm 12 14 6 ) ): Φ ν 10 e SSM prediction ν /E e Data (including theoretical error) +1.01 –0.81 /(2 + m ν 6 8 10 Electron kinetic energy (MeV) +0.093 –0.074
) = (5.05 x y a d / s n t e v E (stat) e 0.005 ν ( ± convolute with predicted spectrum to obtain – elastic scattering of mono-energetic neutrinos e Results from 22400 events (1496 days of data taking) Measured neutrino flux (assuming all SSM prediction: Φ Data/SSM = 0.465 e SSM prediction for electron energy distribution is almost flat between 0 and 2E Recoil electron kinetic energy distribution from ν 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. Why? The two main solar νe sources in the Homestake and water experiments: 3 4 7 – 7 7 He +He →γ+ Be e + Be → νe + Li (Homestake) 7 8 8 8 + p + Be →γ+ B B → Be + e + νe (Homestake, Kamiokande, Super-K) Fusion reactions strongly suppressed by Coulomb repulsion Ec 2 Z1Z2e /d R1 d Potential energy: R2 Z e 1 Z2e d ~R +R 2 2 1 2 ZZ 21 ee hc ZZ 21 197 MeV fm ZZ 21 Ec = = ≈ MeV + RR 21 hc + RR 21 137 + RR 21 fm
Ec ≈ 1.4 MeV for Z1Z2 = 4, R1+R2 = 4 fm
Average thermal energy in the Sun core
-5 kB (Boltzmann constant) = 8.6 x 10 eV/°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 1 2- πη σ E)( = S E)(e measured at energies ~0.1– 0.5 MeV E and assumed to be energy independent ZZ e 2 Tunnel effect: η = 21 v = relative velocity hv
Predicted dependence of the νe fluxes on Tc:
– 7 7 8 From e + Be → νe + Li : Φ(νe)∝Tc
8 8 + 18 From B → Be + e + νe : Φ(νe)∝Tc
N Φ∝Tc ΔΦ/Φ = N ΔTc/Tc How precisely do we know the temperature T of the Sun core?
+ Search for νe from p + p → e + νe + 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 71 – 71 νe + Ga → e + Ge Energy threshold E(νe) > 0.233 MeV reaction sensitive to solar neutrinos + from p + p → e + νe + d (the dominant component) Three experiments: In the Gran Sasso National Lab GALLEX (Gallium Experiment, 1991 – 1997) 150 km east of Rome GNO (Gallium Neutrino Observatory, 1998 – ) Depth 3740 m w.e.
SAGE (Soviet-American Gallium Experiment) 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) 71 Experimental method: every few weeks extract Ge in the form of GeCl4 (a highly volatile substance), convert chemically to gas GeH4, inject gas into a proportional counter, detect 71 – 71 71 radioactive decay of Ge : e + Ge →νe + Ga (half-life τ1/2 = 11.43 d) (Final state excited Ga71 atom emits X-rays: detect K and L atomic transitions) Check of detection efficiency: 71 71 – 71 71 Introduce a known quantity of As in the tank (decaying to Ge : e + As →νe + Ge ) Install an intense radioactive source producing mono-energetic νe near the tank: – 51 51 e + Cr →νe + V (prepared in a nuclear reactor, initial activity 1.5 MCurie equivalent to 5 times the solar neutrino flux), E(νe) = 0.750 MeV, half-life τ1/2 = 28 d Ge71 production rate ~1 atom/day
+6.5 SAGE (1990 – 2001) 70.8 –6.1 SNU +9 SSM PREDICTION: 128 SNU –7 Data/SSM = 0.56 ± 0.05 ( SR: Solar Run) 0.465±0.016 SNO Concluding evidence for solar neutrino oscillations (Sudbury Neutrino Observatory, Sudbury, Ontario, Canada) SNO: detector of Čerenkov light produced in 1000 tons of ultra-pure heavy water D2O contained in an acrylic sphere (diam. 12 m), surrounded by 7800 tons of ultra-pure water H2O
Light collection: 9456 photomultipler tubes, diam. 20 cm, on a spherical surface of 9.5 m radius
Depth: 2070 m (6010 m w.e.) in a Nickel mine
Detection energy threshold: 5.5 MeV (reduced to 3.5 MeV in a recent analysis)
Reconstruct the event position from the measurement of the photomultiplier signal relative timings Solar neutrino detection in the SNO experiment (ES) Neutrino – electron elastic scattering : ν + e– →ν+ e– Directional, σ(νe) ≈ 6 σ(νμ) ≈ 6 σ(ντ) (as in Super-K) – (CC) νe + d → e + p + p Electron angular distribution ∝ 1 − 1 cos(θ ) 3 sun Measurement of the νe energy (most of the νe energy is transferred to the electron) (NC) ν + d →ν+ p + n Identical cross-section for all three neutrino flavours ⇒ measurement of the total neutrino flux from B8 → Be8 + e+ + ν independent of oscillations DETECTION OF ν + d →ν+ p + n Detect neutron capture after “thermalization” Phase I (November 1999 – May 2001): 3 –4 + − n + d → H + γ ( Eγ= 6. 25 MeV, σ = 5x10 b ); γ → Compton electron, e e pair
Phase II (July 2001 – September 2003): add 2 tons of ultra-pure NaCl to D2O 35 36 n + Cl → Cl + several γ’s (
Phase III (November 2004 – November 2006: insert in the D2O volume 3 an array of cylindrical proportional counters (diameter 5 cm) filled with He H3 n n + He3 → p + H3 (0.764 MeV mono-energetic signal, σ = 5330 b) p Use four independent variables to separate the three reactions ( Hatched histograms ES CC NC correspond to Phase II )
Teff Energy distribution (from signal amplitude)
Cosθsun Directionality
β14 Isotropy parameter
3 ρ = (R/R0) Event radial position R0 = 600.5 cm radius of the D2O sphere DATA
cos θsun distribution
Event position: distribution of distance from center 3 ρ = (R / R0) R0 = 600.5 cm radius of D2O sphere Energy distribution (from signal amplitude)
