Neutrino Physics Theory and Phenomenology II

Transcription

1 Neutrino Physics Theory and Phenomenology II André de Gouvêa University PASI 2006 Puerto Vallarta, October 23 November 8, 2006

2 Outline for the Next Three Hours 1. What Boris Already Told You; 2. What We Know We Don t Know Next-Generation ν Oscillations; 3. What We are Not Sure We Don t Know On the LSND Anomaly; 4. Neutrino Masses As Physics Beyond the Standard Model; 5. Ideas for Tiny Neutrino Masses, and Some Consequences; 6. What is Up With Lepton Mixing?; 7. Conclusions. (note: Questions are ALWAYS welcome)

3 Short, Biased List of Recent References: A. Strumia and F. Vissani, hep-ph/ ; R. Mohapatra and A. Yu. Smirnov, hep-ph/ ; R. Mohapatra et al., hep-ph/ ; AdG, hep-ph/ ; AdG, hep-ph/

4 What Boris Told You: Neutrino Have Mass and Mix ν e ν µ ν τ = U e1 U e2 U e3 U µ1 U µ2 U µ3 U τ1 U eτ2 U τ3 tan 2 θ 12 U e2 2 U e1 2 ; tan 2 θ 23 U µ3 2 U e3 sin θ 13 e iδ U τ3 2 ; ν 1 ν 2 ν 3 (update Gonzalez-Garcia, Maltoni, hep-ph/ ) (update Gonzalez-Garcia, Peña-Garay, hep-ph/ ) m 2 1 < m 2 2 m 2 2 m 2 1 m 2 3 m 2 1,2 m 2 13 > 0 Normal Mass Hierarchy m 2 13 < 0 Inverted Mass Hierarchy

5 What We Know We Don t Know (1): Are Neutrinos Majorana Fermions? ν L you ν R? ν L? you (Boris talked about this... ) The neutrino is the only neutral elementary fermion. There is a left-handed one and a right-handed one. as far as we can tell (experiments)... the left-handed has lepton number L = +1, while the right-handed one has L = 1: (ν l ) L + X l + X, while (ν l ) R + X l + + X, so we call (ν l ) R ν l However: If the neutrino is its own antiparticle (Majorana fermion), then the lepton number conservation law must not be exact look for L-violation.

6 What We Know We Don t Know (2) (m 3 ) 2 (m 2 ) 2 (m 1 ) 2 ( m 2 ) sol What is the ν e component of ν 3? (θ 13 0?) Is CP-invariance violated in neutrino oscillations? (δ 0, π?) ( m 2 ) atm ν e ν µ ( 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?) ν τ What is the neutrino mass hierarchy? ( m 2 13 > 0?) ( m 2 ) sol normal hierarchy (m 2 ) 2 (m 1 ) 2 (m 3 ) 2 inverted hierarchy All of these can be addressed in neutrino oscillation experiments if we get lucky, that is if θ 13 is large enough.

7 Hunting For θ 13 (or U e3 ) The best (only?) way to hunt for θ 13 is to look for oscillation effects involving electron (anti)neutrinos, governed by the atmospheric oscillation frequency, m 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

8 Reactor Neutrino Searches for θ 13 L 1 km E ν 5 MeV next-generation: aim at improving CHOOZ bound an order of magnitude. e.g. Double CHOOZ, Daya Bay, etc (João dos Anjos)

9 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 and NOνA. 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.

10 On measuring sin 2 θ 23 (the atmospheric mixing angle) More specifically, we would like to ask whether it is possible to determine: 1. Is it maximal (sin 2 θ 23 = 1/2)? 2. Is sin 2 θ 23 > 1/2 or sin 2 θ 23 < 1/2? Limited information regarding (2) from disappearance channel. P µµ sin 2 2θ 23. Adding P µe sin 2 θ 23 sin 2 2θ 13 does not help! ( ) m P µµ = 1 sin 2 2θ 23 sin L + subleading. 4E In order to resolve this issue, need more information form reactors, atmospheric neutrinos, P eτ cos 2 θ 23 (which required τ appearance and is beyond the reach of standard next-generation LBL experiments usually requires Neutrino Factory).

11 Deciding that θ 23 is not maximal with LBL experiments 5 Conventional Beams 5 JPARC SK 5 NuMI off axis 10 3 ev 2 True value of m ev 2 True value of m ev 2 True value of m True value of sin 2 Θ True value of sin 2 Θ True value of sin 2 Θ 23 5 After ten years 5 JPARC HK 5 NuFact II 10 3 ev 2 True value of m ev 2 True value of m ev 2 True value of m True value of sin 2 Θ True value of sin 2 Θ True value of sin 2 Θ 23 Antusch et al., PRD70, (2004).

