Neutrinos as a Unique Probe: cm

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Juniper Atkinson
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1 Neutrinos as a Unique Probe: cm Particle Physics νn, µn, en scattering: existence/properties of quarks, QCD Weak decays (n pe ν e, µ e ν µ ν e ): Fermi theory, parity violation, quark mixing Neutral current, Z-pole, atomic parity: electroweak unification, field theory, m t ; severe constraint on physics to TeV scale Neutrino mass: constraint on TeV physics, grand unification, superstrings, extra dimensions; seesaw: m ν m 2 q /M GUT P529 Spring,

2 Astrophysics/Cosmology Core of Sun Supernova dynamics Atmospheric neutrinos (cosmic rays) Violent events (AGNs, GRBs, cosmic rays) Large scale structure (dark matter) Nucleosynthesis (big bang - small A; stars iron; supernova - large N) Baryogenesis Simultaneous probes of ν and astrophysics Interior of Earth P529 Spring,

3 Neutrino Oscillations: a first look Weak versus mass eigenstates: ν e }{{} weak = ν 1 cos θ + ν 2 sin θ, ν }{{} µ = ν 1 sin θ + ν 2 cos θ mass t = 0: ν(0) = ν µ (from π + µ + ν µ ) t > 0: ν(t) = ν 1 sin θe ie1t + ν 2 cos θe ie 2t [ ] ν 1 sin θe im2 1 t 2E + ν2 cos θe im2 2 t 2E e iet E i = p 2 + m 2 i E + m2 i /2E where E p for definite p m i (same for definite E or wave packets) P529 Spring,

4 Probability of oscillating to ν e (observe by ν e n e p) P νµ ν e (L) = ν e ν(t) 2 = sin 2 θ cos 2 θ ( m = sin 2 2θ sin 2 2 ) L 4E e im = sin 2 2θ sin 2 [ 1.27 m 2 (ev 2 )L(km) E(GeV) 2 1 t 2E t + e im2 2 t 2 2E t ] m 2 = m 2 2 m2 1, L t µ+ π + ν µ L e ν e p Oscillation length: L osc = 4πE m 2 Survival probability: P νµ ν µ (L) = 1 P νµ ν e (L) P529 Spring,

5 Neutrino Spectra ν Oscillations P νa ν b = sin 2 2θ sin 2 ( m 2 L 4E ) 10 0 KARMEN2 NOMAD MiniBooNE Bugey NOMAD CDHSW CHORUS NOMAD CHORUS LSND 90/99% 3 ν Patterns (U V l ) Solar: LMA (SNO, KamLAND, Borexino) m ev 2, mixing large but nonmaximal Atmospheric + K2K + MINOS: m 2 Atm ev 2, near-maximal mixing Reactor: U e3 small 0.15 m 2 [ev 2 ] Cl 95% Ga 95% CHOOZ all solar 95% SNO 95% ν e ν X ν µ ν τ ν e ν τ ν e ν µ All limits are at 90%CL unless otherwise noted SuperK 90/99% MINOS tan 2 θ K2K KamLAND 95% Super-K 95% 10 2 P529 Spring,

6 Mixings: let ν ± 1 2 (ν µ ± ν τ ): ν 3 ν + ν 2 cos θ ν sin θ ν e ν 1 sin θ ν + cos θ ν e 3 2 m 2 m 2 atm 1 m 2 atm Normal hierarchy 2 1 m2 3 Inverted hierarchy Analogous to quarks, charged leptons ββ 0ν rate very small ββ 0ν if Majorana Degenerate pattern for m m 2 P529 Spring,

7 Mass, Mixing, and Intrinsic Properties Weyl fermion Minimal (two-component) fermionic degree of freedom ψ L ψ c R by CP (ψc R ψ L ) Active Neutrino (a.k.a. ordinary, doublet) in SU(2) doublet with charged lepton normal weak interactions νr c by CP Sterile Neutrino (a.k.a. singlet, right-handed) SU(2) singlet; no interactions except by mixing, Higgs, or BSM ν R νl c by CP Almost always present: Are they light? Do they mix? P529 Spring,

