Putting It All Together: What Do These Results Mean?

Transcription

1 Putting It All Together: What Do These Results Mean? University XXXVIII SLAC Summer Institute Neutrinos: Nature s Mysterious Messangers August 2 13, 2010

2 Outline What We Have Learned: Summary What We Know We Don t Know; Neutrino Masses As Physics Beyond the Standard Model; Some Ideas for the Origin of Neutrino Masses, with Consequences; How Do We Learn More, and Conclusions.

3 Quickly Summarizing What You Learned Both the solar and atmospheric puzzles can be properly explained in terms of two-flavor neutrino oscilations: solar: ν e ν a (linear combination of ν µ and ν τ ): m ev 2, sin 2 θ 0.3. atmospheric: ν µ ν τ : m ev 2, sin 2 θ 0.5 ( maximal mixing ).

4 [Maltoni and Schwetz, arxiv: ]

5 Putting it all together 3 flavor mixing: ν e ν µ = U e1 U e2 U e3 U µ1 U µ2 U µ3 ν 1 ν 2 ν τ U τ1 U eτ2 U τ3 ν 3 Definition of neutrino mass eigenstates (who are ν 1, ν 2, ν 3?): m 2 1 < m 2 2 m 2 2 m 2 1 m 2 3 m 2 1,2 m 2 13 < 0 Inverted Mass Hierarchy m 2 13 > 0 Normal Mass Hierarchy tan 2 θ 12 U e2 2 U e1 2 ; tan 2 θ 23 U µ3 2 U τ3 2 ; U e3 sin θ 13 e iδ [For a detailed discussion see AdG, Jenkins, PRD78, (2008)]

6 It Turns Out That... Two Mass-Squared Differences Are Hierarchical, m 2 12 m 2 13 ; One of the Mixing Angles Is Small, sin 2 θ 13 < Two Puzzles Decouple, and Two-Flavor Interpretation Captures Almost All the Physics: Atmospheric Neutrinos Determine m 2 13 and θ 23 ; Solar Neutrinos Determine m 2 12 and θ 12. (small θ 13 guarantees that m 2 13 effects governing electron neutrinos are small, while m 2 12 m 2 13 guarantees that m 2 12 effects are small at atmospheric and accelerator experiments).

7 Three Flavor Mixing Hypothesis Fits All Data Really Well. Good Measurements of Oscillation Observables [Gonzalez-Garcia, Maltoni, Salvado, arxiv: ]

8 What We Know We Don t Know (i) (m 3 ) 2 (m 2 ) 2 What is the ν e component of ν 3? (θ 13 0?) (m 1 ) 2 ( m 2 ) sol Is CP-invariance violated in neutrino oscillations? (δ 0, π?) ( m 2 ) atm ν e ν µ ν τ ( m 2 ) atm Is ν 3 mostly ν µ or ν τ? (θ 23 > π/4, θ 23 < π/4, or θ 23 = π/4?) What is the neutrino mass hierarchy? ( m 2 13 > 0?) ( m 2 ) sol (m 2 ) 2 (m 1 ) 2 (m 3 ) 2 All of the above can only be addressed with new neutrino normal hierarchy inverted hierarchy oscillation experiments Ultimate Goal: Not Measure Parameters but Test the Formalism (Over-Constrain Parameter Space)

9 1.5 excluded area has CL > 0.95! excluded at CL > #m d & #m s sin 2% 0.5 #m d $ K " ' " V ub! % " We need to do this in the lepton sector! 1.0 CKM f i t t e r Moriond 09! $ K sol. w/ cos 2% < 0 (excl. at CL > 0.95) &

10 The Holy Graill of Neutrino Oscillations CP Violation In the old Standard Model, there is only one a source of CP-invariance violation: The complex phase in V CKM, the quark mixing matrix. Indeed, as far as we have been able to test, all CP-invariance violating phenomena agree with the CKM paradigm: ɛ K ; ɛ K ; sin 2β; etc. Recent experimental developments, however, provide strong reason to believe that this is not the case: neutrinos have mass, and leptons mix! a modulo the QCD θ-parameter, which will be willed away henceforth.

