Lepton Flavor Violation in Left-Right theory

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

References This talk is based on: P. Fileviez Perez, C. Murgui and S. Ohmer, Phys. Rev. D 94 (2016) no.5, 051701 [arxiv:1607.00246 [hep-ph]], P. Fileviez Perez and C. Murgui, Phys. Rev. D 95 (2017) no.7, 075010 [arxiv:1701.06801 [hep-ph]].

Motivation

Left-Right symmetry

Aesthetics Left-Right symmetry

Left-Right symmetry Aesthetics

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

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

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]

Aims Build the simplest LR theory with Majorana neutrinos.

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

Introduction

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

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

Breaking spontaneously the symmetry

Breaking spontaneously the symmetry Φ is not enough :(

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

Up for Majorana neutrinos

Simple Left Right model [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv:1607.00246]

Simple Left Right model [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv:1607.00246] 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)

Simple Left Right model [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv:1607.00246] 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

Simple Left Right model [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv:1607.00246] 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:

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

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

Simple LR: Neutrino masses [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv:1607.00246] 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

Simple LR: Neutrino masses [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv:1607.00246] 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

Simple LR: Low scale see-saw [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv:1607.00246] ( ( ) ( ) νl (ν R ) c) Mν L m D ν νl m D ν Mν R (ν R ) c

Simple LR: Low scale see-saw [P. Fileviez Perez, C. Murgui and S. Ohmer, arxiv:1607.00246] ( ( ) ( ) 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

Simple LR: Neutrino hierarchy M αγ N 1 4π 2 λαβ R [P. Fileviez Perez and C. Murgui, arxiv:1701.06801] 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

Simple LR: Neutrino hierarchy M αγ N 1 4π 2 λαβ R [P. Fileviez Perez and C. Murgui, arxiv:1701.06801] 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,

Simple LR: Neutrino hierarchy M αγ N 1 4π 2 λαβ R [P. Fileviez Perez and C. Murgui, arxiv:1701.06801] 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

Build new theory, So far...

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

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

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.

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.

Lepton Flavor Violation

Current Status CLFV LFV process Current limit Projected limit µ eγ 4,2 10 13 MEG, 2016 6 10 14 MEG-II τ eγ 3,3 10 8 BaBar, 2010 3 10 9 Super KEKB τ µγ 4,4 10 8 BaBar, 2010 10 9 Super KEKB µ eee 1 10 12 SINDRUM, 1988 10 16 Mu3e µal eal 10 16 COMET 6 10 17 Mu2e µti eti 4,3 10 12 SINDRUM II, 1993? µau eau 7 10 13 SINDRUM II, 2006 µpb epb 4,6 10 11 SINDRUM II, 1996

Current Status CLFV

LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv:1701.06801] 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)

LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv:1701.06801] ( ) 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 ( 10 43 x + 78 x 2 49 x 3 + 18 x 3 Log(x) + 4 x 4),

LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv:1701.06801] ( ) 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 2 3 1 6(1 x) 4 ( 10 43 x + 78 x 2 49 x 3 + 18 x 3 Log(x) + 4 x 4), Log(x) +3, x

LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv:1701.06801] ( ) 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 2 3 1 6(1 x) 4 ( 10 43 x + 78 x 2 49 x 3 + 18 x 3 Log(x) + 4 x 4), Log(x) +3, F(x) x 0 5 x 3 1 2 x,

LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv:1701.06801] ( ) 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 2 3 1 6(1 x) 4 ( 10 43 x + 78 x 2 49 x 3 + 18 x 3 Log(x) + 4 x 4), Log(x) +3, F(x) x 0 5 x 3 1 2 x, F(x) x 1 17 12 + 3 20 (1 x).

LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv:1701.06801] 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

LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv:1701.06801] l i l j γ:

LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv:1701.06801] 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 + )

LFV in simple LR: µ eγ [P. Fileviez Perez and C. Murgui, arxiv:1701.06801] 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)

Simple LR: LFV predictions [P. Fileviez Perez and C. Murgui, arxiv:1701.06801] µ e conversion: 10-10 10-14 10-17 10-20 BR(μ e) BR(μ e) 10-8 10-11 DeeMe Mu2e, COMET Ti 10-14 10-18 10-22 10-26 0.2 0.5 1 Au 2 0.2 Mδ+ (TeV) BR(μ e) BR(μ e) 1 2 10-8 10-11 10-15 -19 10 10-23 0.5 Mδ+ (TeV) 10-11 10-14 10-17 -20 10 Pb 0.2 0.5 1 Mδ+ (TeV) 2 DeeMe Mu2e, COMET Al 0.2 0.5 1 Mδ+ (TeV) 2

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

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.

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.

Thanks for your attention!