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Atmospheric NeutrinosMagno V.T. Machado

GFPAE, IF-UFRGShttp://www.if.ufrgs.br/~magnus

Advisor: Profa. Dra. Maria Beatriz Gay Ducati

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Content• Introduction and Motivation

• General Properties of Neutrinos

• Kinematical Limits for Neutrinos masses

• Neutrino Oscillation

• Oscillations in the Vacuum and in the Matter (MSW effect)

• Oscillations in Atmospheric Neutrinos

• Current Status and New Experiments

We will not cover

✗ Role of ν in Astrophysics and Cosmology✗ Theoretical model for Neutrino masses

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Neutrino - A short Curriculum Vitae• [1930] Suggested by Pauli in order to explain the continuum elec-

tron spectrum in β decays and nuclear statistics/spin;

• [1956] Discovered by Reines-Cowan in experiments with νe onreators;

• [1956] B. Pontecorvo introduces the ideia of oscillations (ν → ν)

• [1957] Quiral feature of νe established by Goldhaber-Grodzins-Suniar;

• [1962] Discovering the second flavour νµ;

• [1962] Maki-Nakagaya-Sakata propose oscillation between theexisting ν’s flavours.

• [1974] Discovering the third flavour of lepton (τ );

• [70’s-atual] Oscillations in solar ν’s (Homestake, GALLEX, SA-GE, SNO) and atmospheric (IMB, Soudan-2, Kamiokande, Super-K).

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Why and Where are the ν’s interesting ?• Particle Physics: amazing opportunity to study physics beyond

Standard Model (SM, mν = 0). Small mass is associated to newphysics at scale Λ ∼ 1012 GeV.

• Cosmology: role in big bang nucleosyntesis (limit on Nν. Impor-tant in issues concerning bariogenesis (NB − NB 6= 0). Hot darkmatter.

• Astrophysics: ν’s emitted from termonuclear reactions in stars;information about stellar core. Carry out ∼ 99 % of energy duringexplosion of SN type II (important for the dynamics). Sun is a greatsource to test oscillations (1 a.u.=1.5 108 km).

• Nuclear Physics β decay; X-sections are important in calculatingν fluxes; detection rates; syntesis of elements in SN.

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How many ν’s flavours exist ?• Eletron Neutrino : produced in nuclear β decays (n→ p+e−+νe).

The quiral structure of neutrinos, the parity non-conservation andvector-axial (V-A) structure of weak interactions were established innuclear physics.

•Muon Neutrino: produced in pion and muon decays ( π+ → µ++νµ, µ+ → e+ + νe + νµ).

• Tau Neutrino: produced in lepton flavour τ decays ( τ− → ντ +W−, ντ + e+ + νe, ...).

✓ Studing the process Z0 → ll in weak interactions (Γinv = Γtot −Γvis = 498± 4.2 MeV and Γνν = 166.9 MeV)

Nν =ΓinvΓνν

= 2.994± 0.012

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Kinematical limits for ν’s masses• Studing Tritium decay (T → 3He + e− + νe).All experiments present an excess of electrons number near the

spectrum endpoint, instead of a deficit as expected if mν 6= 0 (pro-bably, unknown systematic effects).

✓

< 2.5 eV [Troitsk]mν1

(95% CL) < 6 eV [Mainz]< 15 eV [PDG]

• Studing the π± decays (π+ → µ+ + νµ)✓ mν2

< 170 keV (90% CL) [PSI]

• Studing the τ± decays (τ− → 5π± + ντ )✓ mν3

< 18.2 MeV (95% CL) [ALEPH]

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Quirality•Weak interactions, which are the reactions where ν takes place,

they are called quiral [V-A, ΦR,L = 12(1± γ5) Φ].

• The να are (right handed) particles, while να are (left handed) par-ticles.

• In the mν = 0 limit, quirality is a good quantum number.

• There is not a clear signal currently if ν’s are Dirac particles orMajorana particles (theoretical models), considering mν = 0. In theSM, ν is a Weyl particle.