11 CP-invariance Violation in Neutrino Oscillations The most promising approach to studying CP-violation in the leptonic sector seems to be to compare P (ν µ ν e ) versus P ( ν µ ν e ). The amplitude for ν µ ν e transitions can be written as A µe = U e2u µ2 ( e i 12 1 ) + U e3u µ3 ( e i 13 1 ) where 1i = m2 1i L 2E, i = 2, 3. The amplitude for the CP-conjugate process can be written as Ā µe = U e2 U µ2 ( e i 12 1 ) + U e3 U µ3 ( e i 13 1 ). [remember: according to unitarty, U e1 U µ1 = U e2 U µ2 U e3 U µ3]

12 In general, A 2 Ā 2 (CP-invariance violated) as long as: Nontrivial Weak Phases: arg(u ei U µi) δ 0, π; Nontrivial Strong Phases: 12, 13 L 0; Because of Unitarity, we need all U αi 0 three generations. All of these can be satisfied, with a little luck: given that two of the three mixing angles are known to be large, we need U e3 0. The goal of next-generation neutrino experiments is to determine the magnitude of U e3. We need to know this in order to understand how to study CP-invariance violation in neutrino oscillations! [Discussed by Gina Rameika]

13 In the real world, life is much more complicated. The lack of knowledge concerning the mass hierarchy, θ 13, θ 23 leads to several degeneracies. Note that, in order to see CP-invariance violation, we need the subleading terms! In order to ultimately measure a new source of CP-invariance violation, we will need to combine different measurements: oscillation of muon neutrinos and antineutrinos, oscillations at accelerator and reactor experiments, experiments with different baselines, etc. [This was discussed by Gina Rameika last week!]

14 What We Know We Don t Know (ii): How Light is the Lightest Neutrino? (m 3 ) 2 (m 2 ) 2 (m 1 ) 2 ( m 2 ) sol So far, we ve only been able to measure neutrino mass-squared differences. ( m 2 ) atm ν e ν µ ν τ ( m 2 ) atm (m 2 ) 2 ( m 2 ) sol (m 1 ) 2 (m 3 ) 2 normal hierarchy m 2 lightest =? inverted hierarchy m 2 = 0 The lightest neutrino mass is only poorly constrained: m 2 lightest < 1 ev 2 (roughly) qualitatively different scenarios allowed: m 2 lightest 0; m 2 lightest m 2 12,13; m 2 lightest m 2 12,13. Need information outside of neutrino oscillations.

15 The most direct probe of the lightest neutrino mass precision measurements of β-decay Observation of the effect of non-zero neutrino masses kinematically. When a neutrino is produced, some of the energy exchanged in the process should be spent by the non-zero neutrino mass. Typical effects are very, very small we ve never seen them! The most sensitive observable is the electron energy spectrum from tritium decay. 3 H 3 He + e + ν Why tritium? Small Q value, reasonable abundances. Required sensitivity proportional to m 2 /Q 2. In practice, this decay is sensitive to an effective electron neutrino mass : m 2 ν e i U ei 2 m 2 i

16 Experiments measure the shape of the end-point of the spectrum, not the value of the end point. This is done by counting events as a function of a low-energy cut-off. note: LOTS of Statistics Needed! t 1/2 = years E 0 = kev e e

17 NEXT GENERATION: The Karlsruhe Tritium Neutrino (KATRIN) Experiment: (not your grandmother s table top experiment!) sensitivity m 2 ν e > (0.2 ev) 2

18 Big Bang Neutrinos are Warm Dark Matter Constrained by the Large Scale Structure of the Universe. Constraints depend on Data set analysed; Bias on other parameters;... Bounds can be evaded with non-standard cosmology. Will we learn about neutrinos from cosmology or about cosmology from neutrinos?

