Neutrinos in the Standard Model

1. Neutrinos in the Standard Model • Neutrinos only interact through the “weak force” • Neutrino interaction with W and Z bosons is (V-A) • Neutrinos are left-handed(Antineutrinos are right-handed) • Neutrinos are massless • Why do they have small mass? • Three types of neutrinos • Electron ne e • Muon nm m • Tau nt t

2. Neutrino Sources for Experimentation • Also: • Supernova Neutrinos( ~10 MeV) • Relic “Big-Bang” Neutrinos(250 meV)

3. 1st Observedpmn decay Highlights of Neutrino History Reines & Cowann Detector Nobel 2002 Observation of neutrinos from the sun and supernovae Davis (Solar n’s in1970) and Koshiba (Supernova n’s1987)

4. Neutrino Interactions • W exchange gives Charged-Current (CC) events and Z exchange gives Neutral-Current (NC) events In CC events the outgoing lepton determines if neutrino or antineutrino

5. n Earth Neutrino Cross Section is Very Small • Weak interactions are weak because of the massive W and Z boson exchange  s weak GF2 (1/MW or Z)4 • For 100 GeV Neutrinos: • s(ne) ~ 10-40and s(np) ~ 10-36cm2compared to s(pp) ~ 10-26cm2 • Mean free path length in Steel ~ 3109 meters! (Need big detectors and lots of n’s) MW ~ 80 GeVMZ ~ 91 GeV

6. Helicity is projection of spin along the particle’s direction Frame dependent (if massive) left-helicity right-helicity Neutrinos in the Standard Model Are Left-Handed(Helicity and Handedness) • Handedness (or chirality) is Lorentz-invariant • Only same as helicity for massless particles. • If neutrinos have mass then left-handed neutrino is: • Mainly left-helicity • But also small right-helicity component  m/E • Neutrinos only interact weakly with a (V-A) interaction • All neutrinos are left-handed • All antineutrinos are right-handed Right-handed neutrinos do not interact in the Standard Model   “Sterile” neutrinos

7. Inverse m-decay:nm + e- m- + ne Total spin J=0 (Helicity conserved) Point scattering    s = 2meEn Neutrino-Electron Scattering • Elastic Scattering:nm + e- nm + e- • Point scattering    s = 2meEn • Electron coupling to Z0 • (V-A): -1/2 + sin2qW • (V+A): sin2qW  Total spin J=0 or 1

8. Charged - Current: W exchange Quasi-elastic Scattering:(Target changes but no break up)nm + n  m- + p Nuclear Resonance Production:(Target goes to excited state)nm + n  m- + p + p0 (N* or D)n + p+ Deep-Inelastic Scattering:(Nucleon broken up)nm + quark  m- + quark’ Neutral - Current: Z0 exchange Elastic Scattering:(Target doesn’t break up or change)nm + N  nm+ N Nuclear Resonance Production:(Target goes to excited state)nm + N  nm+ N + p (N* or D) Deep-Inelastic Scattering(Nucleon broken up)nm + quark  nm + quark Linear rise with energy Resonance Production Neutrino-Nucleon Processes

9. Making Neutrinos Matter • Standard Model assumes that neutrinos are massless • No symmetry property or theoretical reason for mn = 0 • Neutrinos are partners of the massive charged leptons • Could imply right-handed n ’s, Majorana n =nor sterile n’s • Neutrino mass hierarchy ? t m entnm ne • Cosmological Consequences • Neutrinos fill the universe from the Big Bang (109n / m3) Even a small mass (~1 eV) will have effects • Models have hot (n) and coldDark Matter • Massive neutrino affect structure formation such as galaxies and clusters

10. Neutrino Masses in Cosmology

11. Dirac Neutrinos Neutrino and Antineutrino are distinct particles (like their charged lepton partners) Lepton number conserved Neutrino m- Antineutrino  m+ Dirac Mass Term Need to have a right-handed neutrino (Not in the Standard Model) Mass term like e, m, t Majorana Neutrinos Neutrinos and Antineutrinos are the same particle (This can only happen since neutrinos have no charge!) Only difference is “handedness” Neutrinos are left-handed n m- Antineutrinos are right-handed n m+ Lepton number not conserved Neutrino  Antineutrino with spin flip Majorana Mass Term New type of mass Dirac and Majorana Neutrinos

12. See – Saw Mechanism • If only the nL exist, then neutrinos only can have a Majorana mass • But if both nL and nR exist then can have both Majorana and Dirac mass components • If postulate that mL=0, mD=me,m,t << mR= very heavy (since right-handed )and diagonalize the mass matrix Explains? why neutrinos have small mass but predicts very small mixing

13. Direct Neutrino Mass Experiments Direct decay studies have made steady progress but limited • Electron neutrino: • 3H3He + ne + e- • Muon neutrino: • pmnm decays • Tau neutrino: • t (np) nt decays < 2 eV nm(keV) < 170 keV ne(eV) nt(MeV) < 18 MeV

14. Neutrino Oscillations • Direct measurements have difficulty probing small neutrino masses  Use neutrino oscillations • If we postulate: • Neutrinos have (different) mass  Dm2 = m12 – m22 • The Weak Eigenstates are a mixture of Mass Eigenstates Then a pure nm beam at L=0, will develop a ne component as it travels a distance L.