• Dirac particle: (iγµ∂µ −mi) Ψi = 0

• Majorana condition: Ψ = (Ψ)c = C(Ψ)T

• Weyl particle: i∂Ψi = σ.∇φ

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Neutrinos in the Standard Model (SM)• Hadron and lepton decays through weak current (CC) are des-

cribed by the Fermi theory:

LF = −GF√sJCCµ JCC µ †

• The current JCCµ has a hadron and lepton sectors:

JCCµ = JCC (h)µ + JCC (l)

µ

JCC (h)µ = pγµ(gV − gAγ5)n + fπ∂µπ

+ + . . .

JCC (l)µ = νeγµ(1− γ5)e + νµγµ(1− γ5)µ + . . .

•GF ' 1.166×10−5 GeV−2 is the Fermi constant; fπ pion constantdecay; gV,A = 0.98, 1.22 vector and axial-vector nucleon couplings.

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? Interactions in the SM for ν’s

• Standard weak interactions are due to quark and lepton couplingwith gauge bosons W± and Z , described by the interaction Lagran-geans of charged current (CC) and neutral current (NC):

LCCInt = − g

2√

2JCCµ W µ + herm. conj.

LNCInt = − g

2 cos θWJNCµ Zµ

✓ The g is the SU(2)L gauge coupling constant; θW is the weakangle (Weinberg’s).

•Writing explicity only the terms containing the neutrino fields:

JCCµ = 2∑l=e,µ,τ

νlLγµlL + . . .

JNCµ =∑l=e,µ,τ

νlLγµνlL + . . .

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? How are masses generated in the SM

• SM is a quiral gauge theory: quark e lepton masses can be genera-ted only through spontaneous symmetry broke.• Starting by the Yukawa interaction of leptons with the Higgs

scalar fields ( H1, H2 doublet),

LY = hu,ijqLiuR,jH1 + hd,ijqLidR,jH2 + he,ij lLieR,jH2 + h.c.

✓ The vacuum expected values of the Higgs fields, < H1 >= φ1 e< H2 >= φ2 lead to the mass terms,

LM = mu,ijuLiuRj + md,ijdLidRj + me,ijeLieRj + h.c.

mu = huφ1 , md = hdφ2 , me = heφ2 ,

✓ Mass matrices are diagonalized by bi-unitarity transformations,

V (u)muV(u) † = mdiag

u , V (d)mdV(d) † = mdiag

d , V (e)meV(e) † = mdiag

e

• Matrices V , obeying V V † = I , define the transition betweeninteraction eigenstates and mass eigenstates: eLα = V

(e)αi eLi.

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•Matrices V are different for quarks up and down: mixing betwe-en mass eigenstates in the CC interactions,

L(quark) = − g√2

∑α

uLαγµdLαW

+µ + . . . = − g√

2

∑i,j

uLiγµVijdLjW

+µ + . . .

• Vij = V(u) †iα V

(d)αj is the Cabibbo-Kobayashi-Maskawa (CKM) mixing

matrix. Since CKM is complex: CP violations in the weak interacti-ons.

VCKM =

c12c13 s12c13 s13e−iδ13

−s12c23 − c12s23s13eiδ13 c12c23 − s12s23s13e

iδ13 s23c13

s12s23 − c12c23s13eiδ13 −c12c23 − s12c23s13e

iδ13 c23c13

• Notation: cij ≡ cos θij e sij ≡ sin θij, δ13: CP phase.

•Matrix elements determinated (constrained) through semilepto-nic decays.

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✓ Without right-handed neutrinos, mass and interaction eingesta-tes can be chosen in such way that they coincide for leptons. In theSM, there is not mixing in the lepton charged current.

• Leptonic numbers, Le,µ,τ , are separately conserved. In the quarksector only total barionic quantum number is conserved.