19 What We Know We Don t Know (iii) Are Neutrinos Majorana Fermions? ν L you ν R? ν L? you How many degrees of freedom are required to describe massive neutrinos? A massive charged fermion (s=1/2) is described by 4 degrees of freedom: (e L CPT e+ R ) Lorentz (e R CPT e+ L ) A massive neutral fermion (s=1/2) is described by 4 or 2 degrees of freedom: (ν L CPT ν R ) Lorentz (ν R CPT ν L ) MAJORANA DIRAC (ν L CPT ν R ) Lorentz ( ν R CPT ν L )

20 Why Don t We Know the Answer (Yet)? If neutrino masses were indeed zero, this is a nonquestion: there is no distinction between a massless Dirac and Majorana fermion. Processes that are proportional to the Majorana nature of the neutrino vanish in the limit m ν 0. Since neutrinos masses are very small, the probability for these to happen is very, very small: A m ν /E. The smoking gun signature is the observation of LEPTON NUMBER violation. This is easy to understand: Majorana neutrinos are their own antiparticles and, therefore, cannot carry any quantum numbers including lepton number.

21 Weak Interactions are Purely Left-Handed (Chirality): For example, in the scattering process e + X ν e + X, the electron neutrino is, in a reference frame where m E, ( m ) ν e L + R. E If the neutrino is a Majorana fermion, R behaves mostly like a ν e, (and L mostly like a ν e, ) such that the following process could happen: e + X ν e + X, followed by ν e + X e + + X, P ( m E ) 2 Lepton number can be violated by 2 units with small probability. Typical numbers: P (0.1 ev/100 MeV) 2 = VERY Challenging!

22 Search for the Violation of Lepton Number (or B L) Best Bet: search for Neutrinoless Double-Beta Decay: Z (Z + 2)e e 1 disfavoured by 0ν2β mee in ev (next) 2 m 23 (next-next) 2 m 23 < 0 > 0 90% CL (1 dof) disfavoured by cosmology lightest neutrino mass in ev Helicity Suppressed Amplitude m ee E Observable: m ee i U 2 ei m i no longer lamp-post physics!

23 mass (ev) τ b t c TeV GeV What We Are Trying To Understand: µ e s d u MeV NEUTRINOS HAVE TINY MASSES kev LEPTON MIXING IS WEIRD ν 1 ν 2 ν fermion ev mev V MNS V CKM What Does It Mean?

24 Who Cares About Neutrino Masses: Palpable Evidence of Physics Beyond the Standard Model The SM we all learned in school predicts that neutrinos are strictly massless. Massive neutrinos imply that the the SM is incomplete and needs to be replaced/modified. Furthermore, the SM has to be replaced by something qualitatively different. There is only a handful of questions our model for fundamental physics cannot explain properly. These are, in order of palpability (these are personal. Feel free to complain): What is the physics behind electroweak symmetry breaking? (Higgs or not in SM). What is the dark matter? (not in SM). Why does the Universe appear to be accelerating? Why does it appear that the Universe underwent rapid acceleration in the past? (not in SM Is this particle physics? ).

25 Standard Model in One Slide, No Equations The SM is a quantum field theory with the following defining characteristics: Gauge Group (SU(3) c SU(2) L U(1) Y ); Particle Content (fermions: Q, u, d, L, e, scalars: H). Once this is specified, the SM is unambiguously determined: Most General Renormalizable Lagrangian; Measure All Free Parameters, and You Are Done! (after several decades of hard experimental work... ) If you follow these rules, neutrinos have no mass. Something has to give.

26 What is the New Standard Model? [νsm] The short answer is WE DON T KNOW. Not enough available info! Equivalently, there are several completely different ways of addressing neutrino masses. The key issue is to understand what else the νsm candidates can do. [are they falsifiable?, are they simple?, do they address other outstanding problems in physics?, etc] We need more experimental input!

