Neutrino Physics After the Revolution. Boris Kayser PASI 2006 October 26, 2006

Transcription

1 Neutrino Physics After the Revolution Boris Kayser PASI 2006 October 26,

2 What We Have Learned 2

3 The (Mass) 2 Spectrum ν 3 ν 2 ν 1 } Δm 2 sol (Mass) 2 Δm 2 atm or Δm 2 atm ν ν 2 } Δm 2 sol 1 ν 3 Normal Inverted Δm 2 sol = ~ 8 x 10 5 ev 2, Δm 2 atm = ~ 2.7 x 10 3 ev 2 Are there more mass eigenstates, as LSND suggests? 3

4 Leptonic Mixing This has the consequence that ν i > = Σ U αi ν α >. α Flavor-α fraction of ν i = U αi 2. When a ν i interacts and produces a charged lepton, the probability that this charged lepton will be of flavor α is U αi 2. 4

5 The spectrum, showing its approximate flavor content, is sin 2 θ 13 ν 3 ν 2 ν 1 } Δm 2 sol (Mass) 2 Δm 2 atm or Δm 2 atm ν 2 ν 1 } Δm 2 sol ν 3 sin 2 θ 13 Normal Inverted ν e [ U ei 2 ] ν µ [ U µi 2 ] ν τ [ U τi 2 ] 5

6 ν 3 Bounded by reactor exps. with L ~ 1 km From max. atm. mixing, " 3 # " µ +" $ 2 (Mass) 2 Δm 2 atm { { From ν µ (Up) oscillate but ν µ (Down) don t In LMA MSW, P sol (ν e ν e ) = ν e fraction of ν 2 ν 2 ν 1 }Δm 2 sol From distortion of ν e (solar) and ν e (reactor) spectra { From max. atm. mixing, ν 1 + ν 2 includes (ν µ ν τ )/ 2 ν e [ U ei 2 ] ν µ [ U µi 2 ] ν τ [ U τi 2 ] 6

7 The Mixing Matrix Atmospheric Cross-Mixing Solar # & # c 13 0 s 13 e "i* & # c % ( % ( 12 s 12 0& % ( U = % 0 c 23 s 23 ( )% () % "s 12 c 12 0 ( $ % 0 "s 23 c 23 '( % $ "s 13 e i* 0 c ( 13 ' $ % 0 0 1' ( c ij cos θ ij s ij sin θ ij θ 12 θ sol 34, θ 23 θ atm 37-53, θ 13 < ~ 10 δ would lead to P(ν α ν β ) P(ν α ν β ). CP But note the crucial role of s 13 sin θ 13. # e i+ 1 /2 0 0& % ) 0 e i+ 2 /2 ( % 0( % $ 0 0 1( ' Majorana CP phases 7

8 Good Luck Because (Δm 2 sol / Δm 2 atm) << 1 and θ 13 << 1, all confirmed flavor change processes seen so far are effectively two-neutrino processes. Because θ 13 << 1, θ atm θ 23 and θ sol θ 12. This has greatly simplified the analysis of what is happening. 8

9 The Majorana CP Phases The phase α i is associated with neutrino mass eigenstate ν i : U αi = U 0 αi exp(iα i /2) for all flavors α. Amp(ν α ν β ) = Σ U αi* exp( im i2 L/2E) U βi i is insensitive to the Majorana phases α i. Only the phase δ can cause CP violation in neutrino oscillation. 9

10 There Is Nothing Special About θ 13 All mixing angles must be nonzero for CP. For example P (" µ # " e ) $ P (" µ # " e ) = 2cos% 13 sin2% 13 sin2% 12 sin2% 23 sin& ) ' sin (m 2 L, ) sin (m 2 L, ) sin (m 2 L, * 4E - * 4 E - * 4E - In the factored form of U, one can put δ next to θ 12 instead of θ

11 The Open Questions 11

12 What is the absolute scale of neutrino mass? Are neutrinos their own antiparticles? Are there sterile neutrinos? We must be alert to surprises! 12

13 What is the pattern of mixing among the different types of neutrinos? What is θ 13? Is θ 23 maximal? Is the spectrum like or? Do neutrinos violate the symmetry CP? Is P(ν α ν β ) P(ν α ν β )? 13

14 What can neutrinos and the universe tell us about one another? Is CP violation by neutrinos the key to understanding the matter antimatter asymmetry of the universe? What physics is behind neutrino mass? 14