✗ Mass term for ν is generated only in theories beyond StandardModel:

• A νR addition;

• GUT’s theories;

• Larger symmetry groups;

• Extending the Higgs sector, . . .

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? Neutrino mass terms

• Mass terms for ν’s can be 6= from those for leptons and quarks,since they can be Dirac or Majorana particles. Charged leptons can beonly Dirac particles.

L(ν)mass = −nRMnL + c.c.

✗ Two general possibilities for nL :(1) nL contains only ν’s flavour fields:

nL =

νeLνµLντL

, νlL =

3∑i=1

UliνiL (l = e, µ, τ )

✓ The property of νi depends on nR:

• If nR = (νeR νµR ντR), then νi are Dirac fields. Total leptoniccharge is conserved.

• If nR = ((νeL)c (νµL)c (ντR)c), where (νlL)c = CνTlL, the fields areMajorana-like. Leptonic quantum numbers are not conserved

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(2) General case: nL contains also sterile fields, nL = (nlL nsL),which are not present in the LSM (they don’t interact weakly).

• For the mixing, i = 1, . . . , 3 + ns and U is a (3 + ns) × (3 + ns)matrix. The number of sterile ν’s is model dependent.

• If nR = (nL)c, the νi are Majorana particles and the mass term iscalled Dirac-Majorana.

• There is a well-known mechanism for ν’s mass generation (see-saw mechanism): main poit is that leptonic numbers are violated byMajorana mass term (R) at the scale Λ� ΛSM .

✓ The mass spectrum in the see-saw case contains 3 light ν’s (mi)and 3 heavy Majorana particles (Mi ∼ Λ):

mi '(mi

f)2

Mi

� mif (i = 1, 2, 3)

✗ mif is the quark (lepton) mass from the i-th generation (family).

The light ν’s obey a hierarchy relation: m1 � m2 � m3.

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Neutrino oscillation in the Vacuum• Signals for oscillations (transition between different ν’s flavours)

are so far present coming from ν fluxes measurements of solar νe’sand from νµ’s produced in the atmosphere.

• Experiments detect a deficit of the respective fluxes (disappearingof a specific ν flavour).

✓ If there is ν’s mixing, the left-handed components of the interac-tion fields να (α = e, µ, τ, s1, . . .) are linear combinations of n νk fields(k = 1, 2, . . . , n) (Dirac or Majorana) with masses mk.

ναL =

n∑k=1

Uαk νkL

• If all ∆m are small, να state produced in weak process, havingmomentum p� mk: coherent superposition of mass eigenstates.

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|να〉 =

n∑k=1

U ∗αk |νkL〉

• |νk〉: negative helicity state and Ek =√p2 + m2

k ' p +m2k

2p .

✓ Mass eigenstate |νk〉 evolves on time (Schödinger Equation ) fromthe production point (t = 0) to detection,

|να(t)〉 =

n∑k=1

U ∗αke−iEkt |νkL〉

• Expanding the |να(t)〉 state in the |νβ〉 flavour state basis,

|να(t)〉 =∑β

Aνα→νβ |νβ〉

Aνα→νβ(t) =

n∑k=1

Uβk e−iEktU ∗αk

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• A is the transition amplitude for να → νβ at time t (or distanceL ' t).

• The transition probability (for ν : U → U ∗)

Pνα→νβ = |Aνα→νβ(t)|2 =

∣∣∣∣∣n∑k=1

Uβk e−iEktU ∗αk

∣∣∣∣∣2

• Using matrix unitarity,∑

Uβk U∗αk = δαβ and defining ∆m2

kj ≡m2

k −m2j ,

Pνα→νβ =

∣∣∣∣∣δαβ +

n∑k=2

Uβk U∗αk

[exp

(−i∆mk1L

2E

)− 1

]∣∣∣∣∣2

• The transition probability depends on the mixing matrix elements,n− 1 masses differences and L/E parameter.