27 Options include: modify SM Higgs sector (e.g. Higgs triplet) and/or modify SM particle content (e.g. SU(2) L Triplet or Singlet) and/or modify SM gauge structure and/or supersymmetrize the SM and add R-parity violation and/or augment the number of space-time dimensions and/or etc Important: different options different phenomenological consequences

28 νsm One Possibility SM as an effective field theory non-renormalizable operators L νsm y ij L i HL j H 2Λ + O ( 1 Λ 2 ) + H.c. There is only one dimension five operator [Weinberg, 1979]. If Λ 1 TeV, it leads to only one observable consequence... after EWSB L νsm m ij 2 νi ν j ; m ij = y ij v 2 Λ. Neutrino masses are small: Λ v m ν m f (f = e, µ, u, d, etc) Neutrinos are Majorana fermions Lepton number is violated! νsm effective theory not valid for energies above at most Λ. What is Λ? First naive guess is that Λ is the Planck scale does not work. Data require Λ GeV (related to GUT scale?) [note y max 1] What else is this good for? Depends on the ultraviolet completion!

29 The Seesaw Lagrangian A simple a, renormalizable Lagrangian that allows for neutrino masses is L ν = L old λ αi L α HN i 3 i=1 M i 2 N i N i + H.c., where N i (i = 1, 2, 3, for concreteness) are SM gauge singlet fermions. L ν is the most general, renormalizable Lagrangian consistent with the SM gauge group and particle content, plus the addition of the N i fields. After electroweak symmetry breaking, L ν describes, besides all other SM degrees of freedom, six Majorana fermions: six neutrinos. a Only requires the introduction of three fermionic degrees of freedom, no new interactions or symmetries.

30 To be determined from data: λ and M. The data can be summarized as follows: there is evidence for three neutrinos, mostly active (linear combinations of ν e, ν µ, and ν τ ). At least two of them are massive and, if there are other neutrinos, they have to be sterile. This provides very little information concerning the magnitude of M i (assume M 1 M 2 M 3 ) Theoretically, there is prejudice in favor of very large M: M v. Popular examples include M M GUT (GUT scale), or M 1 TeV (EWSB scale). Furthermore, λ 1 translates into M GeV, while thermal leptogenesis requires the lightest M i to be larger than 10 9 GeV. we can impose very, very few experimental constraints on M

31 What We Know About M: M = 0: the six neutrinos fuse into three Dirac states. Neutrino mass matrix given by µ αi λ αi v. The symmetry of L ν is enhanced: U(1) B L is an exact global symmetry of the Lagrangian if all M i vanish. Small M i values are thooft natural. M µ: the six neutrinos split up into three mostly active, light ones, and three, mostly sterile, heavy ones. The light neutrino mass matrix is given by m αβ = i µ αim 1 i µ βi [m 1/Λ Λ = M/µ 2 ]. This the seesaw mechanism. Neutrinos are Majorana fermions. Lepton number is not a good symmetry of L ν, even though L-violating effects are hard to come by. M µ: six states have similar masses. Active sterile mixing is very large. This scenario is (generically) ruled out by active neutrino data (atmospheric, solar, KamLAND, K2K, etc).

32 Constraining the Seesaw Lagrangian sin 2! as Experimentally Excluded m " =...ev M N (ev) [AdG, Huang, Jenkins, arxiv: ]

33 [Aside: Why are Neutrino Masses Small in the M 0 Case?] If µ M, below the mass scale M, L 5 = LHLH Λ. Neutrino masses are small if Λ H. Data require Λ GeV. In the case of the seesaw, so neutrino masses are small if either Λ M λ 2, they are generated by physics at a very high energy scale M v (high-energy seesaw); or they arise out of a very weak coupling between the SM and a new, hidden sector (low-energy seesaw); or cancellations among different contributions render neutrino masses accidentally small ( fine-tuning ).

34 High-energy seesaw has no other observable consequences, except, perhaps,... Baryogenesis via Leptogenesis One of the most basic questions we are allowed to ask (with any real hope of getting an answer) is whether the observed baryon asymmetry of the Universe can be obtained from a baryon antibaryon symmetric initial condition plus well understood dynamics. [Baryogenesis] This isn t just for aesthetic reasons. If the early Universe undergoes a period of inflation, baryogenesis is required, as inflation would wipe out any pre-existing baryon asymmetry. It turns out that massive neutrinos can help solve this puzzle, and you learned all about it from Yossy Nir this week!

