What We Know, and What We Would Like To Find Out Boris Kayser Minnesota October 23, 2008 1
In the last decade, observations of neutrino oscillation have established that Neutrinos have nonzero masses and that Leptons mix. 2
What We Have Learned 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 = ~ 7.6 x 10 5 ev 2, Δm 2 atm = ~ 2.4 x 10 3 ev 2 4
Are There More Than 3 Mass Eigenstates? When only two neutrinos count, e, µ, or τ ( ) = sin 2 2& sin 2 * 1.27'm 2 ev 2 P " # $ " % ( ) ( ) ( ) ( ) L km E GeV Rapid oscillation reported by LSND " µ # " e + -, ~ 1eV 2 in contrast to Δm 2 > Δm 2 atm = 2.4 x 10 3 ev 2 sol = 7.6 x 10 5 ev 2 At least 4 mass eigenstates At least 1 ν Sterile 5
Is the LSND Signal Genuine Neutrino Oscillation? MiniBooNE results up to 9:00 am today suggest that the answer is No. 6
While awaiting further news We will assume there are only 3 neutrino mass eigenstates. 7
Leptonic Mixing This has the consequence that Mass eigenstate ν i > = Σ U αi ν α >. e, µ, or τ α Flavor eigenstate Flavor-α fraction of ν i = U αi 2. PMNS Leptonic Mixing Matrix 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. 8
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 ] 9
The Mixing Matrix Atmospheric Cross-Mixing Solar # 1 0 0 & # c 13 0 s 13 e "i* & # c % ( % ( 12 s 12 0& % ( U = % 0 c 23 s 23 ( )% 0 1 0 () % "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 38-52, 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 10
What Processes Oscillate? 11
KamLAND Evidence for Oscillatory Behavior Survival probability P(ν e ν e ) of reactor ν e L 0 = 180 km is a flux-weighted average travel distance. P(ν e ν e ) actually oscillates! 12
Oscillation Comes From the Coherence of Intermediate ν States ν µ ν e µ + ν e Amp π + Source Detector Intermediate state = " i Amp π + µ + ν i Source e Detector 13
Neutrinos In Final States " Ion 1 # Ion 2 + $; t Are Incoherent In Electron-Capture decays or ( ) = %"( Ion 1 # Ion 2 + $ i ; t) " Atom 1 # Atom 2 + $; t The different mass eigenstates ν i contribute incoherently to the decay rate. i ( ) = %"( Atom 1 # Atom 2 + $ i ; t) i The total decay rate should not oscillate. (Unless the rate for decay to each ν i does.) 14
Litvinov et al. EC decays of H-like 140 Pr and 142 Pm ions in a storage ring at GSI oscillate. Exponential Oscillation 15
Vetter et al. EC decays of neutral 142 Pm atoms at LBNL do not oscillate. Oscillation expected from GSI result Faestermann et al.: EC decays of neutral 180 Re atoms in Munich do not oscillate either. 16
Theoretical Opinion Neutrino mixing can make decay rates oscillate: Faber, Ivanov, Kienle, Kleinert, Lipkin, Reda No it cannot: Giunti, Kienert, Kopp, Lindner, Merle, Peshkin Lipkin: Putting the mother ion in a magnetic field, which is done only in the GSI experiment, makes a difference. To be continued. 17
The Open Questions 18
What is the absolute scale of neutrino mass? Are neutrinos their own antiparticles? Are there sterile neutrinos? We must be alert to surprises! 19
What is the pattern of mixing among the different types of neutrinos? What is θ 13? Is the spectrum like or? Do neutrino matter interactions violate CP? Is P(ν α ν β ) P(ν α ν β )? 20
What can neutrinos and the universe tell us about one another? Is CP violation involving neutrinos the key to understanding the matter antimatter asymmetry of the universe? What physics is behind neutrino mass? 21
The Importance of Some Questions, and How They May Be Answered 22
Does ν = ν? 23
What Is the Question? For each mass eigenstate ν i, and given helicty h, does or ν i (h) = ν i (h) (Majorana neutrinos) ν i (h) ν i (h) (Dirac neutrinos)? Equivalently, do neutrinos have Majorana masses? If they do, then the mass eigenstates are Majorana neutrinos. 24
Majorana Masses Out of, say, a left-handed neutrino field, ν L, and its charge-conjugate, ν Lc, we can build a Majorana mass term m L ν L ν L c (ν) R X ml ν L Quark and charged-lepton Majorana masses are forbidden by electric charge conservation. Neutrino Majorana masses would make the neutrinos very distinctive. 25
Why Majorana Masses Majorana Neutrinos The objects ν L and ν L c in m L ν L ν Lc are not the mass eigenstates, but just the neutrinos in terms of which the model is constructed. m L ν L ν Lc induces ν L ν L c mixing. As a result of K 0 K 0 mixing, the neutral K mass eigenstates are K S,L (K 0 ± K 0 )/ 2. K S,L = K S,L. As a result of ν L ν c L mixing, the neutrino mass eigenstate is ν i = ν L + ν c L = ν + ν. ν i = ν i. 26
SU 2 Why Most Theorists Expect Majorana Masses The Standard Model (SM) may be defined by its ( ) L "U( 1) Y gauge symmetry and its renormalizability, and by its field content. Leaving neutrino masses aside, anything allowed by the SM principles occurs in nature. Majorana mass terms are allowed by the SM principles. Then quite likely Majorana masses occur in nature too. 27
To Determine Whether Majorana Masses Occur in Nature 28
The Promising Approach Seek Neutrinoless Double Beta Decay [0νββ] e e Nucl Nucl We are looking for a small Majorana neutrino mass. Thus, we will need a lot of parent nuclei (say, one ton of them). 29
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 0νββ ν i = ν i 30
Mixing, Mass Ordering, and CP 31
The Central Role of θ 13 Both CP violation and our ability to tell whether the spectrum is normal or inverted depend on θ 13. If sin 2 2θ 13 > 10 (2-3), we can study both of these issues with intense but conventional accelerator ν and ν beams, produced via π + µ + + ν µ and π µ + ν µ. Determining θ 13 is an important step.
