Alain Blondel University of Geneva Neutrino Physics 1. What are neutrinos and how do we know ?

2. The neutrino questions

3. Neutrino mass and neutrino oscillations

4. neutrino oscillations and CP violation

5. on-going and future neutrino experiments on oscillations

6. on-going and future neutrino-less double-beta experiments 7. Conclusions

http://dpnc.unige.ch/users/blondel/conferences/cours-neutrino/

Pauli's letter of the 4th of December 1930Dear Radioactive Ladies and Gentlemen,

As the bearer of these lines, to whom I graciously ask you to listen, will explain to you in more detail, how because of the "wrong" statistics of the N and Li6 nuclei and the continuous beta spectrum, I have hit upon a desperate remedy to save the "exchange theorem" of statistics and the law of conservation of energy. Namely, the possibility that there could exist in the nuclei electrically neutral particles, that I wish to call neutrons, which have spin 1/2 and obey the exclusion principle and which further differ from light quanta in that they do not travel with the velocity of light. The mass of the neutrons should be of the same order of magnitude as the electron mass and in any event not larger than 0.01 proton masses. The continuous beta spectrum would then become understandable by the assumption that in beta decay a neutron is emitted in addition to the electron such that the sum of the energies of the neutron and the electron is constant... I agree that my remedy could seem incredible because one should have seen those neutrons very earlier if they really exist. But only the one who dare can win and the difficult situation, due to the continuous structure of the beta spectrum, is lighted by a remark of my honoured predecessor, Mr Debye, who told me recently in Bruxelles: "Oh, It's well better not to think to this at all, like new taxes". From now on, every solution to the issue must be discussed. Thus, dear radioactive people, look and judge.Unfortunately, I cannot appear in Tubingen personally since I am indispensable here in Zurich because of a ball on the night of 6/7 December. With my best regards to you, and also to Mr Back.Your humble servant. W. Pauli Wolfgang PauliNeutrinos: the birth of the idea1930dNdEEfew MeVe- spectrum in beta decayne

Neutrinos: direct detection 1953The anti-neutrino coming from the nuclear reactor interacts with a proton of the target, giving a positron and a neutron. 4-fold delayed coincidenceReines and CowanThe target is made of about 400 liters of water mixed with cadmium chloride

The positron annihilates with an electron of target and gives two simultaneous photons (e+ + e- ) . The neutron slows down before being eventually captured by a cadmium nucleus, that gives the emission of 2 photons about 15 microseconds after those of the positron.

All those 4 photons are detected and the 15 microseconds identify the "neutrino" interaction.

Parity violation in Co beta decay: electron is left-handed (C.S. Wu et al)

Neutrino helicity measurement M. Goldhaber et al Phys.Rev.109(1958)1015 neutrinos have negative helicity (If massless this is the same as left-handed)

Step I neutrino emission Step II photon emission Step IV photon filter through magnetic ironStep III photon absorption/emission Step V photon detection in NaI cristal E = 961 keV/c (1 v (Sm*) /c) E > 961 keV/cI,IIIIIIVV

Step I -- sourceelectron spin oriented opposite magnetic fieldJz = +1/2 = +1 -1/2BBJz = -1/2 = -1 +1/2neutrino spin is in direction of magnetic field(conservation of angular momentum)

Sm* and neutrino have the same helicityphoton from Sm* carries that spin too.

EnergiesNB:

Goldhaber experiment -- STEP II Photon emissionSm*E = 961 keV/c (1 + v (Sm*) /c)

E > 961 keV/cSm*E = 961 keV/c (1 - v (Sm*) /c)

E < 961 keV/c

STEP III photon absorption and reemission The photon must have enough energy to raise Sm to excited state. This happens only if the Sm* is emitted in the same direction and thus E > 961 keV/c(a few eV is enough, 6 eV is Doppler shift)

The dependence of signal in the NaI cristal is recorded as function of magnetic field -- in analyzing magnet and -- in magnetic filter

STEP IV magnetic filter

Step I neutrino emission Step II photon emission Step IV photon filter through magnetic ironStep III photon absorption/emission Step V photon detection in NaI cristal E = 961 keV/c (1 v (Sm*) /c) E > 961 keV/cI,IIIIIIVV

Goldhaber experiment -- Summary --

the positive neutrino helicity situation could be detected if it existed but is not. the negative neutrino helicity situation is detected

The neutrino emitted in K capture is left-handed.

Ray Davis established that (anti) neutrinos from reactors do not interact with chlorine to produce argon reactor : n p e- ne or ne ? these ne dont do ne + 37Cl 37Ar + e-

they are anti-neutrinos!

