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Enrique FernándezUniv. Autónoma Barcelona/IFAE

Neutrino oscillations: status and plans

Trobada de Nadal, Univ. Barcelona, Dec 21-22, 2005

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Neutrino properties

Neutrinos are somewhat special particles. This is mainly due to the fact that they only interact weakly.At low energies (MeV’s), the cross-section for

interacting with 1 nucleon is very small, ~ 10-40 cm2. This implies that they are “invisible” in most cases. The charged current weak interaction is also very peculiar: it only acts on the left-handed chiral projection of particle spinors (right-handed, for antiparticles). It does not conserve P (nor CP). Spin effect are thus very strong.

They also have a very small mass, compared with that of the other elementary particles.

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mu= 400 md= 400 me= 0.5 me< 0.0000022

mc= 1,600 ms= 500 m= 106 m< 0.000170

mt=175,000 mb=4,300 m= 1,776 m< 15.5

Quarks LeptonesQuark and Lepton masses in units of MeV/c2

mi<0.00000071From CMB anisotropies:

Neutrino properties

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Neutrinos in the SM

In the SM there are 3 lepton families, each containing a charged lepton and a neutrino.Neutrinos are massless particles and each family lepton number (as well as global lepton number) is conserved.

These assumptions, in particular the massless assumption, were built up from experiments.

The neutrino has three states (weak eigenstates): e, , By definition these are the states that couple to the W together with the corresponding charged leptons.

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Massive neutrinos and neutrino oscillationsIn 1998 there was a turning point in neutrino physics. Data from atmospheric neutrinos collected by the Superkamiokande detector showed that there were neutrino oscillations. As we will see neutrino oscillations requires that neutrinos have mass and that there is lepton mixing.The SK results were preceded by many experiments on solar neutrinos that showed a deficit, with respect to solar models, on the number of neutrinos coming from the Sun.New solar neutrino experiments, in particular SNO (Sudbury Neutrino Observatory) have now shown unequivocally that the deficit of solar neutrinos is also due to oscillations.

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What do we mean by oscillations?

(ref.: B. Kaiser, hep-ph/0506165).

Let’s assume that a neutrino of flavor , , is produced at the source. When it interacts at the target it does so as a neutrino of a different flavor, .

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Oscillation requires both mixing between the leptons and massive neutrinos.Suppose that there are several neutrino mass states i. Mixing means that the state produced together with charged lepton l is a superposition of different i:

The set of all U*i (for 3 i) form a unitary matrix. Inverting

it:

Neutrino Oscillations:

e

PMNS3

2

1

Pontecorvo-Maki-Nakagawa-Sakata matrix

U*i= amplitude of W+ decay to li

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The oscillation probability is given by the square of the amplitude:

Neutrino Oscillations:

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Neutrino Oscillations:

In the rest frame:

In terms of laboratory variables:

To interfere coherently, the different i have to have the same E. (if they had the same p the phase would be exp (-i(Ei-Ej)t) which, averaged over t, would be zero, unless Ei=Ej).The momentum is given by (for mi

2<<E2):

Therefore the phase is:

(constant for all i, thus not contributing to the probability)

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Neutrino oscillations. Squaring the amplitude:

The oscillation implies that lepton family number is no longer conserved.

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This is entirely similar to what happens in the case of the quarks, where favor is not conserved in weak decays, e.g

(uds) p (uud)+ (du)The reason for the non-conservation of “quark family number” or “flavor” is quark mixing, the fact that weak and mass eigenstates are different.

u d’ c s’ t b’

bsd

CKMbsd

'''

Neutrino Oscillations:

The difference is that we produce weak-interaction quarks (in the weak decay of the ) but observe them as mass states (in the p or ).

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Neutrino oscillations. Squaring the amplitude:

From this expression we see that:

1) as required by CPT invariance.

2) In general (if U complex):

CP violation.

The above formula is very complicated but nature has been kind enough as to make it simple in certain cases of interest.

3) The sin2[..L/E] gives “oscillatory” pattern.

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Neutrino oscillation:

To gain some understanding of the above formula write:

For a given term to be relevant the argument of sin2() should not be much smaller than /2, otherwise sin2( ) is too small. It can also be that for a given experiment only one mixing angle is relevant.The bottom line is that in some cases the oscillation can be treated as a two-family mixing.

cos sin-sin cos

PMNSU

GeVEkmLeVm

ELcm ijij

22222 27.1sin4

3sin

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Neutrino oscillation:

Oscillation probabilities (2 neutrino case; relevant for CNGS beam):

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The first clear signature of oscillations came from the SuperKamiokande experiment in 1998

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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.

SuperKamiokande detector principle

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SuperKamiokande events (fairly typical)

muon electron

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Evidence for neutrino oscillations

SK atmospheric

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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

The evidence for oscillations: solar neutrinos

About 2 radioactive atoms/day!

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The evidence for oscillations: solar neutrinos

The measurement was repeated by other experiments using Galium instead of Clorine. All of them saw less neutrinos than expected.This was known as the “solar neutrino problem”.Kamiokande, and later SK, measured the “elastic-scattering” reaction

x + e- → x + e-

where x is mostly e.

e e

e

ee-

e- e-e-

e- e-

W Z

Z

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The evidence for oscillations: solar neutrinos

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The evidence for oscillations: solar neutrinos

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Definive solution of the Solar neutrino puzzle

The Sudbury Neutrino Observatory (SNO)

SNO: 1 kT of D2O (heavy water) surrounded by 7.8kT of ultra pure H2O.

