Cosmic Neutrinos. Chris Quigg Fermilab. XXXV SLAC Summer Institute Dark Matter 10 August 2007

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1 Cosmic Neutrinos Chris Quigg Fermilab XXXV SLAC Summer Institute Dark Matter 10 August 2007

2 Neutrinos are abundant! Each second, some neutrinos made in the Sun pass through your body. Each second, about 10 3 neutrinos made in Earth s atmosphere by cosmic rays pass through your body. Other neutrinos reach us from natural (radioactive decays of elements inside the Earth) and artificial (nuclear reactors, particle accelerators) sources. Inside your body are more than 10 7 neutrino relics from the early universe. ν i, ν i number density now: 56 cm 3, (1 + z) 3 Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 2 / 56

3 Neutrinos in the electroweak theory ν τ ν µ ν e τ µ L L e L u L d L c L s L t L b L Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 3 / 56

4 Neutrinos in the electroweak theory ν 3 ν 2 ν 1 τ µ L L e L µ R ν 2 e ν R 1 ν 3 τ R u R d R c R s R t R b R u L c L s L t L b L d L Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 4 / 56

5 Leptons are observed as free particles Lepton Mass Lifetime ν e < 2 ev e (44) MeV > y (90% CL) ν µ < 0.19 MeV (90% CL) µ (94) MeV (4) 10 6 s ν τ < 18.2 MeV (95% CL) τ ± 0.20 MeV ± s All spin- 1 2, pointlike ( < few cm) kinematically determined ν masses consistent with 0 (ν oscillations nonzero, unequal masses) Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 5 / 56

6 Tritium β-decay spectrum 3 H 3 He e ν e : Q kev a) b) m = 0 ev 2 x m = 1 ev Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 6 / 56

7 ν mass limits (e-associated) Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 7 / 56

8 KATRIN aims for m ν < 0.2 ev Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 8 / 56

9 Neutrino flavor change neutrinos have mass SuperK Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 9 / 56

10 The essence of neutrino oscillations If neutrinos of definite flavor (ν e, ν µ, ν τ ) are superpositions of different mass eigenstates (ν 1, ν 2, ν 3 ) the mass eigenstates evolve in time with different frequencies... and so the superposition changes in time Beam created as flavor ν α evolves into a flavor mixture Suppose ν α = ν 1 cos θ + ν 2 sin θ; ν β = ν 1 sinθ + ν 2 cosθ: After distance L, beam created as ν α with energy E has P α β = sin 2 2θ sin 2 ( m 2 L/4E ) Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 10 / 56

11 SuperK Atmospheric (535 day) Now (2293 day) Downward ν travel 15 km, upward ν up to km Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 11 / 56

12 MINOS ν µ Deficit Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 12 / 56

13 Atmospheric Neutrino Summary 2 ( min 2.3) 2 ( min 4.61) Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 13 / 56

14 SuperK All-Sky Map in Neutrinos (νe νe) 4p 4 He + 2e + + 2ν e + 25 MeV Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 14 / 56

15 Solar neutrinos: measure three reaction rates [CC] Charged-current dissociation: sensitive to ν e flux ν e d e p p W -exchange [NC] Neutral-current dissociation: sensitive to total ν flux ν l d ν l p p Z-exchange [ES] Elastic scattering: sensitive to ν e (ν µ + ν τ ) flux σ(ν µ,τ e ν µ,τ e) = G 2 F m ee ν 2π σ(ν e e ν e e) = G 2 F m ee ν 2π [ L 2 e + R 2 e/3 ] Z-exchange [ (Le + 2) 2 + R 2 e /3] W + Z-exchange L l = 2 sin 2 θ W ; R l = 2 sin 2 θ W 1 2 Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 15 / 56

16 Solar neutrino observations: SuperK & SNO Total flux agrees with solar model, but only 30% arrive as ν e Solar ν emerge as ν 2 s -1 ) 6 cm -2 ( 10 φ µτ BS05 SSM 6 φ 68% C.L. 5 4 NC φ µτ 68%, 95%, 99% C.L SNO φ CC SNO φnc SNO φes SK φes 68% C.L. 68% C.L. 68% C.L. 68% C.L ( 10 cm -2 s -1 ) Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 16 / 56 φ e