35 Mass (ev) 10 0 Dark Matter(?) Pulsar Kicks Oscillations ν 6 ν 5 ν 4 [AdG, Jenkins, Vasudevan, PRD75, (2007)] ν s3 ν s2 ν s1 ν τ ν µ ν e Also effects in 0νββ, tritium beta-decay, supernova neutrino oscillations, NEEDS non-standard cosmology. ν ν 2 ν

36 Fourth Avenue: Higher Order Neutrino Masses from L = 2 Physics. Imagine that there is new physics that breaks lepton number by 2 units at some energy scale Λ, but that it does not, in general, lead to neutrino masses at the tree level. We know that neutrinos will get a mass at some order in perturbation theory which order is model dependent! For example: SUSY with trilinear R-parity violation neutrino masses at one-loop; Zee model neutrino masses at one-loop; arxiv: and many others neutrino masses at two loops; etc

37 arxiv: [hep-ph] Effective Operator Approach (there are 129 of them if you discount different Lorentz structures!) classified by Babu and Leung in NPB619,667(2001) 11 b L i L j Q k d c Q l d c ɛ ik ɛ jl y d v 2 (16π 2 ) 2 Λ ββ0ν 12 a L i L j Q i ū c Q j ū c yu 2 v ββ0ν (16π 2 ) 2 Λ 12 b L i L j Q k ū c Q l ū c ɛ ij ɛ kl yu 2 g2 v ββ0ν (16π 2 ) 3 Λ 13 L i L j Q i ū c L l e c ɛ jl y l y u v 2 (16π 2 ) 2 Λ ββ0ν 14 a L i L j Q k ū c Q k d c ɛ ij y d y u g 2 v 2 (16π 2 ) 3 Λ ββ0ν 14 b L i L j Q i ū c Q l d c ɛ jl y d y u v 2 (16π 2 ) 2 Λ ββ0ν 15 L i L j L k d c L i ū c ɛ jk y d y u g 2 v 2 (16π 2 ) 3 Λ ββ0ν 16 L i L j e c d c ē c ū c ɛ ij y d y u g 4 v 2 (16π 2 ) 4 Λ 2 ββ0ν, LHC 17 L i L j d c d c dc ū c ɛ ij y d y u g 4 v 2 (16π 2 ) 4 Λ 2 ββ0ν, LHC 18 L i L j d c u c ū c ū c ɛ ij y d y u g 4 v 2 (16π 2 ) 4 Λ 2 ββ0ν, LHC 19 L i Q j d c d c ē c ū c ɛ ij yd y 2 y u v 2 lβ (16π 2 ) 3 Λ 1 ββ0ν, HElnv, LHC, mix 20 L i d c Q i ū c ē c ū c y y d yu 2 lβ 21 a L i L j L k e c Q l u c H m H n y ɛ ij ɛ km ɛ l y u v 2 1 ln (16π 2 ) 2 Λ 21 b L i L j L k e c Q l u c H m H n y ɛ il ɛ jm ɛ l y u v 2 kn (16π 2 ) 2 Λ 22 L i L j L k e c L k ē c H l H m g ɛ il ɛ 2 jm 23 L i L j L k e c Q k dc H l H m y ɛ il ɛ l y d v 2 jm (16π 2 ) 2 Λ (16π 2 ) 3 v 2 16π π 2 (16π 2 ) 3 v π 2 40 ββ0ν, mix Λ + v ββ0ν Λ 2 + v2 Λ ββ0ν ββ0ν Λ + v2 40 ββ0ν Λ 2 24 a L i L j Q k d c Q l d c H m H i ɛ jk ɛ lm y 2 d (16π 2 ) 3 v 2 Λ ββ0ν 24 b L i L j Q k d c Q l d c H m yd H i ɛ jm ɛ 2 kl 25 L i L j Q k d c Q l u c H m H n y ɛ im ɛ jn ɛ d y u v 2 kl (16π 2 ) 2 Λ (16π 2 ) 3 v 2 26 a L i L j Q k d c L i ē c H l H m y ɛ jl ɛ l y d km 26 b L i L j Q k d c L k ē c H l H m y ɛ il ɛ l y d v 2 jm (16π 2 ) 2 Λ 1 16π 2 (16π 2 ) 3 v π ββ0ν Λ + v ββ0ν Λ 2 40 ββ0ν Λ + v2 40 ββ0ν Λ 2 27 a L i L j Q k d c Q i dc H l H m ɛ jl ɛ km g 2 v 2 (16π 2 ) 3 Λ ββ0ν 27 b L i L j Q k d c Q k dc H l H m ɛ il ɛ jm g 2 v 2 (16π 2 ) 3 Λ ββ0ν 28 a L i L j Q k d c Q j ū c H l H i ɛ kl y d y u v 2 (16π 2 ) 3 Λ ββ0ν 28 b L i L j Q k d c Q k ū c H l H i ɛ jl y d y u v 2 (16π 2 ) 3 Λ ββ0ν 28 c L i L j Q k d c Q l ū c H l y H i ɛ d y u v 2 jk ββ0ν (16π 2 ) 3 Λ 29 a L i L j Q k u c Q k ū c H l H m yu ɛ il ɛ 2 v 2 1 jm + v ββ0ν (16π 2 ) 2 Λ 16π 2 Λ 2 29 b L i L j Q k u c Q l ū c H l H m ɛ ik ɛ jm g 2 v 2 (16π 2 ) 3 Λ ββ0ν 30 a L i L j L i ē c Q k ū c H k H l y ɛ l y u v 2 jl All Together ββ0ν ν (16π 2 ) 3 Λ 30 b L i L j L m ē c Q n ū c H k H l ɛ ik ɛ jl ɛ mn y ly u v v ββ0ν (16π 2 ) 2 Λ 16π 2 Λ 2