Extract all components (ES, CC, NC, background) by maximum likelihood method Number of events: CC: 2176 ± 78 ES: 279 ± 26 NC: 2010 ± 85 Background from external neutrons: 128 ± 42 Solar neutrino fluxes, as measured from the three signals:
6 −2 −1 ΦCC = ( 1.72 ± 0.05 ± 0.11 ) x 10 cm s Note: ΦCC ≡Φ(νe) + 0.15 6 −2 −1 Calculated assuming that ΦES = ( 2. 34 ± 0.23 − 0.14 ) x 10 cm s all incident neutrinos are νe + 0.28 +1.01 6 −2 −1 Φ ( ν) = 5.05 x 106 cm−2s−1 ΦNC = ( 4. 81 ± 0. 19 − 0.27 ) x 10 cm s SSM –0.81 (stat) (syst)
ΦCC + 0.028 differs from 1 = 0.358 ± 0.021 − 0.029 by 10 standard deviations ΦNC The TOTAL solar neutrino flux agrees with SSM predictions (determination of the solar core temperature to ~ 0.5% precision) Composition of solar neutrino flux on Earth: ~ 36% νe ; ~ 64% νμ +ντ (ratio νμ /ντ unkown) DEFINITIVE EVIDENCE OF SOLAR NEUTRINO OSCILLATIONS Difference between the measured values of ΦCC and ΦES
CC ν e )( Φ≡Φ=Φ e
NC ν e Φ+Φ=Φ ν μ + Φ ν τ )()()( ≡ Φ e + Φ μτ
σ ES ν ,τμ)( 1 ES ν e )( +Φ=Φ []μ νντ )()( e Φ+Φ≈Φ+Φ μτ νσeES )( 6 Solar νe disappearance: interpretation
Hypothesis: two – neutrino mixing Vacuum oscillations
νe energy spectrum measured on Earth Φ(νe) = Pee Φ0(νe) (Φ0(νe) ≡νe energy spectrum at production)
Probability to detect νe on Earth : L [m] 2 2 2 L E [MeV] Pee −= θ m ≈Δ 0.33)267.1()sin2(sin1 E Δm2 [eV2]
Solar neutrino energy in SNO, Super-K experiments E = 5 – 15 MeV Variation of Sun – Earth distance during data taking (the Earth orbit is an ellipse) ΔL = 5.01 x 109 m (
Check dependence of Pee on E and L Spectral distortions
Super-K 2002 Data/SSM
Electron kinetic energy (MeV)
– SNO: νe + d → e + p + p electron energy distribution
SNO: data / SSM prediction
νe deficit independent of energy within measurement errors (no spectral distortions) Seasonal modulation
2 Yearly variation of the Sun - Earth distance: 3.3% ⇒ seasonal modulation of the solar neutrino flux
Expected seasonal variation from the variation of solid angle in the absence of oscillations: ~ 6.6%
Days from start of data taking
The observed effect is consistent with the expected solid angle variation L [m] 2 2 ⎛ 2 L ⎞ 2 2 ⎛ L ⎞ Pee −= θ ⎜ 267.1)sin2(sin1 Δm ⎟ −= )sin2(sin1 ⎜πθ⎟ ≈ 0.33 E [MeV] ⎝ E ⎠ ⎝ λ ⎠ Δm2 [eV2]
8 For oscillation lengths λ << ν source dimension (~ 0.15 RO ≈ 1 x 10 m); << Earth diameter (~ 1.3 x 107 m)
Pee is independent of E and L :
2 2 ⎛ L ⎞ 1 2 Pee −= ()sin2sin1 ⎜πθ⎟ 1−= θ ≥ 0.5)2(sin ⎝ λ ⎠ 2 in disagreement with the experimental result ~ 0.33
Neutrino oscillations in vacuum do not describe the observed solar νe deficit NEUTRINO OSCILLATIONS IN MATTER Neutrino refractive index in matter (L. Wolfenstein, 1978) 2π p: neutrino momentum n 11 +=ε+= Nf )0( N: density of scattering centers p2 f(0): scattering amplitude at θ = 0°
In vacuum: += mpE 22 Plane wave in matter: Ψ = ei(np•r –E’t) p 2 ′ )( 22 EmnpE +≈+= ε (|ε | << 1) E Energy conservation: E = E′ +V V ≡ neutrino potential energy in matter p2 2π V −=ε−= Nf )0( EE V <0: attractive potential (n >1) V >0: repulsive potential (n <1) Neutrino potential energy in matter 1. Z-boson exchange (the same for the three neutrino types) ν ν 2 2 Z Z =−= pF (NG(e)V(p)V − sin41 θw ) Z 2 GF: Fermi constant 2 −= NG(n)V Np (Nn): proton (neutron) density e,p,n e,p,n Z 2 nF θw: weak mixing angle
2. W- boson exchange (only for νe!) − νe e Z V [eV] .NG ×≈= 105672 −14 ρ W+ W eF A
3 − electron density matter density [g/cm ] e νe
NOTE: V(ν) = – V( ν ) Example: νe – νμ mixing in a constant density medium (identical results for νe – ντ mixing) Evolution ⎛ νe ⎞ ∂ν In the “flavour” representation: =ν ⎜ ⎟ equation: =ν iH ⎝νμ ⎠ ∂t 2x2 matrix 2 2 01 1 ee MM eμ 01 += VEH Z )( + 2 2 + VW 10 2E μe MM μμ 00
M 2 M 2 (Remember: 22 pMp E +≈+≈+ for M << p) p 22 E
2 1 M (μ Δ−= m22 θ )2cos μ 2 2 += mm 2 ee 2 1 2 2 2 2 1 2 −=Δ mmm 1 2 MM 2 Δ== m 2 2sin θ eμ μe 2 1 M 2 (μ Δ+= m22 θ )2cos NOTE: m1, m2, θ are defined in vacuum μμ 2 2 2 01 1 M ee + 2 MEV eW μ += VEH Z )( + 2 2 10 2E M μe M μμ
diagonal term: no mixing Term inducing νe–νμ mixing ρ = constant H is time - independent H diagonalization ⇒ eigenvalues and eigenvectors 1 1 Eigenvectors M 2 2 ξμ)( Δ±+= m2 ξθ2 Δ+− m 222 2sin)()2cos( θ in matter 2 2 Z EV 10512.12 −7 ρ×≈≡ξ E [eV2] (ρ in g/cm3, E in MeV) W A Mixing angle in matter: ξ = Δm2cos 2θ ≡ ξ ⇒ maximum mixing 2 res Δm 2sin θ (θm = 45°) even if the mixing angle in vacuum 2tan θm = 2 is very small: “MSW resonance ” Δm 2cos −ξθ (discovered by Mikheyev and Smirnov in 1985) Mass eigenvalues M2 as a function of ξ Z EV 10512.12 −7 ρ×≈≡ξ E m 2 W A 2 2 2 ξres Δ= m 2cos θ m1
Oscillation length in matter: Δm2 m = λλ Δm2 ξθ2 Δ+− m 222 2sin)()2cos( θ (λ ≡ oscillation length in vacuum) λ For ξ = ξ res: λ = m 2sin θ