12 sin 2 Θ σ 2 σ σ Appearance + Disappearance not Enough Reactors Can Resolve Degeneracy Hiraide et al., hep-ph/ sin 2 2Θ 13

13 (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

14 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,

15 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 NOνA, T2K, and neutrino factories. 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 is well-known (I assume Boris explained this), 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.

16 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.

17 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.

18 ASIDE this is how the solar mass ordering was determined (m 3 ) 2 (m 2 ) 2 (m 1 ) 2 ( m 2 ) sol Of course, m 2 12 is positive-definite. What I mean by the solar mass ordering is whether ν e is mostly heavy (ν 2 ) ( m 2 ) atm ν e or mostly light (ν 1 ). ν µ ( m 2 ) atm ν τ Matter effects in the Sun have uniquely determined that the electron-type ( m 2 ) sol (m 2 ) 2 (m 1 ) 2 } (m 3 ) 2 neutrino is mostly light. normal hierarchy inverted hierarchy NOTE: this is a two-flavor effect!

19 Determining the Mass Hierarchy via Oscillations vanishing U e3 route hep-ph/ , hep-ph/ , hep-ph/ In the case of two-flavors, the mass-hierarchy can only be determined in the presence of matter effects: vacuum neutrino oscillations are not sensitive to the mass hierarchy. In the case of three-flavors, this is not the case: vacuum neutrino oscillation probabilities are sensitive to the neutrino mass hierarchy. This does not depend on whether U e3 vanishes or not.

20 How does one compare the two mass hierarchies and determines which one is correct? The question I address is the following: For a positive choice of m 2 13 = m 2+ 13, is there a negative choice for m 2 13 = m 2 13 that yields identical oscillation probabilities? If the answer is yes, then one cannot tell one mass hierarchy from the other. If the answer is no, then one can, in principle, distinguish the two possibilities. More concretely: fix m (which I ll often refer to as m2 13) and define x so that m 2 13 = m x. Question: Is there a value of x that renders P ( m ) = P ( m2 13 )? Note: x is such that m 2 13 is negative. It turns out that x s that almost do the job are of order m 2 12.

21 I will concentrate on survival probabilities (which will be the only relevant ones in the U e3 0 limit): ( P αα = 1 4 U α1 2 U α2 2 sin 2 12 L 2 ( 4 U α1 2 U α3 2 sin 2 13 L 2 ( 4 U α2 2 U α3 2 sin 2 23 L 2 ij m 2 ij/2e. Note that 23 = It is easy to see how the different hierarchies lead to different results. In the normal case, 13 > 23, while in the inverted case 13 < 23. Hence, all one needs to do is establish which frequency is associated to which amplitude (governed by the U αi s). ) ) ),

22 More detail: { [ P αα + Pαα = 4 U α3 2 U α1 2 X = x/2e. + U α2 2 [ ( sin 2 13 L 2 sin 2 ( ( )L 2 ) ) ( )] sin 2 ( 13 X)L 2 sin 2 ( ( X)L 2 There is no choice of x that renders this zero for all L and E, unless (i) U α2 2 = U α1 2 (known not to happen) or (ii) 12 = 0 (also does not happen) or (iii) one of the U αi s vanishes (could happen in the case of P ee ). )]},

23 Life is not this simple. Most experimental set-ups looking for U e3 effects concentrate on L and E so that 13 L 1. This means that 12 L 1. It turns out that x = 2 U α2 2 U α1 2 + U α2 2 m2 12, renders P + αα P αα = O( 12 L) 2. There are two ways around this problem. One is to make sure you consider large 12 L values. The other is to note that different α s yeild different values of x. Both are very, very challenging...

24 P µµ L=295 km m 2 13 = ev m 2 13 = ev 2 (s) m 2 13 = ev 2 (d) m 2 12 = ev 2, sin 2 2θ 12 = 0.83, sin 2 2θ 23 = 1 E (GeV) The small 12 L problem: in this case x = 2 m 2 12 cos 2 θ 12 (= ev 2 ). This would be the situation at a short baseline experiment: even with quasi-infinite statistics one would still end up with two different values of m 2 13, one for each hierarchy hypothesis.

25 P µµ P µµ E (GeV) L=6000 km E (GeV) m 2 13 = ev 2 m 2 13 = ev 2 (d) m 2 12 = ev 2, sin 2 2θ 12 = 0.83, sin 2 2θ 23 = 1 There is hope! But can we see the fast oscillations at low energies?

