neutrino novelties: pointers to new physics? dae golden jubilee colloquium institute of mathematical...

Neutrino Novelties:Pointers to new physics?

DAE Golden Jubilee ColloquiumInstitute of Mathematical Sciences, Chennai

May 19, 2004

Amitava RaychaudhuriUniversity of Calcutta

May 19, 2004IMSC, Chennai

A. Raychaudhuri 2 of 28

Neutrino Novelties

• Experimental results: solar and atmospheric neutrinos

• Neutrino oscillations, neutrino mass and mixing

• Massive fermions

c ? (Majorana neutrino)

• Standard model



Neutrino Novelties (contd)

• India-based neutrino observatory (INO)

• See-saw models, Left-right symmetry

• Extra dimensions

• Supersymmetry

• Looking ahead



Neutrino properties

• Three types: e , µ, (sterile ?)• Mass limits:m(e) < 2.5 eV (Tritium beta decay) m(µ) < 0.19 MeV (Pion decay) m() < 18.2 MeV ( decay)

• From cosmology: ∑ m < 24 eV (Energy Density of the Universe) ∑ m < 0.71 eV (WMAP Satellite: CMBR anisotropy)

• Majorana neutrino( =c)? 02β <m> 0.39+0.27

-0.28 eV

(76Ge Heidelberg Moscow)

• Neutrino interactions: Only weak interactions (CC and NC) (e +e e +e ) ~ 10-43 cm2 c.f. ~ 10-27 cm2 (em), ~10-23 cm2 (strong) • Sterile : No weak interactions



Solar and Atmospheric Neutrinos



Solar neutrinos

• Sun generates heat and light through fusion reactions4p 4He + 2 e+ + 2 e + 25 MeV (i)

• Just like sunlight, solar neutrinos are reaching us (day & night!)

• Reaction (i) does not take place in one go. Rather, it is the consequence of a cycle of reactions, e.g. p + p 2H + e+ + e pp neutrinos

The e energy spectra from these reactions are well-known.

• Robust prediction of the number of solar neutrinos as a function of energy is possible. These have been detected by several expts. • But …



Solar neutrino results

Expt Obsvd/Predn Eth (MeV) Type

Homestake 0.335 ± 0.029 0.8 Radiochemical

e + 37Cl 37Ar + e_ (CC)

GNO, SAGE, 0.584 ± 0.039 0.233 Radiochemical

Gallex e + 71Ga 71Ge + e_ (CC)

SuperK 0.459 ± 0.017 5.0 Water Cerenkov

e + e e + e (CC + NC)

SNO CC 0.347 ± 0.027 6.75 Cerenkov

e + d p + p + e_ (CC)

SNO NC 0.894 ± 0.004 + d n + p + (NC)



Neutrino interactions

Neutrinos have two kinds of weak interactions

CC (Radiochemical, SK, SNO), NC (SK, SNO)

e e, p e, n

e, n e e, n W Z

Charged Current (CC) Neutral Current (NC)



Atmospheric neutrinos

Neutrinos are produced in the atmospherefrom cosmic ray pion and kaon decayse.g. (- µ- + µ), (µ

- e- + e + µ)and the charge conjugate processesTypical energy ~ 1 GeV

Expectation: R =(# µ+ µ)/(# e+e) ≈ 2

SuperK: Robs/Rmc =0.635±0.035±0.083 (sub-GeV) = 0.604±0.065±0.065 (multi-GeV)

No. of µ depends on zenith angle (up-down asymmetry)No such effect for e

up

down

detector

Earth

atmosphere



Neutrino Oscillations



Neutrino oscillations

• A quantum mechanical phenomenon relying on the superposition principle.

• In the oscillation of a pendulum, the bob alternately reaches the left and right end-points of the trajectory.

• During travel, a e becomes a µ and then back again to a e. This oscillation process continues.

Prob(e µ, L) = 4 c2 s2 sin2(L/ λ) where λ = 4 E/ ∆, ∆ = (m1

2 – m22), s = sinθ, c = cosθ.

