Selected topic in neutrino physics

Petr Vogel, Caltech

• Overview of oscillation phenomenology• KamLAND, a culmination of half

century of reactor neutrino studies• Neutrinoless double beta decay: from

rates to Majorana masses• Mechanism of lepton number violation• An example of model building

New era of neutrino physics

1. Atmospheric neutrino oscillations

(in particular zenith angle dependence of the muon neutrino flux, confirmed by K2K)

2. Solar neutrino deficit

(in particular the difference in neutrino fluxes deduced from the charged and neutral current reaction rates)

3. KamLAND

(reactor e disappearance, oscillations seen with the terrestrial sources)

4. LSND oscillation observations

(unconfirmed, but soon to be checked; if correct all bets are off)

Consequences:• At least some neutrinos are massive. Lower limits are 50 and 10 meV, upper limit ~ 2 eV from tritium decay, or alternatively,

m < 1 eV from cosmology and astrophysics.

• Mixing exists. Two mixing angles are large, one is small)

• But we do not know the absolute mass scale• We do not know the behavior under charge

conjugation• We know nothing about CP symmetry of leptons

This is a first clear manifestation of “physics beyond the Standard model”.

(entries evaluated for Ue3 = 0.1,near the middle of allowed range)

Neutrino mass and oscillations:An overview

In the standard electroweak model neutrinos are massless and the lepton flavors are exactly conserved. Formally this is a consequence of the absence of the

right-handed weak singlet components. Neutrino masses do not arise even through loop effects.

Charged lepton and neutrino fields form doublets in SU(2)L:

From the width of Z it follows that N = 2.984 +- 0.008. BBN is compatible with 3 flavors and disfavors 4.

Neutrino mass is generated by a phenomenological mass

term, connecting the left and righthanded fields:

The mass is analogous to the mass term of charged leptons, it might violate flavor, but conserves the lepton number.The Majorana mass might exist if there are no additiveconserved charges. It violates the total lepton number.For N lefthanded neutrinos i and n sterile j

Mhas N + n Majorana eigenstates kc = k.

For N lefthanded neutrinos there are N masses, N(N-1)/2 mixing angles, (N-1)(N-2)/2 CP phases, and (N-1) Majorana phases.

NxN unitary mixing matrix has 2N2 real parameters.

N is used for normalization, N(N-1) for orthogonality,N is absorbed by charged lepton phases.

Thus N2 is left. N phases can be eliminated bychoosing the phases of the charged lepton fields.There are N(N-1) parameters left.

(N-1)(N-2)/2 CP phases + (N-1) Majorana phases =N(N-1)/2 phases altogether

N(N-1)/2 angles

Altogether N(N-1) mixing parameters + N-1 mass differences + 1 mass scale

Basic formulae for vacuum oscillations:

Parametrization of the 3x3 mixing (MNS or PMNS) matrix:

(or E in MeV and Losc in m)

Since is small, solar, and ~ atm

Majorana phases i do not affect flavor oscillations

The magnitude of CP or T violation in flavor oscillations is

where ij = (mi2 – mj

2)L/4E.Thus the size of the effect is the same in all channels.CP violation is possible only when all three angles and all three mass differences are nonvanishing.

sin

Oscillations in matter:

When neutrinos propagate in matter, additional phase appears,

due to effective neutrino-matter interaction with electrons(only for electron neutrinos and antineutrinos):

And with nucleons for all active neutrinos:

The additional phase is then

And the corresponding oscillation length is

The equations of motion can be rewritten either in thevacuum mass eigenstate basis,

Or in the flavor eigenstate basis

In either case the matter eigenstates depend on L0, Losc,

and on the vacuum mixing angle

There is a resonance, i.e. maximum mixing, ifLosc/Locos2 = 1.

In practical units the ratio Losc/Lo is

We can thus consider several special cases:

Why is the survival probability increasing again for large E?

At resonance the two eigenvalues are essentially degenerate,and there is a probability Px for jumping from one eigenstateto another.

Since cos2m(max) ~ -1, and at high energies Px ~ 1,<P(e -> e)> -> cos2

Thus solar neutrinos (from 8B decay observed in SK and

SNO) actually “do not oscillate”. They areborn as the heavier eigenstate and propagate

likethat all the way to a detector.The fact that the oscillation parameters derived

fromthe solar and reactor e agree is a sign of not only

CPT invariance but test the whole concept of vacuum

and matter oscillations.

Atmosphericneutrinos.Best fitm32

2 ~ 2x10-3eV2,sin22 > 0.94

Allowed regions of parameter space (2003)

8.2-0.5+0.6x10-5(2004)

Present status of our knowledge of oscillation parameters

LSND – fly in the ointment

L = 30 m, E= 20-50 MeV, “decay at rest spectrum”

Oscillations -> e, 87.9 +- 22.4 +- 6.0 events,oscillation probability 0.264 +- 0.067 +- 0.45 %

Most of the parameter range excluded by reactorand KARMEN experiments, but a sliver with0.2 < m2 < 10 eV2 remains.

Requires existence of sterile neutrinos !!!

At present tested by Mini-BOONE at Fermilab, waitand see……(until 2005 at least)

Reminder, direct neutrino mass mesurement

1) Time of flight – not sensitive enough2) Two body decays, e.g. -> not sensitive

enough3) Three body decay ( decay of 3H)

This is essentially model independent, based on kinematics only. Incoherent sum,m = ( |Uei|2 mi

2)1/2 is determined.Present limit 2.5 – 2.8 eV, planned sensitivity~0.3eV (KATRIN).

Cosmological constraints

The presently observed distribution of matter (throughhigh resolution galaxy surveys) and CMB are both

affectedby the presence of massive neutrinos in the early

Universe.Combined analysis is sensitive to mi.