15 The Importance of the Questions, and How They May Be Answered 15

16 Most of the questions will be discussed by André de Gouvêa. I will focus on one question 16

17 Are Neutrinos Their Own Antiparticles? 17

18 What Is the Question? For each mass eigenstate ν i, does or ν i = ν i (Majorana neutrinos) ν i ν i (Dirac neutrinos)? Equivalently, is the Lepton Number L defined by L(ν) = L(l ) = L(ν) = L(l + ) = 1 conserved? If not, then nothing distinguishes ν i from ν i. We then have Majorana neutrinos. 18

19 How Can the Standard Model be Modified to Include Neutrino Masses? 19

20 The S(tandard) M(odel) l W ν and Z ν ν couplings conserve the Lepton Number L defined by L(ν) = L(l ) = L(ν) = L (l + ) = 1. So do the Dirac charged-lepton mass terms m l l L l R l + ( ) l + X m l 20 ( )

21 Original SM: m ν = 0. Why not add a Dirac mass term, m D ν L ν R ( ) ν X m D ( ) ν Then everything conserves L, so for each mass eigenstate ν i, ν i ν i (Dirac neutrinos) [L(ν i ) = L(ν i )] The SM contains no ν R field, only ν L. To add the Dirac mass term, we had to add ν R to the SM. 21

22 Unlike ν L, ν R carries no Electroweak Isospin. Thus, no SM principle prevents the occurrence of the Majorana mass term m R ν Rc ν R But this does not conserve L, so now ν i = ν i (Majorana neutrinos) [No conserved L to distinguish ν i from ν i ] ν X ν m R We note that ν i = ν i means ν i (h) = ν i (h) helicity 22

23 The objects ν R and ν R c in m R ν Rc ν R are not the mass eigenstates, but just the neutrinos in terms of which the model is constructed. m R ν Rc ν R induces ν R ν R c mixing. As a result of K 0 K 0 mixing, the neutral K mass eigenstates are As a result of ν R mass eigenstate is K S,L (K 0 ± K 0 )/ 2. ν R c mixing, the neutrino ν i = ν R + ν R c = ν + ν. 23

24 Many Theorists Expect Majorana Masses The Standard Model (SM) is defined by the fields it contains, its symmetries (notably Electroweak Isospin Invariance), and its renormalizability. Leaving neutrino masses aside, anything allowed by the SM symmetries occurs in nature. If this is also true for neutrino masses, then neutrinos have Majorana masses. 24

25 The presence of Majorana masses ν i = ν i (Majorana neutrinos) L not conserved are all equivalent Any one implies the other two. (Recent work: Hirsch, Kovalenko, Schmidt) 25

26 To Determine If Neutrinos Are Majorana Particles 26

27 How Can We Demonstrate That ν i = ν i? We assume neutrino interactions are correctly described by the SM. Then the interactions conserve L (ν l ; ν l + ). An Idea that Does Not Work [and illustrates why most ideas do not work] Produce a ν i via Spin ν Pion Rest Frame i µ π + + Give the neutrino a Boost: β π (Lab) > β ν (π Rest Frame) νi Lab. Frame π + µ + 27

28 The SM weak interaction causes µ + ν i Target at rest Recoil ν i = ν i means that ν i (h) = ν i (h). helicity If ν i our ν i = ν i, will make µ + too. 28

29 Minor Technical Difficulties β π (Lab) > β ν (π Rest Frame) E π (Lab) > m π E ν (π Rest Frame) m ν i E π (Lab) > 10 5 TeV if m ν ~ 0.05 ev Fraction of all π decay ν i that get helicity flipped ( ~ i m ν i E ν (π Rest Frame) ) 2 ~ if m ν ~ 0.05 ev Since L-violation comes only from Majorana neutrino masses, any attempt to observe it will be at the mercy of the neutrino masses. (BK & Stodolsky) i 29

30 The Idea That Can Work Neutrinoless Double Beta Decay [0νββ] e e i ν i ν i W W Nucl Nuclear Process Nucl If we start with a lot of parent nuclei (say, one ton of them), we can cope with the small neutrino masses. Observation would imply L and ν i = ν i. 30

31 Whatever diagrams cause 0νββ, its observation would imply the existence of a Majorana mass term: Schechter and Valle (ν) R e e 0νββ ν L W u d d u W (ν) R ν L : A Majorana mass term 31

32 In SM vertex i Nucl e e ν i ν i U ei U ei W W Nuclear Process Nucl Mixing matrix Mass (ν i ) the ν i is emitted [RH + O{m i /E}LH]. Thus, Amp [ν i contribution] m i Amp[0νββ] m i U ei2 m ββ i 32

33 The proportionality of 0νββ to mass is no surprise. 0νββ violates L. But the SM interactions conserve L. The L violation in 0νββ comes from underlying Majorana mass terms. 33