✓ If there is not mixing (U = I) and/or ∆mk1/E � 1 for anyk = 2, . . . , n, transitions don’t occur (Pνα→νβ = δαβ)

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✓ The ν’s oscillations can be observed only if it occurs ν’s mixingand at least one ∆m2 satisfies the condiction ∆m2 ≤ E/L.

• The larger the L/E parameter, the smaller the ∆m2 values ana-lized in the experiment.

EXPERIMENT L [km] E [GeV] ∆m2 [eV2]

Accelerator (short baseline) 0.1 1 10Reators 0.1 10−3 10−2

Accelerator (long baseline) 103 10 10−2

Atmospheric 104 1 10−4

Solar 108 10−3 10−11

(1)

✓ As a consequence of the CPT invariance, one hasPνα→νβ = Pνβ→να

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? The two generation oscillation case

• The simpler hypothesis for experiments on ν’s oscillations is thetwo flavour mixing.

Pνα→νβ =

∣∣∣∣δαβ + Uβ2U∗α2

[exp

(−i∆m

2L

2E

)− 1

]∣∣∣∣2•∆m2 = m2

2 −m21 and α and β are e, µ or µ, τ , so on.

✓ Probability determinated only from elements of U which con-nect ν’s flavours with mass eigenstate ν2 (or ν1).

✗ The choice for U is arbitrary. In general, it is inspired in therotation matrices( desconsidering phases in the U elements),

U =

(Uα1 Uα2Uβ1 Uβ2

)=

(cos θ sin θ− sin θ cos θ

)• The mixing angle between the 2 flavours is denoted by θ.

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✗ Transition and survival probabilities

Pνα→νβ = 4|Uα2|2 |Uβ2|2 sin2

(∆m2L

4E

)= sin2 2θ sin2 (L/Losc)

Pνα→να = 1− Pνα→νβ , Losc =4πE

∆m2= 2.47

E [MeV ]

∆m2 [eV 2]m

✓ The transition probability is a periodic function of L/Losc.

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? The exclusion plots

• Several experiments with ν’s on reators and accelerators (SBL) don’thave found indications for oscillations.

✗ These data provide a upper bound for the transition probability,which it implies in a exclusion region in the parameter space ∆m2 andsin2 2θ.

•At large ∆m2 (Losc � L), sin2(L/Losc) oscillates fastly as a func-tion of energy. In the real world, ν’s have a spectrum, so one measu-res only a averaged transition probability,

< Pνα→νβ >=1

2sin2 2θ

• < Pνα→νβ > is independend from ∆m2. From an experimentalupper bound < Pνα→νβ >sup, one obtains a vertical line in the exclusi-on plot.

• In the large sin2 2θ region, the bound curve in the exclusion plot

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is given by,

∆m2 '√< Pνα→νβ >sup

1.27√

sin2 2θ < L2 >< E−2 >(2)

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Oscillations and Transitions in the Matter•When ν’s propagate in dense matter, the medium interactions af-

fect their properties.

✗ Purely incoherent inelastic scatterings ν−p produce a cross sectionvery small σ ∼ 10−43 cm2 (E/1 MeV)2.

✓ Coherent frontal elastic interactions: interference amplifies effects.

• Medium effects described by effective potential: it depends onmatter density and composition (Mikheyev-Smirnov-Wolfenstein).

• An example: evolution effective potential for νe in a mediumwith electrons, protons and neutrons,

H(e)C =

GF√2

∫d3pef (Ee, T )

× 〈〈e(s, pe)|e(x)γα(1− γ5)νe(x)νe(x)γα(1− γ5)e(x)|e(s, pe)〉〉

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• f (Ee, T ): electron energy dist. function in the medium, whichis assumed to be homogeneous and isotropic. 〈...〉: average over e−

spinors and sum over all e−’s in the medium.

• Ne(pe): electron density number having momentum pe. Ne =∫d3pef (E − e, T )Ne(pe) is the e− density number.