8 Fermion Mass Transition between right and left Weyl spinors: m ψ L ψ R + m ψr ψ L m ( ψl ψ R + ψ R ψ L ) ( m 0 by ψ L,R phase changes) Dirac Mass Connects two distinct Weyl spinors (usually active to sterile): m D ( ν R + ν R ) = m D ν D ν D h ν ν R Dirac field: ν D + ν R 4 components, L = 0 t 3 L = ±1 2 Higgs doublet Why small? (Large dimensions? Higherdimensional operators? String instantons?) φ 0 m D = h ν ν = 2h ν ϕ 0 P529 Spring,

9 Majorana Mass Connects Weyl spinor with itself: m T 2 ( νl ν c R + νc R m S 2 ( ν c L ν R + ν R ν c L Majorana fields: ν M + ν c R = νc M ) = m T 2 ν M ν M (active) ) = m S 2 ν MS ν MS (sterile) ν c R m T m T The Standard Electroweak Theo h T ν MS ν c L + ν R = ν c M S 2 components, L = ±2, self-conjugate φ 0 T Active: t 3 L = ±1 (triplet or higher-dimensional operator) Sterile: t 3 L = 0 (singlet or bare mass) φ 0 φ 0 Phase of or ν c L fixed by m T,S 0 P529 Spring,

10 Neutrinoless Double Beta Decay (ββ 0ν ) L = 2: Majorana mass only (m ββ m T ) p e e p m ββ W W n n Other mechanisms, e.g., R P violation in supersymmetry P529 Spring,

11 Mixed Models Can have simultaneous Majorana and Dirac mass terms L = 1 2 ( ) ( ( ) ν 0 L ν }{{ L 0c mt m D ν 0c R } m D m S νr 0 weak eigenstates ) + h.c. m T : L = 2, t 3 L = 1 (Majorana) m D : L = 0, t 3 L = 1 2 (Dirac) m S : L = 2, t 3 L = 0 (Majorana) P529 Spring,

12 Mass eigenvalues: A ν L ( ) ( ) mt m D A ν m D m R = m1 0 }{{ S 0 m } 2 M=M T (Majorana) mass eigenstates: ν im = ν il + ν c ir = νc im, i = 1, 2 ( ν1l ν 2L ) = A ν L ( ν 0 L ν 0c L ), ( ν c 1R ν c 2R ) = A ν R ( ν 0c R ν 0 R ) M = M T (unlike Dirac mass matrix) A = Aν R P529 Spring,

13 Special Cases L = 1 2 ( ν 0 L ν 0c L ) ( ) ( m T m D ν 0c R m D m S ν 0 R ) + h.c. Majorana (m D = 0): m 1 = m T : ν 1L = ν 0 L, νc 1R = ν0c R m 2 = m S : ν 2L = ν 0c L, νc 2R = ν0 R P529 Spring,

14 Dirac (m T = m S = 0): m 1 = +m D : ν 1L = 1 (ν 0 L + ν0c L ), νc 1R = 1 (ν 0c R + ν0 R ) 2 2 m 2 = m D : ν 2L = 1 (ν 0 L ν0c L ), νc 2R = 1 (ν 0c R ν0 R ) 2 2 Dirac ν (4 components) equivalent to two degenerate ( m 1 = m 2 ) Majorana ν s with m 1 = m 2 and 45 mixing (cancel in ββ 0ν ) Useful description for Dirac limit of general case Recover usual Dirac expression L = m D 2 ( ν 1Lν c 1R ν 2Lν c 2R ) + h.c. = m D( ν 0 L ν0 R + ν0 R ν0 L ) No ν 0 L ν0c L or ν0c R ν0 R mixing L conserved P529 Spring,

15 Seesaw (a.k.a. minimal or Type I seesaw) (m S m D,T ) : m 1 m T m2 D m S : ν 1L ν 0 L m D m S ν 0c L ν0 L, m 2 m S : E.g., m T = 0, m D = O(m u,e,d ), m S = O(M X GeV): ν 2L m D ν 0 L m + ν0c L S ν0c L φ 0 T φ S m 1 m 2 D /m S m D ν R ν R ν 1M ν 0 L + ν0c R (active) Lower m S possible (even TeV) φ 0 φ 0 Heavy ( sterile) ν 2M decouples at low energy ν 2M decays leptogenesis P529 Spring,

