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Lepton Mixing and Neutrino Mass

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Lepton Mixing and Neutrino Mass Lepton Mixing and Neutrino Mass v Werner Rodejohann T -1 (MPIK, Heidelberg) mv = m L - m D M R m D Strasbourg MANITOP Massive Neutrinos: Investigating their July 2014 Theoretical Origin and Phenomenology 1 Neutrinos! 2 Literature ArXiv: • – Bilenky, Giunti, Grimus: Phenomenology of Neutrino Oscillations, hep-ph/9812360 – Akhmedov: Neutrino Physics, hep-ph/0001264 – Grimus: Neutrino Physics – Theory, hep-ph/0307149 Textbooks: • – Fukugita, Yanagida: Physics of Neutrinos and Applications to Astrophysics – Kayser: The Physics of Massive Neutrinos – Giunti, Kim: Fundamentals of Neutrino Physics and Astrophysics – Schmitz: Neutrinophysik 3 Contents I Basics I1) Introduction I2) History of the neutrino I3) Fermion mixing, neutrinos and the Standard Model 4 Contents II Neutrino Oscillations II1) The PMNS matrix II2) Neutrino oscillations II3) Results and their interpretation – what have we learned? II4) Prospects – what do we want to know? 5 Contents III Neutrino Mass III1) Dirac vs. Majorana mass III2) Realization of Majorana masses beyond the Standard Model: 3 types of see-saw III3) Limits on neutrino mass(es) III4) Neutrinoless double beta decay 6 Contents I Basics I1) Introduction I2) History of the neutrino I3) Fermion mixing, neutrinos and the Standard Model 7 I1) Introduction Standard Model of Elementary Particle Physics: SU(3) SU(2) U(1) C × L × Y oR +R Species # eR bR tR sR Quarks 10P 10 cR io dR i+ uR ie oL Leptons 3 13 +L eL tL Charge 3 16 cL uL bL sL dL Higgs 2 18 18 free parameters... + Gravitation + Dark Energy + Dark Matter + Baryon Asymmetry 8 Standard Model of Elementary Particle Physics: SU(3) SU(2) U(1) C × L × Y oR +R Species # eR bR tR sR Quarks 10P 10 cR io dR i+ uR ie oL Leptons 3 13 +L eL tL Charge 3 16 cL uL bL sL dL Higgs 2 18 + Neutrino Mass mν 9 Standard Model∗ of Particle Physics add neutrino mass matrix mν (and a new energy scale?) Species # Quarks 10P 10 Leptons 3 13 Charge 3 16 Higgs 2 18 10 Standard Model∗ of Particle Physics add neutrino mass matrix mν (and a new energy scale?) Species # Species # Quarks 10P 10 Quarks 10P 10 Leptons 3 13 Leptons 12 (10) 22 (20) −→ Charge 3 16 Charge 3 25 (23) Higgs 2 18 Higgs 2 27 (25) 11 Supersymmetry Astrophysics LHC ILC cosmic rays supernovae ... BBN Cosmology ... Dark Matter Baryon Asymmetry ... NEUTRINOS Flavor physics GUT quark mixing ... SO(10) see−saw proton... decay 12 Supersymmetry Astrophysics LHC ILC cosmic rays supernovae ... BBN Cosmology ... Dark Matter Baryon Asymmetry ... NEUTRINOS Flavor physics GUT quark mixing ... SO(10) see−saw proton decay ... 13 General Remarks Neutrinos interact weakly: can probe things not testable by other means • – solar interior – geo-neutrinos – cosmic rays Neutrinos have no mass in SM • – probe scales m 1/Λ ν ∝ – happens in GUTs – connected to new concepts, e.g. new representations of SM gauge group, Lepton Number Violation particle and source physics ⇒ 14 Contents I Basics I1) Introduction I2) History of the neutrino I3) Fermion mixing, neutrinos and the Standard Model 15 I2) History 1926 problem in spectrum of β-decay 1930 Pauli postulates “neutron” 16 1932 Fermi theory of β-decay 1956 discovery