A LOOK INTO THE PHYSICS OF NEUTRINOS

J A Grifols, UAB

Viña del Mar, 11-15 Dec 06

• Neutrino weak interactions

• Neutrino masses

• Neutrino mixing and oscillations

• Static properties

• Dirac or Majorana?

• Absolute neutrino masses

• Neutrinos in Cosmology and Astrophysics

Weak interactions of neutrinos

with

Neutrino masses

weak eigenstates are NOT mass eigenstates

i) construct with

Then, the most general MAJORANA mass term

upon diagonalization of the complex & symmetric matrix

we get

where

are Majorana neutrinos ( )ckk

ii) alternatively,

introduce

and write the most general DIRAC mass term

diagonalization thereof

leads to

where

are DIRAC neutrino fields

Neutrino oscillations A neutrino of definite flavor is produced at t=0

and has probability amplitude to be found in flavor state after time t

'

withand

Thus, the (vacuum) transition probability is

P’s depend on 2 mass-squared differences, 3 mixing angles & 1 CP phase

The key parameter is the “oscillation length”

2

4

m

ELosc

Oscillations can be observed in an experiment if

oscLL

Experiments fall roughly into 2 cathegories: i) atmospheric and long baseline accelerator experiments on the one hand & ii) solar and reactor long baseline experiments on the other. Analysis of data shows that

30

1223

212

m

mand 2

132 105sin

Then, neglecting small quantities and ,

oscillations in i) (for which holds) are mainly

and thus

E

Lm212 13

2sin

)1(2

223 O

E

Lm

)cos1(2sin1)( 222323

221

ELmP

For experiments in cathegory ii), is relevant and the survival probabilities again can be given by standard 2-flavor formulas, i.e.

212m

)cos1(2sin1)( 221212

221

EL

ee mP

for reactor (KamLAND) experiments, or

for solar MSW matter oscillations.

In short, oscillations in atmospheric-LBL and solar-KamLAND domains decouple.

),,(sin)( 21212

2)2,1(ematteree mPP

A brief survey of experiments i)

Super-Kamiokande atmospheric experiment

if there were no oscillations, electron & muon events from up/down going should satisfy

,e

)cos()(cos ,, zeze NN

electron events satisfy this equality but muon events don’t

004.0035.0551.0)50020(

)000,13500(

kmLD

kmLU

best fit gave

12sin

105.2

232

23223

eVm

Further support for disappearence is provided by

K2K experiment MINOS experiment

produced at KEK accelerator Fermilab-Soudan, 730km

and detected at SKamiokande, 250km apart

away

112 were observed and 204 events

expected (if no oscillations) observed,

expected (no oscillations)

best fit best fit

2.96.81.158

12sin

1064.2

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23223

eVm

15298

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ii) Solar-KamLAND domain

All solar neutrino experiments (Homestake, GALLEX-GNO, SAGE and Super-Kamiokande) show a factor 2-3 less rate than expected by the SSM.

The SNO experiment gave model independent evidence for oscillations via reactions

charged current

neutral current

ee

pnd

pped

xx

xx

e

elastic scattering

From CC the flux of on Earth is obtained

From NC the flux of on Earth is obtained

SNO results:

e ,,e

031.0023.0340.0,,

flux

flux

e

e

Thus, about a factor 3 less solar electron neutrinos reach the Earth because they convert into other flavors on their way from the Sun to the Earth.

The total flux measured is in agreement with the SSM prediction:

Additional model independent evidence for oscillations comes from the reactor KamLAND experiment:

In the Kamiokande mine the antineutrinos from 53 reactors in Japan are detected through . Their average distance to the detector is 170km.

events were expected (no oscillations)

258 events were observed

From a global analysis of solar & KamLAND data,

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nepe

24365

09.007.012

2256.04.0

212 45.0tan;100.8

Vm

Static properties

Majorana neutrinos have neither charge nor magnetic/electric dipole moments. This follows from

and

that implies

However Dirac neutrinos (with mass) can have magnetic moment (and EDM, if CP is not conserved)

Tc C

1CC T

0

0

5

Indeed, the SM (with RH neutrino added) predicts a magnetic dipole moment:

which is extremely small.

The best empirical limits on MDM come from astrophysics:

A larger MDM would cause excessive energy depletion from globular-cluster red giant cores via the plasma process (all flavors).

BeVm

)(102.3 119

B12103

Dirac or Majorana?

Best way to decide is neutrinoless double β decay:

eZAZA 2)2,(),(

MoXeTeGe 10013613076 ,,, and other even-even nuclei

Majorana ν

The matrix element for the 0νββ-decay is proportional to an effective Majorana mass .

Most competitive lower bounds on 0νββ-decay half-lives are,

i ieimUm 2

)(105.5)(

)(109.1)(231300

2/1

257602/1

CuricinoyearsTeT

MoscowHeidelbergyearsGeT

eVm )2.112.0(

New experiments in 0νββ-decay are presently being prepared (CUORE, GERDA,EXO, MAJORANA, …). Goal is to reach

.10 2eVfewm

What is the absolute scale of neutrino masses?

From ν oscillations we only know mass squared differences. No absolute ν mass values are known. Upper bounds come from laboratory experiments and astrophysics/cosmology.

Tritium β-decay experiments: eeHeH 33

Mainz and Troitsk experiments give

H3

eVmUm ii

ei 3.222

The future Katrin experiment foresees a sensitivity

eVm 2.0

Astrophysics/Cosmology

Bounds on neutrino masses have been derived from various astrophysical/cosmological settigs, e.g. Supernova 1987A, Lyman-α forests studies, Galaxy redshift surveys, CMB anisotropies, cosmic energy density, …

The “classical” Gerstein-Zeldovich limit

Light neutrinos (i.e. relativistic at neutrino decoupling, when T~1MeV) populate the Universe today (~100 per cubic cm). If they are nonrelativistic today, they contribute to the known matter density .

Indeed,

Observationally , and since

m

i

i

eV

mh

932

15.02 hm m

eVmi

i 14

The most powerful constraint comes from the CMB radiation data in conjunction with the power spectrum obtained from Large Scale Structure (LSS) surveys.

After their decoupling at T~1MeV, relativistic neutrinos free-stream at almost the speed of light and outflow from regions smaller than the horizon so that density perturbations at those scales are effectively erased. This comes to an end when neutrinos become non-relativistic and cluster with the cold components of dark matter. Hence, for all physical scales smaller than the size of the horizon at the time when neutrinos turn non-relativistic, the growth of perturbations is hindered.

In Fourier space, scales are characterized by their “wavenumber” k and this limiting scale is given by

Neutrino mass influences cosmic structure formation at small scales (i.e. ).

MpcheVmk mnr /)1/(03.0 2/12/1

nrkk

The power spectrum is defined as , i.e. the variance of the Fourier transformed density fluctuations. The power loss at small scales induced by a non-zero neutrino mass can be parameterized by

W.Hu et al., PRL 80 (1998) 5255

2)( kkP

mP

P

8

From the large samples of data in galaxy redshift surveys, such as the 2dFGRS, the power spectrum of matter fluctuations can be analyzed and bounds on neutrino masses inferred. These bounds are particularly strong when the WMAP results on cosmological parameters (most importantly on and ) are incorporated in the analysis.

In this way, cosmology sets the limit

and cosmologists claim that future data will be sensitive to

2hm h

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SUMMARY

• 4 oscillation parameters are known (with approximate accuracies)

• The parameter is bounded

• The CP phase δ is unknown• Cosmology sets a bound on absolute mass

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