38 (a) LNV Operator ν α yv (b) γ, g W, Z yv ν β ν α yv (c) γ, g W, Z yv y H ē yβ ν β ν α ν β ν α H + y e y α h 0 ν β ν α h0 h 0 h 0 y ē y β H ν β v (d) v v (e) v

39 Number Of Operators Directly Accessible Colliders g 2 CLFV EDM Log(Λ/TeV) Dim 5 Dim 7 Dim 9 Dim 11 Out of direct reach if not weakly-coupled (?) (seesaw)

40 [arxiv: [hep-ph]] H e c d c Order-One Coupled, Weak Scale Physics Q L φ 4 φ 3 φ 1 φ 2 Can Also Explain Naturally Small Majorana Neutrino Masses: Multi-loop neutrino masses from lepton number H d c d c violating new physics. L νsm 4 i=1 M iφ i φi + iy 1 QLφ 1 + y 2 d c d c φ 2 + y 3 e c d c φ 3 + λ 14 φ1 φ 4 HH + λ 234 Mφ 2 φ3 φ 4 + h.c. m ν (y 1 y 2 y 3 λ 234 )λ 14 /(16π) 4 neutrino masses at 4 loops, requires M i 100 GeV! WARNING: For illustrative purposes only. Details still to be worked out. Scenario most likely ruled out by charged-lepton flavor-violation, LEP, Tevatron, and HERA.

41 How Do We Learn More? In order to learn more, we need more information. Any new data and/or idea is welcome, including searches for charged lepton flavor violation; searches for lepton number violation; (µ eγ, µ e-conversion in nuclei, etc) (neutrinoless double beta decay, etc) precision measurements of the neutrino oscillation parameters; searches for fermion electric/magnetic dipole moments (Daya Bay, NOνA, etc) (electron edm, muon g 2, etc);

42 precision studies of neutrino matter interactions; collider experiments: (Minerνa, NuSOnG, etc) (LHC, etc) Can we see the physics responsible for neutrino masses at the LHC? YES! Must we see it? NO, but we won t find out until we try! we need to understand the physics at the TeV scale before we can really understand the physics behind neutrino masses (is there low-energy SUSY?, etc).

43 CONCLUSIONS The venerable Standard Model has finally sprung a leak neutrinos are not massless! 1. we have a very successful parametrization of the neutrino sector, and we have identified what we know we don t know Well-defined experimental program. 2. neutrino masses are very small we don t know why, but we think it means something important. 3. we need a minimal νsm Lagrangian. In order to decide which one is correct we need to uncover the faith of baryon number minus lepton number (0νββ is the best [only?] bet).