2 NOTE: for νe oscillations the MSW resonance exists only if Δm cos2θ > 0 Δm2 > 0, cos2θ > 0 (θ < 45º) or Δm2 < 0, cos2θ < 0 (θ > 45º) 2 2 2 DEFINITION (to remove the ambiguity): Δm = m2 –m1 > 0 Matter effects in solar neutrino oscillations 100 Solar density Solar neutrinos are produced in a high – density medium (the solar core). 10 Variable density along the neutrino path: ρ = ρ(t) ρ Oscillations in solar matter [g/cm3] Time evolution: Hν = i ∂ν / ∂ t 1 H (2 x 2 matrix) depends on time via ρ(t) 0.1 H has no eigenvectors R/RO Numerical solution of the evolution equation 0. 0.2 0.4 0.6 0.8 for fixed Δm2 and mixing angle θ (values in vacuum): ⎛1⎞ )0( =ν ⎜ ⎟ (pure νe at production) ⎝0⎠ ⎛ ν∂ ⎞ )0()( +ν=δν ⎜ ⎟ iH )0()0()0( δν−ν=δ (δ = very small time interval) ⎝ ∂t ⎠t=0
⎛ ν∂ ⎞ tt )()( +ν=δ+ν ⎜ ⎟ ttiHt )()()( δν−ν=δ ⎝ ∂t ⎠t
until the neutrino emerges from the Sun. Then, propagation in vacuum to Earth, and through Earth matter if needed (for night-time at detector site) νe production with ξ > ξres
2 2 0 m 2sin θΔ 00 m 2cos θΔ=ξ 2tan =θ < 0 m >θ 45 res m m2 2cos ξ−θΔ
0 0 At production : e cos m 1 sin m νθ+νθ=ν 2
Z For 10512.1 −7 ρ×≈ξ [g/cm3 ]E[]MeV m2 2cos θΔ> [eV 2 ] A
the ν2 component of νe is larger than the ν1 component
For antineutrinos ξ changes sign (ξ < 0) Æ no MSW resonance for νe propagating in matter “Adiabatic” solutions (negligible variation of matter density oven an oscillation length)
The ν1 and ν2 amplitudes do not change along the neutrino path in matter
2 M 2 2 νν∝ )t( Area 2 1 νν∝ )t(
θm < 45° θm > 45°
ν production Exit from Sun e
At exit from Sun (in vacuum) ν2 has a larger νμ component than ν1 “Best fit” to SNO data
Best fit: m2 ×=Δ 1057.4 − eV 25 2 θ = 447.0tan 2 χ Ndof = 72/8.73/
Confidence levels for two-parameter fits 2 2 2 CL Δχ =χ −χ min 68.27% 2.30 90% 4.61 95% 5.99 99% 9.21 99.73% 11.83
NOTE: tan2θ is used instead of sin22θ because sin22θ is symmetric around θ = 45° 0 θ 0 θ 0 θ =+=−=− 0 +θ )45(2sin)290sin()290sin()45(2sin MSW solutions exist only if θ < 45° Best fit to all solar neutrino experiments including a re-analysis of SNO Phase I and II data with detection threshold reduced to 3.5 MeV B.Aharmim et al., Phys. Rev. C81, 055504 (2010)
Best fit:
+2.13 2 −5 2 Δm = (5.89 − 2.16 ) x 10 eV
+0.038 2 tan θ = 0.457 −0.041
+1.07 θ = (32.82 − 1.24 ) º
2 χ / Ndof = 67.5 / 89 KamLAND
Confirmation of solar νe oscillations using antineutrinos from nuclear reactors
CPT invariance: Posc(να – νβ) = Posc ( νβ – να )
same disappearance probability for νe and νe
Nuclear reactors: strong, isotropic νe sources from β − decay of fission fragments Energy spectrum (E ≤10 MeV,
νe source : nuclear reactors in Japan
Total thermal power 70 GW >79% of the νe flux from 26 reactors, 138 < L < 214 km Distance weighted average:
6 –2 –1 Expected νe flux ≈1.3x 10 cm s (all reactors at full power, no oscillations) Expected oscillation length for Δm2 = 5 x 10–5 eV 2 : < λosc > ≈ 160 km KamLAND: detector
1000 tons liquid scintillator
Transparent nylon balloon
Mineral oil
Acrylic sphere Photomultipliers (1879) (coverage: 35% of 4π)
External anticoincidence against cosmic rays (pure H2O ) 13 m 225 photomultipliers 18 m KamLAND: final results S. Abe et al., Phys. Rev. Lett. 100, 221803 (2008)
Effect of scintillator contamination from α radioactivity
Expected number of events for no oscillation : 2179 ± 89 (syst.) Background: 276.1 ± 23.5 events Number of observed events: 1609 KamLAND: νe disappearance probability L P −= 2 θ 2 Δm2 0 )267.1(sin)2(sin1 ee E 2 + 14.0 − 25 Δm = − 13.0 ± ×10)15.058.7( eV Best fit 2 + 10.0 + 10.0 θ = − 07.0 (stat)56.0tan − 06.0 (syst)
L0 = 180 km source - detector average distance Solar – KamLAND fit comparison Best fit to all solar neutrino data + KamLAND
2 2 2 −5 2 Combined best fit : Δm21 ≡ m2 − m1 = (7.59 ± 0.21) x 10 eV 2 + 0.040 + 1.16 tan θ12 = 0.457 – 0.029 ⇒θ12 = (34.06 –0.84 )° 2 χ / Ndof = 81.4 / 106 BOREXINO An experiment at the Gran Sasso National Laboratories
Goal: Detection of elastic scattering process
ν + e → ν + e (dominated by νe) in liquid scintillator Scintillation light >> Čerenkov light → detection threshold < < 1 MeV Scintillator: pseudocumene (PC) + PPO; “buffer liquid”: PC + DMP (no scintillation)
Real – time experiment
Scintillation light is ISOTROPIC → no signal correlation with the Sun direction The signal solar origin has been verified over several years of data-taking by observing the seasonal modulation induced by the excentricity of the Earth orbit around the Sun Measurement of the solar νe deficit at energies Eν < 1 MeV
νe survival probability vs. energy
Expected behaviour from the measured oscillation parameters
Matter effects small important “Atmospheric” neutrinos Primary cosmic ray Main sources of atmospheric neutrinos: interacting in ethe atmosphere ± ± ± π , K →μ + νμ( νμ) ± → e + νe( νe) + νμ(νμ) For energies E <2GeV most pions and muons decay before reaching the Earth: ν+ν μμ ≈ 2 ν+ν ee At higher energies most muons reach the Earth before decaying: +ν ν μμ > 2 DETECTOR ν+ν ee (increasing with E ) Atmospheric neutrino energies: 0.1 — 100 GeV Very low event rates: ~100 /year for a 1000 ton detector Typical uncertainty on the atmospheric neutrino fluxes: ± 30% (from uncertainties on the primary cosmic ray spectrum, on hadron production, etc.)
