Lepton Flavor Violation in Left-Right theory

Transcription

1 Lepton Flavor Violation in Left-Right theory Clara Murgui IFIC, Universitat de Valencia-CSIC

2 References This talk is based on: P. Fileviez Perez, C. Murgui and S. Ohmer, Phys. Rev. D 94 (2016) no.5, [arxiv: [hep-ph]], P. Fileviez Perez and C. Murgui, Phys. Rev. D 95 (2017) no.7, [arxiv: [hep-ph]].

3 Motivation

4 Left-Right symmetry

5 Aesthetics Left-Right symmetry

6 Aesthetics Left-Right symmetry

7 Aesthetics Left-Right symmetry

8 Left-Right symmetry Aesthetics

9 Left-Right symmetry Aesthetics

10 Left-Right symmetry Aesthetics Origin of P parity violation naturally explained

11 Left-Right symmetry Aesthetics Origin of P parity violation naturally explained m ν 0 as a natural output

12 Left-Right symmetry Aesthetics Origin of P parity violation naturally explained m ν 0 as a natural output [J. C. Pati and A. Salam, 1974], [R. N. Mohapatra and J. C. Pati, 1975] [G. Senjanovic and R. N. Mohapatra, 1975]

13 Aims Build the simplest LR theory with Majorana neutrinos.

14 Aims Build the simplest LR theory with Majorana neutrinos. Study phenomenological implications of Lepton Flavor Violation in its context.

15 Introduction

16 Minimal content in LR models G. Senjanovic, Nucl. Phys. B 153 (1979) 334. Gauge symmetry: SU(2) R SU(2) L U(1) B L

17 Minimal content in LR models G. Senjanovic, Nucl. Phys. B 153 (1979) 334. Gauge symmetry: SU(2) R SU(2) L U(1) B L Matter content: Q L = l L = ( ul ( νl ) (2, 1, 1/3), d L ) Q R = (2, 1, 1), l R = e L ( νr ( ur e R ) (1, 2, 1/3), d R ) (1, 2, 1).

18 Minimal content in LR models G. Senjanovic, Nucl. Phys. B 153 (1979) 334. Gauge symmetry: SU(2) R SU(2) L U(1) B L Matter content: Q L = l L = ( ul ( νl ) (2, 1, 1/3), d L ) Q R = (2, 1, 1), l R = e L ( νr ( ur ( φ 0 Scalar content: Φ = 1 φ + ) 2 φ 1 φ 0 (2, 2, 0), 2 e R ) (1, 2, 1/3), d R ) (1, 2, 1). L Y = Q L (Y 1 Φ + Y 2 Φ)QR + l L (Y 3 Φ + Y 4 Φ)lR

19 Breaking spontaneously the symmetry

20 Breaking spontaneously the symmetry Φ is not enough :(

21 Breaking spontaneously the symmetry Φ is not enough :(

22 Breaking spontaneously the symmetry Φ is not enough :( Doublets H L and H R [G. Senjanovic, 1978] Triplets L and R [R. N. Mohapatra and G. Senjanovic, 1975] Dirac neutrinos Majorana neutrinos

23 Up for Majorana neutrinos

24 Simple Left Right model [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv: ]

25 Simple Left Right model [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv: ] Extra content: ( ) H + H L = L HL 0 (1, 2, 1), H R = ( ) H + R HR 0 (2, 1, 1) and δ + (1, 1, 2)

26 Simple Left Right model [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv: ] Extra content: ( ) H + H L = L HL 0 (1, 2, 1), H R = ( ) H + R HR 0 (2, 1, 1) and δ + (1, 1, 2) Minimal (d.o.f) LR with triplets LR doublets + singlet Scalar content L (1, 3, 2) R (3, 1, 2) H L (1, 2, 1) H R (2, 1, 1) δ + (1, 1, 2) d.o.f. 6 5

27 Simple Left Right model [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv: ] Extra content: ( ) H + H L = L HL 0 (1, 2, 1), H R = ( ) H + R HR 0 (2, 1, 1) and δ + (1, 1, 2) Minimal (d.o.f) BUT extra couplings:

28 Simple Left Right model [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv: ] Extra content: ( ) H + H L = L HL 0 (1, 2, 1), H R = ( ) H + R HR 0 (2, 1, 1) and δ + (1, 1, 2) Minimal (d.o.f) BUT extra couplings: Assumption: LR symmetry explicity broken λ L λ R

29 Simple LR: Neutrino masses L Y Q L (Y 1 Φ + Y 2 Φ)QR + l L (Y 3 Φ + Y 4 Φ)lR < Φ >= ( ) v1 0 0 v 2, Fermion masses M U = Y 1 v 1 + Y 2 v 2 M D = Y 1 v 2 + Y 2 v 1 M E = Y 3 v 2 + Y 4 v 1 M D ν = Y 3 v 1 + Y 4 v 2