17 Absolute scale of neutrino masses is not yet known Normal spectrum Inverted spectrum m2 2 m2 1 = m2 = ev 2 m3 2 m2 1 = m2 atm = ev 2 ρ c 3H0 2/8πG N = 1.05h ev cm 3 = ev cm 3 (56ν i + 56 ν i ) cm 3 i m ν i < 50 ev Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 17 / 56

18 Expectations for relic neutrinos Relate to Cosmic Microwave Background: dn γ (T) d 3 p = 1 (2π) 3 1 exp(p/t) 1, p: relic momentum, T: photon temperature n γ (T) = 1 d 3 p (2π) 3 1 exp (p/t) 1 = 2ζ(3) T 3, π 2 T 0 = (2.725 ± 0.002) K: n γ0 n γ (T 0 ) 410 cm 3 Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 18 / 56

19 Expectations for relic neutrinos ν decoupled around 1 MeV (0.1 s), were not reheated by e + e annihilation: T ν /T = ( 4 11) 1/3 (below me ). T ν0 = ( 4 11) 1/3 T0 = K ev. dn νi (T ν ) d 3 p n νi (T ν ) = = 1 (2π) 3 1 exp(p/t ν ) d 3 p (2π) 3 1 exp (p/t ν ) + 1 = 3ζ(3) 4π 2 T 3 ν = 3 22 n γ(t). Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 19 / 56

20 Expectations for relic neutrinos In the present Universe, n νi 0 = n ν c i 0 n νi (T ν0 ) 56 cm 3 rms neutrino momentum: pν T ν ev not necessarily small on scale of m ν Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 20 / 56

21 i m ν i Summed neutrino masses [ev] Normal Inverted Lightest neutrino mass [ev] Fraction of critical density (%) Ω ν >(1.2,2.2) 10 3 for (normal, inverted) spectrum Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 21 / 56

22 i m ν i : cosmological constraints Top four use Baryon Acoustic Oscillations S. Dodelson, Fermilab KEK ν School: Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 22 / 56

23 Quark & charged-lepton masses Mass/WeakScale e charged leptons up quarks down quarks u d m c s t t b 10-6 If neutrinos have Dirac masses, ν Yukawa couplings < Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 23 / 56

24 Summary of ν mixing parameters Define ν = (ν 1, ν 2, ν 3 ) l L = (e L, µ L, τ L ) L (q) CC = g 2 ν γ µ V l L W + µ + h.c., V: ν mixing matrix V = V e1 V e2 V e3 V µ1 V µ2 V µ3 V τ1 V τ2 V τ3 Convention: ν 1, ν 2 : solar pair, m 1 < m 2 ν 3 separated by m 2 atm; above or below? Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 24 / 56

25 Experiment tells us... V = < V = c 23 s 23 0 s 23 c 23 c 13 0 s 13 e iδ s 13 e iδ 0 c 13 c 12 s 12 0 s 12 c < θ 12 < 38 : solar 35 < θ 23 < 55 : atm θ 13 < 10 CP phase δ unconstrained s ij = sin θ ij, c ij = cosθ ij Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 25 / 56

26 Neutrino Mixing (representative θ 12, θ 23 values, θ 13 = 10 ) tau mu e Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 26 / 56

27 Quark Mixing (Components: V uα 2, etc.) u: d' c: s' t: b' b s d Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 27 / 56

28 Neutrino Mixing (θ 12, θ 23 variations, θ 13 = 10 ) tau mu e Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 28 / 56

29 Neutrino Mixing (θ 12, θ 23 fixed, δ variations, θ 13 = 10 ) tau mu e Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 29 / 56

30 Varieties of neutrino mass: Dirac mass Chiral decomposition of Dirac spinor: ψ = 1 2(1 γ 5 )ψ + 1 2(1 + γ 5 )ψ ψ L + ψ R Dirac mass connects LH, RH components of same field L D = D( ψ L ψ R + ψ R ψ L ) = D ψψ = mass eigenstate ψ = ψ L + ψ R (invariant under global phase rotation ν e iθ ν, l e iθ l, so that lepton number is conserved) Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 30 / 56