Incertainty on the νμ / νe ratio : ± 5% Atmospheric neutrino detection νμ + Nucleon →μ+ hadrons: presence of a long, minimum – ionizing track (the muon) – + νe + n → e + p, νe + p → e + n : presence of an electromagnetic shower (νe interactions with multiple hadron production cannot be easily distinguished from Neutral Current interactions ν + N → ν + hadrons ) Event identification in water Čerenkov detectors Muon track: 41° dE/dx consistent with ionization minimum; well defined edges of Čerenkov light ring Electromagnetic shower: high dE/dx (many secondary electrons); fuzzy edges of Čerenkov light ring (from the shower angular aperture) Direct measurement of the electron / muon separation by exposing a 1000 ton water Čerenkov detector (a small copy of Super-K) to electron and muon beams from a proton accelerator. Measured probability of wrong identification ~2% Measurement of the νμ / νe ratio: first hints for a new phenomenon Water Čerenkov detectors: Kamiokande (1988), IMB (1991), Super-K (1998) Conventional calorimeters (iron plates + proportional tubes): Soudan2 (1997) (νμ/νe)measured R = = 0.65 ± 0.08 (νμ/νe)predicted Atmospheric neutrino events in Super-K Distance between interaction point and inner detector walls ≥1 meter
(April 96 – July 01)
H2O radiation length ≈ 36 cm → energetic electrons are totally absorbed in ~8 m of water
lepton (e/μ) energy [GeV] An additional event sample: Up – going muons from νμ interactions in the rock
Note: down – going muons are mainly π → μ decays in the atmosphere traversing the mountain rock and reaching the detector Measurement of the zenith angle distribution
Definition of the zenith angle θ : Polar axis along the local vertical axis, Earth atmosphere pointing downwards Down-going : θ = 0º detector Up-going: θ = 180° Horizontal : θ = 90°
L (distance between neutrino production point and detector) Earth Local vertical axis depends on zenith angle 104 θ = 0º— 180º L = ~10 —~12800 km [Km] 103
L Search for oscillations with variable distance L Strong angular correlation between incident neutrino and produced electron/muon for E >1GeV: 102 ν α ≈ 25°at E = 1 GeV; α α → 0 for increasing E Uncertainty on neutrino e/μ 10 production point ±5 km –1. –0.5 0. 0.5 1. cosθ Zenith angle distribution in Super-K
No oscillation (χ2 = 456.5 / 172 degrees of freedom)
2 −3 2 2 νμ – ντ oscillation (best fit): Δm = 2.5x10 eV , sin 2θ = 1.0 χ2 = 163.2 / 170 degrees of freedom Zenith angle distributions in the Super‐K experiment
Evidence for νμ disappearance over ~1000 — 10000 km distance
Atmospheric νe flux compatible with no oscillation.
The most plausible interpretation: νμ – ντ oscillation Super-K ντ + N →τ + X requires E(ντ) > 3.5 GeV; fraction of τ → μ decays ≈ 18%
Region of oscillation parameters –3 2 –3 2 1.9 x 10 < |Δm32 | <3.0x 10 eV 2 sin 2θ23 >0.90 (confidence level 90%)
Oscillation parameters accessible with long baseline experiments using neutrino beams from high‐energy accelerators Three –neutrino mixing
Three mass eigenvalues: m1 , m2 , m3 2 2 2 − 25 21 2 mmm 1 ×±=−≡Δ 10)18.053.7( eV (Solar neutrino experiments + KamLAND)
2 2 2 − 23 32 3 mmm 2 ×≈−≡Δ 105.2 eV (Atmospheric neutrinos)
Only two independent Δm2 values: 2 2 2 2 2 2 2 31 3 1 ( 3 2 ) ( 2 −+−=−≡Δ mmmmmmm 1 ) Three –neutrino oscillations are described by three angles (θ12 , θ13 , θ23) + a phase angle δ inducing violation of CP – symmetry
⎛ ν ⎞ ⎛ UUU ⎞⎛ ν ⎞ ⎛ cc sc es iδ− ⎞⎛ ν ⎞ e 11 12 13 1 ⎜ 1312 1213 13 ⎟ 1 ⎜ ⎟ ⎜ ⎟⎜ ⎟ iδ iδ ⎜ ⎟ ⎜ ν μ ⎟ = ⎜ 21 22 UUU 23 ⎟⎜ ν 2 ⎟ ⎜ −−= 2313121223 − 2313122312 scesssccesscsc 2313 ⎟⎜ ν 2 ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ iδ iδ ⎟⎜ ⎟ ⎝ ν τ ⎠ ⎝ 31 32 UUU 33 ⎠⎝ ν 3 ⎠ ⎝ − 1323122312 −− 1312232312 ccesscscesccss 2313 ⎠⎝ ν 3 ⎠
cik ≡ cosθik; sik ≡ sinθik For Dirac neutrinos the matrix U is the neutrino mixing unitary matrix; for Majorana neutrinos, there are two additional phases which do not contribute to CP – violation in neutrino oscillations:
⎛ ν ⎞ ⎛ M M UUU M ⎞⎛ ν ⎞ ⎛ UUU ⎞⎛ 001 ⎞⎛ ν ⎞ e ⎜ 11 12 13 ⎟ 1 11 12 13 1 ⎜ ⎟ M M M ⎜ ⎟ ⎜ ⎟⎜ iα 2/ ⎟⎜ ⎟ ⎜ ν μ ⎟ = ⎜ 21 22 UUU 23 ⎟⎜ ν 2 ⎟ = ⎜ 21 22 UUU 23 ⎟⎜ 0 e 0 ⎟⎜ ν 2 ⎟ ⎜ ⎟ ⎜ M M M ⎟⎜ ⎟ ⎜ ⎟⎜ iβ 2/ ⎟⎜ ⎟ ⎝ ν τ ⎠ ⎝ 31 32 UUU 33 ⎠⎝ ν 3 ⎠ ⎝ 31 32 UUU 33 ⎠⎝ 00 e ⎠⎝ ν 3 ⎠
For Majorana neutrinos, all phases contribute to the “effective νe mass” in the ββ0ν decay rate formula: 2 2 M mν = ∑()1i mU i i Two –neutrino mixing: a good approximation to describe solar νe and atmospheric νμ oscillations
2 ‐3 2 Atmospheric νμ : |Δm32 | ≈ 2.5 x 10 eV
For a νμ at the oscillation peak :
2 ⎛ 2 L ⎞ 2 L π ⎜ 27.1sin Δm32 ⎟ =1 27.1 m32 =Δ ⎝ E ⎠ E 2
2 ‐5 2 For the same L/E the amplitude of the oscillation driven by Δm21 = 7.5 x 10 eV is ⎛ Δπ m2 ⎞ sin 2 ⎜ 21 ⎟ ≈ 0022.0 ⎜ 2 ⎟ ⎝ 2 Δm32 ⎠ 2 2 negligible effect because Δm21 << | Δm32 |