30 Simple LR: Neutrino masses L Y Q L (Y 1 Φ + Y 2 Φ)QR + l L (Y 3 Φ + Y 4 Φ)lR < Φ >= ( ) v1 0 0 v 2, Fermion masses M U = Y 1 v 1 + Y 2 v 2 M D = Y 1 v 2 + Y 2 v 1 M E = Y 3 v 2 + Y 4 v 1 M D ν = Y 3 v 1 + Y 4 v 2 In the limit Y 3 Y 4 and v 2 v 1, M D ν is tiny M E Y 4 v 1 ( Mν D v ) 2 = v 1 Y 3 + M E v 1 2

31 Simple LR: Neutrino masses [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv: ] L λ L l L l L δ + + λ R l R l R δ + + λ 1 H T L iσ 2 ΦH R δ + λ 2 H T L iσ 2 ΦHR δ + h.c. H 0 L H 0 R δ + φ + j ν L/R e e ν L/R φ 0 i

32 Simple LR: Neutrino masses [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv: ] L λ L l L l L δ + + λ R l R l R δ + + λ 1 H T L iσ 2 ΦH R δ + λ 2 H T L iσ 2 ΦHR δ + h.c. H 0 L H 0 R δ + φ + j ν L/R e e ν L/R φ 0 i

33 Simple LR: Neutrino masses [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv: ] L λ L l L l L δ + + λ R l R l R δ + + λ 1 H T L iσ 2 ΦH R δ + λ 2 H T L iσ 2 ΦHR δ + h.c. H 0 L H 0 R δ + φ + j ν L/R e e ν L/R φ 0 i

34 Simple LR: Neutrino masses [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv: ] L λ L l L l L δ + + λ R l R l R δ + + λ 1 H T L iσ 2 ΦH R δ + λ 2 H T L iσ 2 ΦHR δ + h.c. H 0 L H 0 R δ + φ + j ν L/R e e ν L/R (M L ν) αγ = (M R ν) αγ = 1 φ 0 i 4π 2 λαβ L me β 1 4π 2 λαβ R me β ( ) M 2 ] hi Log V 5i [(Y 3 )βγ V2i (Y 4 )βγ V1i + α γ, i m 2 e β ( ) M 2 ] hi Log V 5i [(Y 3) βγ V1i (Y 4) βγ V2i + α γ. i m 2 e β

35 Simple LR: Low scale see-saw [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv: ] ( ( ) ( ) νl (ν R ) c) Mν L m D ν νl m D ν Mν R (ν R ) c

36 Simple LR: Low scale see-saw [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv: ] ( ( ) ( ) νl (ν R ) c) Mν L m D ν νl m D ν Mν R (ν R ) c

37 Simple LR: Low scale see-saw [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv: ] ( ( ) ( ) νl (ν R ) c) Mν L m D ν νl m D ν Mν R (ν R ) c M αγ ν [(md ν ) αγ ] 2 (M R ν) αγ M αγ N (M R ν) αγ = 1 4π 2 λαβ R m e β i Log ( M 2 hi m 2 e β ) V 5i [ Y βγ 3 V 1i m e β δ βγ v 1 V 2i ] + α γ

38 Simple LR: Neutrino hierarchy M αγ N 1 4π 2 λαβ R [P. Fileviez Perez and C. Murgui, arxiv: ] m e β i Log ( M 2 hi m 2 e β ) V 5i [ Y βγ 3 V 1i m e β δ βγ v 1 V 2i ] + α γ

39 Simple LR: Neutrino hierarchy M αγ N 1 4π 2 λαβ R [P. Fileviez Perez and C. Murgui, arxiv: ] m e β i Log ( M 2 hi m 2 e β ) V 5i [ Y βγ 3 V 1i m e β δ βγ v 1 V 2i ] + α γ Limit v 2 v 1 and Y 3 Y 4,

40 Simple LR: Neutrino hierarchy M αγ N 1 4π 2 λαβ R [P. Fileviez Perez and C. Murgui, arxiv: ] m e β i Log ( M 2 hi m 2 e β ) V 5i [ Y βγ 3 V 1i m e β δ βγ v 1 V 2i ] + α γ Limit v 2 v 1 and Y 3 Y 4, (M N ) αβ 4π 2 v λ αβ R (m2 e α m 2 e β ) 1

41 Simple LR: Neutrino hierarchy M αγ N 1 4π 2 λαβ R [P. Fileviez Perez and C. Murgui, arxiv: ] m e β i Log ( M 2 hi m 2 e β ) V 5i [ Y βγ 3 V 1i m e β δ βγ v 1 V 2i ] + α γ Limit v 2 v 1 and Y 3 Y 4, (M N ) αβ 4π 2 v λ αβ R (m2 e α m 2 e β ) 1

42 Build new theory, So far...

43 So far... Build new theory, with usual properties of a LR theory,

44 So far... Build new theory, with usual properties of a LR theory, with simplest higgs sector to generate Majorana neutrinos,

45 So far... Build new theory, with usual properties of a LR theory, with simplest higgs sector to generate Majorana neutrinos, which predicts light sterile neutrinos.