16 Active-sterile (ν 0 L ν0c L ) mixing (LSND) No active-sterile mixing for Majorana, Dirac, or seesaw m D and m S (and/or m T ) both small and comparable: Mechanism? Pseudo-Dirac ( m T, m S m D ): Small mass splitting, small L violation, e.g., m T = ɛ, m S = 0 m 1,2 = m D ± ɛ/2 Reactor and accelerator disappearance limits? Cosmological implications? P529 Spring,

17 Extension to Three Families Dirac mass: L D = ν 0 L M Dν 0 R + ν0 R M D ν0 L ν 0 L ν0 1L ν 0 2L ν 0 3L = A, ν 0 R ν0 1R ν 0 2R ν 0 3R = A ν R ν R M D = arbitrary 3 3 Dirac mass matrix A ν L M DA ν R = m m m 3 P529 Spring,

18 Leptonic weak charge lowering current J lµ W = 2ē Lγ µ V l = (ē µ τ )γ µ (1 γ 5 )V l ν 1 ν 2 ν 3 U V l = A e L A (PMNS) matrix (leptonic analog of CKM) is Pontecorvo-Maki-Nakagawa-Sakata Choose, e L phases: remove 5 unobservable phases from V l (choose ν R, e R phases for real non-negative masses) U = c 23 s 23 c 13 0 s 13 e iδ c 12 s 12 0 s 12 c s 23 c }{{ 23 s } 13 e iδ 0 c }{{ }}{{} atmospheric reactor limits Solar c ij cos θ ij, s ij sin θ ij, δ = CP -violating phase (if s 13 0) (s ij, δ CKM angles/phase) P529 Spring,

19 More on unobservable phases: Most general unitary 3 3 PMNS matrix Û: 3 angles, 6 phases J lµ W = (ē µ τ )γµ (1 γ 5 )Û ν 1 ν 2 ν 3 Û = e iβ e iα e iβ 2 0 }{{} U 0 e iα e iβ 3 s ij,δ 0 0 e iα 3 β i, α j not determined by diagonalization (Û Û = ÛÛ = I) Only depends on α j β i can choose α 3 = 0 Redefine ν jl e iα jν jl, e il e iβ ie il Û U (Independent) e ir, ν jr phases chosen so that m ei, m νj 0 P529 Spring,

20 Majorana mass: L T = 1 2 ( ) ν L 0 M T νr 0c + ν0c R M T ν0 L Diagonalize: M T A ν L M T A ν R by ν0 L = A, ν 0c R = Aν R νc R But ψ al ψ c br = ψ bl ψ c ar, where ψc R = C ψ T L Therefore M T = M T T A = Aν R Phases determined by m i 0 two unremovable Majorana phases in U (observable in ββ 0ν?) U = c 13 0 s 13 e iδ c 12 s 12 0 e iα c 23 s s 12 c e iα s 23 c 23 s }{{} 13 e iδ 0 c }{{}}{{}}{{} atmospheric, s s , δ=? Solar, s Majorana only Same results for active sector in seesaw model P529 Spring,

21 General case (3 active and 3 sterile): L = 1 2 ( ν 0 L ν 0c L ) ( M T M D MD T M S ) ( ν 0c R ν 0 R ) + h.c. M D, M T = MT T, M S = MS T are Majorana mass eigenstates Majorana, Dirac, seesaw, active-sterile mixing (LSND) limits Can also have > 3 or < 3 sterile P529 Spring,

22 Neutrino Counting Invisible Z width: N ν = 3 + N ν N ν = 0.015(9) (also counts light ν (1/2), triplet Majoron + scalar (2), etc.) Cosmology: big bang nucleosynthesis, large scale structure P529 Spring,

23 Dirac or Majorana ββ 0ν nn ppe e (m ββ i U 2 ei m i) Magnetic or electric dipole moments Dirac: may have diagonal ( νσ αβ νf αβ ) or transition ( ν i σ αβ ν j F αβ, i j) moments Majorana: only transition moments (diagonal Dirac from off-diagonal Majorana) One loop (Dirac): µ i 3eG F m i ( 19 m i 2π 2 (much larger in some models) Laboratory, astrophysical limits: µ < µ B 1 ev) µb p e e p n m ee ev W m ββ W General theory prediction Disfavored by 0ΝΒΒ decay m IO m NO Disfavored by cosmology m ev Winter, n P529 Spring,