2 ‐3 2 For solar νe the oscillation driven by |Δm31 | ≈ 2.5 x 10 eV can also be neglected 2 because the ν3 component of νe is small : sin (2θ13) ≈ 0.1 Wide band neutrino beams from accelerators Focusing of positively or negatively charged hadrons to produce an almost parallel beam with wide momentum distribution using “magnetic horns” (invented at CERN in 1963 by S. Van der Meer) The horns are followed by a long decay tunnel under vacuum
Axially symmetric conductors Pulsed current Cylindrically symmetric magnetic field perpendicular to the hadrons produced in the target
Changing the direction of the current pulse selects opposite charge hadron beams + − π ( → νμ ) π ( → νμ ) “On – axis” neutrinos (emitted at decay angles θ = 0º with respect to the hadron beam) have a wide momentum distribution. “Off –axis” beams have narrower energy distributions but lower fluxes
off – axis ν beam θ μ π+ parallel beam π+ beam axis
* * E E : νμ energy in the ν energy at fixed θ : E = π+ rest frame (0.03 GeV) μ − θβγ)cos1( (from Lorentz transformation) π π γπ = Eπ /mπ βπ = vπ /c
+ + π → μ + νμ decay E(νμ) GeV νμ energy versus π+ momentum
for different νμ angles θ For θ > 0 neutrino beams are enriched in monoenergetic neutrinos but flux is reduced by a factor ~4
Monoenergetic neutrinos: p (GeV/c) first oscillation maximum at L = λosc / 2 π Project Distance L < Eν > ν beam type Status K2K 250 km 1.3 GeV on – axis completed MINOS 735 km few GeV on – axis data – taking CNGS 732 km 17 GeV on – axis completed T2K 295 km ~0.6 GeV off – axis data - taking NOνA 810 km ~1.6 GeV off – axis under construction
– Energy threshold for ντ + N →τ + X: Eν >3.5GeV – Event rate ~1 νμ →μ event / year for one ton detector mass need detector masses of several kiloton. Angular divergence of the νμ beam from pion decay : π+ θ Beam axis
pT 0.03GeV + + θ ≈ ≈ = 3 mrad at 10 GeV νμ from π →μ νμ decay pL Eν [GeV ]
Neutrino beam lateral dimensions: 100 m – 1 km for L > 100 km no problem to hit the far detector The neutrino flux decreases as L–2 at large distance L K2K
12 GeV proton L=250 km synchrotron Neutrino beam: 95% νμ 4% νμ 1% νe
Near detector Near detector: measurement of νμ flux and νμ interaction rate in the absence of oscillation 1 kton water Čerenkov counter: similar to Super-K; fiducial mass 25 ton Muon chambers: measurement of muon energy spectrum from π → μ decay
Events fully contained in the Super-K detector, Evis >30MeV: + 12 predicted (Posc = 0): 151 −10 events ; observed: 107 events
2 –3 2 2 Best fit: Δm23 = 2.2 x 10 eV ; sin 2θ23 = 1 (in agreement with atmospheric νμ results) Probability of no oscillation 5 x 10 −5 (equivalent to 4 standard deviations) MINOS experiment Neutrino beam from Fermilab to Soudan (an old iron mine in Minnesota): L = 735 km
Accelerator: Fermilab Main Injector (MI) 120 GeV proton synchrotron High beam intensity (0.4 MW): 4x1013 protons per cycle (1.9 s) 4x1020 protons / year Decay tunnel : 700 m NUMI beam (“Neutrinos from Main Injector”)
The neutrino beam average energy can be changed by varying the target – magnetic horn distance and the horn current
Aerial view of the Fermilab accelerators MINOS: Far detector
Octagonal tracking calorimeter diameter 8 m Iron plates 2.54 cm thick Plastic scintillator 4 cm wide strips between adjacent iron plates 2 modules, each 15 m long total mass 5400 tons, fiducial mass 3300 tons. 484 scintillator planes ( 26000 m2) Magnetized iron plates: toroidal field, B = 1.5 T
MINOS: Near detector “Octagonal” tracking calorimeter , 3.8x4.8 m Construction similar to far detector 282 magnetized iron plates Total mass 980 tons, fiducial mass 100 tons Installed 250 m downstream of the decay tunnel end Start – up of data – taking: 2005 MINOS: far detector 2014 MINOS RESULTS – + νμ + N → μ + X and νμ + N → μ + X events 2014 MINOS RESULTS – νμ + N → μ + X events
2 − 23 Best fit: m23 ×±=Δ 10)09.034.2( eV 2 + 020.0 ( 23 )=θ 980.02sin − 022.0 The T2K experiment
T2K (Tokai to Kamioka): experiment to measure θ23 using a 2.5º off‐axis neutrino beam of ~ 0.6 GeV produced at J‐PARC and aimed at the Super‐K detector (L = 295 km); T2K includes a near detector. J‐PARC (Japan Proton Accelerator Research Complex): 30 GeV high intensity proton synchrotron at JAERI (Tokai) in operation since 2009 T2K results : νμ disappearance K. Abe et al., Phys. Rev. Lett. 112 (2014) 181801
2 − 23 Best fit: m23 ×±=Δ 10)06.044.2( eV 2 + 001.0 ( 23 )=θ 999.02sin − 017.0 CNGS (CERN Neutrinos to Gran Sasso) Search for ντ appearance at L = 732 km – Predicted number of ντ + N →τ + X (Nτ) events: Emax Φ= P σ )()()( dEEEEAN τ ∫ μ μτ τ Normalization: 5.3 GeV depends on detector mass , τ – production νμ flux running time, detection cross-section efficiency , etc.