26 Other Tool? Non-Oscillation Experiments (U e3 = 0, m = ev 2, m 2 13 = ev 2 ) 10 1 m ee ev ev m νe m νe ev10 1 Normal Inverted 10 2 Σ = m 1 + m 2 + m Σ ev m 2 ν e i U ei 2 m 2 i m ee i U 2 ei m i m 1 U e1 2 e iα 1 + m 2 U e2 2 e iα 2 + m 3 U e3 2 e 2iδ

27 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.

28 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 ). A µe = U e1u µ1 + U e2u µ2 e i 12, +U e3u µ3 e i 13 where 1i = m2 1i L 2E. The amplitude for the CP-conjugate process is. Ā µe = U e1 U µ1 + U e2 U µ2e i 12, +U e3 U µ3e i 13

29 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!

30 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.

31 <P(ν)> <P(ν)> cp + matter, m 2 31 >0 cp, m 2 31 >0 cp + matter, m 2 31 <0 cp, m 2 31 <0 0 π/2 π 3π/ (a) <E ν >=0.5GeV (b) <E ν >=1GeV Need to determine other oscillation parameters in order to realistically study CP-invariance violation (c) <E ν >=1.5GeV <P(ν)> (d) <E ν >=2GeV <P(ν)> [Minakata, Nunokawa, hep-ph/ ]

32 ASIDE: How many new CP-violating parameters in the neutrino sector? If the neutrinos are Majorana fermions, there are more physical observables in the leptonic mixing matrix. Remember the parameter counting in the quark sector: 9 (3 3 unitary matrix) 5 (relative phase rotation among six right-handed quark fields) 4 (3 mixing angles and 1 CP-odd phase).

33 If the neutrinos are Majorana fermions, the parameter counting is quite different: there are no right-handed neutrino fields to absorb CP-odd phases: 9 (3 3 unitary matrix) 3 (three right-handed charged lepton fields + overall phase) 6 (3 mixing angles and 3 CP-odd phases). There is CP-invariance violating parameters even in the 2 family case: 4 2 = 2, one mixing angle, one CP-odd phase.

34 L ē L V MNS W µ γ µ ν L ē L (M e )e R ν t L(M ν )ν L + H.c. Write V = E iξ/2 V E iα/2, where E iα = diag(e iα 1, e iα 2, e iα 3 ), L ē L V MNSE iα/2 W µ γ µ ν L ē L E iξ/2 (M e )e R ν t L(M ν )ν L ξ phases can be absorbed by e R, α phases cannot go anywhere!

35 V MNS = U e1 U e2 U e3 U µ1 U µ2 U µ3 U τ1 U eτ2 U τ3 e iα 1/ e iα 2/ e iα 3/2. It is easy to see that the Majorana phases never show up in neutrino oscillations (A U αi U β i ). Furthermore, they only manifest themselves in phenomena that vanish in the limit m i 0 after all they are only physical if we know that lepton number is broken. A(α i ) m i /E tiny! END ASIDE

36 DO WE REALLY KNOW EVERYTHING ABOUT THE NEW ν s? (Some of) What We Don t Know We Don t Know Given that neutrinos have mass and we are in position to probe whether neutrino are endowed with other unexpected properties, including, an electric/magnetic dipole moment; a finite lifetime. We are also able to search for New neutrino contact interactions; New neutrino degrees of freedom (sterile neutrinos). Finally, we can ask whether the leptonic sector respects a variety of fundamental symmetries, including Lorentz invariance; CPT invariance.

37 Example: New Neutrino Matter Interactions These are parameterized by effective four-fermion interactions, of the type: L NSI = 2 ( ) 2G F ( ν α γ µ ν β ) ɛ f fl f αβ L γ µ fl + ɛ f fr f αβ R γ µ fr + h.c. where f, f = u, d,... and ɛ f f αβ are dimensionless couplings that measure the strength of the four-fermion interaction relative to the weak interactions. While some of the ɛs are well constrained (especially those involving muons), some are only very poorly known. These are best searched for in neutrino oscillation experiments, where they mediate anomalous matter effects: H mat = 2G F n e 1 + ɛ ee ɛ eµ ɛ eτ ɛ eµ ɛ µµ ɛ µτ ɛ eτ ɛ µτ ɛ ττ, ɛ αβ = f=u,d,e ɛ ff n f αβ n e Such Effects Will Be Probed By The Same Neutrino Oscillation Experiments!

