Lepton and baryon number violation

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1 Lepton and baryon number violation some remarks Goran Senjanović ICTP LBV09-MADISON 1

2 NOT a summary talk. Will not refer to talks by: Pilaftsis, Wagner, Agashi, Kile, Garbrecht, Lavignac, Friedland, Mustafayev - 1/4 3/4 of summary talk? only some aspects of direct tests of B and L violation: fact and fancy LBV09-MADISON 2

3 Some History VIOLATION OF LEPTON NUMBER: L = 2 neutrino-less double beta decay ββ0ν Racah 37 Furry, 38 over the years: T 1/ yr (double beta decay - when single not possible: T 1/ yr) Goeppert-Mayer, 35 LBV09-MADISON 3

4 inspired by the paper of Majorana Teoria simmetrica dell elettrone e del positrone Il Nuovo Cimento Vol.14 (1937) p.171 last paper before his disappearance written only for the professorship position in Napoli LBV09-MADISON 4

5 BARYON NUMBER VIOLATION proton rather stable Feel it in your bones: roughly τ p year otherwise killed by radiation Goldhaber, fifties? Nath, Dorsner, Pati LBV09-MADISON 5

6 Proton stability BARYON NUMBER Weyl 29 Stuckelberg 39 Wigner 49 DOGMA LBV09-MADISON 6

7 Reines, Cowan, Goldhaber, Phys. Rev. 96, 1157 (1954) In view of the fundamental nature of such an assumption, it seemed of interest to investigate the extent to which the stability of nucleons could be experimentally demonstrated. neutrino detectors τ p yr yr LBV09-MADISON 7

8 in the 50 s: n n oscillations but not pursued until 70 s talks by Kamyshkov and Babu theoretically a long shot, but very interesting - implies physics not far from M W LBV09-MADISON 8

9 THE ONLY GOOD (GLOBAL) SYMMETRY IS A BROKEN (GLOBAL) SYMMETRY B, L not unbroken gauge symmetries - unless g ( ) - Charge conservation and the lifetime of the electron? τ e yr (e ν + γ) Moe, Reines 65 p decay, ββ0ν THEORY LBV09-MADISON 9

10 Standard Model B,L exact (except for anomalies = irrelevant at T = 0) effective theory: higher dimensional operators STAND OUT L = LLHH M L L = Y ij QQQL M B probes M L GeV probes M B GeV? Ideal windows to high-scale physics Weinberg 79 LBV09-MADISON 10

11 Lepton Number Violation Motivation: neutrinos are massive With the SM degrees of freedom ν masses parametrized by Weinberg d = 5 effective operator L = Y ij L i HHL j M L - left-handed leptonic doublet H - Higgs doublet (with a vev v) (M ν ) ij = Y ij v 2 M neutrino mass - Majorana LBV09-MADISON 11

12 not so much a clue why m ν m ± M arbitrary - not necessarily large Y arbitrary - not necessarily large talk by Langacker but a case for Majorana: connects m ν to new physics VIOLATION OF LEPTON NUMBER: L = 2 neutrino-less double beta decay ββ0ν same sign charged lepton pairs in colliders Keung, G.S., 83 LBV09-MADISON 12

13 M = GeV corresponds to Y of order one PERTURBATIVE CUT-OFF However, small Yukawas are natural in a sense of being protected by symmetries. still: Y but: Y e 10 5, Y t 1 for M 100GeV Keep M free and look for theoretical predictions (grand unification) LBV09-MADISON 13

14 Origin of neutrino mass: seesaw fermion singlet N (1 C, 1 W, Y = 0) TYPE I SEESAW Minkowski, 77; Mohapatra, G.S., 79 Gell-Mann et al, 79; Glashow, 79; Yanagida, 79 boson weak triplet (1 C, 3 W, Y = 2) TYPE II SEESAW Lazarides et al, 80; Mohapatra, G.S., 80 fermion weak triplet T F (1 C, 3 W, Y = 0) TYPE III SEESAW Foot et al, 86 I and II very well studied, III almost ignored in the past LBV09-MADISON 14

15 type I, III: mediators fermionic singlets (triplets) - at least two needed H H ν N N ν Y D T F T F YD Integrate N(T F ) out: Y Y 2 D M 100GeV : Y D 10 6 LBV09-MADISON 15

16 type II: mediator = bosonic (1, 3, 2) (one is enough) H H ν ν Y integrate out M ν = Y v Y possibly large if v small ( natural = controlled by lepton number) LBV09-MADISON 16