24 Tritium β spectrum (KATRIN) m ν e ( i U ei 2 m 2 i Absolute Mass Scale ) 1/2 2 ev 0.2 ev Large scale structure: Σ i m i (0.5 1) ev O(0.05) ev If ββ 0ν observed (m ββ 0.01 ev) inverted or degenerate P529 Spring,

25 P529 Spring,

26 Neutrino Oscillations and Propagation The two flavor case: ν e }{{} weak = ν 1 cos θ + ν 2 sin θ, ν }{{} µ = ν 1 sin θ + ν 2 cos θ mass t = 0: ν(0) = ν µ (from π + µ + ν µ ) t > 0: ν(t) = ν 1 sin θe ie1t + ν 2 cos θe ie 2t [ ] ν 1 sin θe im2 1 t 2E + ν2 cos θe im2 2 t 2E e iet P529 Spring,

27 Probability of oscillating to ν e (appearance experiment) P νµ ν e (L) = ν e ν(t) 2 = sin 2 θ cos 2 θ ( m = sin 2 2θ sin 2 2 ) L 4E e im m 2 L/4E large 2 1 t 2E t + e im2 2 t 2 2E t 1 2 sin2 2θ µ+ π + ν µ L e ν e p m 2 = m 2 2 m2 1, Oscillation length: L osc = 4πE m 2 L t Survival probability (disappearance experiment): P νµ ν µ (L) = 1 P νµ ν e (L) P529 Spring,

28 Three or More Families ν(0) = ν a }{{} weak = i U ai ν i }{{} mass ν(t) i U ai ν i e im2 i t 2E P νa ν b (L) = ν b ν(t) 2 =δ ab 4 Re ( ( ) U ai U biu aj U ) bj sin 2 ij L 4E i<j + 2 Im ( ( ) U ai U biu aj U ) ij L bj sin }{{} 2E i<j CP violating ij m 2 i m2 j Rephasing invariant P529 Spring,

29 Antineutrinos P νal ν bl (L) =δ ab 4 Re ( ( ) U ai U biu aj U ) bj sin 2 ij L 4E i<j +2 Im ( ( ) U ai U biu aj U ) ij L bj sin }{{} 2E i<j CP violating P νal ν bl (L) U U P νbl ν al (L) P ν c ar ν c br (L) = P ν bl ν al (L) (by CP T ) =δ ab 4 i<j Re ( U ai U biu aj U bj 2 i<j Im ( U ai U biu aj U bj ( ) ) sin 2 ij L 4E ( ) ) ij L sin 2E P529 Spring,

30 Propagation in Matter Coherent forward scattering in matter potential (cf optics) Two flavor oscillations in vacuum: ν(t) = a c a(t) ν a i d dt ( ca (t) c b (t) ) = m2 4E ( ) ( cos 2θ sin 2θ ca (t) sin 2θ cos 2θ c b (t) ) In matter (different interactions of ν a and ν b ): ν µ e e ν e ν e e Z W Z ν µ e ν e e ν e e P529 Spring,

31 i d dt ( ca (t) c b (t) ) = n = m2 4E cos 2θ + G F 2 n m 2 4E sin 2θ m 2 4E m 2 4E sin 2θ cos 2θ G F n e for ν el ν µl, ν τ L 0 for ν µl ν τ L n e 2 1n n for 1 2 n n for ν el νl c ν µl, ν τ L νl c 2 n ( ca (t) c b (t) ) Signs reversed for ν c R, ν R Solar (MSW), atmospheric (not sterile; (hierarchy), supernovae also WNC), long baseline MINOS vs νr c : new flavor-dependent matter interaction? (to mimic CP T violation) P529 Spring,

32 Long Baseline (LBL) Oscillation Experiments 3 ν oscillations, small s 13 and m 2 (Akhmedov et al, JHEP 04, 078): P ν µ νe = α 2 sin 2 2θ 12 c 2 sin 2 A s 2 sin 2 (A 1) A 2 13 s2 23 (A 1) 2 where α = + 2 α s 13 sin 2θ 12 sin 2θ 23 cos( + δ) m2 m 2 Atm 0.03, δ δ and A A for P νµ ν e, A > 0 (normal),, A < 0 (inverted) sin A A sin(a 1) A 1 = m2 Atm L 4E, A = 2 2EGF n e m }{{ 2 Atm } matter In principle, determine s 13, δ, hierarchy (easier if s 13 from reactor) P529 Spring,