31 Varieties of neutrino mass: Dirac mass Add RH neutrino N R to the standard-model spectrum N R : SU(2) L singlet with Y = 0, so sterile L (ν) D = ζ [ ν ( Ll φ)nr + N R ( φ L l ) ] m D ( νl N R + N ) R ν L m D = ζ ν v/ 2 Some argue that ζ ν < is unnatural, while the range ζ t 1 to ζ e few 10 6 is only puzzling. But all Dirac masses involve physics beyond the standard model. Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 31 / 56

32 Varieties of neutrino mass: Majorana mass Neutrinos: no color, no Q: their own antiparticles? Majorana fermions Charge conjugate of RH field is LH: ψ c L (ψc ) L = (ψ R ) c Majorana joins LH, RH components of conjugate fields L MA L MB = A( ν c R ν L + ν L ν c R ) = A χχ = B( ν c Lν R + ν R ν c L) = B ωω for which the mass eigenstates are χ ν L + ν c R = χc = ν L + (ν L ) c ω ν R + ν c L = ω c = ν R + (ν R ) c Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 32 / 56

33 Lepton number violation Majorana ν: no conserved additive quantum number L M violates lepton number by two units Majorana ν can mediate ββ 0ν decays (Z, A) (Z + 2, A) + e + e Detecting ββ 0ν would offer decisive evidence for Majorana nature of ν Active ν L mass generated by I = 1 Higgs with vev or effective operator containing two I = 1 Higgs combined to transform as I = 1. 2 Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 33 / 56

34 Neutrino observatories: expectations Cosmic ν flux may exceed atmospheric background at E ν few TeV prospect for sources characterize sources study ν properties Sources include AGN (at 10 2 Mpc) 1 Mpc m pp or pγ numbers of π + π 0 π π + + π 0 + π 2γ + 2ν µ + 2 ν µ + 1ν e + 1 ν e Φ 0 std = {ϕ0 e = 1 3,ϕ0 µ = 2 3,ϕ0 τ = 0} (ν = ν) Detection (in volumes 1 km 3 ) (ν µ, ν µ )N (µ,µ + ) + anything Can we achieve efficient, calibrated (ν e, ν e ) detection? Good (ν τ, ν τ ) detection, NC capability desirable Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 34 / 56

35 ν µ N µ + anything d 2 σ dxdy = 2G2 F ME ( ν M 2 ) 2 W [ xq(x,q 2 π Q 2 + MW 2 ) + x q(x,q 2 )(1 y) 2] q(x,q 2 ) = u v(x,q 2 ) + d v (x,q 2 ) + u s(x,q 2 ) + d s (x,q 2 ) 2 2 +s s (x,q 2 ) + b s (x,q 2 ) q(x,q 2 ) = u s(x,q 2 ) + d s (x,q 2 ) 2 + c s (x,q 2 ) + t s (x,q 2 ), (EHLQ) x = Q 2 /2Mν y ν/e ν ν E ν E µ...isoscalar nucleon Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 35 / 56

36 νn µ +... Cross Sections CTEQ6 EHLQ EHLQ, unevolved HERA M. H. Reno Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 36 / 56

37 νn µ +... Interaction Lengths Solar diameter Earth diameter Lunar diameter n B cm 3 Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 37 / 56

38 νe cross sections σ [cm 2 ] E ν [GeV] At low energies: σ( ν e e hadrons) > σ(ν µ e µν e ) > σ(ν e e ν e e) > σ( (ν e e ν µ µ) > σ( ν e e ν e e) > σ(ν µ e ν µ e) > σ( ν µ e ν µ e) Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 38 / 56

