Enrique Fernández Univ. Autónoma Barcelona/IFAE

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Enrique FernándezUniv. Autónoma Barcelona/IFAE

Neutrino Oscillations: a km-scale Quantum Phenomenon

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The Neutrino Hypothesis

circa-1930: If nuclear -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.

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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…

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for 2-body decay

What Pauli was saying:

End point and shape of the spectrum depend on neutrino mass.

This method of measuring the mass, still in use, gives m< 2.2 eV/c2.

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Fermi’s Theory of Weak-Interactions

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Pauli “invented” the neutrino and Fermi (in 1934) made an extremely successful theory of weak interactions based on it:

are Dirac spinors ; i are 4X4 complex matrices ; currents can be Scalar, Vector, Axial Vector, Pseudoscalar o Tensor.

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Fermi’s Theory of Weak-Interactions

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Fermi’s theory lead to some predictions:

+ decay:

electron capture:

inverse -decay:

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Observed by Jolliot-Curie in 1934.

Observed by Alvarez in 1938.

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…

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Neutrino discovery

Remember inverse-beta-decay

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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…

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Neutrino discovery

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

Pr

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14460

8939

14459

8938

14458

8937

14457

8936

14456

23592

Nd

Y

SrCe

RbLa

nKrBaU

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“Typical” nuclear bomb:

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Neutrino discovery

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Neutrino discovery

The project was actually approved at Los Alamos!

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Neutrino discovery

A much better idea:

Put a detector at some distance from the core of a nuclear reactor.

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Use delayed coincidence between e+ annihilation and neutron capture

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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)

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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.

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_6028

6027 eNiCo

Experiment of C.S. Wu et al (1956).

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

Measure electrons from -decay of polarized Co nuclei.

is a pseudoscalar, it changes sign under parity.

eN p

If parity is conserved should be zero. The measured value was close to -1.

eN p

eN p

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Peculiar neutrino & weak-interaction propertiesLee 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.

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)1()0( *15262

15263 SmeEu

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 . The polarization of the measures the helicity of the neutrino (in a non-trivial way!).

Neutrinos have negative helicity.

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Peculiar neutrino & weak-interaction propertiesBUT… 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.

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.

There could be right-handed neutrinos and left-handed antineutrinos, but they would not interact weakly!

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Peculiar neutrino & weak-interaction propertiesWe 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:

R is a distinct state from L

The neutrino field is a 4 component spinor

Majorana neutrinos:

R is the antineutrino of L

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.

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More than one neutrinoSo far we have seen only electron-neutrinos, e. These neutrinos are produced together with electrons in -decay.

But there was another particle, “like the electron” but heavier: the muon. This particle should decay into an electron and a gamma

→e+

through the diagram:

But this decay did not occur.

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More than one neutrinoFurthermore in the late 40’s it became clear that the muon decayed into more than one particle. Presumably the unseen particles were neutrinos:

→ e + + Were the neutrinos the same?

There was a particle that decayed into a muon and a (presumably) neutrino: the pion.

→

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More than one neutrinoWith the new accelerators it became plausible to make intense beams. The idea occurred independently to Schwartz and Pontecorvo.

Accelerator

Target and Magnetic

Horn

k

shielding

detector

protons

→

→e o ?

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More than one neutrinoAn 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

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3 neutrino families

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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.

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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:

iii tiEt )exp()(

Neutrino oscillations

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21

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sincos

e

Let’s assume, for simplicity, that we have only two families:

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Neutrino oscillations

After some algebra:

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

)()( tP ee

)/(sin2sin)( 22osce xP

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2

22

5.2

mmm

eVm

MeVEkmosc

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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

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The solar neutrino problem (s)The total luminosity is very well measured:

L = 3.846x1026 watts

All fusion reaction amount to:4p 4He + 2e+ + 2e (Q=24.68 MeV)

Assuming that ’s and kinetic energy (except that of the ’s) go to heat, the heat production per reaction is

W= Q+4mec2-<E’s> =26.1 MeV

The total number of ne’s produced by the Sun is then:

N = 2 L /W = 1.8x3038e . s-1

Flux on Earth surface = 6.4x1010 e/cm2s-1 (day and night)

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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.

MeVAreCl 814.0E *3718

3717

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SSM Prediction: 7.7 SNU (5.9 for 8B, 1.15 for 7Be, 0.65

others)

1 SNU=10-36 captures/(atom sec)

Measurement:2.560.160.16 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.

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The problem was finally solved in 2002 with the results of SNO, beautifully confirmed by KAMLAND this year.

But more later.

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The atmospheric connection.

41.4m

39.3m

Outer detector

1867 of 8” PMT

50 ktons of pure H2O at 1000 m depth

A new era of detectors: SuperKamiokande

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

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Superkamiokande Atmospheric Data

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1

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0

The detected reaction is:

e + X e- + X’

The reactions

+ X - + X’

+ X - + X’

are not possible E < m, m

Back to Solar Neutrinos

e

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In addition to charged-current reactions

),,( ' elXlXl

there are neutral current reactions

'XX ll The probles is to detect them:

A special case is + e- + e- which is that detected in SK. This reaction proceeds through both CC and NC but they are indistinguishable.

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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)

e + D p + p + e- (CC)

l + D l + p + n (NC) (l = e,,)

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.

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Detector located in Ni mine at 2000m depth.

Sudbury Neutrino Observatory (S N O)

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

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In the SNO experiment there are 3 reactions measured:

e + d → p + p + e- CC

x + e- → x + e- ES (as in SK)

x + d → p + n + x NC

In D2O the events are selected statistically, from characteristic variables for each reaction.

Derived from NC

12.024.012.023.0

09.006.009.005.0

39.2

76.1

SNOES

SNOCC

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KAMLAND reactor experiment:Nuclear reactors are very intense sources of e from the -decay of the neutron-reach fission fragments.

Each fission results into 6 e of various energies.

Detection through inverse -decay (as in Reines-Cowan experiment).

KAMLAND:

liquid scintillator.

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KAMLAND reactor experiment:

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Global fits to atmospheric and solar

sin2 23 almost maximal

sin2 12 large

sin2 13 < 0.05

m2atm ~ 3x10-3 eV2

m2solar ~ 3x10-5 eV2

But things could be more complicated.

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In oscillations the big unknown now is 13.

Future

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.

Enrique Fernández Univ. Autónoma Barcelona/IFAE

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