Lee and YangNeutrinos the properties1960In 1960, Lee and Yang realized that if a reaction like

- e-

is not observed, this is because two types of neutrinos exist nm and ne

- e- n + ne

otherwise - e- n + nhas the same Quantum numbers as - e-

Two Neutrinos1962 Schwartz Lederman Steinberger Neutrinos fromp-decay onlyproduce muons (not electrons)

when they interact in matterAGS Proton BeamnmW-hadrons

m-

N

Neutrinos the weak neutral currentGargamelle Bubble ChamberCERNDiscovery of weak neutral current

nm + e nm + e

nm + N nm + X (no muon)

previous searches for neutral currents had been performed in particle decays (e.g. K0->mm) leading to extremely stringent limits (10-7 or so)

early neutrino experiments had set their trigger on final state (charged) lepton!

nm

nm

e-Ze-elastic scattering of neutrino off electron in the liquid

1973 Gargamelle

experimental birth of the Standard model

Gargamelle Charged Current event

Gargamelle neutral current event (all particles are identified as hadrons)

eneduFirst familymc2=0.0005 GeVmc2 ?=?

Neutrino Interactions

Tau Neutrino in DONUT experiment (Fermilab) 2000

Observation of tau-neutrino in ALEPH at LEP e+e- W+ W- (hadrons)+ + -

quasi-elastic:

Neutrino cross-sectionsat all energies NC reactions (Z exchange) are possible for all neutrinos

ne,m,t

ne,m,t

e-Ze-CC reactions

very low energies(E e- + AZ+1N inverse beta decay of nuclei

medium energy (50 e+ + n

Threshold for muon reaction 110 MeVThreshold for tau reaction 3.5 GeV

above 700 MeV pion production becomes abundant and above a few GeV inelastic (diffusion on quark folloed by fragmentation) dominates

ne,m,t

e,m,t

e-Wne

Total neutrino nucleon CC cross sectionsWe distinguish:

quasi-elastic single pion production (RES region, e.g. W

Quasi-elastic reaction +n->lepton +pThe limiting value depends onthe axial massUnder assumption of dipole vector form-factors:(from Naumov)(A. Ankowski)Huge experimental uncertainty

J=0 ==> Cross section is isotropic in c.m. system

Quasielastic scattering off electrons ( Leptons and quarks L.B.Okun)J=0high energy limit(neglect muon mass)

Total cross sectionQuasi-elastic scattering off electrons

Differential cross section in c.m. system

J=1

At high energies interactions on quarks dominate: DIS regime: neutrinos on (valence) quarksJ=0pduumulti-hadron systemwith the right quantum numberx= fraction of longitudinal momentum carried by struck quarky= (1-cosq)/2 for J=0 isotropic distributiond(x)= probability density of quark d with mom. fraction x neglect all masses!s = xS = 2mE x

At high energies interactions on quarks dominate: DIS regime: anti-neutrinos on (valence) quarksJ=1pduumulti-hadron systemwith the right quantum numberx= fraction of longitudinal momentum carried by struck quarky= (1-cosq)/2 for J=1 distribution prop. to (1-y)2 (forward favored)u(x)= probability density of quark u with mom. fraction x s = xS = 2mE x

there are also (gluons) and anti-quarks at low x (sea) (anti)neutrinos on sea-(anti)quarksJ=0pmulti-hadron systemwith the right quantum numberfor J=0 (neutrino+quarks or antineutrino+antiquarks) isotropicfor J=1 (neutrino+antiquarks or antineutrino+quarks) (1-y)2 qi(x), = probability density of quark u with mom. fraction x s = xS = 2mE xgluon

Neutral Currentselectroweak theory

CC: g = e/sinqWNC: g=e/sinqWcosqW

NC fermion coupling = g(I3 - QsinqW)

I3= weak isospin = +1/2 for Left handed neutrinos & u-quarks, -1/2 for Left handed electrons muons taus, d-quarks0 for right handed leptons and quarks

Q= electric charge qW= weak mixing angle. J=0the parameter can be calculated by remembering that for these cross sections we have the W (resp Z)propagator, and that the CC/NC coupling is in the ratio cosqWthus r2 = mW4/ (mZ4 cosqW)=1 at tree level in the SM, but is affected by radiative corrections sensitive to e.g. mtop

J=1gLu = 1/2 - 2/3 sinqW

gRu = - 2/3 sinqW(sum over quarks and antiquarks as appropriate)

J=0J=1scattering of nm on electrons:(invert the role of R and L for antineutrino scattering)

neW-ne

neW-nee-e-e-e-only electron neutrinosonly electron anti- neutrinosthe scattering of electron neutrinos off electrons is a little more complicated (W exchange diagram)

eneduFirst familymc2=0.0005 GeVmc2 ?=?

