Neutrino Oscillations: a km-scale Quantum Phenomenon Enrique Fernández Univ. Autónoma Barcelona/IFAE

The Neutrino Hypothesis circa-1930: If nuclear b-decay is a two-body decay  energy cannot be conserved  the spin-statistics connection does not hold e.g. energy conservation implies that the electron should have a fixed energy. Observation tells us that the spectrum of the electron is continuous.

The Neutrino Hypothesis These two “problems” lead W. Pauli to postulate the existence of a particle that escaped detection: (4 December 1930, Zürich) Dear radioactive ladies and gentlemen: ...I have hit upon a desperate remedy to save the “exchange theorem” and the energy theorem. Namely [there is] the possibility that there could exist in the nuclei electrically neutral particles that I wish to call neutrons... … But I don’t feel secure enough to publish anything about this idea… … I admit that my remedy may appear to have a small a priori probability because neutrons, if they exist, would probably long ago have been seen. However, only those who wager can win…

The Neutrino Hypothesis What Pauli was saying: for 2-body decay End point and shape of the spectrum depend on neutrino mass. This method of measuring the mass, still in use, gives mn< 2.2 eV/c2.

Fermi’s Theory of Weak-Interactions Pauli “invented” the neutrino and Fermi (in 1934) made an extremely successful theory of weak interactions based on it: are Dirac spinors ; Gi are 4X4 complex matrices ; currents can be Scalar, Vector, Axial Vector, Pseudoscalar o Tensor.

Fermi’s Theory of Weak-Interactions Fermi’s theory lead to some predictions: b+ decay: Observed by Jolliot-Curie in 1934. electron capture: Observed by Alvarez in 1938. inverse b-decay: Predicted by Bethe and Peierls. Bethe and Bacher (1936): …there is only one process which neutrinos can certainly cause. That is the inverse beta process, consisting of the capture of a neutrino by a nucleus together with the emission of an electron (positron). … It seems practically impossible to detect neutrinos in the free state…

Neutrino discovery Or may be not… Remember inverse-beta-decay Is it possible to detect neutrinos by means of this reaction? Neutrino cross-sections are small, very small. Today we know that the cross-section for the above reaction is of the order of 10-40cm2. The “mean free path” of such neutrinos in, say in a block of Lead, is of the order of 1 light year!. Detecting neutrinos is next to impossible. Or may be not…

Neutrino discovery The “atomic age” made available very intense sources of neutrinos: nuclear bombs and nuclear reactors. “Typical” nuclear bomb:

Neutrino discovery

Neutrino discovery The project was actually approved at Los Alamos!

Neutrino discovery A much better idea: Put a detector at some distance from the core of a nuclear reactor. Use delayed coincidence between e+ annihilation and neutron capture

Neutrino discovery On June 14, 1956, Reines and Cowan sent a telegram to Pauli: “We are happy to inform you that we have definitely detected neutrinos from fission fragments by observing inverse beta decay of protons…” 1995 Nobel Prize to Reines (shared with M. Perl)

Peculiar neutrino & weak-interaction properties Parity is not conserved in weak interactions. T. D. Lee and C. N. Yang (1950): To decide univocally whether parity is conserved in weak interactions one must perform an experiment to determine whether weak interactions differentiate the right from the left. A relatively simple possibility is to measure the angular distribution of the electrons coming from beta decays of oriented nuclei…an asymmetry of the distribution…constitutes an unequivocal proof that parity is not conserved in beta decays.

Peculiar neutrino & weak-interaction properties Experiment of C.S. Wu et al (1956). Measure electrons from b-decay of polarized Co nuclei. Polarization is obtained by aligning nuclear spins with external magnetic field. What the experiment measured was that is, the correlation between nuclear spin and electron momentum. The quantity is a pseudoscalar, it changes sign under parity. If parity is conserved should be zero. The measured value was close to -1.

Peculiar neutrino & weak-interaction properties Lee and Yang interpretation (1957): The antineutrino is always emitted with helicity +1. Lee and Yang formulated the 2-component neutrino theory: neutrinos  left (negative) helicity antineutrinos  right (positive) helicity Neutrinos “should” have zero mass.

Peculiar neutrino & weak-interaction properties The actual proof that the neutrino has negative helicity was done by M. Goldhaber and collaborators in 1958: The Sm* nucleus recoils from the neutrino. It decays to the ground state by emitting a g. The polarization of the g measures the helicity of the neutrino (in a non-trivial way!). Neutrinos have negative helicity.

Peculiar neutrino & weak-interaction properties BUT… R. Feynman and M. Gell-Mann concluded that the weak interaction is V-A (1958): Weak interaction acts on the:  left-handed component of particles.  right-handed component of antiparticles. There could be right-handed neutrinos and left-handed antineutrinos, but they would not interact weakly! For massless particles handeness and helicity are equivalent. The Co and Eu experiments do not necessarily imply that the neutrinos are massless. But zero-mass neutrinos were nevertheless incorporated into the SM, , since there was no evidence to the contrary.

Peculiar neutrino & weak-interaction properties We will see later that in fact neutrinos have mass. Therefore there could be right-handed neutrinos and left-handed antineutrinos. For a neutral particle (all charges equal to zero) there are two possibilities:  Dirac neutrinos: nR is a distinct state from nL The neutrino field is a 4 component spinor  Majorana neutrinos: nR is the antineutrino of nL The neutrino is its own antiparticle! We still do not know which is the case. The only hope to check this is neutrinoless double-beta-decay.