νμ – ντ oscillation probability (Pμτ ): 2 2 2 2 L 22 22 ⎛ L ⎞ Pμτ = 2(sin θ23 m32 ≈Δ 2(sin27.1)27.1(sin) θ23 Δm32 ))( ⎜ ⎟ E ⎝ E ⎠
2 –3 2 Good approximation for : L = 732 km, E > 3.5 GeV, Δm32 ≈ 2.5x10 eV Emax σ E)( N ≈ 2 2(sin61.1 θ Δ ))( Lm 222 Φ E)( τ dE τ 23 32 ∫ μ 2 5.3 GeV E
The neutrino beam is designed to maximize Nτ average νμ energy ≈ 17 GeV corresponding to first oscillation peak at ~8400 km from νμ source > > 732 km CNGS: neutrino beam production
Pulsed magnetic lenses
Proton beam (400 GeV) from the CERN SPS Search for ντ appearance at Gran Sasso OPERA experiment
No near detector (negligible ντ production at the proton target) OPERA experiment: detect τ– by observing its decays to one charged particle(~85%) Mean τ decay path ≈1mm ⇒ need very high space resolution Photographic emulsion: space resolution ~1μm 200 μm plastic base
“Brick”: 56 1mm thick Pb plates 50 μm emulsion layers interleaved with 57 emulsion films Brick internal structure and tightly packed
“Bricks” arranged into “walls” : one “wall” = 2850 bricks “Walls” arranged into two “super-modules” → ~150,000 bricks ≈ 1.25 ktons in total Each super-module is followed by a magnetic spectrometer Planes of orthogonal scintillating strips are inserted between walls to provide the trigger and to identify the brick where the neutrino interacted. Immediate removal of the brick, emulsion development and automatic measurement using computer – controlled microscopes
Present status of OPERA experiment
• Data –taking (2008 – 2012) completed • 19 505 neutrino events recorded • So far, analysis completed for 75% of the events (emulsion scanning + measurement) • 4 events consistent with τ production and decay have been identified • expected background 0.23 ± 0.05 events
• Evidence for ντ appearance with a statistical significance of 4.2 σ The first OPERA event consistent with τ− production N. Agafonova et al., Phys. Letters B 691 (2010) 138
− Event interpretation: ντ + N → τ + hadrons − ρ + ντ 2γ π− + πº ICARUS detector (proposed by C. Rubbia in 1977) Possibly the ideal detector for all future neutrino experiments 600 ton liquid Argon in two adjacent containers Container dimensions 3.6 x 3.9 x 19.9 m3 Time Projection Chamber (TPC): electrons from primary ionization drift in the liquid and are collected by read-out wires → 3-dimensional event reconstruction Number of primary ionization electrons from a charged particle at minimum ionization ~ 6000 / mm of track length Electron drift without recombination over lengths of ~1.8 m require ultra-pure Argon (concentration of electro-negative impurities <10-10) Drift velocity ~ 1.5 mm/μs for electric fields ~ 0.5 kV/cm Liquid Argon density 1.4 g/cm3 Radiation length 14 cm
DETECTOR INSTALLED AT GRAN SASSO; FILLED AT MID MAY 2010, DATA – TAKING COMPLETED IN 2012 ICARUS UV scintillation light from liquid Argon is collected by photomultiplier tubes located behind the read-out wires The scintillation signal is necessary to localize the event along the drift direction
ICARUS AT GRAN SASSO: Liquid Argon total mass (600 tons) not large enough for studies of long baseline neutrino oscillations but useful to demonstrate the detector potential for future, very high mass neutrino detectors ICARUS at Gran Sasso: νμ Charged‐Current event – νμ + nucleon → μ + hadrons ICARUS at Gran Sasso: νe Charged‐Current event – νe + nucleon → e + hadrons ICARUS at Gran Sasso: neutrino Charged‐Current event ν + nucleon → ν + hadrons Measurement of θ13
νe disappearance experiments with antineutrinos from nuclear reactors 2 −3 2 For E = 3 MeV (average reactor νe energy) and |Δm31 | ≈ 2.5 x 10 eV the νe disappearance probability has a maximum at L ≈ 1500 m
Nb. Nb. Dist. Experiment Site Year sin2(2θ ) det. reactors (m) 13
Chooz, 998 CHOOZ 1998 1 2 < 0.17 France 1114
Yonggwang, 290 (11.3 ± 1.3 ± 1.9) RENO 2012 2 6 Korea 1380 x 10–2 360, 500, Daya Bay, +0.8 –2 Daya Bay 2012 8 6 1540, (9.8 −0.9) x 10 China 1910
Chooz, 998 (10.9 ± 3.0 ± 2.5) Double‐CHOOZ 2012 1 2 France 1114 x 10–2 Daya Bay experiment (on the East coast of China, 55 km North‐East of Hong Kong
EH: underground experimental hall NPP: Nuclear Power Plant : reactor Distance EH3 – Daya Bay NPP ≈ 1900 m
20 ton Gd‐loaded liquid scintillator Liquid scintillator (“γ – catcher” )
+ νe + p → e + n Neutron capture by Gd → γ –rays, ΣEγ ≈ 8.1 MeV Each detector is immersed in water and surrounded by counters to reject cosmic ray background Daya Bay results F.P. An et al., PRL 112 (2014) 061801
EH3 detectors (at the longest distance from reactors) show the largest νe deficit νμ – νe appearance : series expansion for three‐flavor neutrino oscillation probability in matter E.K. Akhmedov et al., JHEP 04 (2004) 078 2 B )1(sin ω− P 2 sinsin4)( 2 θθ=ν−ν μ e 13 23 B − )1( 2 Bω B − ω])1sin[()sin( δ−ωθθθα+ )cos()2sin()2sin(sin2 13 12 23 B B −1 2 Bω)(sin 22 cos)2(sin 2 θθα+ 12 23 B2 (assuming constant matter density)