38 Solar Neutrinos SuperK and SNO have measured, with great precision, high energy solar neutrinos, E ν > 5 MeV. The next natural step is to measure low energy (E ν < 1 MeV) solar neutrinos. In order to do this, we need deep underground detectors. These are not your typical LBL detector. Different techniques have been proposed in order to obtain sensitivity to sub-mev neutrinos and reduce radioactive backgrounds. We don t expect significant improvements as far as solar parameters are concerned, but solar neutrinos could play a big role in the case of new new physics (and I won t talk about astrophysics at all). Important ingredients: strong magnetic fields (time dependency?), large, smoothly varying matter density, effect, very low neutrino energies.

39 We Have Only Precisely Studied a Tiny Fraction of the Solar νs! Vacuum - Matter transition P 0.6 cos 4 θ 13 (1-1 sin 2 2θ 12 ) Low E β= 23/2 G F cos 2 θ 13 n e E ν 2 m 21 E High E cos 4 θ 13 sin 2 θ and we have only looked at the boring side of the LMA solution!

40 Non-Standard ν Interactions and Low-Energy Solar νs Friedland et al. PLB594, 347 (2004). m 2 (ev 2 ) LMA-II LMA-I LMA-II LMA-I LMA-0 tan 2 θ tan 2 θ 1 LMA 0 ɛ ee ɛ ττ sin 2 θ 23 = ɛ eτ sin θ 23 = 0.15 [WARNING: This is old KamLAND data]

41 What We Are Not Sure We Don t Know: 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 observed in another experimental setup.

42 If oscillations m2 1 ev2 strong evidence for ν µ ν e does not fit into 3 ν picture; Beam Excess Beam Excess p(ν _ µ ν_ e,e+ )n p(ν _ e,e+ )n other scheme ruled out (solar, atm);? scheme disfavored (sbl searches); 3 ν s CPTV ruled out (KamLAND, atm); µ eν e ν e ruled out (KARMEN, TWIST); scheme works (finely tuned?); 4 ν s CPTV 0 heavy decaying sterile neutrinos; L/E ν (meters/mev)? 3 νs and Lorentz-invariance violation; something completely different.

43 m 2 (ev 2 /c 4 ) Karmen Bugey 90% (L max -L < 2.3) 99% (L max -L < 4.6) CCFR NOMAD sin 2 2θ Karmen has a similar sensitivity to ν µ ν e, but a shorter baseline (L = 18 m) Other curves are failed searches for ν µ disappearance (CCFR), ν e disapperance (Bugey), etc Remember: P µe = sin 2 2θ sin 2 [ 1.27 ( ) m ( 2 L ) ( MeV ) ] ev 2 m E

44 ( m 2 ) atm ν e ( m 2 ) LSND ν µ ν τ ( m 2 ) LSND ν s ( m 2 ) atm ( m 2 ) sol ( m 2 ) sol 2+2 requires large sterile effects in either solar or atmospheric oscillations, not observed

45 m 2 (ev 2 ) a) b) c) d) sin 2 2θ µe p LSND (10-2 ) (χ 2 NSBL ) min (χ 2 LSND ) min In 3+1, sin 2 2θ LSND = sin 2 2θ µe 4 U e4 2 U µ4 2, while for disappearance searches sin 2 2θ αα 4 U α4 2 (1 U α4 2 ). nontrivial constraints from short-baseline disappearance searches!...

46 ... but one can still speak of a best fit region. m 2 (ev 2 ) a) b) c) sin 2 2θ µe p LSND (10-2 ) (χ 2 SBL ) min

47 3+1+1 Fits Introduce an Extra m 2 and Effective Mixing Angle. U e B C Can only be better than 3+1 fit (decoupling) 0.12 D A The fit works by splitting the constraints imposed by short baseline data between the m 51 2 (ev 2 ) m 2 51 (ev2 ) two frequencies, whose effect add up at LSND. Is this finely tuned? In what sense? m 41 2 (ev 2 )

48 8 6 8 χ χ U µ U µ U e χ U e χ 2 [Courtesy of Michel Sorel]

49 LSND Challenge Summarized The LSND effect is very small (P µe 0.3%). No other experiment has achieved better sensitivity to ν µ ν e, except for the Karmen experiment L (L/E) dependency necessary! It is, then, always the case that a small effect at LSND translates into a much larger effects elsewhere (atmospheric/solar neutrinos, short baseline experiments, etc). We have, so far, failed to find a consensus, feel good solution to the LSND anomay. Does this mean it is wrong? Of course, not! a a Some have experimental complaints about LSND. None seem to be entirely convincing, and qualify, at best, as well-justified suspicion that something is afoot...