Quark upcharge 2/3Quark downcharge -1/3Electroncharge -1Neutrino charge 0some remarkable symmetries:

each quark comes in 3 colors

sum of charges is

-1 + 0 + 3 x ( 2/3 - 1/3) = 0

this turns out to be a necessary condition for the stability of higher order radiative corrections

1989 The Number of Neutrinoscollider experiments: LEP Nn determined from the visible Z cross-section at the peak (most of which are hadrons): the more decays are invisible the fewer are visible: hadron cross section decreases by 13% for one more family of neutrinos

in 2001: N = 2.984 0.008

Neutrino mysteriesNeutrinos have mass (we know this from oscillations, see later) neutrinos are massless or nearly so (while me=5.105eV/c2, mtop=1.7 1011eV/c2) mass limit of 2.2eV/c2 from beta decay mass limit of

KATRIN experiment programmed to begin in 2008. Aim is to be sensitive to mn e < 0.2 eV

New experiment KATRIN at KARLSRUHE aims at mc2 ~ 0.2 eV

The future of neutrino physicsThere is a long way to go to match direct measurements of neutrino masses with oscillation resultsand cosmological constraintsWhat IS the neutrino mass?????

Direct exploration of the Big Bang -- Cosmology

measurements of the large scale structure of the universe using a variety of techniques

-- Cosmic Microwave Background -- observations of red shifts of distant galaxies with a variety of candles.Big news in 2002 : Dark Energy or cosmological constant

large scale structure in space, time and velocity is determined by early universe fluctuations, thus by mechanisms of energy release (neutrinos or other hot dark matter)

the robustness of the neutrino mass limits.

Formation of Structure

mn = 0 eVmn = 1 eVmn = 7 eVmn = 4 eVadding hotneutrino darkmatter erasessmall structureHalzen

Recent Cosmological Limits on Neutrino MassesAuthorsSmn/eV(limit 95%CL)Data / PriorsSpergel et al. (WMAP) 2003[astro-ph/0302209] 0.69WMAP, CMB, 2dF, s8, HSTHannestad 2003[astro-ph/0303076]1.01WMAP, CMB, 2dF, HSTTegmark et al. 2003[astro-ph/0310723]1.8WMAP, SDSSBarger et al. 2003[hep-ph/0312065]0.75WMAP, CMB, 2dF, SDSS, HSTCrotty et al. 2004[hep-ph/0402049]1.00.6WMAP, CMB, 2dF, SDSS& HST, SNHannestad 2004[hep-ph/0409108]0.65WMAP, SDSS, SN Ia gold sample,Ly-a data from Keck sample Seljak et al. 2004[astro-ph/0407372]0.42WMAP, SDSS, Bias,Ly-a data from SDSS sample NB Since this is a large mass this implies that the largest neutrino mass is limit/3Halzen

http://map.gsfc.nasa.gov/

see e.g.http://www.nu.to.infn.it/Neutrino_Cosmology/

Neutrinos astrophysical neutrinosRay Davis

since ~1968 Solar Neutrino Detection600 tons of chlorine. Detected neutrinos E> 1MeV

fusion process in the sunHomestake Detector solar : pp pn e+ ne (then D gives He etc) these ne do ne + 37Cl 37Ar + e- they are neutrinos The rate of neutrinos detected is three times less than predicted!

solar neutrino puzzle since 1968-1975!

solution: 1) solar nuclear model is wrong or 2) neutrino oscillate

ne solar neutrinosSun = Fusion reactorOnly ne producedDifferent reactionsSpectrum in energyCounting experiments vs flux calculated by SSMBUT ...