15. Derivation of Oscillation Formula(A favorite graduate exam problem today) See if you can derive the 1.27factor in the formula by recoveringfrom the hbar = c =1.

16. Oscillation Formula Parameters nmDisappearance neAppearance

17. Current Situation: Three Experimental Indications for Neutrino Oscillations Atmospheric NeutrinosL = 15 to 15,000 km E =300 to 2000 MeV LSND ExperimentL = 30m E = ~40 MeV Solar NeutrinosL = 108 km E =0.3 to 3 MeV Dm2 = ~ 2 to 8 10-5eV2ProbOSC = ~100% Dm2 = .3 to 3 eV2ProbOSC = 0.3 % Dm2 = ~ 1 to 7 10-3 eV2 ProbOSC = ~100%

18. Make ’s fromp,K m n decays Only n’s left ! Make ’s and K’s Slow down and stopall m’s in shielding MiniBooNE Neutrino Beam

19. 50m Decay Pipe Magnetic Horn MiniBooNE Neutrino Beam Variable decay pipe length (2 absorbers @ 50m and 25m) 8 GeV Proton Beam Transport p  m n One magnetic Horn, with Be target Detector

20. The MiniBooNE Detector • 12 meter diameter sphere • Filled with 950,000 liters (900 tons) of very pure mineral oil • Light tight inner region with 1280 photomultiplier tubes • Outer veto region with 241 PMTs. • Oscillation Search Method:Look for ne events in a pure nm beam

21. Particle Identification By Phototube Hit Pattern • Charged particles produce Čerenkov photons at a constant angle as they go through the oil • This shows up as a ring of hits in the phototubes mounted inside the MiniBooNE sphere • Pattern of phototube hits tells the particle type Stopping muon event

22. MiniBooNE Now Taking Data(Examples of two early data events) Charged Currentnm + n  m- + pwith outgoing muon (1 ring) Neutral Currentnm + n  nm + p0 + pwith outgoing p0  gg (2 rings)

23. Animation Each frame is 25 ns with 10 ns steps. Low High Early Late Muon Identification Signature:m  e nm ne after ~2msec Charge (Size) Time (Color)

24. Three Positive Signals Solar Neutrinos Atmospheric Neutrinos Low-E Accelerator Neutrinos Many negative searches Current Neutrino Oscillation Signals

25. Scenario: MiniBooNE Confirms LSNDThree Dm2solar , Dm2atm , Dm2LSND Possible explanations • Atmospheric result is a mixture of Dm2solar and Dm2LSND • Difficult to fit all data with this model (hep-ph/000416) • Introduce a 4th (or more) sterile neutrino • 2+2 Model: • Atmospheric or Solar (or both) have oscillation fractions to ns such that fSolar + fAtmos = 1 Super-K Atmospheric: fAtmos< 0.25 @ 90%CL SNO + Super-K Solar: fSolar<0.50 @ 90%CL • Model still possible but at the edge(Extension: 3active +3sterile model can work)

26. 3+1 Model: Atmospheric: nm nt Solar: LMA nem,t LSND: nmse Solar oscillations are to a 50%/50% mixture of nm and nt LSND nme oscillations are through high mass, mainly ns state with small admixture of nm and e 3+1 Model

27. If CPT is violated the Model accommodates solar, atmospheric, and LSND without sterile neutrinos Just allow the antineutrino Dm2 to be bigger than the neutrino Tests Kamland usesne’s from a set of reactors In this model, Kamland will see no oscillation signal MiniBooNE can run with both nm andnm In this model, will see no oscillations for nm ne but oscillations at the LSND rate fornme CPT Violation (Barenboim, Borissov, Lykken,Smirnov, Murayama, Yanagida;hep-ph 0201080)

28. Matter-Antimatter Asymmetry (B  0)from Leptogenesis • Hard to generate a baryon asymmetry (B  0) using quark matrix CP violation • Generate L  0 using CP or CPT violation in the lepton sector • B-L processes then convert neutrino excess to baryon excess. • Sign and magnitude ~correct to generate baryon asymmetry in the universe d gives CP violation Why?

29.  N3 N3 Matter-Antimatter Asymmetry (B  0)from Leptogenesis • Hard to generate a baryon asymmetry (B  0) using quark matrix CP violation • Generate L  0 in the early universe from CP (or CPT) violation in heavy neutrino N3 vs.decays (only needs to be at the 10-6 level) • B-L processes then convert neutrino excess to baryon excess. • Sign and magnitude ~correct to generate baryon asymmetry in the universe with mN > 109 GeV and mn < 0.2 eV n Mixing n Mixing

30. Summary • Neutrinos have mass and flavor mixing • Observed masses and differences are much smaller than charged lepton partners ?? • Mixings are very large  near 100% ?? But expect small mixings if mn is from the “See-Saw” • If all indications true, need to add more neutrinos (“sterile”, heavy?) • Neutrinos may have an important role in producing the baryon-antibaryon asymmetry in the universe

31. Maybe it was the ns !