50 In summary, the best solution (my opinion) to the LSND anomaly we have been able to concoct is 3+2 neutrino oscillations (or 3+3, 3+4, etc). While a good fit can be obtained, it seems to be taylor made. Why haven t LSND effects been observed in disappearance experiments? There are many left-over theoretical complaints. What are these sterile neutrinos? [LEP data tell us there are only three light neutrinos that couple to the Z-boson...] Why are they so light? Sterile neutrinos are theoretically expected to be very heavy... Can we say anything about the expected sterile active neutrino mixing? Can LSND oscillations be predicted?...

51 LSND Anomaly to be resolved by the MiniBooNE experiment: Ongoing experiment at Fermilab designed to definitively test the LSND anomaly with different beam and systematics. LSND: µ + ν µ ν e MiniBooNE: π + ν µ ν e Results expected in the very near future (!?)

52 Outline for the Next Three Hours 1. What Boris Already Told You; 2. What We Know We Don t Know Next-Generation ν Oscillations; 3. What We are Not Sure We Don t Know On the LSND Anomaly; 4. Neutrino Masses As Physics Beyond the Standard Model; 5. Ideas for Tiny Neutrino Masses, and Some Consequences; 6. What is Up With Lepton Mixing?; 7. Conclusions. (note: Questions are ALWAYS welcome)

53 mass (ev) τ µ b s t c TeV GeV NEUTRINOS e d u MeV HAVE MASS kev albeit very tiny ones ν 1 ν 2 ν generation ev mev SO WHAT?

54 Only Palpable Evidence of Physics Beyond the Standard Model The SM we all learned in school predicts that neutrinos are strictly massless. Hence, 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 palpabiloity (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? ).

55 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.

56 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, and it looks like it may be coming in the near/intermediate future!

57 The νsm Take 1 SM as an effective field theory non-renormalizable operators L νsm λ ij L i HL j H 2M + O ( 1 M 2 ) + H.c. There is only one dimension five operator [Weinberg, 1979]. If M 1 TeV, it leads to only one observable consequence... after EWSB L νsm m ij 2 νi ν j ; m ij = λ ij v 2 M. Neutrino masses are small: M 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 M. What is M? First naive guess is that M is the Planck scale does not work. Data require M < GeV (anything to do with the GUT scale?) What else is this good for? Depends on the ultraviolet completion!

58 Note that this VERY similar to the discovery weak interactions. Imagine the following model: U(1) E&M + e(q = 1), µ(q = 1), ν e (q = 0), ν µ (q = 0). The most general renormalizable Lagrangian explains all QED phenomena once all couplings are known (α, m f ). New physics: the muon decays! µ e ν e ν µ. This can be interpreted as evidence of effective four fermion theory (nonrenormalizable operators): 4G F 2 γ g γ (ēγ γ ν) ( νγ γ µ), Γ γ = 1, γ 5, γ µ,... Prediction: will discover new physics at an energy scale below 1/GF 250 GeV. We know how this turned out W ±, Z 0 discovered slightly below 100 GeV!

59 Full disclosure: All higher dimensional operators are completely negligible, except those that mediate proton decay, like: λ B M 2 QQQL The fact that the proton does not decay forces M/λ B to be much larger than the energy scale required to explain neutrino masses. Why is that? We don t know...

60 νsm Take 2 The Higgs sector could be more complicated. We add to the SM a complex Higgs triplet ξ = (ξ ++ ξ + ξ 0 ) T, which can couple to lepton doublets 2 2 κ αβl cα ξl β + h.c.. If the neutral component of ξ develops a vacuum expectation value u, the neutrinos acquire a Majorana mass m αβ u κ αβ. Lots of questions Why is u so small? Where are these ξ (note that they also couple to charged leptons) heavy fields. Other technical issues render proper realizations of this ugly.

61 The νsm Take 3 Why don t we just enhance the fermion sector of the theory? One may argue that it is trivial and simpler to just add L Yukawa = y iα L i HN α + H.c., and neutrinos get a mass like all other fermions: m iα = y iα v Data requires y < Why so small? Neutrinos are Dirac fermions. B L exactly conserved. νsm is a renormalizable theory. This proposal, however, violates the rules of the SM (as I defined them)! The operator M N 2 NN, allowed by all gauge symmetries, is absent. In order to explain this, we are forced to add a symmetry to the νsm. The simplest candidate is a global U(1) B L. U(1) B L is upgraded from accidental to fundamental (global) symmetry.

62 Standard Model in One Slide, No Equations, Encore 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. This model has accidental global symmetries. In particular, the anomaly free global symmetry is preserved: U(1) B L.

63 New Standard Model, Dirac Neutrinos 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, N, scalars: H); Global Symmetry U(1) B L. Once this is specified, the SM is unambiguously determined: Most General Renormalizable Lagrangian; Measure All Free Parameters, and You Are Done. Naively not too different, but nonetheless qualitatively different enhanced symmetry sector!