• Effective Hamiltonian and potential (CC) for νe in matter:

H(e)C =

GFNe√2νe(x)γ0(1− γ5)νe(x)

VC = 〈νe|∫d3x H

(e)C |νe〉 =

GFNe√2

2

V

∫d3x u†νuν =

√2GFNe

• Potential expressed in terms of matter density ρ,

VC =√

2GFNe ' 7.6

(Ne

Np + Nn

)ρ

1014g/cm3eV

✓ Earth: ρ ∼ 10g/cm3 (VC = 10−13 eV). Sun (core) : ρ ∼ 100g/cm3

(VC = 10−12 eV).

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? Evolution equation in matter

• Effective Hamiltonian written using H0 (vacuum) and potential V ,

H = H0 + V

H0 = −iγ0~γ~∂ + γ0m, V =

( √2GFNe 0

0 0

)(3)

• Flavour oscillation probability is calculated in similar way as inthe vacuum case.

H|να(t)〉 = E|να(t)〉

✓ The free Hamiltonian is known in the mass eigenstates basis. Inthe flavour basis, H = UH0U

† + V .

• The corresponding matter mixing angle is given by as a functionof the vacuum mixing angle and Ne,

tan 2θmat =∆m2

2E sin 2θ∆m2

2E sin 2θ −√

2GFNe

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• The flavour transition probability has a similar expression as inthe vacuum case, where θ → θmat and Losc → Lmat,

Pνα→νβ = |〈νβ||να(t)〉|2 ' sin 2θmat sin2 L

Lmat

Lmat =2√

(∆m2

2E sin 2θ −√

2GFNe)2 + (∆m2

2E sin 2θ)2

• The mixing angle θmat has a typical resonant behavior, and maxi-mal mixing (θmat = 45◦) is reached when,

√2GFNe =

∆m2

2Esin 2θ

✓ The relation above is known as MSW resonance condition. It re-quires that ∆m2

2E sin 2θ is positive.

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Atmospheric Neutrinos• Atmospheric neutrinos are produced in cascades started by cos-

mic rays collisions (protons, He, ions) with the atmosphere.

proton + Air → π±(K±) + X

π±(K±) → µ± + νµ(νµ)

µ± → e± + νe(νe) + νµ(νµ)

• The absolute fluxes are known with an uncertainty ∼ 20%. Theratio between ν’s from 6= flavours are known with uncertainty∼ 5%.

✓ Since νe’s are mostly produced in π → µνµ, followed by µ →eνµνe, the νµ and νe expected ration is 2 : 1.

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• Anomaly in atmospheric ν’s (νmu’s disappearing)

(νµ + νµ/νe + νe)Obs(νµ + νµ/νe + νe)MC

6= 1

• The double ratio diminishes uncertainties associated with abso-lute normalizations of the calculated fluxes and systematic errors.

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✓ Weak interactions of ν’s detected in experiments with a hugevolume and located in deep underground (small ν cross section and shieldfor background)

✗ Two experimental methods (detection types):

• Calorimeters: charged particles generated by ν interactions ionizea gas (trajectories are reconstructed). [Frejus, NUSEX, Soudan-2].

•Cherenkov detectors: targets for ν are a huge volume of water over-covered by photomultipliers (detecting Cherenkov light). [IMD, Kami-okande, Super-Kamiokande].

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? Events selection in Cherenkov detectors

• Fully Contained events (FC): all Cherenkov light is deposited in theinner detector.

✗ These events FC are classified as: sub-GeV (Evis ≤ 1.33 GeV) andmulti-GeV (Evis ≥ 1.33 GeV).

• Partially Contained events (PC): múon track deposites part of Che-renkov radiation in the external detector.

? Indirect detection of ν’s out of detector

• High energies νµ’s indirectly detected, observing produced µ’s nearthe detector (upgoing µ’s).

✗ If µ’s stop in detector: stopping muons (Eν ∼ 10 GeV).

✗ If µ’s cross the detector: through-going muons (Eν ≥ 100 GeV).