of ν¯e by Cowan and Reines (NP 1985) 1957 Pontecorvo suggests neutrino oscillations 1958 helicity h(ν )= 1 by Goldhaber V A e − ⇒ − 1962 discovery of νµ by Lederman, Steinberger, Schwartz (NP 1988) 1970 first discovery of solar neutrinos by Ray Davis (NP 2002); solar neutrino problem 1987 discovery of neutrinos from SN 1987A (Koshiba, NP 2002) 1991 Nν = 3 from invisible Z width 1998 SuperKamiokande shows that atmospheric neutrinos oscillate 2000 discovery of ντ 2002 SNO solves solar neutrino problem 2010 the third mixing angle 17 Future History 20ab CP shown to be violated 20cd mass ordering determined 20ef Dirac/Majorana nature shown 20gh value of neutrino mass measured 20ij new physics discovered 20kl ??? 18 Contents I Basics I1) Introduction I2) History of the neutrino I3) Fermion mixing, neutrinos and the Standard Model 19 I3) Neutrinos and the Standard Model SU(3) SU(2) U(1) SU(3) U(1) with Q = I + 1 Y c × L × Y → c × em 3 2 νe Le = (2, 1) e ∼ − L e (1, 2) R ∼ − ν (1, 0) total SINGLET!! R ∼ oR +R eR bR tR sR cR d io u R i+ R ie oL +L eL tL cL uL bL sL dL 20 Masses in the SM: = g L Φ e + g L Φ˜ ν + h.c. −LY e R ν R with ∗ ∗ + 0 νe ∗ φ φ L = and Φ=˜ iτ2 Φ = iτ2 = e φ0 φ+ L − after EWSB: Φ (0, v/√2)T and Φ˜ (v/√2, 0)T h i → h i → v v Y = ge eL eR + gν νL νR + h.c. me eL eR + mν νL νR + h.c. −L √2 √2 ≡ in a renormalizable, lepton number conserving model with Higgs doublets the ⇔ absence of νR means absence of mν 21 Quark Mixing g + µ CC = W uL γ V dL −L √2 µ with u =(u,c,t)T , d =(d,s,b)T Quarks have masses they mix ↔ mass matrices need to be diagonalized ↔ flavor states not equal to mass states ↔ results in non-trivial CKM (Cabibbo-Kobayashi-Maskawa) matrix: 0.97427 0.00015 0.22534 0.00065 0.00351+0.00015 ± ± −0.00014 V = 0.22520 0.00065 0.97344+0.00016 0.0412+0.0011 | | ± −0.00016 −0.0005 0.00867+0.00029 0.0404+0.0011 0.999146+0.000021 −0.00031 −0.0005 −0.000046 small mixing related to hierarchy of masses? 22 Contents II Neutrino Oscillations II1) The PMNS matrix II2) Neutrino oscillations II3) Results and their interpretation – what have we learned? II4) Prospects – what do we want to know? 23 II1) The PMNS matrix Analogon of CKM matrix: g µ − CC = ℓL γ U νL W −L √2 µ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix ∗ να = Uαi νi connects flavor states να (α = e, µ, τ) to mass states νi (i = 1, 2, 3) mass terms go like ℓL ℓR and νL νR (?) (flavor = mass if m = 0 U = ½) ν ⇒ 24 Number of parameters in U for N families: complex N N 2 N 2 2 N 2 × unitarity N 2 N 2 − rephase ν , ℓ (2 N 1) (N 1)2 i i − − − a real matrix would have 1 N (N 1) rotations around ij-axes 2 − in total: families angles phases 2 1 0 3 3 1 4 6 3 N 1 N (N 1) 1 (N 2) (N 1) 2 − 2 − − this assumes νν¯ mass term, what if Majorana mass term νT ν ? 25 Number of parameters in U for N families: complex N N 2 N 2 2 N 2 × unitarity N 2 N 2 − rephase ℓ N N(N 1) α − − a real matrix would have 1 N (N 1) rotations around ij-axes 2 − in total: families angles phases extra phases 2 1 1 1 3 3 3 2 4 6 6 3 N 1 N (N 1) 1 N (N 1) N 1 2 − 2 − − Extra N 1 “Majorana phases” because of mass term νT ν − (absent for Dirac neutrinos) 26 Majorana Phases connected to Majorana nature, hence to Lepton Number Violation • I can always write: U = UP˜ , where all Majorana phases are in • P = diag(1, eiφ1 , eiφ2 , eiφ3 ,...): 