Neutrino Novelties: Pointers to new physics?

1. Neutrino Novelties:Pointers to new physics? DAE Golden Jubilee Colloquium Institute of Mathematical Sciences, Chennai May 19, 2004 Amitava Raychaudhuri University of Calcutta

2. Neutrino Novelties • Experimental results: solar and atmospheric neutrinos • Neutrino oscillations, neutrino mass and mixing • Massive fermions •   c ? (Majorana neutrino) • Standard model A. Raychaudhuri

3. Neutrino Novelties (contd) • India-based neutrino observatory (INO) • See-saw models, Left-right symmetry • Extra dimensions • Supersymmetry • Looking ahead A. Raychaudhuri

4. 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)? 02β <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 A. Raychaudhuri

5. Solar and Atmospheric Neutrinos A. Raychaudhuri

6. Solar neutrinos • Sun generates heat and light through fusion reactions 4p  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 … A. Raychaudhuri

7. 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) A. Raychaudhuri

8. 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 WZ Charged Current (CC) Neutral Current (NC) A. Raychaudhuri

9. Atmospheric neutrinos Neutrinos are produced in the atmosphere from cosmic ray pion and kaon decays e.g. (- µ- + µ), (µ-  e-+ e+ µ) and the charge conjugate processes Typical 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 down detector up Earth atmosphere A. Raychaudhuri

10. Neutrino Oscillations A. Raychaudhuri

11. 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 µand then back again to a e. This oscillation process continues. Prob(eµ, L) = 4 c2 s2 sin2(L/ λ) where λ = 4 E/ ∆, ∆ = (m12 – m22), s = sinθ, c = cosθ. • The oscillation wavelength (and hence probability!) depends on the neutrino energy. Key combination: Δ . (L/E) µ µ t e e e e µ A. Raychaudhuri

12. 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, τwhile 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. A. Raychaudhuri

13. 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> sinθe-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 + mi2/2p (E1 - E2)t = (m12 – m22)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) A. Raychaudhuri

14. More on  oscillations • Essential ingredients: (i)  = m12 - m22  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  A. Raychaudhuri

15. 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? A. Raychaudhuri

16. Neutrino Mass A. Raychaudhuri

17. 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) A. Raychaudhuri

18. 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. A. Raychaudhuri

19. 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 (02β process) • Normal double beta decay (22β) : X  Y + 2 e- + 2e • Neutrino-less double beta decay (02β) : X  Y + 2 e- (<m>2) • Look for peak in 2e- invariant mass • Current limit <m> < 0.2 eV. A. Raychaudhuri

20. How to get m 0? • The mundane way is to add a Rto 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 A. Raychaudhuri

21. New Physics A. Raychaudhuri

22. 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? A. Raychaudhuri

23. Extra Dimensional models (an example) World is (4+d) dim (bulk)  4 dim branes Sterile 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 + 2R Either N(x,y) or n(x) with n = 0,±1,±2,…… Note m(n) = n/R (from y y piece in kinetic term) A. Raychaudhuri

24. 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. A. Raychaudhuri

25. 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. A. Raychaudhuri

26. 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. A. Raychaudhuri

27. 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. X Ĩ X     e- A. Raychaudhuri

28. Looking Ahead • Mixingbetween 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 A. Raychaudhuri