64 On very small Yukawa couplings We would like to believe that Yukawa couplings should naturally be of order one. Nature, on the other hand, seems to have a funny way of showing this. Of all known fermions, only one (1) has a natural Yukawa coupling the top quark! Regardless there are several very different ways of obtaining naturally very small Yukawa couplings. They require the more new physics.

65 Example 1: Non-Anomalous, Gauged U(1) ν Add to the SM a new, non-anomalous U(1) ν under which both SM fermions and the right-handed neutrinos transform. Charges are heavily constrained by anomaly cancellations and the fact that quarks and charged leptons have relatively large masses. One can choose U(1) ν charges so that all neutrino masses are forbidden by gauge invariance. This way, neutrino masses are only generated after U(1) ν is spontaneously broken, a and only through higher dimensional operators, suppressed by a new ultraviolet scale Λ. Neutrino masses are small either because Λ is very large (this is the usual high energy seesaw) or because it is a consequence of a very high dimensional operator: m ν ( ϕ Λ) p, where p is a large integer exponent. a Assume U(1) ν is spontaneous broken when SM singlet scalar Φ gets a vev, Φ ϕ.

66 After U(1) ν breaking see-saw Lagrangian plus left left neutrino mass: L ik ɛ p ik Li (λ ν ) ik n k H + ɛ q ij (h L ) ij Lc i ij Λ L jhh + kk ɛ rkk Λ n c k(h R ) kk nk, λ ν neutrino Yukawa coupling, h L left left coupling), and h R right right Majorana mass term). i, j = 1, 2, 3, k, k = 1... N. Only allowed for integer values of p, q, and r. After electroweak symmetry breaking, (3 + N) (3 + N) neutrino mass matrix M ν : M ν v 2 Λ hl ɛ q v(λ ν ɛ p ) vλ ν ɛ p Λh R ɛ r Lots of possibilities. If there are no integer q and r Dirac Neutrinos, with suppressed masses (m ν vɛ p ) [M.C. Chen, B. Dobrescu, AdG, work in progress].

67 Example 2: Extra-Dimensional Theories Large Extra Dimensions, with right-handed neutrinos in the bulk: m ν = λv ( MD M Pl ) δ/d Randall-Sundrum Models: left-handed, right-handed neutrinos live very close to the ultra-violet brane, the Higgs lives in the infra-red brane small Yukawa couplings from very small small overlap of the 5-dimensional wave-functions (Grossman, Neubert).

68 Fat Branes: λ e 1 2 µ2 (f i f j ) 2, where f i are the positions of the different fermion fields in the extra-dimension, all of width 1/µ. easy to get very small, very hierarchical masses. Tricky bit is the large mixing angles. Barenboim, Branco, AdG, Rebelo, hep-ph/

69 Massive Neutrinos and the Seesaw Mechanism 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.

70 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 around GeV. we can impose very, very few experimental constraints on M

71 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 λ αim 1 i λ βi. 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).

72 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!

73 In the old SM, (electroweak) baryogenesis does not work not enough CP-invariance violation, Higgs boson too light. Neutrinos help by providing all the necessary ingredients for successful baryogenesis via leptogenesis. Violation of lepton number, which later on is transformed into baryon number by nonperturbative, finite temperature electroweak effects (in one version of the νsm, lepton number is broken at a high energy scale M). Violation of C-invariance and CP-invariance (weak interactions, plus new CP-odd phases). Deviation from thermal equilibrium (depending on the strength of the relevant interactions).

74 E.g. thermal, seesaw leptogenesis, L y iα L i HN α M αβ N 2 N α N β + H.c. N 1 L L N 1 N 2, 3 H L L N 1 N 2, 3 [Fukugita, Yanagida] H H L H H L-violating processes L N 1, 2, 3 L L N 1, 2, 3 H L N 1, 2, 3 H y CP-violation H H N 1 U 3 H H N 1 H L L L N 1 H H L deviation from thermal eq. constrains combinations of M N and y. L Q 3 U 3 Q 3 Q 3 U 3 need to yield correct m ν N 1 H N 1 H N 1 H H L L not trivial! L A L A A L N 1 L N 1 L N 1 L L H H [G. Giudice et al, hep-ph/ ] H A H A A H

75 E.g. thermal, seesaw leptogenesis, L y iα L i HN α M αβ N 2 N α N β + H.c. maximal nb / nγ SM 3σ ranges heaviest ν mass m 3 in ev maximal nb / nγ MSSM 3σ ranges heaviest ν mass m 3 in ev [G. Giudice et al, hep-ph/ ] It did not have to work but it does MSSM picture does not quite work gravitino problem (there are ways around it, of course...)