2 families: • cos θ sin θ 1 0 U = sin θ cos θ 0 eiα − 27 3 families: U = R R˜ R P • 23 13 12 −iδ 1 0 0 c13 0 s13 e c12 s12 0 = 0 c s 0 1 0 s c 0 P 23 23 − 12 12 0 s c s eiδ 0 c 0 0 1 − 23 23 − 13 13 iδ c12 c13 s12 c13 s13 e = s c c s s e−iδ c c s s s e−iδ s c P − 12 23 − 12 23 13 12 23 − 12 23 13 23 13 s s c c s e−iδ c s s c s e−iδ c c 12 23 − 12 23 13 − 12 23 − 12 23 13 23 13 with P = diag(1, eiα, eiβ) 28 Contents II Neutrino Oscillations II1) The PMNS matrix II2) Neutrino oscillations II3) Results and their interpretation – what have we learned? II4) Prospects – what do we want to know? 29 II2) Neutrino Oscillations (in Vacuum) Neutrino produced with charged lepton α is flavor state ν(0) = ν = U ∗ ν | i | αi αj | ji evolves with time as ν(t) = U ∗ e−i Ej t ν | i αj | j i amplitude to find state ν = U ∗ ν : | βi βi | ii (ν ν , t)= ν ν(t) = U U ∗ e−i Ej t ν ν A α → β h β| i βi αj h i| j i δij ∗ −i Ei t | {z } = Uαi Uβi e 30 Probability: P (ν ν , t) P = (ν ν , t) 2 α → β ≡ αβ |A α → β | ∗ ∗ −i (Ei−Ej ) t = Uαi Uβi Uβj Uαj e ij αβ P e−i∆ij Jij | {z } =|... = {zEXERCISE!} ∆ P = δ 4 Re αβ sin2 ij + 2 Im αβ sin∆ αβ αβ − {Jij } 2 {Jij } ij j>i j>i X X with phase 1 ∆ = 1 (E E ) t 1 p2 + m2 p2 + m2 L 2 ij 2 i − j ≃ 2 i i − j j 2 m2 m2−m2 1 mi j q i j 2 pi (1 + 2p2 ) pj (1p + 2p2 ) L 4E L ≃ i − j ≃ 2 2 2 1 m m ∆m L GeV ∆ = i − j L 1.27 ij 2 ij 4 E ≃ eV2 km E ! 31 ∆ P = δ 4 Re αβ sin2 ij + 2 Im αβ sin∆ αβ αβ − {Jij } 2 {Jij } ij j>i j>i X X α = β: survival probability • α = β: transition probability • 6 2 requires U = ½ and ∆m = 0 • 6 ij 6 Pαβ = 1 conservation of probability • α ↔ Pαβ invariant under U eiφα U eiφj • Jij αj → αj Majorana phases drop out! ⇒ 32 CP Violation In oscillation probabilities: U U ∗ for anti-neutrinos → Define asymmetries: ∆ = P (ν ν ) P (ν ν )= P (ν ν ) P (ν ν ) αβ α → β − α → β α → β − β → α αβ = 4 Im ij sin∆ij j>i {J } P 2 families: U is real and Im αβ = 0 α,β,i,j • {Jij } ∀ 3 families: • ∆m2 ∆m2 ∆m2 ∆ = ∆ = ∆ = sin 21 L + sin 32 L + sin 13 L J eµ − eτ µτ 2 E 2 E 2 E CP ∗ ∗ where JCP = Im Ue1 Uµ2 Ue2 Uµ1 1 = 8 sin2θ12 sin2θ23sin2θ13 cos θ13 sin δ 2 vanishes for one ∆mij = 0 or one θij = 0 or δ = 0, π 33 Two Flavor Case Uα1 Uα2 cos θ sin θ αα 2 2 1 2 U = = 12 = Uα1 Uα2 = sin 2θ U U sin θ cos θ ⇒J | | | | 4 β1 β2 − ∆m2 and transition probability is P = sin2 2θ sin2 21 L αβ 4 E 34 35 amplitude sin2 2θ • maximal mixing for θ = π/4 ν = 1 (ν + ν ) • ⇒ α 2 1 2 q 2 2 E eV oscillation length Losc = 4π E/∆m21 = 2.48 GeV ∆m2 km • 21 2 2 L Pαβ = sin 2θ sin π ⇒ Losc is distance between two maxima (minima) e.g.: E = GeV and ∆m2 = 10−3 eV2: L 103 km osc ≃ 36 37 L L : fast oscillations sin2 πL/L = 1 ≫ osc h osci 2 and P = 1 2 U 2 U 2 = U 4 + U 4 αα − | α1| | α2| | α1| | α2| sensitivity to mixing 38 L L : fast oscillations sin2 πL/L = 1 ≫ osc h osci 2 and P = 2 U 2 U 2 = U 2 U 2 + U 2 U 2 = 1 sin2 2θ αβ | α1| | α2| | α1| | β1| | α2| | β2| 2 sensitivity to mixing 39 L L : hardly oscillations and P = sin2 2θ (∆m2L/(4E))2 ≪ osc αβ sensitivity to product sin2 2θ ∆m2 40 large ∆m2: sensitivity to mixing small ∆m2: sensitivity to sin2 2θ ∆m2 maximal sensitivity when ∆m2L/E 2π ≃ 41 Characteristics of typical oscillation experiments 2 2 Source Flavor E [GeV] L [km] (∆m )min [eV ] (−) (−) −1 2 4 −6 Atmosphere νe , νµ 10 ..
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