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Zenite Angle measurements

✓ The zenite angle measures the charged leptons direction in rela-tion to the detector vertical.

✓ Downward (upward) particles correspond to cos θz = +1(−1).Coming in the horizontal direction (cos θz = 0).

✓ Atmospheric ν’s are produced isotropically at∼ 15 km above theEarth ground.

✓ Experiments (Kamiokande, Super-K) indicate that the deficit isdue to ν’s coming from above the horizontal direction (cos θz < 0).

✓ The ν’s entering in the top of the detector cross ∼ 15 km, whileupgoing ν’s cross∼ 104 km.

✓ Strong νµ deficit indication, mainly from upward muons.

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The Up-Down Asymmetry• At high energies, the Earth magnetic field is small and the ex-

pected number of events would not depend on zenite angle.

✗ Super-K found strong cos θz dependence for multi-GeV events.

• The up-down integral asymmetry (U − D),

A =U − DU +D

• For muons

Aµ = −0.316± 0.042(stat)± 0.005(syst)

• For electrons

Ae = −0.036± 0.067(stat)± 0.020(syst)

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Deficit interpretation through Oscillations• Angular distribution of FC ( E ∼ 1 GeV): deficit mostly from

L ∼ 102 − 104 km. Oscillation phase should be maximal, requiring∆m2 ∼ 10−4 − 10−2 eV2.

• Assuming that all upward νµ (multi-GeV events) oscillate in dif-ferent flavour, the up-down asymmetry is approximatelly given by|Aµ| = sin2 2θ/(4− sin2 2θ).

✗ At 1σ level, |Aµ| > 0.27 requiring mixing angle almost maximal,sin2 2θ > 0.85.

✓ Expected number of contained events µ or e-like

Nµ = Nµµ + Neµ , Ne = Nee + Nµe

Nαβ = ntT

∫d2Φα

dEνd(cos θν)καPαβ

dσ

dEβ

ε(Eβ)dEνdEβd(cos θν)dh

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• Upward muons: effective fluxes for stopping and through-goingmuons, convolute the survival probability for νµ’s with correspondingfluxes for muons produced by ν’s interacting in the Earth.

Φµ(θ)S,T =1

A(Lmin, θ)

∫ ∞

Eµ,min

dΦµ(Eµ, cos θ)

dEµd cos θAS,T (Eµ, θ)dEµ

dΦµ

dEµd cos θ= NA

∫ ∞

Eµ

dEµ0

∫ ∞

Eµ0

dEν

∫ ∞

0dX

∫ ∞

0dh κνµ(h, cos θ, Eν)

dΦνµ(Eν, θ)

dEνd cos θPµµ

dσ(Eν, Eµ0)

dEµ0Frock(Eµ0, Eµ, X)

✓ A(Lmin, θ) = AS(Eµ, θ) + AT (Eµ, θ): detector area projected byinner path-lengths larger than Lmin(= 7 m in Super-K). AS e AT arethe effective areas for stopping e through-going muon trajectories.

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Oscillation Channels? Transition channel νµ → νe

✗ Channel excluded at high confidence level (CL):

✓ High precision data from Super-K: contained events for νe arewell described considering no oscillation for normalization and angu-lar dependence.

✓ Excluded also by the reactor CHOOZ experiment, which doesn’tshow evidence for νe deficit.

? Transition channel νµ → ντ (νs)

✗ These oscillation hypothesis explain consistently data on atmosphe-ric ν’s.

✓ Total event rates is consistent with large ∆m2 values.

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✓ Best fit: ∆m2 = 2.6 × 10−3, sin2 2θ = 0.97 (for νµ → ντ ) and∆m2 = 3× 10−3, sin2 2θ = 0.61 (for νµ → νs)

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Current status and new experiments✓ Strong evidence for ν oscillation and mixing;

✓ In atmospheric ν’s , deviations of the expected double ratio betweenνµ/νe and strong dependence on zenite angle

✓ More probable channel νµ → ντ (global atmospheric-solar-reactoranalysis, mixing among 3 ν’s flavours) : 1.9 10−3 < ∆m2

atm < 6 10−3;0.4 < tan2 θatm < 3.