17 Seesaw scenario: add new heavy particles and integrate them out talks by Bajc, Gavela, Tulin by itself not more useful than just Weinberg operator: trade physical couplings Y in d=5 to unknown masses of new particles and unknown (unphysical) couplings such as Y D or Y however, new phenomenology LBV09-MADISON 17

18 side remark: infinitely many see-saws if you add more than one (type) particle; to have a coupling: L - Higgs - fermion Higgs iso-spin 3/2, fermion iso-spin 2 (seesaw IV) Higgs iso-spin 2, fermion iso-spin 5/2 (seesaw V) Higgs iso-spin 5/2, fermion iso-spin 3 (VI) Higgs iso-spin 3, fermion iso-spin 7/2 (VII)... LBV09-MADISON 18

19 Fermi theory of low energy weak interactions: PERTURBATIVE CUT-OFF: 300 GeV effective four fermion interaction preferred to the W picture for more than two decades until we had a theory of W (and Z) : SU(2) L U(1) correlates different processes at low energies E << M W M W scale reached only a decade later LBV09-MADISON 19

20 The theory behind L-R symmetric theories Pati, Salam; Mohapatra, G.S., 74,75 SU(2 L ) SU(2) R U(1) B L W L implies W R : parity restoration at high energy ν L implies ν R (N): massive neutrinos LBV09-MADISON 20

21 seesaw: connects neutrino mass to scale of parity restoration M N M WR m ν M 2 W L /M WR Minkowski 77; Mohapatra, G.S. 79 V-A limit: M WR infinite neutrinos massless VIOLATION OF LEPTON NUMBER LBV09-MADISON 21

22 Neutrino-less double beta decay n p W e m ν e W n p LBV09-MADISON 22

23 76 Ge 76 Se ee ν ν T 1/ yr cannot decay into 76 As - heavier for Majorana neutrino masses 76 Ge 76 Se ee (HMBB) Heidelberg - Moscow: T 1/ yr IGEX (International GErmanium Experiment) T 1/ yr CUORICINO (test for CUORE - Cryogenic Underground Observatory for Rare Events) NEMO3 (Neutrino Ettore Majorana Observatory) LBV09-MADISON 23

24 future - probe yr CUORE (Cryogenic Underground Observatory for Rare Events) EXO (Enriched Xenon Observatory) GERDA (GERmanium Detector Array) SuperNEMO LBV09-MADISON 24

25 A LL M ν ee p GeV 1 (p 100MeV ) probes ee element of the neutrino mass matrix: eV M ee ν = ΣU 2 ei m i = cos 2 θ 13 (m 1 e 2iβ cos 2 θ 12 + m 2 e 2iα sin 2 θ 12 ) + m 3 sin 2 θ 13 Depends on hierarchy normal: m 1 m 2 m 3 inverse: m 3 m 1 m 2 degenerate: m 1 m 2 m 3 talk by Atre LBV09-MADISON 25

26 OITSK 1 disfavoured by 0Ν2Β 10-1 disfavoured by cosmology.1 1 in ev mee in ev % CL (1 dof) m 2 23 <0 m 2 23 >0 disfavoured by cosmology lightest neutrino mass in ev LBV09-MADISON 26

27 nucleus Present bound on m ee /h in ev 76 Ge 0.35 HM 76 Ge 0.38 IGEX 130 Te 0.42 Cuoricino 100 Mo 1.7 NEMO3 136 Xe 2.2 DAMA/LXe Sensitivity to m ee /h in ev.025 GERDA.025 MAJORANA.033 CUORE.052 EXO.055 SuperNEMO Table 1: Left: present constraints at 90% CL. Right: future sensitivities. The factor h 1 reminds that 0ν2β elements are uncertain. h - uncertainty in nuclear physics new GERDA: ev Strumia, Vissani 2007 talk by Engel LBV09-MADISON 27

28 SM with Majorana neutrino NOT complete in general m ν not directly connected to ν0ββ decay: depends on the completion of the SM Example: W R contribution even with y D, m ν 0 LBV09-MADISON 28

29 n p W R e m N e W R n p ( ) 4 A RR ML 1 M R M N 10 8 GeV for M R 2T ev and M N 100GeV Mohapatra, G.S., 80 LBV09-MADISON 29

30 ββ0ν NOT necessarily a probe of neutrino mass still, in the context of SM measures m ee and thus Majorana phases not enough to probe the origin of neutrino mass LBV09-MADISON 30

31 Colliders To trace see-saw : measure L = 2 in colliders Keung, G.S., 83 produce right-handed neutrinos through W R j W R d N j l W R ū l LBV09-MADISON 31