39 Influence of neutrino oscillations Flux at Earth Φ = {ϕ e, ϕ µ, ϕ τ } Φ 0 = {ϕ 0 e, ϕ0 µ, ϕ0 τ } source fluxes Vacuum oscillation length is short; for m 2 = 10 5 ev 2, L osc = 4πE ν / m Mpc (E ν /1 ev)...a fraction of Mpc even for E ν = ev ν oscillate many times between cosmic source and terrestrial detector Also, over long paths, cosmic neutrinos are vulnerable to decay processes that would not affect terrestrial or solar experiments. Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 39 / 56

40 ... Neutrino Oscillations (flavor) ν α = i V αiν i (mass) Idealize sinθ 13 = 0, sin2θ 23 = 1, write x = sin 2 θ 12 cos 2 θ 12. V ideal = c 12 s 12 0 s 12 / 2 c 12 / 2 1/ 2 s 12 / 2 c 12 / 2 1/ 2 Transfer matrix X: Φ 0 (source) Φ (detector); Over many oscillations, 1 2x x x X ideal = 1 x 2 (1 x) 1 2 (1 x) 1 x 2 (1 x) 1 2 (1 x) X ideal : Φ 0 std {ϕ e = 1 3,ϕ µ = 1 3,ϕ τ = 1 3 } Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 40 / 56

41 With current constraints... Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 41 / 56

42 After current generation... Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 42 / 56

43 Reconstructing the ν Mixture at the Source ν µ, ν τ fully mixed can t fully characterize Φ 0 Reconstruct ν e fraction at source using X ideal : ϕ 0 e = (ϕ e x)/(1 3x) Extreme ϕ e implicates unconventional physics Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 43 / 56

44 Influence of neutrino decays Nonradiative decays ν i (ν j, ν j ) + X not very constrained: τ/m > 10 4 s/ev If only lightest neutrino survives, flavor mix at Earth is independent of composition at source Normal hierarchy m 1 < m 2 < m 3 : ϕ α = U α1 2 Φ normal {0.70,0.17,0.13} Inverted hierarchy m 1 > m 2 > m 3 : ϕ α = U α3 2 Φ inverted {0,0.5,0.5} far from Φ std = { 1 3, 1 3, 1 3 } Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 44 / 56

45 Energy-dependent composition as marker of ν decays E ν = ε(1 s/ev)/(τ ν /m ν ) L/(100 Mpc) Normal hierarchy Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 45 / 56

46 Energy-dependent composition as marker of ν decays E ν = ε(1 s/ev)/(τ ν /m ν ) L/(100 Mpc) Inverted hierarchy Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 46 / 56

47 UHE ν annihilation on ν relics Barenboim, Mena, CQ m ν = 10 5 ev Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 47 / 56

48 Interaction lengths on Z 0 resonance: Dirac Majorana ν number density now: 56 cm 3, (1 + z) Mpc = 39 Gly Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 48 / 56

49 Fable: l-o-o-o-o-o-n-g path (10 4 or 10 5 Mpc) in current U m l = 10 5 ev m l = 10 3 ev Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 49 / 56

50 Flavor ratios probe the mass hierarchy... Normal m l = 10 5 ev Inverted Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 50 / 56

51 Incorporate evolution of U back to z = 20 m l = 10 5 ev m l = 10 3 ev Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 51 / 56

52 Flavor ratios probe the mass hierarchy(z < 20) Normal m l = 10 5 ev Inverted Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 52 / 56

53 Relic neutrinos are moving targets... z = 20 z = 0 T ν0 = K = ev T ν (1 + z) Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 53 / 56

54 Incorporate evolution of U back to z = 20, Fermi motion m l = 10 5 ev m l = 10 3 ev Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 54 / 56

55 Flavor ratios probe mass hierarchy(z < 20, Fermi motion) Normal m l = 10 5 ev Inverted Chris Quigg (Fermilab) Cosmic Neutrinos 2007 SLAC Summer Institute 55 / 56

56 Dark Matter: The Contest What should be the theme of SSI 2010? Propose a title and give a two-sentence description to appear on the SSI 2010 web page. Justify your choice in one tightly reasoned paragraph. Winners receive valuable prizes and untold glory Deadline for entries: 17h00 Thursday Award ceremony: Friday morning