2EV × −4 )/(10512.1 ρEAZ W term describing matter effects B = 2 = 2 Δm31 Δm31 2 Δ 2 2 L Δm21 m31 > 0 (normal hierarchy) 267.1 Δ=ω m =α ≈α )03.0( 2 31 ; 2 Δm < 0 (inverted hierarchy) E Δm31 31
3 2 2 ρ (g/cm ) ; E (GeV) ; L (km) ; Δmik (eV )
To calculate P( νμ – νe) change δ →−δ , VW →−VW matter effects induce an apparent CP‐violation which can be separated from the CP‐violation in the mixing matrix (δ ≠ 0) by the dependence on neutrino energy Note the weak dependence on the CP-violating phase δ coming from terms to first order in α (|α| ≈ 0.03) Present experiments
to search for long baseline νμ – νe oscillations at accelerators
Experimental method:
Select events consistent with a νe Charged – Current interaction (no muon, presence of an electromagnetic shower consistent with an electron)
Main source of background events: the νe beam contamination (typically ~1%) Measure background event rate in the near detector (no oscillation) Predict backgrounds for the far detector Compare far detector data with predictions MINOS: search for νμ– νe and νμ– νe oscillations P. Adamson et al., PRL 110 (2013) 171801 Baseline 735 km
2 + 4.8 −2 Best fit: sin (2θ13) = (6.4 − 3.7 ) x 10 (normal mass hierarchy)
2 + 6.8 −2 sin (2θ13) = (11.7 − 6.2 ) x 10 (inverted mass hierarchy) T2K: search for νμ– νe oscillations K. Abe et al., PRL 112 (2014) 061802 Baseline 295 km In the Far Detector (Super‐K) observe 28 single electron events Predicted background 4.92 ± 0.55 events
2 + 0.038 Best fit: sin (2θ13) = 0.140 − 0.032 (normal mass hierarchy)
2 + 0.045 sin (2θ13) = 0.170− 0.037 (inverted mass hierarchy) NOνA: search for νμ– νe oscillations Esperiment approved in 2008 to use the Fermilab NUMI beam Off – axis neutrino beam (14.8 mr off –axis) Baseline 810 km, neutrino beam energy ~1.6 GeV Detector (on surface): 15,000 ton liquid scintillator in plastic rectangular tubes 15.5 m long, section 3.9cm x 6cm Data taking expected to start soon
Future project: DUNE (Deep Underground Neutrino Experiment) A 40 000 ton Liquid Argon TPC to be installed in the Sanford Underground Research Facility at Homestake (South Dakota, U.S.A.) Depth 4 200 m w.e. Distance from the neutrino source (NUMI beam at Fermilab) ~ 1300 km Start of data –taking in the years > 2020 Physics goals: • Solve the mass hierarchy problem • Study CP violation in neutrino mixing
by comparing νμ – νe with νμ – νe oscillations 2 −3 2 First νμ – νe oscillation peak for L=1300 km and Δm31 = 2.4 x 10 eV : Eν ≈ 2.5 GeV probability
appearance e ν
2 The sign of Δm31 can be determined only if matter effects are present: 2EV × −4 )/(10512.1 ρEAZ W 3 2 x −3 2 B = 2 = 2 ±≈ 3.0 for Z/A=½ , ρ = 4 g/cm , E=2.5 GeV, Δm31 =2.4 10 eV Δm31 Δm31 2 The sign of B depends on the relative sign of VW ( ν or ν ) and of Δm31 st The effect of the CP‐violating phase δ is different for the 1 (Eν ≈ 2.5 GeV) nd and 2 (Eν ≈ 0.8 GeV) oscillation peak because of the matter effect Eν dependence Expected results from the DUNE experiment (from simulations)
Normal hierarchy m3 > m1
Inverted hierarchy m3 < m1
Assumptions: 34 kton Liquid Argon TPC (Far Detector) ; 3 years data‐taking at proton beam power 1.2 MW (present NUMI power ~ 0.7 MW) Other ideas under discussion Beta beams Produce intense beams of radioactive isotopes undergoing β decay Acceleration to GeV energies and injection into a storage ring with long straight sections 6 6 − He → Li + e + νe :
pure νe or νe beams to study νe – νμ and νe – νμ oscillations
Neutrino factories Multi‐GeV muon storage rings with long straight sections pointing to neutrino detectors: + Store μ Æ νμ , νe beams − Store μ Æ νμ , νe beams Neutrino fluxes and energy spectra precisely predicted from μ± decay kinematics The project requires “muon cooling” (compression of muon beam phase space) to match the acceptance of the accelerating and storage rings. R&D on muon cooling has started >10 years ago with no conclusive results yet. Do additional neutrinos exist? Hints from the LSND beam‐dump experiment at Los Alamos in the 1990s
π± Veto counter Proton beam 800 MeV θ kin. energy ν target Detector + beam dump
shielding 70–90% + Decay At Rest (DAR) ~75% + DAR 100% + π νμ μ νμ e νe Decay In Flight (DIF) ~5% Proton-nucleus ~20% collisions μ– p →ν n Nuclear absorption capture≥90% μ Kinetic energy 800 MeV DIF few % – – DAR ≤10% 30–10% π νμ μ The only ν e– ν ν ν μ e e e ≤ 10–3 source νe Two similar experiments Experiment LSND KARMEN Los Alamos Linear Neutron Spallation Accelerator Proton Accelerator Facility ISIS (R.A.L., U.K.) Proton kin. energy 800 MeV 800 MeV Proton current 1000 μA 200 μA Single tank 512 independent cells Detector (liquid scintillator) (liquid scintillator + Gd) Detector mass 167 tons 56 tons Event localization PMT timing cell size Distance from ν 29 m 17 m source Angle between 11° 90° proton and neutrino Data‐taking period 1993 –98 1997 – 2001 Protons on target 4.6 x 1023 1.5 x 1023 + + Neutrino energy spectra from π →μ νμ decay at rest