32 direct test of parity restoration direct test of lepton number violation determination of W R and N masses Ferrari et al, 99 Gninenko et al, 07 LHC: probes W R up to 3 TeV and ν R in GeV for integrated luminosity of 30 fb 1 talk by Mellado LBV09-MADISON 32

33 of course, you can trade W R for W L - only needs huge cancellations in Yukawas - a long shot talks by Atre and Bajc for other possibilities: can be used to measure seesaw parameters - in particular Majorana phases talks by Bajc and Wang a Tao of L violation@colliders (and collaborators) LBV09-MADISON 33

34 one can give up L-R, but keep B-L (gauged - still needs N) talks by Blanchet, Spinner interesting in itself, and more freedom - the scale can be low even in GUT talk by Nelson B-L gauge boson as light as 10 MeV! - just forget about unification LBV09-MADISON 34

35 Determining the scale seesaw scale: GRAND UNIFICATION LBV09-MADISON 35

36 SO(10) : a predictive L-R theory minimal models predict neutrino masses and mixings but M R large: GeV SU(5) more interesting for colliders Bajc talk LBV09-MADISON 36

37 GUTs and PROTON DECAY Pati, Salam 73, 74 Georgi, Glashow 74 charge quantization gauge coupling unification magnetic monopoles proton decay predicts Goldhaber: many rushed underground LBV09-MADISON 37

38 Proton decay rush calorimeter Kolar Gold Field - Kolar district (Kamataka, India) NUSEX - Mont Blanc (Alps, France) FREJUS - Frejus tunnel (Alps, France) SOUDAN- Soudan underground mine (Minnesota, US) Cherenkov IMB - Morton salt mine (Ohio, US) Kamiokande - Mozumi mine (Hida, Japan) atmospheric neutrino oscillations Super-Kamiokande talk by Kearns LBV09-MADISON 38

39 Channel τ p (10 33 years) p e + π p µ + π p µ + K p e + K p νk (1.5?) n e + K 0.02 n e K important to improve indication of low scale LBV09-MADISON 39

40 Minimal SU(5) Georgi, Glashow 74 caused the underground rush: fast proton decay τ p yr Higgs: 24 H (GUT Higgs)+5 H (SM Higgs) matter: 3(10 F + 5 F ) asymmetric matter, fine tuning (D-T splitting) - but simple and predictive LBV09-MADISON 40

41 if NO higher dimensional operators: p decay branching ratios predicated only V CKM mixings Mohapatra, 79 bad mass relations: m d = m e LBV09-MADISON 41

42 RULED OUT gauge couplings do not unify even with thresholds: 24 H = (8 c, 1 W ) + (1 c, 3 W ) + (1 c, 1 W ) + goldstones neutrinos massless (as in the SM) LBV09-MADISON 42

43 α 3 α 2 α 1 log(e/gev ) LBV09-MADISON 43

44 Minimal extensions that cure both problems: talk of Bajc LBV09-MADISON 44

45 15 H : type II seesaw 15 H = (1 C, 3 W ) + (6 C, 1 W ) + [(3 C, 2 W ) leptoquarks] possibly light leptoquarks Doršner, Fileviez Pérez 05 LBV09-MADISON 45

46 24 F : type I + III seesaw PREDICTIVE 24 F = (8 C, 1 W ) + (1 C, 3 W ) + (1 C, 1 W ) + (3 C, 2 W ) + ( 3, 2 W ) less than TeV light triplet fermion - LHC decays violate lepton number and probe neutrino mass matrix Bajc, G.S. 06 Bajc, Nemevšek, G.S. 07 Arhrib, Bajc, Ghosh, Han, Huang, Puljak, G.S. 09 LBV09-MADISON 46

47 PROTON DECAY both cases fast proton decay: τ p yr LBV09-MADISON 47

48 underground rush continues MINIMAL SUPERSYMMETRIC SU(5) Dimopoulos, Georgi 81 low energy supersymmetry stabilize hierarchy sin 2 θ W = great success when confirmed by LEP Ibanez, Ross 80 Dimopulos, Raby, Wilczek 80 Einhorn, Jones 81 Marciano, G.S. 81 LBV09-MADISON 48

49 α 3 α 2 α 1 log(e/gev ) LBV09-MADISON 49

50 supersymmetric unification heavy top Marciano, G.S experiment: sin 2 θ W = 0.21 for ρ 1 grows with ρ Needed: ρ > 1 loops large Y t heavy top: m t 200 GeV LBV09-MADISON 50