Sterile Neutrinos CDHSW 10 0 KARMEN2 NOMAD MiniBooNE Bugey NOMAD CHORUS NOMAD CHORUS LSND 90/99% 1 st class oscillations: ν a ν b, both active m 2 [ev 2 ] 10 3 10 6 10 9 10 12 Cl 95% Ga 95% CHOOZ all

33 Sterile Neutrinos CDHSW 10 0 KARMEN2 NOMAD MiniBooNE Bugey NOMAD CHORUS NOMAD CHORUS LSND 90/99% 1 st class oscillations: ν a ν b, both active m 2 [ev 2 ] Cl 95% Ga 95% CHOOZ all solar 95% SNO 95% ν e ν X ν µ ν τ ν e ν τ ν e ν µ All limits are at 90%CL unless otherwise noted SuperK 90/99% MINOS tan 2 θ K2K KamLAND 95% Super-K 95% nd class: active sterile LSND: third ij sterile ν s LSND + MiniBooNE: sterile ν s and CP violation (but reactor, accelerator disappearance; other ν e appearance; cosmology?) ν c L appearance (need new interactions) Non-orthogonal light neutrinos (from mixing with heavy) P529 Spring,

34 m2 atm m 2 LSND m 2 LSND m 2 m 2 atm m 2 P529 Spring,

35 Models No unbroken gauge symmetry forbids Majorana mass for active ν s Seesaw leptogenesis (heavy ν 2M decay in Type I) But New TeV physics or string constraints may forbid seesaw Appropriate masses not automatic (e.g., SO(10) Higgs 126 or HDO) so that Majorana may be negligible Alternative baryogenesis (e.g., electroweak) Other plausible mechanisms for both Majorana and Dirac (especially in strings) Type, mechanism, scale is open question P529 Spring,

36 Small Dirac masses Usually forbid bare mass (string? U(1)?) Higher dimensional operator (m D ν ϕ S /M P ) Large extra dimension (wave function overlap) String instanton Non-holomorphic soft h ν ν R φ 0 ν R φ S φ 0 φ S P529 Spring,

37 Small Majorana masses The Standard Electroweak Theory Higgs triplet (spontaneous L excluded) Stringy Weinberg operator h T νl φ 0 T φ 0 φ 0 φ 0 φ 0 Heavy ν R (Type I seesaw) Heavy Higgs triplet (Type II seesaw) φ S ν R ν R h S h T φ 0 T κ Loops (new scalars) TeV (extended) seesaws φ 0 φ 0 φ 0 φ 0 φ 0 φ 0 R P violation φ 0 Typeset by FoilTEX ν µl e e ν el h φ φ 0 P529 Spring,

38 Outstanding Issues (intrinsic properties) Scale of underlying physics? (string, GUT, TeV?) (LHC, flavor) Mechanism? (seesaw, LED, HDO, stringy instanton?)(indirect: LHC) Hierarchy, U e3, leptonic CP violation? (mechanism, leptogenesis) (long baseline, reactor, ββ 0ν, supernova) Absolute mass scale? (cosmology) (β decay, cosmology, ββ 0ν, supernova) Dirac or Majorana? (mechanism, scale, leptogenesis) (ββ 0ν ) Baryon asymmetry? (leptogenesis, electroweak baryogenesis, other?) (indirect: LHC) P529 Spring,

Neutrino Basics. m 2 [ev 2 ] tan 2 θ. Reference: The Standard Model and Beyond, CRC Press. Paul Langacker (IAS) LSND 90/99% SuperK 90/99% MINOS K2K

Neutrino Basics. m 2 [ev 2 ] tan 2 θ. Reference: The Standard Model and Beyond, CRC Press. Paul Langacker (IAS) LSND 90/99% SuperK 90/99% MINOS K2K Neutrino Basics CDHSW m 2 [ev 2 ] 10 0 10 3 10 6 10 9 KARMEN2 Cl 95% NOMAD MiniBooNE Ga 95% Bugey CHOOZ ν X ν µ ν τ ν τ NOMAD all solar 95% SNO 95% CHORUS NOMAD CHORUS LSND 90/99% SuperK 90/99% MINOS K2K