76 Relationship to Low Energy Observables? In general... no. This is very easy to understand. The baryon asymmetry depends on the (high energy) physics responsible for lepton-number violation. Neutrino masses are a (small) consequence of this physics, albeit the only observable one at the low-energy experiments we can perform nowadays. see-saw: y, M N have more physical parameters than m ν = y t M 1 N y. There could be a relationship, but it requires that we know more about the high energy Lagrangian (model depent). The day will come when we have enough evidence to refute leptogenesis (or strongly suspect that it is correct) - but more information of the kind I mentioned earlier is really necessary (charged-lepton flavor violation, collider data on EWSB, lepton-number violation, etc).

77 ( There are other kinds of leptogenesis, of which I ll say nothing Nonthermal leptogenesis Type-II see-saw leptogenesis Dirac leptogenesis Soft leptogenesis Lindner et al; Murayama and Pierce Grossman et al; Giudice et al.... )

78 Low-Energy Seesaw [AdG PRD72,033005)] Lets peek in the other end of the M spectrum. What do we get? Neutrino masses are small because the Yukawa couplings are very small λ [10 6, ]; No standard thermal leptogenesis right-handed neutrino way too light; No obvious connection with other energy scales (EWSB, GUTs, etc); Right-handed neutrinos are propagating degrees of freedom. They look like sterile neutrinos; Sterile active mixing can be predicted hypothesis is falsifyable. Sterile neutrinos could be Gods gift to all our puzzles! Small values of M are natural (in the thooft sense). In fact, theoretically, no value of M should be discriminated against!

79 10 4 Dark Matter(?) [AdG, Jenkins, Vasudevan, hep-ph/ ] 10 3 Pulsar Kicks ν 6 ν s3 ν s2 ν s1 Also effects in 0νββ, 10 2 ν τ ν µ tritium beta-decay, supernova neutrino oscillations, ν e NEEDS non-standard cosmology Mass (ev) 10 0 LSND ν 5 ν 4 ν ν 2 ν

80 Understanding Fermion Mixing The other puzzling phenomenon uncovered by the neutrino data is the fact that Neutrino Mixing is Strange. What does this mean? It means that lepton mixing is very different from quark mixing: V MNS [ (V MNS ) e3 < 0.2] V CKM WHY? They certainly look VERY different, but which one would you label as strange?

81 In the quark sector, the small mixing angles are interpreted, together with the hierarchical quark masses, as evidence for extra structure in the SM, i.e., there is some underlying dynamical principle (symmetry) capable of telling one quark flavor from another. The same must be true in the leptonic sector. After all, charged lepton masses are also hierarchical (we don t know whether the same is true for the neutrinos yet...) and, if GUTs have anything to do with Nature, quarks and leptons may well be different low-energy manifestations of a more fundamental unified fermion. Hence, there should also be a dynamical principle which naturally explains the form of the MNS matrix. (or should there?... ) First Prediction: V CKM V MNS driving force before 1998 SK results, turned out to be completely wrong.

82 André de Gouvêa! " #! " $ % & '( ) * +, -. / 0 1/ "! "! ) % 9 : ; ; < = % :. > 2 A - B CB D " E F " C D " E G. 2 A - > H I > $! B! " J 0 /!! " #, 2 >. B! " K C# D " E F - L M!! " # m 2 13 > 0 typical prediction of all Type-I seesaw GUT models inverted hierarchy requires more flavor structure Albright,hep-ph/ N 2 O P K! K! 3 #! " B! Q > H Q! "! 5 = < R = S % <. / 0 1/ 2 H 2 B! "!. T U > B "! "!!! M D " E F!!! " V * 7 8 ) % 9 : ; ; < = % ' < 9 0 / W 4 / B B $ 0 / W 4 / B!$!$. > / N 2 2 B! "! # J / 0 B B! #!!!! $!!!B U 2 P T 2 B M! K!!! "!!!! # J B K!! " B X < R = S % < 9 Y T J - I 0 B #! #!!!! $!!! " B W > T B Q! "!. T J - U > I 0 M! "!!! B D " E F!!! " Z > M "!! " B $ [ 9 < < \ 9 7 ], 2 ^ /? P - M M $! B! " _ 0 2 L ` T M! "! a M B b 0 2 H c! K! b 4 T H c d C M d " CM D " E F e f 7 % g h : T / 4 i / H 0 M M d C " d C j < f ) % ; 7 * ' k 7 = ' ) f l % ) S m < f h 7 f g < ; < f =? T n - M K! #!!! "! $!!! [from reactor white paper] Theoretical predictions: The literature on this subject is very large. The most exciting driving force (my opinion) is the fact that one can make bona fide predictions: U e3, CP-violation, mass-hierarchy unknown! Unfortunately, theorists have done too good a job, and people have successfully predicted everything... More data needed to sort things out. October I27/28, > 2 " o 2006 Z T! I / 0 > / 2 T > T T T 0 / T 0!