51 M GUT GeV (? see below) τ p (d = 6) 10 35±1 yr Seemed out of reach LBV09-MADISON 51

52 New contribution: d = 5 operators through the exchange of heavy color triplet Higgsino (T and T ) (partners of doublets D and D from 5 H and 5 H ) 1 M T qq qẽ Weinberg 82 Sakai, Yanagida 82 LBV09-MADISON 52

53 u y u ẽ c ē T gaugino T u d y d d c talks by Nath, Pati LBV09-MADISON 53

54 G T q q q l B-L conserved as before G T α 4π y u y d m gaugino M T m 2 f GeV 2 for y u y d 10 4 m gaugino 100 GeV m f TeV M T GeV τ p(d = 5) yr RULED OUT!? LBV09-MADISON 54

55 uncertainties: f spectrum and mixings Bajc, Fileviez-Pérez, G.S. 02 wrong mass relations: m e = m d correct mass relations lose connection between D and T couplings LBV09-MADISON 55

56 cure for bad mass relations: higher dimensional operators Ellis, Gaillard 79 increase M GUT Bachas, Fabre, Yanagida 96 increase M T Bajc, Fileviez-Pérez, G.S H = (8 c, 1 W ) + (1 c, 3 W ) + (1 c, 1 W ) + goldstones split the triplet and octet masses: threshold effects LBV09-MADISON 56

57 ( ) M GUT = MGUT 0 M 0 1/2 GUT 2m 8 ( ) 5/2 M T = MT 0 m 3 m 8 M 0 GUT GeV M 0 T GeV Murayama, Pierce 01 d = 4 m 3 = 4m 8 M T = 32M 0 T 1017 GeV M GUT (m GeV) τ p 10 3 τ 0 p (d = 5) yr Bajc, Fileviez-Pérez, G.S. 02 LBV09-MADISON 57

58 Minimal Supersymmetric SU(5) VIABLE Prediction : p K + ν µ dominant B-L accidental symmetry in proton decay: qqql??? LBV09-MADISON 58

59 R(p) must be broken neutrino masses...+ λ 1 u c d c d c + λ 2 q l d c = d c mediates d = 6 proton decay = λ 1 λ (=?) possible decay: n e + K + B + L conserving B - L violating Vissani 96 LBV09-MADISON 59

60 R(p) breaking = unstable neutralino L 0 at colliders neutrino gaugino mixing Θ ν gaugino mν M gaugino only possible DM in the minimal model: gravitino LBV09-MADISON 60

61 3/2 γ + ν Γ(3/2 γν) = 1 32π m 3 3/2 M 2 P l GeV Θ 2 ν gaugino 1 32π m 3 3/2 M 2 P l (τ sec) m ν M gaugino m 3/2 10 GeV talk by Porod for more possibilities beyond MSSM Buchmuller SUSY09 LBV09-MADISON 61

62 SO(10) Georgi 74 ; Fritzch, Minkowski 74 Unifies a fermion family: 16 F Right-handed neutrino: N M N M W : see-saw Supersymmetry: R(p) = gauge symmetry Mohapatra 86 Renormalizable version R(p) remains exact LSP stable DM Aulakh, Benakli, G.S. 96 ; Aulakh et al. 00 LBV09-MADISON 62

63 More Higgs 10 H + (126 H N mass) Deshpande, Keith, Pal 93 Acampora et al. 94 Bajc, Melfo, G.S., Vissani 05 Bertolini, Di Luzio, Malinsky 09 NO realistic predictive model LBV09-MADISON 63

64 Supersymmetric SO(10) Aulakh, Mohapatra 82 Clark, Kuo, Nakagawa 82 Babu, Mohapatra 92 Bajc, G.S., Vissani 02 Aulakh, Bajc, Melfo, G.S., Vissani H H (holomorphic) predictive (no higher dimensional operators) LBV09-MADISON 64

65 after initial success... tension between neutrino mass and proton decay when pinned down precisely seems to work only with m M W (split supersymmetry) d = 6 p-decay with predicted branching ratios and fast overall decay (borderline) Bajc, Doršner, Nemevšek 08 example of how model may decide on the low energy effective theory Bajc, G.S. 04 LBV09-MADISON 65

66 Partial mean life (10 33 years) p decay modes Model predictions Lifetime bounds Fraction (Γ i /Γ) p π 0 e > % p π 0 µ > % p K 0 e > % p K 0 µ > % p ηe > % p ηµ > % p K + ν > % p π + ν 10.9 > % LBV09-MADISON 66