• The oscillation wavelength (and hence probability!) depends on the neutrino energy. Key combination: Δ . (L/E)

µ µ

µ

e

e

e

et



Neutrino oscillations (contd)How does this help?

• Solar detectors are sensitive primarily to e. Some (Cl, Ga and SNO CC) are totally insensitive to µ, τ while SK has a smaller sensitivity (about 1/6). Only SNO NC is equally sensitive to all. If some e have oscillated to µ when they reach the detector, then count will be less (except in SNO NC).

• Atmospheric e, µ are detected through the e-, µ- they produce. At their smaller (L/E), e oscillation hardly occurs, but the µ

oscillates to τ, which do not produce µ-. This reduces the measured ratio R. Also, the zenith angle dependence seen for µ is explained.

• Solar (atmospheric) results cross-checked by KAMLAND reactor (K2K long baseline) expt. LSND result awaiting confirmation.



Quantum Mechanics of neutrino oscillations

Neutrino stationary states: |1>, |2> mass m1, m2

Neutrino flavour eigenstates: |e>, | µ>

Two different bases: |e> = |1> cosθ + |2> sinθ

|µ> = -|1> sinθ + |2> cosθ

|e> produced at t = 0 |Ψ(0)> = |e> = |1> cos θ + |2> sinθ

At a later time: |Ψ(t)> = |1> cos θ e-iE1t + |2> sinθ e-iE2t

Prob(e µ, L) = |< µ |Ψ(t)>|2 = 4 c2 s2 |e-iE1t - e-iE2t|2

Neutrinos are ultra-relativistic: p >> m Ei = (p2 + mi2)½ ≈ p + mi

2/2p

(E1 - E2)t = (m12 – m2

2)t /2p ≡ (∆/2p)t = L ∆/2E

Prob(e µ, L) = 4 c2 s2 sin2(L/ λ) where λ = 4 E/ ∆

Survival Prob. = Prob(e e, L) = 1 - Prob(e µ, L)



More on oscillations

• Essential ingredients: (i) = m12 - m2

2 0, (ii) sin 2 0.

• Matter effect: Mass is a measure of inertia. In a medium, inertia (and hence mass) changes. Neutrino mass and mixing affected by medium (MSW effect)

• Solar neutrino problem: = 6.07 x 10-5 eV2 (ii) tan2 = 0.41 (Best fit -- MSW LMA)

e oscillates to another `active’ neutrino (SNO NC ≈ 1)

• Atmospheric neutrino anomaly: = 3 x 10-3 eV2 (ii) sin2 2 = 1 (Best fit)

µ oscillates to



India-based Neutrino Observatory (INO)• Neutrino detector being planned in India• Advantages: Good mountain coverage (reduce cosmic rays) Only low latitude neutrino detector site in the world.• Location: Pushep (Nilgiris, near Ooty) or Rammam (Near

Darjeeling)• Observatory will eventually house several experiments• ICAL Design: 32 kT magnetised (1 Tesla) Iron, Resistive Plate Chamber (RPC) detectors • R & D Work being pursued: a) Site survey, geological study, tunneling plans, cost estimate b) Prototype detector fabrication, magnet design, engineering c) Detector simulation• Physics goals: a) L/E dip -- a clinching oscillation signal -- in atmospheric b) End detector for neutrino factory: Longest baseline expt?



Neutrino Mass



Fermion mass

• Left- and right-handed fermions: = L+ R

• Fermion mass couples left to right:

m = m(R L + L R)

• Neutrinos only left-handed. If there is only left-handed (or right-handed) component then m=0.

• Caveat: presence of L (c)R , a right-handed field but of opposite charge. m L(c)R violates charge conservation. Majorana mass for neutrinos. (L = 2)



Standard Model

• The Standard Model describes strong and electroweak interactions.