44 4. We know very little about the new physics uncovered by neutrino oscillations. It could be renormalizable boring Dirac neutrinos. It could be due to Physics at absurdly high energy scales M 1 TeV high energy seesaw. How can we ever convince ourselves that this is correct? It could be due to very light new physics. Prediction: new light propagating degrees of freedom sterile neutrinos It could be due to new physics at the TeV scale either weakly coupled, or via a more subtle lepton number breaking sector. Predictions: charged lepton flavor violation, collider signatures! 5. We need more experimental input and more seems to be on the way (this is a data driven field). We only started to figure out what is going on. 6. There is plenty of room for surprises, as neutrinos are very narrow but deep probes of all sorts of physical phenomena. Remember that neutrino oscillations are quantum interference devices potentially very sensitive to whatever else may be out there (e.g., Λ GeV).

45 Backup Slides...

46 The LSND Anomaly The LSND experiment looks for ν e coming from π + µ + ν µ decay in flight; µ + e + ν e ν µ decay at rest; produced some 30 meters away from the detector region. It observes a statistically significant excess of ν e -candidates. The excess can be explained if there is a very small probability that a ν µ interacts as a ν e, P µe = (0.26 ± 0.08)%. However: the LSND anomaly (or any other consequence associated with its resolution) is yet to be convincingly observed in another experimental setup.

47 Low energy excess, naively rules out LSND (2 flavors). But ν ν... [R. Van de Water at Neutrino 2010] Consistent with LSND, but statistically less significant.

48 Very Unclear Still... LSND: strong evidence for ν µ ν e Beam Excess Beam Excess p(ν _ µ ν_ e,e+ )n p(ν _ e,e+ )n other L/E ν (meters/mev) If oscillations (??) m 2 1 ev 2 does not fit into 3 ν picture; scheme ruled out (solar, atm); scheme ruled out; 3 ν s CPTV ruled out (KamLAND, atm); µ eν e ν e ruled out (KARMEN, TWIST);? scheme; 4 ν s CPTV? heavy decaying sterile neutrinos; 3 νs and Lorentz-invariance violation; something completely different.

49 3+1+1 Fits Introduce an Extra m 2 and New Mixing Parameters CP-violating phase [Maltoni, Schwetz, arxiv: [hep-ph]] Mini-BooNE and LSND fit perfectly, including low-energy excess (MB300). However, severely disfavored by disappearance data, especially if MB300 is included [3σ 4σ (?)].

50 Prediction for low-energy seesaw: Neutrinoless Double-Beta Decay The exchange of Majorana neutrinos mediates lepton-number violating neutrinoless double-beta decay, 0νββ: Z (Z + 2)e e. For light enough neutrinos, the amplitude for 0νββ is proportional to the effective neutrino mass 6 m ee = U eim i U 2 eim i + ϑ 2 eim i. i=1 However, upon further examination, m ee = 0 in the ev-seesaw. The contribution of light and heavy neutrinos exactly cancels! This seems to remain true to a good approximation as long as M i 1 MeV. ( ) [ M = 0 µ T µ M i=1 i=1 m ee is identically zero! ] [AdG PRD 72, (2005)]

51 (lack of) sensitivity in 0νββ due to seesaw sterile neutrinos [AdG, Jenkins, Vasudevan, hep-ph/ ] 0.3 M ee (ev) Σ M ee = Q U 2 ei m i Q 2 + m i 2 Region Required to explain Pulsar kicks and warm dark matter M ee : ν light M ee : ν light + ν heavy Q = 50 MeV m (ev): Heaviest sterile neutrino mass 6

52 Weak Scale Seesaw, and Accidentally Light Neutrino Masses [AdG arxiv: [hep-ph]] MAX Γ(H νn)/γ(h bb - ) M H =120 GeV What does the seesaw Lagrangian predict for the LHC? Nothing much, unless... M N GeV, Yukawa couplings larger than naive expectations H νn as likely as H b b! (NOTE: N lq q or ll ν (prompt) Weird Higgs decay signature! ) m 4 (GeV) (plus Lepton-Number Violation at the LHC)