+ e νμ νe νe detection: the “classical” way ν + p → e+ + n e Energy (MeV)
prompt signal delayed signal from np → γd
KARMEN beam time structure Repetition rate 50 Hz
Expect νμ →νe oscillation signal within ~10 μs after beam pulse
time (ns) LSND beam time structure Repetition rate 120 Hz no correlation between event time and beam pulse
0 600 μs LSND: evidence for νμ – νe oscillations Positrons with 20 < E < 60 MeV N(beam-on) – N(beam-off) = 49.1 ± 9.4 events Neutrino background = 16. 9 ± 2.3
νe signal = 32.2 ± 9.4 events –2 Posc = (0.264 ± 0.067 ± 0.045) x 10
KARMEN: no evidence for νμ – νe oscillations Positrons with 16 < E < 50 MeV : 15 events Total background: 15.8 ± 0.5 events
–2 Posc < 0.085 x 10 (conf. level 90%)
Consistency of KARMEN and LSND results in a limited region of the oscillation parameters because of the different detector distance L: L = 29 m (LSND); L = 17 m (KARMEN) 2 2 The LSND νμ – νe oscillation signal with Δm ≈ 0.2 – 2 eV requires the existence of a 4th neutrino: 2 2 2 2 2 2 2 1 3 2 1 mmmmmm 3 =−+−+− 0)()()(
2 2 –5 2 2 2 –3 2 m2 -m1 ≈ 7.5 x 10 eV ; |m3 -m2 | ≈ 2.4 x 10 eV 2 2 2 2 2 2 2 → |m1 -m3 | = |m3 -m2 |±(m2 -m1 ) << 0.2 – 2 eV
Measurement of the Z – boson width at LEP: number of neutrinos Nν = 2.984 ± 0.008 ⇒ the 4th neutrino does not couple to W or Z ⇒ no interaction with matter: “sterile neutrino”–the mixing matrix dimensions are at least 4 x 4 4 α = e μ τ ,,, s ν α = ∑Uαkν k k=1 2 4 2 4 ⎛ Δk1 ⎞ 2 2 P μ ννe )( =− ∑ μkek k )exp( e μ11 +=− ∑ μkek exp⎜− iUUUUtiEUU t ⎟ ( 1 kk −=Δ mm 1 ) k =1 k =2 ⎝ 2E ⎠
For the LSND experiment oscillation effects associated with Δ12 and Δ23 are negligible: 2 3 2 ⎛ Δ41 ⎞ 2 ⎛ L ⎞ P μ ννe )( =− ∑ μ + ekek μ 44 exp⎜− iUUUU ⎟ = 4 e UUt μ 44 ⎜ 267.1sin Δ41 ⎟ ];[( MeVEmL ])[ k =1 ⎝ 2E ⎠ ⎝ E ⎠
4 With 4 neutrinos: 6 mixing angles ; UU = 0 from unitarity ∑ μkek 3 CP – violating phases (Dirac ν) k =1 or 6 CP – violating phases (Majorana ν) MiniBooNE at Fermilab An experiment to verify the LSND oscillation signal
8 GeV proton Beryllium target synchrotron
Predicted flux L ≈ 500 m fluxes ν L similar to LSND experiment E
(arbitrary units) NO NEAR DETECTOR
Eν [GeV] MiniBooNE detector
Spherical tank, diameter 12 m, filled with 807 ton mineral oil Collect both Čerenkov light (directional) and scintillation light. Fiducial mass 445 tons Optically isolated inner region (1280 photomultiplier tubes, diam. 20 cm) External shell used for anticoincidence (240 photomultiplier tubes)
Particle identification based on the different behaviour of electrons, muons, pions and on the Čerenkov light ring configuration MiniBooNE final results A.A. Aguilar‐Arevalo et al., Phys. Rev. Lett. 110 (2013) 161801
Energy distribution of single –electron events MiniBooNE: data –expected backgrounds and fits
νe excess in data 78.4 ± 28.5 events (2.8 σ significance)
consistent with νμ – νe oscillation
νe excess in data 162.0 ± 47.8 events (3.4 σ significance)
Fit to νμ – νe oscillation gives poor χ2 / ndf = 22.8/8.8 MiniBooNE oscillation parameters from fits Best fit sin22θ=0.004, Δm2=1.0 eV2 sin22θ=0.2, Δm2=0.1 eV2 Include exclusion regions from previous experiments + ICARUS at Gran Sasso New short baseline experiment at Fermilab to verify the existence of a 4th neutrino 3 Liquid Argon TPCs at different distances on the neutrino beam from the 8 GeV booster
600 tons
170 tons
260 tons
Two new buildings at ~100 m and ~600 m from neutrino source ICARUS T600 is presently at CERN for upgrades and tests Expected start of data –taking: Spring 2018 CONCLUSIONS
Neutrinos have mass ≠ 0 and mix. Present values (from PDG 2014): 2 2 2 −5 2 Δm21 ≡ m2 – m1 =(7.53 ± 0.18)x10 eV 2 2 2 −3 2 Δm32 ≡ m3 – m2 = (2.44 ± 0.06)x10 eV (Normal mass hierarchy) = – (2.52 ± 0.07)x10−3 eV2 (Inverted mass hierarchy)
Two large mixing angles: θ12 = (33.5 ±0.8)° ; θ23 = (44.1 ±3.1)°; θ13 = (8.9 ±0.4)° (very different from the CKM quark mixing matrix, where the largest angle is θC ≈ 13°)
The mass hierarchy problem (is ν1 or ν3 the lightest mass eigenstate?) should be solved by the next long baseline experiments (NOνAor, more probably, DUNE) An Inverted Mass Hierarchy would be good news for experiments on double β decay
and for the Tritium experiment KATRIN on direct νe mass measurement Future long baseline experiments should also detect CP violation by comparing
νμ – νe and νμ – νe oscillation probabilities Does a 4th, sterile neutrino exist? Answer probably by the year 2020 from the next short baseline experiment with 3 Liquid Argon TPC detectors at Fermilab Large volume Liquid Argon TPCs appear to be the preferred detector for future neutrino experiments.