Reactor Experiments To Determine θ 13 Looking for disappearance of reactor ν e, which have E ~ 3 MeV, while they travel L ~ 1.5 km is the cleanest way to determine θ 13. P(ν e Disappearance) = = sin 2 2θ 13 sin 2 [1.27Δm 2 atm (ev2 )L(km)/E(GeV)] 33
Accelerator Experiments Accelerator neutrino experiments can also probe θ 13. Now it is entwined with other parameters. In addition, accelerator experiments can probe whether the mass spectrum is normal or inverted, and look for CP violation. All of this is done by studying ν µ ν e and ν µ ν e while the beams travel hundreds of kilometers. 34
The Mass Spectrum: or? Generically, grand unified models (GUTS) favor GUTS relate the Leptons to the Quarks. However, Majorana masses, with no quark analogues, could turn into. 35
How To Determine If The Spectrum Is Normal Or Inverted Exploit the fact that, in matter, e ( ) ν e W ( ) ν e e affects ν and ν oscillation (differently), and leads to P(ν µ ν e ) P(ν µ ν e ) > 1 ; < 1 ; Note fake CP Note dependence on the mass ordering 36
Q : Does matter still affect ν and ν differently when ν = ν? A : Yes! Spin ν e + W + ν Spin ν e W ν The weak interactions violate parity. Neutrino matter interactions depend on the neutrino polarization. 37
Do Neutrino Interactions Violate CP? The observed CP in the weak interactions of quarks cannot explain the Baryon Asymmetry of the universe. Is leptonic CP, through Leptogenesis, the origin of the Baryon Asymmetry of the universe? (Fukugita, Yanagida) 38
Leptogenesis In Brief The most popular theory of why neutrinos are so light is the See-Saw Mechanism ( Yanagida; Gell-Mann, Ramond, Slansky; Mohapatra, Senjanovic; Minkowski ν ( { Familiar light neutrino Very heavy neutrino } N The very heavy neutrinos N would have been made in the hot Big Bang. 39
The heavy neutrinos N, like the light ones ν, are Majorana particles. Thus, an N can decay into l or l +. If neutrino oscillation violates CP, then quite likely so does N decay. In the See-Saw, these two CP violations have a common origin: One Yukawa coupling matrix. Then, in the early universe, we would have had different rates for the CP-mirror-image decays N l + ϕ + and N l + ϕ This would have led to unequal numbers of leptons and antileptons (Leptogenesis). Then, Standard-Model Sphaleron processes would have turned 1/3 of this leptonic asymmetry into a Baryon Asymmetry. + Standard-Model Higgs 40
Electromagnetic Leptogenesis (Bell, B.K., Law) A new, alternative leptogenesis scenario in which the leptonic asymmetry arises from Γ(N l + ϕ 0 + + + W ) Γ(N l ϕ 0 + W ) Heavy EW singlet neutrino This too can produce the observed Baryon Asymmetry of the universe. Has the link between CP in neutrino oscillation and the Baryon Asymmetry been broken? 41
No These new couplings lead to neutrino masses. If leptogenesis is driven by these couplings, then the neutrino masses probably are too. CP-violating couplings will lead to CP-violating mass matrices, which in turn will lead to CP violation in oscillation. As in standard leptogenesis, CP in neutrino oscillation and CP in the early universe are linked. 42
How To Search for CP In Neutrino Oscillation Look for P(ν α ν β ) P(ν α ν β ) 43
Q : Can CP violation still lead to P(ν µ ν e ) P(ν µ ν e ) when ν = ν? A : Certainly! Compare " i π + ν µ ν e µ + ν U µi * i exp ( 2 "im i L 2E ) U ei e Detector with " i π µ ν µ ν e ν i ( ) 2 U µi exp "im i L 2E U * ei e + Detector 44
Summary We have learned a lot about the neutrinos in the last decade. What we have learned raises some very interesting questions. We look forward to answering them. 45