83 [Albright and Chen, hep-ph/ ] pessimist We can t compute what U e3 is must measure it! (same goes for the mass hierarchy, δ)

84 Qualitative descriptions of why V MNS and V CKM could turn out to be so different in a GUT theory [apologies to experts in the audience]: Large neutrino mixing comes from M N remember, while m f = yv, m ν = y t M 1 N y SU(5) inspired mixing: left-handed leptons and right-handed down-type quarks are in a 5 of SU(5), while everyone else is in a 10. If the 5 s are strongly mixed, we would only be able to see it in the leptonic sector, since one is always free to redefine right-handed fermions without physical consequences (because of left-handedness of weak interactions). [ interesting consequences in quark flavor physics if one adds SUSY] large mixing induced via renormalization group running...

85 Something Completely Different (?) maybe we are asking the wrong question! Notice that quark mixing is the one that fits the strange label this is why we are convinced that there is some hint of more fundamental physics hidden in the CKM matrix! Lepton mixing, on the other hand, seems quite ordinary. Maybe the MNS matrix is what one should expect if there was no fundamental principle hidden behind neutrino mixing. Neutrino Mass Anarchy Anarchy is resistant against hierarchical charged lepton masses, GUT constraints. The relevant questions are 1-can we test whether the idea is plausible and 2-can we learn anything from it? (yes, and yes!) My only complaint is the fact that θ 23 is maximal. But when should we start worrying about this? (to be discussed in the next-to-next slide)

86 Lower Bound for U e3 2 [AdG, Murayama, PLB573, 94 (2003)] P(KS) (one dimensional) σ according to the anarchical hypothesis, the probability density distribution for θ 13 is given by P (cos 4 θ 13 ) 1 [Haba, Murayama, PRD63, (2001)] σ The probability that U e3 2 is larger than 0.01 is around 95%, EXCLUDED by CHOOZ and if U e3 2 turns out to be smaller, the anarchical hypothesis is ruled out! sin 2 θ 13 (Prob. distribution for CP-phase: P (δ) 1)

87 generic predictions for subleading parameters. Note correlations between U e3 and cos 2θ 23, plus dependency on mass-hierarchy. Case Texture Hierarchy U e3 cos 2θ 23 (n.s.) cos 2θ 23 Solar Angle m 2 A 13 m Normal 2 12 m O(1) 2 m 2 12 O(1) 13 m B m Inverted m 2 12 m m m 2 13 O(1) m 2 C 2 13 m Inverted 2 12 m m 2 13 O(1) 2 12 m 2 13 cos 2θ 12 m2 12 m Anarchy m Normala > 0.1 O(1) O(1) a One may argue that the anarchical texture prefers but does not require a normal mass hierarchy. What About Maximal Atmospheric Mixing? [enlarged from AdG, PRD69, (2004)] Textures are another way to parametrize neutrino mixing and to try and understand salient features: U e3 1, cos 2θ 23 1, m 2 12 m2 13, etc. Usually quark independent.

88 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 (µ eγ, etc); searches for lepton number violation (neutrinoless double beta decay, etc); precision measurements of the neutrino oscillation parameters; searches for fermion electric/magnetic dipole moments (electron edm, muon g 2, etc); searches for new physics at the TeV scale we need to understand the physics at the TeV scale before we can really understand the physics behind neutrino masses (is the low-energy SUSY?, etc).

89 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. 2. neutrino masses are very small we don t know why, but we think it means something important. 3. lepton mixing is very different from quark mixing we don t know why, but we think it means something important. 4. we need a minimal νsm Lagrangian. In order to decide which one is correct (required in order to attack 2. and 3. above) we must uncover the faith of baryon number minus lepton number (0νββ is the best [only?] bet).

90 5. We need more experimental input and more seems to be on the way (this is a truly data driven field right now). We only started to figure out what is going on. 6. The fact that neutrinos have mass may be intimately connected to the fact that there are more baryons than antibaryons in the Universe. How do we test whether this is correct? 7. 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., M seesaw GeV). 8. Finally, we need to resolve the LSND anomaly. If MiniBooNE agrees with the LSND result, life will be much more interesting!