✓ Data from reactors, sin θreat ≤ 0.22 (small Ue3) ensure that com-bined analysis (( 3 ν’s flavour mixing) can be approximated by inde-pendent effective analysis considering only 2 ν’s flavour mixing.

✓ Great interest for possibilities of discrimination between the ντand νs channels.

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✗ Confirmed the oscillation hypothesis, then the next step is to me-asure precisely (to contraint) the mixing matrix elements using datafrom solar, atmospheric and reactors-accelerators ν’s.

✗ Forthcoming experiments will test L/Eν and the appearing ofντ , a better statistics and constraints to the elements of U .

•UNO: under discussion, 20 times Super-K. It will allow to detectsinals of τ appearance.

• AQUA-RICH: L/Eν in high resolution.

•MONOLITH: calorimeter of magnetised tracking. It can to sepa-rate ν and ν’s initiated events and to measureL/Eν at high precision.

• Others : AMANDA, ICARUS, Augier, . . .

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✗ HARD THEORETICAL-EXPERIMENTAL WORK IN THE NEARFEATURE . . .

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References on Neutrinos

Text Books

☞ C.W Kim, A. Pevsner, Neutrinos in Physics and Astrophysics, vol.8, Harwood Academic Press, Chur, Switzerland (1993).

☞ R.N. Mohapatra, P.B. Pal, Massive Neutrinos in Physics and As-trophysics, vol. 41, World Scientific, Singapore (1991).

☞ F. Boehm, P. Vogel, Physics of Massive Neutrinos, Cambridge Uni-versity Press, Cambridge (1989).

☞ J.N. Bahcall, Neutrino Physics and Astrophysics, Cambridge Uni-versity Press, Cambridge (1987).

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Reviews

☞ T.K. Gaisser, M. Honda, Flux of Atmospheric Neutrinos, [hep-ph/0203272];

☞ M.C. Gonzalez-Garcia, Y. Nir , Developments in Neutrino Physics,[hep-ph/0202058];

☞ W. Buchmuller, Neutrinos, Grand Unification and Leptogenesis, [hep-ph/0204288];

☞ F. Halzen, D. Hooper, High-energy Neutrino Astronomy: The Cos-mic Ray Connection, [astro-ph/0204527];

☞ S.M. Bilenky, C. Giunti, W. Grimus, Phenomenology of NeutrinoOscillations, Prog. Part. Nucl. Phys. 43 (1999);

☞ K. Zuber, On the physics of massive neutrinos, Phys. Rept. 305,295-364 (1998);

☞ P. Fisher, B. Kayser, K.S. McFarland, Neutrino Mass and Oscillati-on, Ann. Rev. Nucl. Part. Sci. 49, 481 (1999);

☞ W.C. Haxton, B.R. Holstein, Neutrino Physics, Am. J. Phys. 68, 15(2000).

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Sites in the Web

☞ GEFAN, Grupo de Estudos de Fisica e Astrofisica de Neutrinos, http://www.ifi.unicamp.br/neutrinos

☞ Book on ν’s in the Web (Neutrinos Matter), http://www-boone.fnal.gov/about/nusmatter

☞ Historic site on ν (Neutrino History) http://wwwlapp.in2p3.fr/neutrinos/aneut.html

☞ Central of links about ν’s (The Neutrino Oscillation Industry site),http://www.hep.anl.gov/ndk/hypertext/nu_industry.html

☞ Database with the main experiments on ν (The Ultimate NeutrinoPage), http://cupp.oulu.fi/neutrino/

☞ Super-Kamiokande Homepage, http://geb.phys.washington.edu/local_web/SuperK/aaa_SuperK_home.html

☞ John Bahcall Homepage, http://www.sns.ias.edu/~jnb/