More than one neutrino m→e+g So far we have seen only electron-neutrinos, ne. These neutrinos are produced together with electrons in b-decay. But there was another particle, “like the electron” but heavier: the muon. This particle should decay into an electron and a gamma m→e+g through the diagram: But this decay did not occur.

More than one neutrino Furthermore in the late 40’s it became clear that the muon decayed into more than one particle. Presumably the unseen particles were neutrinos: m→ e + n + n Were the neutrinos the same? There was a particle that decayed into a muon and a (presumably) neutrino: the pion. p→ m + n

Target and Magnetic Horn More than one neutrino With the new accelerators it became plausible to make intense n beams. The idea occurred independently to Schwartz and Pontecorvo. → m + n n+N→e o m? k p n p m n protons Target and Magnetic Horn detector shielding Accelerator

More than one neutrino An experiment was done at the Brookhaven 30 GeV accelerator in 1962. Out of 29 events none was compatible with an electron in the final state. 1988 Nobel Prize

3 neutrino families

3 neutrino families If neutrinos are massless there is no interaction that will mix the 3 families. Lepton-family number as well as global lepton number are conserved. But if the neutrino had mass, there could be mixing through the same Higgs mechanism that gives mass to the particles. Mass eigenstates and weak eigenstates do not need to be the same, as it indeed happens with the quarks.

Neutrino oscillations In the early sixties, Pontecorvo suggested that if neutrinos had mass they could oscillate. Assume we start with a pure neutrino of a given family at t=0, and let it evolve freely. After time t: Let’s assume, for simplicity, that we have only two families:

Neutrino oscillations Suppose that we create a beam of pure nm at some source at t=0. Question: what is the probability of finding a ne in a detector located at a distance x from the source of the nm flux? After some algebra:

The solar neutrino problem (s) In 1960 R. Davies started with an experiment to detect solar neutrinos. The original motivation was to check the mechanism for producing energy in the Sun

The solar neutrino problem (s) The total luminosity is very well measured: L = 3.846x1026 watts All fusion reaction amount to: 4p  4He + 2e+ + 2ne (Q=24.68 MeV) Assuming that g’s and kinetic energy (except that of the n’s) go to heat, the heat production per reaction is W= Q+4mec2-<En’s> =26.1 MeV The total number of ne’s produced by the Sun is then: Nn = 2 L /W = 1.8x3038 ne . s-1 Flux on Earth surface = 6.4x1010 ne/cm2s-1 (day and night)

The solar neutrino problem (s) The flux of solar neutrinos is very large but their detection is very difficult. The pioneer experiment of R.Davies took place at the Homestake Mine in S. Dakota (at 1350m depth). Large (600 tons) of Perchloroethylene (C2Cl4). The detection method is radiochemical.

The solar neutrino problem (s) SSM Prediction: 7.7 SNU (5.9 for 8B, 1.15 for 7Be, 0.65 others) 1 SNU=10-36 captures/(atom sec) Measurement:2.560.160.16 SNU The measurement was repeated by many experiments with different techniques (e.g. Galium instead of Clorine). All of them (except one) saw less neutrinos than expected.

The solar neutrino problem (s) The problem was finally solved in 2002 with the results of SNO, beautifully confirmed by KAMLAND this year. But more later.

The atmospheric connection. Outer detector 1867 of 8” PMT A new era of detectors: SuperKamiokande 50 ktons of pure H2O at 1000 m depth

The atmospheric connection. Detect Cherenkov light produced by charged lepton l from reacction n+N l +X (l=e,m), or e- from n+e-n+e- . Detector operates in real time and has directional information.

The atmospheric connection.

The atmospheric connection.

Superkamiokande Atmospheric Data

Back to Solar Neutrinos 1 The detected reaction is: ne ne + X  e- + X’ nm .5 nt The reactions nm + X  m- + X’ nt + X  t- + X’ are not possible En < mm, mt 

In addition to charged-current reactions there are neutral current reactions The probles is to detect them: A special case is n + e-  n + e- which is that detected in SK. This reaction proceeds through both CC and NC but they are indistinguishable.

One way to distinguish (proposed by H. H One way to distinguish (proposed by H. H. Cheng in 1984) is to use D2O (heavy water) as target, instead of water. In deuterium (D) ne + D  p + p + e- (CC) nl + D  nl + p + n (NC) (l = e,m,t) In the last reaction the p and n break apart if the energy is abobe 2.22 MeV. The free neutron is captured, liberating 6.25 MeV. But its detection is difficult... Another problem is how to get tons of heavy-water.

Sudbury Neutrino Observatory (S N O) Detector located in Ni mine at 2000m depth.

1kT of D20, surrounded by tank of 7.8 kT of ultrapure H2O.

In the SNO experiment there are 3 reactions measured: ne + d → p + p + e- CC nx + e- → nx + e- ES (as in SK) nx + d → p + n + nx NC In D2O the events are selected statistically, from characteristic variables for each reaction. Derived from NC

KAMLAND reactor experiment: Nuclear reactors are very intense sources of ne from the b-decay of the neutron-reach fission fragments. Each fission results into 6 ne of various energies. Detection through inverse b-decay (as in Reines-Cowan experiment). KAMLAND: liquid scintillator.

KAMLAND reactor experiment:

Global fits to atmospheric and solar sin2 q23 almost maximal sin2 q12 large sin2 q13 < 0.05 Dm2atm ~ 3x10-3 eV2 Dm2solar ~ 3x10-5 eV2 But things could be more complicated.

Future In oscillations the big unknown now is q13. CP violation?. Neutrino “super-beams” Cosmic Neutrinos (from Super-Novae to unexpected). Large projects underway. The neutrino is a special particle and there is still a lot of “conventional” physics to be done with neutrinos.