• Mediated by gluons, W-boson, Z-boson, and photon.• Fermions: Left- and right-handed quarks, left- and right-

handed charged leptons, left-handed neutrino.

• Masses of W, Z , quarks and leptons via Higgs mechanism.

• No R in SM Neutrino is massless. Chosen for consistency with information of that era.



Majorana Neutrino?

• Can the neutrino be its own anti-particle? ( ≡ c ?)

The photon is its own anti-particle. (Also 0)• In such an event, lepton number is not conserved!

• Consequence Neutrino-less double beta decay (02β process)

• Normal double beta decay (22β) : X Y + 2 e- + 2e

• Neutrino-less double beta decay (02β) : X Y + 2 e- (<m>2)

• Look for peak in 2e- invariant mass

• Current limit <m> < 0.2 eV.



How to get m 0?

• The mundane way is to add a R to the SM.

• This solves the problem but has no explanation of the smallness of m.

• This is the major hurdle in neutrino model building. To explain the smallness, one always needs new physics associated with some heavy scale, M. For Majorana mass, lepton number violation is also needed.

• Generic form of see-saw: m = (const)/M



New Physics



Simplest new physics

• Left-right symmetric model R required by symmetry.

• Nature is parity violating. Left-right symmetry is broken at a high energy scale, MR.

• Neutrino mass matrix: MR » m

• Two majorana neutrinos: L (mass m), R (mass MR)

• See-saw mass formula: m = (m2)/MR.

• Pati-Salam model and other grand unified theories contain left-right symmetry.

• How to test for MR?

RMm

m0



Extra Dimensional models (an example)

World is (4+d) dim (bulk) 4 dim branesSterile neutrino, N, (and gravity) in bulk, other particles in 4d

brane.

Consider d=1. Coordinates: (x,y)Extra dimension compactified (y coordinate a circle) y y + 2R

Either N(x,y) or n(x) with n = 0,±1,±2,……

Note m(n) = n/R (from y y piece in kinetic term)

])()([2

1),( // RinynRinyn exex

RyxN



Extra Dimensional models (contd.)

Instead of n (with n = 0,±1,±2,...) one often defines Mn = (n + -n)/2 and M’n = (n - -n)/2 with n = 1,2,...and masses (n/R).

Coupling of ordinary L with N only at y=0.

Effective coupling of L with an infinite number of sterile neutrinos. Infinite dimensional mass matrix.

Has been used to address the solar neutrino problem.

)2()(1

0

n

nLRL MMmyNm



Supersymmetry

Bosons Fermions

Supersymmetry puts bosons and fermions in a supermultiplet Superfield: L ≡ (l, Ĩ ), U = (u, ũ)

Many attractive features. Search is on for squarks and sleptons.

Interactions written as a superpotential in terms of superfields.



Supersymmetry (contd.)

Supersymmetric interactions can violate lepton and baryon number.

Baryon number violation implies proton decay. This is not seen!

Often, an additional symmetry, R-parity, was imposed on the superpotential to exclude all baryon number and lepton number violating terms. R-parity conservation requires SUSY particles to be produced in pairs.

Now it is realized that one can retain L-violating terms to generate a neutrino mass and yet maintain proton stability.



Supersymmetry (contd.)

One loop diagrams generate neutrino mass. e.g.,

Notice that Lepton number

is violated at each vertex

by one unit.

L = 2 (Majorana mass)

Here, the slepton mass is the heavy scale. Further suppression through loop factors.

Ĩ

e- X

X



Looking Ahead• Mixing between three neutrinos

• CP-violation in lepton sector• Majorana neutrinos• Sterile neutrinos• Neutrino factories: Long base-line, pure and intense beams• INO• Neutrino mass matrix• Large mixing vs. small quark mixing: RG effect? • New physics: new interactions, symmetries, etc.• Alternatives to massive neutrinos, e.g. VEP• Astroparticle physics: e.g. Supernova, Nucleosynthesis

neutrino novelties: pointers to new physics? dae golden jubilee colloquium institute of mathematical...

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