Located at 2000m depth at the INCO mine in Sudbury, Ontario, Canada.

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Definive solution of the Solar neutrino puzzle

A neutrino of E>2.2 MeV can disociate the Deuterium nucleous, into proton and neutron. This NC process takes place for any neutrino species.

SNO

SNO detects 3 reactions:e + D p + p + e- (CC)

x + e- → x + e- (ES; like SK)

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

The neutron is captured producing 6.25 MeV.

But detecting a single neutron is difficult...

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Definive solution of the Solar neutrino puzzle

SNO Results

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Oscillation signaturesAtmospheric neutrino disappear, but, is it due to oscillations?A controlled accelerator experiment: K2K (KEK to Kamioka).

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K2K (KEK to Kamioka)

monitormonitor Near detectors

(ND)

+

Target+Horn200m

decay pipe

SK

100m ~250km

12GeV protons~1011/2.2sec(/10m10m)

~106/2.2sec(/40m40m)

~1 event/2days

Signal of oscillation at K2K Reduction of events Distortion of energy spectrum

(monitor the beam center)

1º tilt downwards

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SK Events

(BG: 1.6 events within 500s 2.4×10-3 events in 1.5s)

TSKTspill

GPS

SKTOF=0.83msec

107 events

Decay electron cut.

20MeV Deposited Energy

No Activity in Outer DetectorEvent Vertex in Fiducial VolumeMore than 30MeV Deposited Energy

Analysis Time Window

500sec

5sec

TDIFF. (s)

-0.2TSK-Tspill-TOF1.3secfor 0.89x1020 p.o.t.

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K2K near-detector complex

• 1KT Water Cherenkov Detector (1KT)• Scintillating-fiber/Water sandwich Detector (SciFi)• Lead Glass calorimeter (LG) before 2002• Scintillator Bar Detector (SciBar) after 2003• Muon Range Detector (MRD)

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Oscillation signatures

E. Aliu et al., Phys. Rev. Letters 94:081802, 2005.

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KAMLAND Reactor Experiment

“Solar” neutrino oscillations in a controlled reactor-experiment

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Evidence for neutrino oscillationsSK atmospheric

K2K

Solar experiments

KAMLAND reactor exp.

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Neutrino oscillations:In addition to the Solar (+Kamland) and Atmospheric (+K2K), there are two other very relevant experiments: Chooz reactor experiment. Sees no oscillation of

reactor e over a baseline of 1 Km.

conveniently ignored

Excess of 87.9±22.4±6.0 events!

LSND accelerator experiment. Sees positive signal of oscillations of → e over 30 m baseline

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Results of the analysis of the oscillation data

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Results of the analysis of the oscillation data

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Mixing angles:

12 sol 34º2º23 atm 45º3º13 < 12º (at 3) sin213≡|Ue3|2 < 0.04

m2atm≡ m2

32=m23-m2

2 = [(2.40.3)x10-3 eV2]

m2sol≡ m2

21=m22-m2

1 = (0.80.3)x10-5 eV2

12/3 e 21/3 e 30% e

Oscillation parameters

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In view of the results it is convenient to parameterize the PMNS matrix as:

Parameterization of the PMNS matrix

CP violation phase

U 1 0 00 c23 s23

0 s23 c23

c13 0 s13ei

0 1 0 s13e

i 0 c13

c12 s12 0 s12 c12 0

0 0 1

solar

Links atmospheric & solar sectors

atmospheric

cij≡cosij sij≡sinij

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Solar Oscillations and the MSW effect

The solar neutrinos pass through the very dense Sun core. Electron neutrinos can interact forward with the solar matter in two ways, while mu or tau neutrinos only do so through NC.

Forward interactions cannot be distinguished from no-interaction at all coherent scattering, which affects propagation through matter. The extra term for e gives an extra phase to mass eigenstates which interplays with that which gives rise to oscillations. The effect has the opposite sign for neutrinos and antineutrinos (has nothing to do with CP violation).

e e e

e e e e

e

Z W

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Formulae are similar to those in vacuum with the replacement:

2

22m

ENGx eF

2222 )2(cos2sin xmmm M

)2(cos2sin2sin2sin 2sin 2

222

xM

+ for neutrinos

- for antineutrinos

sign of depends on sign of m2

Solar Oscillations and the MSW effect

x > 1

x < cos212

Pee

E 1 MeV

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Accelerator experiments and their primary goals:

MiniBoone (FNAL): prove or disprove LSND

K2K (KEK-Kamioka): check SK, improve m

MINOS (FNAL-Soudan) check SK, improve m, 13?OPERA (CERN-LNGS) see appearance in beamT2K (KEK-Kamioka) try to measure 13 . . .

Noa (FNAL-Nth Minn.) try to measure 13 . . .

Many ideas for future 13, CP-violation, ...

Near

Term

Longer

Term

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Conclusions

• Neutrinos played a crucial role in establishing the Standard Model.

• Neutrinos have mass and mix. This is physics beyond the Standard Model.

• The masses and pattern of mixing is quite different from that of quarks. This may be a hint to the physics beyond the SM.

• Accelerator experiments permit the control of E, L and the initial neutrino state. They will have a role in elucidating fully the pattern of masses and mixings.

• Progress will require a variety of experiments at different energies and baselines.