67 126 H 16 H breaks R(p) Babu, Barr, Raby, Lucas, Dermisek, Mohapatra, Berezhiani, Nesti, Pati, Tavartkiladze, Wilczek... GUT not sufficient, needs physics beyond. Some rather detailed studies of textures and sfermion spectrum talks by Pati, Raby more ambitious (apparentely): one Higgs only (144 H ) - needs more matter - trade-off talk by Nath LBV09-MADISON 67

68 no consensus on the simple predictive theory LBV09-MADISON 68

69 GUT: generic predictions? M GUT M W effective operator expansion SM symmetry: SU(3) SU(2) U(1) expansion in M W /M B or m p /M B where M B is the scale responsible for p decay (GUT with desert picture: M B = M GUT ) LBV09-MADISON 69

70 leading d = 6: only 4 operators O 1 = (u R d R ) (q L l L ) O 2 = (q L q L ) (u R e R ) gauge boson and scalar O 3 = (q L q L ) (q L l L ) O 4 = (u R d R ) (u R e R ) scalar Weinberg 79; Wilczek, Zee 79; Abbott, Wise 80 gauge meson dominance red (only two operators) B-L automatic accidental talk by Doršner LBV09-MADISON 70

71 Isospin relations Γ(p l + R π0 ) = 1 2 Γ(n l+ R π ) = 1 2 Γ(p νπ+ ) = Γ(n ν π 0 ) Γ(p l + L π0 ) = 1 2 Γ(n l+ L π ) s goes out p K + ν n K + l n K l + and more (not completely generic) Weinberg 81 Weldon, Zee 81 Fileviez Pérez 04 LBV09-MADISON 71

72 R(p) violation n K + e Vissani 96 d s d l H / m 3 in GUT: m M GUT suppression : M W /M GUT also n π + e LBV09-MADISON 72

73 MESSAGE n K + e n K e + low energy source of proton decay limits roughly yr urge experimentalists to improve them LBV09-MADISON 73

74 Proton decay: matrix elements non-relativistic quark model, bag model, chiral lagrangians, lattice Ioffe 81 Tomozawa 82 Krasnikov, Pivovarov, Tavkhelidze 82 Meljanac, Palle, Picek, Tadic 82 Donoghue, Golowich 82 Claudson, Hall, Wise 82 Brodsky et al. 84 Gavela et al. 89 Tsutsui et al. 04 Claudson, Hall, Wise 82 LBV09-MADISON 74

75 lattice still in progress Aoki, Dawson, Noaki, Soni 06 chiral langrangians + lattice leading terms in (momentum/gev) expansion Claudson, Hall, Wise 82 Aoki et al 08 LBV09-MADISON 75

76 two coefficients: α (Vector Meson) and β (Scalar Meson): Lattice α = ± (stat) ± (syst) GeV 3 β= ± (stat) ± (syst) GeV 3 Aoki et al 08 works best for soft pions but here momentum up to 500 MeV. Higher orders? LBV09-MADISON 76

77 Grand Unification: NO complete accepted theory most models: τ p yr especially SUSY minimal SU(5) ruled out- minimal extension LHC physics minimal SUSY SU(5) viable gravitino unstable dark matter LBV09-MADISON 77

78 test of GUT desert picture limits yr n K + l n K l + above decays - low energy physics, below TeV connection between p decay and LHC LBV09-MADISON 78

79 Proposed experiments HYPER-Kamiokande Cherenkov detector - MEGATON 3M -(Megaton, Modular, Multipurpose) Homestake - DUSEL (Deep Underground Science and Engineering Lab) MEMPHYS - (MEgaton Mass PHYSics) Fréjus - LAGUNA (Large Apparatus Grand Unification and Neutrino Astrophysics) project p l + π 0 LBV09-MADISON 79

80 Liquid Argon Detector kt LANNDD (Liquid Argon Neutrino Nucleon Decay Detector) Homestake - DUSEL? GLACIER (Giant Liquid Argon Charge Imaging ExpeRiment) Europe - Laguna Liquid scintillator - 50 kt LENA (Low Energy Neutrino Astronomy) Europe - Laguna p νk + LBV09-MADISON 80

81 talk by Kearns rather realistic (pessimistic) - expect yr by 2040!? I for one can wait, but hope he is wrong LBV09-MADISON 81

Proton decay theory review

Proton decay theory review Borut Bajc J. Stefan Institute, Ljubljana, Slovenia Lyon, 12 1 Introduction STANDARD MODEL: renormalizable level: accidental B and L conservation (no invariants that violate