34 How Large is m ββ? How sensitive need an experiment be? Suppose there are only 3 neutrino mass eigenstates. (More might help.) Then the spectrum looks like atm ν 3 sol < ν 2 ν1 or ν sol < 2 ν 1 atm ν 3 34

35 m ββ m i U ei2 # & # c 13 0 s 13 e "i* & # c % ( % ( 12 s 12 0& % ( U = % 0 c 23 s 23 ( )% () % "s 12 c 12 0 ( $ % 0 "s 23 c 23 '( % $ "s 13 e i* 0 c ( 13 ' $ % 0 0 1' ( # e i+ 1 /2 0 0& % ) 0 e i+ 2 /2 ( % 0( % $ 0 0 1( ' The e (top) row of U reads (U e1, U e2, U e3 ) = (c 12 c 13 e i" 1 /2, s12 c 13 e i" 2 /2, s13 e #i$ ) θ 12 θ 34, but s 13 2 <

36 If the spectrum looks like sol < atm m 0 then m ββ m 0 [1 - sin 2 2θ sin 2 ( )] ½. Solar mixing angle m 0 cos 2θ m ββ m 0 At 90% CL, m 0 > 47 mev (SuperK); cos 2θ > 0.28 (SNO), so ν 3 m ββ > 13 mev. α 2 α 1 2 { Majorana CP phases 36

37 If the spectrum looks like then ν 3 sol < atm 0 < m ββ < Present Bound [( ) ev]. (Petcov et al.) Analyses of m ββ vs. Neutrino Parameters Barger, Bilenky, Farzan, Giunti, Glashow, Grimus, BK, Kim, Klapdor-Kleingrothaus, Langacker, Marfatia, Monteno, Murayama, Pascoli, Päs, Peña-Garay, Peres, Petcov, Rodejohann, Smirnov, Vissani, Whisnant, Wolfenstein, Review of ββ Decay: Elliott & Vogel Evidence for 0νββ with m ββ = ( ) ev? Klapdor-Kleingrothaus 37

38 Electromagnetic Properties of Majorana Neutrinos Majorana neutrinos are very neutral. No charge distribution: CPT[ ] + = + + But for a Majorana neutrino, [ ] [ ] CPT ν ν i = i 38

39 No magnetic or electric dipole moment: [ ] [ ] = µ µ e + e But for a Majorana neutrino, ν i = ν i Therefore, µ [ν ] = [ν ] i µ i = 0 39

40 Possible Information From Neutrino Magnetic Moments Both Majorana and Dirac neutrinos can have transition magnetic dipole moments µ: µ γ ν i For Dirac neutrinos, ν j µ < µ Bohr For Majorana neutrinos, µ < Present bound Present bound = 7 x µ Bohr ; Wong et al. (Reactor) 3 x10 12 µ Bohr ; Raffelt (Stellar E loss) 40

41 An observed µ below the present bound but well above µ Bohr would imply that neutrinos are Majorana particles. However, a dipole moment that large requires L-violating new physics below 100 TeV. ( Bell, Cirigliano, Davidson, Gorbahn, Gorchtein, ) Ramsey-Musolf, Santamaria, Vogel, Wise, Wang Neutrinoless double beta decay at the planned level of sensitivity only requires this new physics at GeV, near the Grand Unification scale. 41

42 Enjoy The Rest Of The School! 42

43 Backup Slides 43

44 What Is the Absolute Scale of Neutrino Mass? ν 3 Δm2 atm } ν Flavor Change (Mass) 2 0 ν 2 1?? Δm 2 sol } Tritium Decay, Double β Decay Cosmology How far above zero is the whole pattern? 44

45 A Cosmic Connection Oscillation Data Δm 2 atm < Mass[Heaviest ν i ] Cosmological Data + Cosmological Assumptions Σ m i < ( ) ev. Mass(ν i ) ( Seljak, Slosar, McDonald) Pastor If there are only 3 neutrinos, 0.04 ev < Mass[Heaviest ν i ] < ( ) ev ~ Δm 2 atm Cosmology 45

46 Wouldn t the dependence on neutrino mass be eliminated by a Right-Handed Current? e e SM LH current W L ν R m L ν L md ν R RH current Nucl Nuclear Process W R Nucl The SM LH current does not violate L. An identical current, but of opposite handedness, wouldn t violate L either. We still need the L-violating Majorana neutrino mass to make this process occur. 46

47 With a RH current at one vertex, Amp[0νββ] (ν mass) 2. Contributions with a RH current at one vertex are not likely to be significant. BK, Petcov, Rosen Enqvist, Maalampi, Mursula 47