Majorana Fermions (Neutrinos) in Particle Physics S. T. Petcov SISSA/INFN, Trieste, Italy, and Kavli IPMU, University of Tokyo, Japan School on Topological and Symmetry-Broken Phases TU Dresden, Germany August 17, 2017 Plan of the Lectures 1. Preliminary Remarks. 2. Massive Neutrinos, Neutrino Mixing and Oscillations: Brief Overview. 3. The Three Neutrino Mixing: what we have learned. 4. Open Questions in the Physics of Massive Neutrinos and Future Progress. 5. The Nature of Massive Neutrinos I: Massive Majorana versus Massive Dirac Neutrinos. 6. The Nature of Massive Neutrinos II: Origins of Dirac and Majorana Massive Neutrinos (Deneral Discussion). 7. Determining the Nature of Massive Neutrinos: Neutrinoless Double Beta Decay. 8. The Nature of Massive Neutrinos III: The Seesaw Mechanisms of Neutrino Mass Generation. 9. Leptogenesis Scenario of Generation of the Baryon Asymmetry of the Universe. 2 10. Future LBL Neutrino Oscillation Experiments on sgn(∆m31) and CP Violation (brief overview). 11. Conclusions. S.T. Petcov, Summer School, TU Dresden, 17/08/2017 3 Families of Fundamental Particles: Quarks+Leptons νe u νµ c ντ t + their antiparticles e d µ s τ b p>= uud >, n>= ddu >,... • | | | | Electromagnetic interaction: the photon γ (q’s,e,µ,τ) • Strong interaction: 8 Gluons G (only q’s) • Weak interaction: W , Z0 (all: q’s, l , ν ) • ± ± l Gravitational interaction: the graviton g (all ) • EM, Strong and Gravitational Interactions have symme- tries: particle antiparticle (C), Left–Right or Mirror (P), and Combined↔ CP (Strong CP Problem?) not respected by Weak Interactions. All Fundamental Interactions obey CPT-symmetry: particle antiparticle, Left–Right, t t. ↔ →− Universe: there are no antiparticles. S.T. Petcov, Summer School, TU Dresden, 17/08/2017 3 Families of Fundamental Particles νe u νµ c ντ t + their antiparticles e d µ s τ b 3 types (flavours) of active ν s andν ˜ s • ′ ′ The notion of “type” (“flavour”) - dynamical; • + + νe: νe + n e + p; νµ: π µ + νµ; etc. → − → The flavour of a given neutrino is Lorentz invariant. • ν = ν ,ν ˜ =˜ν , l = l = e,µ,τ; ν =ν ˜ , l,l = e,µ,τ. • l 6 l′ l 6 l′ 6 ′ l 6 l′ ′ The states must be orthogonal (within the precision of the corresponding data): ν ν = δ , ν˜ ν˜ = δ , h l′| li l′l h l′| li l′l ν˜ ν = 0. h l′| li S.T. Petcov, Summer School, TU Dresden, 17/08/2017 The Charged Current Weak Interaction Lagrangian: CC g α (x)= ¯l(x)γα (1 γ5) ν (x) W (x)+h.c., Llep − 2√2 − lL l=Xe,µ,τ W ±: MW = 80 GeV, g(=∼ 0.6) – SU(2)L. The Neutral Current Weak Interaction Lagrangian: 2 2 NC g + (g′) α (x)= ν¯ (x)γα ν (x) Z (x) , Lν − q 2 lL lL l=Xe,µ,τ Z0 boson: M = 92 GeV, g (= 0.4) – U(1) − Z ′ ∼ YW For example, µ decay, µ νµ + e +¯νe: − − − → − µ νµ + virtual W νµ + e +¯νe − → − → − S.T. Petcov, Summer School, TU Dresden, 17/08/2017 We live in a sea of neutrinos. S.T. Petcov, Summer School, TU Dresden, 17/08/2017 S.T. Petcov, Summer School, TU Dresden, 17/08/2017 S.T. Petcov, Summer