The interactionn Signal Composition:(BP04+N14 SSM+ n osc)pep+hep0.15 SNU ( 4.6%)7Be0.65 SNU (20.0%)8B2.30 SNU (71.0%)CNO 0.13 SNU ( 4.0%)Tot 3.23 SNU 0.68 1sExpected Signal (BP04 + N14)8.2 SNU +1.81.8 1s The Pioneer: Chlorine Experiment

Generalities on radiochemical experiments

expected (no osc)

8.5+-1.8

131+-11

131+-11

Data used for R determination N runsAverageefficiencyHot chem checkSource calibRex [SNU]Chlorine(Homestake Mine);South Dakota USA1970-19931060.958 0.00736ClNo2.55 0.17 0.18 6.6% 7%2.6 0.3GALLEX/GNOLNGS Italy1991-2003124??37AsYestwice51Crsource69.3 4.1 3.6 5.9% 5%

SAGEBaksanKabardino Balkaria1990-ongoing104??NoYes51Cr37Ar70.5 4.8 3.7 6.8% 5.2%70.5 6.0

Super-K detector39.3 m41.3 mWater Cerenkov detector50000 tons of pure light water10000 PMTs

Missing Solar Neutrinos

Possible explications:

wrong SSMNO. Helio-seismologywrong experimentsNO. Agreement between different techniquesornes go into something elseOscillations? Only fraction of the expected flux is measured !

neutrino definitions

the electron neutrino is present in association with an electron (e.g. beta decay)

the muon neutrino is present in association with a muon (pion decay)

the tau neutrino is present in association with a tau (Wtn decay)

these flavor-neutrinos are not (as we know now) quantum states of well defined mass (neutrino mixing)

the mass-neutrino with the highest electron neutrino content is called n1

the mass-neutrino with the next-to-highest electron neutrino content is n2

the mass-neutrino with the smallest electron neutrino content is called n3

Lepton Sector MixingPontecorvo 1957

Neutrino Oscillations (Quantum Mechanics lesson 5)sourcepropagation in vacuum -- or matterdetectionweak interaction produces flavour neutrinos

e.g. pion decay p mnnm> = a n1 > + b n2 > + g n3 >

n (t)> = a n1 > exp( i E1 t) + b n2 > exp( i E2 t) + g n3 > exp( i E3 t) weak interaction: (CC)

nm N m- C

or ne N e- C

or nt N t- C

P ( m e) = < ne n (t)>2Energy (i.e. mass) eigenstates propagateLt = proper time L/E is noted U1

is noted U2

is noted U3 etc.

Oscillation ProbabilityHamiltonian= E = sqrt( p2 + m2) = p + m2 / 2pfor a given momentum, eigenstate of propagation in free space are the mass eigenstates!Dm2 en ev2 L en kmE en GeV

LA MECANIQUE QUANTIQUE DES OSCILLATIONS DE NEUTRINOS On traitera dabord un systme deux neutrinos pour simplifier Propagation dans le vide: on crit le Hamiltonien pour une particule relativiste(NB il y a l une certaine incohrence car la mcanique quantique relativiste utilise des mthodes diffrentes. Dans ce cas particulirement simple les rsultats sont les mmes.)

On se rappellera du 4-vecteur relativiste Energie Impulsion

Dont la norme est par dfinition la masse (invariant relativiste) et scrit

(mc2)2 = E2 - (pc)2

Dou lnergie:

On considre pour simplifier encore le cas de neutrinos dont la quantit de mouvement est connue ce qui fait que le Hamiltonien va scrire ainsi dans la base des tats de masse bien dfinie:

LA MECANIQUE QUANTIQUE DES OSCILLATIONS DE NEUTRINOS Pour le cas de deux neutrinos, dans la base des tats de masse bien dfinie: Cependant les neutrinos de saveur bien dfinie sont des vecteurs orthogonaux de ce sous espace de Hilbertt deux dimensions, mais diffrents des neutrinos de masse bien dfinie: Levolution dans le temps des tats propres et scrit:

Lvolution dans le temps scrit maintenant

LA MECANIQUE QUANTIQUE DES OSCILLATIONS DE NEUTRINOS Si nous partons maintenant au niveau de la source (t=0) avc un tat et que nous allons dtecter des neutrinos une distance L (soit un temps L/c plus tard) la probabilit Quand on observe une interaction de neutrino dobserver une interaction produisant un electron ou un muon seront donns par le calcul de

LA MECANIQUE QUANTIQUE DES OSCILLATIONS DE NEUTRINOS En utilisant:

LA MECANIQUE QUANTIQUE DES OSCILLATIONS DE NEUTRINOS On a donc trouv:Le terme doscillation peut tre reformul:

mlangeoscillation

LA MECANIQUE QUANTIQUE DES OSCILLATIONS DE NEUTRINOS Les units pratiques sont Les nergies en GeVLes masses mc2 en eVLes longeurs en km

On trouve alors en se souvenant que

kmPExemple de probabilit en fonction de la distance la source pour E= 0.5 GeV, m212 = 2.5 10-3 (eV/c2)2