53 Hunting For θ 13 (or U e3 ) The best way to hunt for θ 13 is to look for oscillation effects involving electron (anti)neutrinos, governed by the atmospheric oscillation frequency, m 2 13 (other possibility, precision measurement of ν µ disappearance... ). One way to understand this is to notice that if θ 13 0, the ν e state only participates in processes involving m Example: ( ) m P ee 1 sin 2 2θ 13 sin L 4E + O ( m 2 12 m 2 13 ) 2

54 ν µ ν e at Long-Baseline Experiments REQUIREMENTS: ν µ beam, detector capable of seeing electron appearance. This is the case of Superbeam Experiments like T2K (2009) and NOνA (2012). Gina discused these in detail. or ν e beam and detector capable of detecting muons (usually including sign). This would be the case of Neutrino Factories (µ + e + ν µ ν e ) and Beta Beams (Z (Z ± 1)e ν e ). In vaccum ( ) P µe = sin 2 θ 23 sin 2 2θ 13 sin 2 m 2 13 L + subleading. 4E Sensitivity to sin 2 θ 13. More precisely, sin 2 θ 23 sin 2 2θ 13. This leads to one potential degeneracy.

55 (m 3 ) 2 (m 2 ) 2 (m 1 ) 2 ( m 2 ) sol ν e The Neutrino Mass Hierarchy ( m 2 ) atm ν µ ( m 2 ) atm ν τ which is the right picture? ( m 2 ) sol (m 2 ) 2 (m 1 ) 2 (m 3 ) 2 normal hierarchy inverted hierarchy

56 Why Don t We Know the Neutrino Mass Hierarchy? Most of the information we have regarding θ 23 and m 2 13 comes from atmospheric neutrino experiments (SuperK). Roughly speaking, they measure ( ) m P µµ = 1 sin 2 2θ 23 sin L 4E + subleading. It is easy to see from the expression above that the leading term is simply not sensitive to the sign of m On the other hand, because U e3 2 < 0.05 and m2 12 m 2 13 we are yet to observe the subleading effects. < 0.06 are both small,

57 Determining the Mass Hierarchy via Oscillations the large U e3 route Again, necessary to probe ν µ ν e oscillations (or vice-versa) governed by m This is the oscillation channel that (almost) all next-generation, accelerator-based experiments are concentrating on, including the next generation experiments T2K and NOνA. In vaccum ( ) P µe = sin 2 θ 23 sin 2 2θ 13 sin 2 m 2 13 L + subleading, 4E so that, again, this is insensitive to the sign of m 2 13 at leading order. However, in this case, matter effects may come to the rescue. As I discussed already, neutrino oscillations get modified when these propagate in the presence of matter. Matter effects are sensitive to the neutrino mass ordering (in a way that I will describe shortly) and different for neutrinos and antineutrinos.

58 If 12 m2 12 2E terms are ignored, the ν µ ν e oscillation probability is described, in constant matter density, by ( P µe P eµ sin 2 θ 23 sin 2 2θ13 eff sin 2 eff eff 13 = 13 L 2 ), sin 2 2θ13 eff = 2 13 sin2 2θ 13, ( eff 13 )2 ( 13 cos 2θ 13 A) sin2 2θ 13, 13 = m2 13 2E, A ± 2G F N e is the matter potential. It is positive for neutrinos and negative for antineutrinos. P µe depends on the relative sign between 13 and A. It is different for the two different mass hierarchies, and different for neutrinos and antineutrinos.

59 P eµ = 1-P ee sign(a)=sign(cos2θ) replace sign(cos 2θ) sign( m 2 13 ) A=0 (vacuum) sign(a)=-sign(cos2θ) L(a.u.) Requirements: sin 2 2θ 13 large enough otherwise there is nothing to see! 13 A matter potential must be significant but not overwhelming. eff 13 L large enough matter effects are absent near the origin.

60 [Maltoni and Schwetz, arxiv: ] Hint for non-zero sin 2 θ 13? You decide... (see claim by Fogli et al., arxiv: )