School, TU Dresden, 17/08/2017 S.T. Petcov, Summer School, TU Dresden, 17/08/2017 S.T. Petcov, Summer School, TU Dresden, 17/08/2017 S.T. Petcov, Summer School, TU Dresden, 17/08/2017 S.T. Petcov, Summer School, TU Dresden, 17/08/2017 10 ν Solar Neutrinos: Φ = 6.5 10 ⊙ , E¯ 1 MeV. Earth ∼ × cm2 s ∼ SN Neutrinos: E¯ 10 MeV ∼ Φ carries 99% of the released E ( 1053 ergs). SN ∼ Relic Neutrinos (Cosmic Background νs): t 1 sec, E 10 4 eV, n 330 ν . U ∼ ∼ − CB ∼ cm2 Atmospheric Neutrinos, νµ, ν¯µ, νe, ν¯e, E 0.2 10 GeV. ∼ − Reactor ν¯e, E 3 MeV: NPS 1 GWT ∼ : 1020 ν¯e . thermal ∼ sec Accelerator νµ, ν¯µ, E 1 100 GeV. ∼ − S.T. Petcov, Summer School, TU Dresden, 17/08/2017 Data (relativistic ν’s): ν (˜ν ) - predominantly LH ( RH). • l l Standard SU(2) U(1) Theory: ν ,ν ˜ - ν (x); L × YW l l lL νlL(x) form SU(2)L doublets with lL(x), l = e,µ,τ: νlL(x) ; lR(x) SU(2)L singlets , l = e,µ,τ . l (x) − L No (compelling) evidence for existence of (relativistic) • ν’s (˜ν’s) which are predominantly RH (LH): νR (˜νL.) If νR,ν ˜L exist, must have much weaker interaction than νl,ν ˜l: νR,ν ˜L - “sterile”, “inert”. B. Pontecorvo, 1967 In the formalism of the ST, νR andν ˜L - RH ν fields νR(x); can be introduced in the ST as SU(2)L singlets. No experimental indications exist at present whether the SM should be minimally extended to include νR(x), and if it should, how many νR(x) should be introduced. S.T. Petcov, Summer School, TU Dresden, 17/08/2017 νR(x) appear in many extensions of the ST, notably in SO(10) GUT’s. The RH ν’s can play crucial role i) in the generation of m(ν) = 0, 6 ii) in understanding why m(ν) ml, mq, iii) in the generation of the observed≪ matter-antimatter asymmetry of the Universe (via leptogenesis). The simplest hypothesis is that to each νlL(x) there cor- responds a νlR(x), l = e,µ,τ. ST + m(ν)=0: Ll = const., l = e,µ,τ; L Le + Lµ + Lτ = const. ≡ S.T. Petcov, Summer School, TU Dresden, 17/08/2017 There have been remarkable discoveries in neutrino physics in the last 19 years. ∼ S.T. Petcov, Summer School, TU Dresden, 17/08/2017 Compellings Evidence for ν Oscillations − ν : SK UP-DOWN ASYMMETRY − atm θ , L/E dependences of µ like events Z− − − Dominant νµ ντ K2K, MINOS, T2K; CNGS (OPERA) → ν : Homestake, Kamiokande, SAGE, GALLEX/GNO − ⊙ Super-Kamiokande, SNO, BOREXINO; KamLAND Dominant νe νµ,τ BOREXINO → ν¯e (from reactors): Daya Bay, RENO, Double Chooz − Dominant ν¯e ν¯µ,τ → T2K, MINOS, NOνA (accelerators νµ, ν¯µ): νµ νe,ν ¯µ ν¯e → → S.T. Petcov, Summer School, TU Dresden, 17/08/2017 Compelling Evidences for ν Oscillations: ν mixing − n ν >= U ν >, ν : m =0; l = e,µ,τ ; n 3; | l lj∗ | j j j 6 ≥ jX=1 n ν (x)= U ν (x) , ν (x): m =0; l = e,µ,τ . lL lj jL jL j 6 jX=1 B. Pontecorvo, 1957; 1958; 1967; Z. Maki, M. Nakagawa, S. Sakata, 1962; U is the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino mixing matrix. ν , m = 0: Dirac or Majorana particles. j j 6 Data: at least 3 νs are light: ν1,2,3, m1,2,3 < 1 eV. ∼ S.T. Petcov, Summer School, TU Dresden, 17/08/2017 The Charged Current Weak Interaction Lagrangian: CC g α (x)= ¯l(x)γα (1 γ5) ν (x) W (x)+h.c., L − 2√2 − lL l=Xe,µ,τ n ν (x)= U ν (x) , ν (x): m =0; l = e,µ,τ . lL lj jL jL j 6 jX=1 S.T. Petcov, Summer School, TU Dresden, 17/08/2017 1 0.8 0.6 0.4 Survival Probability 0.2 ν ν 3- best-fit oscillation Data - BG - Geo e 2-ν best-fit oscillation 0 20 30 40 50 60 70 80 90 100 110 L /Eν (km/MeV) 0 e KamLAND: L/E Dependence (reactorν ¯e, L¯ =180 km, E = (1.8 - 10) MeV) − S.T. Petcov, Summer School, TU Dresden, 17/08/2017 ν¯e ν¯e 1.0 → baseline = 180 Km 0.8 P = 1 - sin 22 sin 2 m2L/4 E ee θ (∆ ν) 0.6 ee P 0.4 0.2 0.0 0 5 10 15 E in MeV ν S.T. Petcov, Summer School, TU Dresden, 17/08/2017 Dr. T. Kajita, Prof. A. McDonald, Nobel Prize for Physics winners, 2015 S.T. Petcov, Summer School, TU Dresden, 17/08/2017 ✳ ✥❛ ✤ ✽ ✾✿❀ ❁ ❂ ❀ ✾❃❄❅ ❈ ❱❈ ❋❂● ❋✾❍■❋✿❂■ ✾❋● ❋❈ ❲● ❏✾❋❂✿❏ ❂ ● ✫✯ ❏✾❍❍■❂ ❂ ❈❈ ❃❀■P❈ ● ▼ ✿❖❀❈✿❂❈ ● ❀❖▼❈● ▲ ✻ ❯ ❘ ❊ ✻❚ ❊ ✼ ❇ ❡✁ ✂ ✄☎ ♦✆ ✝☎ ✞ ✐✟❡ ❙✠❡ ✡✐✁ ☛ ❇ ❡✁ ✂✄☎ ♦✆✝☎ ✞ ✐✟❡ ◆❡ ☞ ✌♦ ✐✟♦✍ ✎ ✞ ✐✟❡ ✞☎②✎✐✡ ✎ s ♦✍ ✄✐❡ ✎ ✞ ✐✟❡ ✷ ✏ ✑ ✒ ✷ ✏ ✑✓ ✷ ✏ ✑✔ ✷ ✏ ✑✕ ✷ ✏ ✑✷ ❑ ✙ ✤✙ ✙ ✤✙✉ ❛ ❛ ❛ ✜ ✢ ★ ✯ ✫★ ✰ ✱ ✇ ❑ ❛ ✖✗✘✙✚ ✛✚✉ ❛✜✢ ✣✤ ✥ ❨✙✬❛ ✜✭ ✮❛✜✭ ❛ ✜ ✢ ✣✤ ✥ ❆✣ ✚ ✣ ✳✚ ✴✚ ✉ ✙ ❛ ✜ ✢ ✣✤ ✥ ✱ ★ ✣✤✥ ❑t❑ ❛ ✜✢ ✲t ❑ ❛ ❛ ✘ ❛ ❛ ❛✣✙ ✜ ❛ ❛ ✘❛ ❛ ❛✣✙ ✜ ❑ ❛ ✖✛ ❆ ❛ ❛✣✙ ✜ ❉ ✦ ✦ ✧★✩✩ ✪ ★✫ ★ ❉ ✦ ✦ ✧★✩✩ ✪ ★✫ ★ ✰ ❉ ✧★✩✩ ✪ ★✫ ★ ❛ ❛✣✙ ✜ ✧★✩✩ ✪ ★✫ ★ ❆ ✣✤✚ ✘ ✜❛ ✢ ❛✜✢ ✲❛✉ ❛❛✉ ✙ ❑ ❛ ✙ ✣❛ ❛✜✢ ✣✤ ✥ ❨ ✙ ✤✙ ✳✚ ✴✚✉ ✙ ❛ ✜ ✢ ✣✤ ✥ ✫ ✫ ✵ ✶ ✯ ❉ ★ ✩ ✹ ★ ✯ ✫★ ✣✤ ✥ ✳ ❛ ❛✣✙ ✜ ✳✚ ✥ ❑ ❛ ❛ ✣✙ ✜ ✳✚ ✥ ❑ ❛ ❛✣✙ ✜ ✰ ✸ ✧★✩✩ ✪ ★✫ ★ ✺ ✫ ✧★✩✩ ✪ ★ ✫ ★ ✺ ✫ ✧★✩✩ ✪ ★✫ ★ S.T. Petcov, Summer School, TU Dresden, 17/08/2017 S.T. Petcov, Summer School, TU Dresden, 17/08/2017 The Pontecorvo Prize for 2016 (24/02/2017): Prof. Yifang Wang (Daya Bay), Prof. Soo-Bong Kim (RENO), Prof. K. Nishikawa (T2K) ”For their outstanding contributions to the study of the neutrino oscillation phenomenon and to the measurement of the Theta13 mixing angle in the Daya Bay, RENO and T2K experiments.” The relatively large value of the “reactor” angle θ13 =∼ 0.15 measured in the Daya Bay, RENO and Double Chooz experiments, indications for which were obtained first in the T2K experiment, opened up the possibility to search for CP violation effects in neutrino oscillations. S.T. Petcov, Summer School, TU Dresden, 17/08/2017 These data imply that mνj <<< me,µ,τ , mq, q = u, c, t, d, s, b < < 6 For mνj 1 eV: mνj/ml,q 10− ∼ ∼ 2 < < 2 For a given family: 10− ml,q/mq 10 ∼ ′ ∼ S.T. Petcov, Summer School, TU Dresden, 17/08/2017 These discoveries suggest the existence of New Physics beyond that of the ST. S.T. Petcov, Summer School, TU Dresden, 17/08/2017 The New Physics can manifest itself (can have a variety of different “flavours”): In the existence of more than 3 massive neutrinos: n> 3 (• n = 4, or n = 5, or n = 6,...). In the Majorana nature of massive neutrinos. • In the observed pattern of neutrino mixing and in the values• of the CPV phases in the PMNS matrix.