46 So far... Build new theory, with usual properties of a LR theory, with simplest higgs sector to generate Majorana neutrinos, which predicts light sterile neutrinos. Study phenomenological implications of Lepton Flavor Violation in its context.

47 Lepton Flavor Violation

48 Current Status CLFV LFV process Current limit Projected limit µ eγ 4, MEG, MEG-II τ eγ 3, BaBar, Super KEKB τ µγ 4, BaBar, Super KEKB µ eee SINDRUM, Mu3e µal eal COMET Mu2e µti eti 4, SINDRUM II, 1993? µau eau SINDRUM II, 2006 µpb epb 4, SINDRUM II, 1996

49 Current Status CLFV

50 LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv: ] l i l j γ: W + R/L γ δ + j γ µ ν i/n i e µ ν i/n i e (a) (b)

51 LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv: ] ( ) L g 2 e m µ m 2 R 64π 2 MW 2 (V N ) ei (VN) µi F Ni R m 2, i W R ( ) R g 2 e m µ m L 64π 2 MW 2 (V ν ) ei (Vν 2 ) µi F νi L m 2, W L A WR A WL i F(x) = 1 6(1 x) 4 ( x + 78 x 2 49 x x 3 Log(x) + 4 x 4),

52 LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv: ] ( ) L g 2 e m µ m 2 R 64π 2 MW 2 (V N ) ei (VN) µi F Ni R m 2, i W R ( ) R g 2 e m µ m L 64π 2 MW 2 (V ν ) ei (Vν 2 ) µi F νi L m 2, W L A WR A WL i F(x) = F(x) x (1 x) 4 ( x + 78 x 2 49 x x 3 Log(x) + 4 x 4), Log(x) +3, x

53 LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv: ] ( ) L g 2 e m µ m 2 R 64π 2 MW 2 (V N ) ei (VN) µi F Ni R m 2, i W R ( ) R g 2 e m µ m L 64π 2 MW 2 (V ν ) ei (Vν 2 ) µi F νi L m 2, W L A WR A WL i F(x) = F(x) x (1 x) 4 ( x + 78 x 2 49 x x 3 Log(x) + 4 x 4), Log(x) +3, F(x) x 0 5 x x,

54 LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv: ] ( ) L g 2 e m µ m 2 R 64π 2 MW 2 (V N ) ei (VN) µi F Ni R m 2, i W R ( ) R g 2 e m µ m L 64π 2 MW 2 (V ν ) ei (Vν 2 ) µi F νi L m 2, W L A WR A WL i F(x) = F(x) x (1 x) 4 ( x + 78 x 2 49 x x 3 Log(x) + 4 x 4), Log(x) +3, F(x) x 0 5 x x, F(x) x (1 x).

55 LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv: ] Limit m Ni M WR g 2 e m µ R 128π 2 m Ni M WR g 2 Rm µ 3e 64π 2 m Ni M WR g 2 3 m µ R 1280π 2 MW 2 R A W R L M i W 4 (VN)ei(V N) µim 2 N i R ( i Log m 2 N i M 2 W R ) (V N) ie(v N) iµ 1 m 2 N i i (VN)ei(V N) µi M 2 W R m 2 N i M 2 W R

56 LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv: ] l i l j γ:

57 LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv: ] l i l j γ: A δ+ L = e 4π 2 m µ m 2 δ + i c,d (λ R) ce λ dµ R Vci N (V N) di G G(x) = 1 6x + 3x2 + 2x 3 6x 2 Log(x) 12(1 x) 4 ( m 2 Ni m 2 δ + )

58 LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv: ] l i l j γ: A δ+ L = e 4π 2 m µ m 2 δ + i c,d (λ R) ce λ dµ R Vci N (V N) di G ( m 2 Ni m 2 δ + ) (1)

59 Simple LR: LFV predictions [P. Fileviez Perez and C. Murgui, arxiv: ] µ e conversion: BR(μ e) BR(μ e) DeeMe Mu2e, COMET Ti Au Mδ+ (TeV) BR(μ e) BR(μ e) Mδ+ (TeV) Pb Mδ+ (TeV) 2 DeeMe Mu2e, COMET Al Mδ+ (TeV) 2

60 Conclusions New left-right model with the simplest scalar sector to generate Majorana neutrinos.

61 Conclusions New left-right model with the simplest scalar sector to generate Majorana neutrinos. The model predics light right-handed neutrinos with a peculiar hierarchy.

62 Conclusions New left-right model with the simplest scalar sector to generate Majorana neutrinos. The model predics light right-handed neutrinos with a peculiar hierarchy. Predictions for lepton flavor violating processes testable in the current and new generation of experiments.

63 Thanks for your attention!