Lepton Flavor Violation in Left-Right theory · Left-Right symmetry • Aesthetics • Origin of...

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

•

Left-Right symmetry

• Aesthetics

Left-Right symmetry

• Aesthetics

Left-Right symmetry

• Aesthetics

Left-Right symmetry

• Aesthetics

•

Left-Right symmetry

• Aesthetics

•

Left-Right symmetry

• Aesthetics

• Origin of P parity violation naturally explained

• mν 6= 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]

Left-Right symmetry

• Aesthetics






Left-Right symmetry

• Aesthetics






Aims

� Build the simplest LR theory with Majorana neutrinos.

� Study phenomenological implications of Lepton Flavor Violation in itscontext.

Aims

� Build the simplest LR theory with Majorana neutrinos.


Introduction

Minimal content in LR modelsG. Senjanovic, Nucl. Phys. B 153 (1979) 334.

• Gauge symmetry: SU(2)R ⊗ SU(2)L ⊗ U(1)B−L

• Matter content:

QL =

(uL

dL

)∼ (2, 1, 1/3) , QR =

(uR

dR

)∼ (1, 2, 1/3) ,

`L =

(νL

eL

)∼ (2, 1,−1) , `R =

(νR

eR

)∼ (1, 2,−1) .

• Scalar content: Φ =

(φ0

1 φ+2φ−1 φ0

2

)∼ (2, 2, 0),

−LY = QL(Y1Φ + Y2Φ̃)QR + `L(Y3Φ + Y4Φ̃)`R



• Matter content:

QL =

(uL

dL

)∼ (2, 1, 1/3) , QR =

(uR

dR

)∼ (1, 2, 1/3) ,

`L =

(νL

eL

)∼ (2, 1,−1) , `R =

(νR

eR

)∼ (1, 2,−1) .


(φ0

1 φ+2φ−1 φ0

2

)∼ (2, 2, 0),




• Matter content:

QL =

(uL

dL

)∼ (2, 1, 1/3) , QR =

(uR

dR

)∼ (1, 2, 1/3) ,

`L =

(νL

eL

)∼ (2, 1,−1) , `R =

(νR

eR

)∼ (1, 2,−1) .


(φ0

1 φ+2φ−1 φ0

2

)∼ (2, 2, 0),


Breaking spontaneously the symmetry

• Φ is not enough :(







Doublets HL and HR

[G. Senjanovic, 1978]

• Dirac neutrinos

Triplets ∆L and ∆R

[R. N. Mohapatra and G. Senjanovic, 1975]

• Majorana neutrinos

Up for Majorana neutrinos

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

• “Extra” content:

HL =

(H+

LH0

L

)∼ (1, 2, 1), HR =

(H+

RH0

R

)∼ (2, 1, 1) and δ+ ∼ (1, 1, 2)

• “Minimal” (d.o.f)

Scalar content d.o.f.

LR with triplets ∆L ∼ (1, 3, 2) 6∆R ∼ (3, 1, 2)

LR doublets + singletHL ∼ (1, 2, 1)

5HR ∼ (2, 1, 1)δ+ ∼ (1, 1, 2)



HL =

(H+

LH0

L

)∼ (1, 2, 1), HR =

(H+

RH0

R

)∼ (2, 1, 1) and δ+ ∼ (1, 1, 2)





5HR ∼ (2, 1, 1)δ+ ∼ (1, 1, 2)



HL =

(H+

LH0

L

)∼ (1, 2, 1), HR =

(H+

RH0

R

)∼ (2, 1, 1) and δ+ ∼ (1, 1, 2)





5HR ∼ (2, 1, 1)δ+ ∼ (1, 1, 2)



HL =

(H+

LH0

L

)∼ (1, 2, 1), HR =

(H+

RH0

R

)∼ (2, 1, 1) and δ+ ∼ (1, 1, 2)


• BUT extra couplings:

Assumption: LR symmetry explicity broken→ λL 6= λR



HL =

(H+

LH0

L

)∼ (1, 2, 1), HR =

(H+

RH0

R

)∼ (2, 1, 1) and δ+ ∼ (1, 1, 2)


• BUT extra couplings:

Assumption: LR symmetry explicity broken→ λL 6= λR

Simple LR: Neutrino masses

• −LY ⊃ QL(Y1Φ + Y2Φ̃)QR + `L(Y3Φ + Y4Φ̃)`R

• < Φ >=

(v1 00 v2

), Fermion masses

MU = Y1v1 + Y2v∗2MD = Y1v2 + Y2v∗1ME = Y3v2 + Y4v∗1MDν = Y3v1 + Y4v∗2

• In the limit Y3 � Y4 and v2 � v1, MDν is tiny

ME ≈ Y4v∗1

MDν = v1

(Y3 + ME

v∗2|v1|2

)

Simple LR: Neutrino masses

• −LY ⊃ QL(Y1Φ + Y2Φ̃)QR + `L(Y3Φ + Y4Φ̃)`R

• < Φ >=

(v1 00 v2

), Fermion masses

MU = Y1v1 + Y2v∗2MD = Y1v2 + Y2v∗1ME = Y3v2 + Y4v∗1MDν = Y3v1 + Y4v∗2

• In the limit Y3 � Y4 and v2 � v1, MDν is tiny

ME ≈ Y4v∗1

MDν = v1

(Y3 + ME

v∗2|v1|2

)

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

−L ⊃ λL`L`Lδ+ + λR`R`Rδ

+ + λ1HTL iσ2ΦHRδ

− + λ2HTL iσ2Φ̃HRδ

− + h.c.

νL/R νL/Re e

δ+

H0L H0

R

φ0i

φ+j

(MLν)

αγ=

14π2 λ

αβL meβ

∑i

Log

(M2

hi

m2eβ

)× V5i

[(Y†3 )

βγV∗2i − (Y†4 )βγV∗1i

]+ α↔ γ ,

(MRν)

αγ=

14π2 λ

αβR meβ

∑i

Log

(M2

hi

m2eβ

)× V5i

[(Y3)

βγV∗1i − (Y4)βγV∗2i

]+ α↔ γ .





− + h.c.

νL/R νL/Re e

δ+

H0L H0

R

φ0i

φ+j

(MLν)

αγ=

14π2 λ

αβL meβ

∑i

Log

(M2

hi

m2eβ

)× V5i

[(Y†3 )


]+ α↔ γ ,

(MRν)

αγ=

14π2 λ

αβR meβ

∑i

Log

(M2

hi

m2eβ

)× V5i

[(Y3)


]+ α↔ γ .





− + h.c.

νL/R νL/Re e

δ+

H0L H0

R

φ0i

φ+j

(MLν)

αγ=

14π2 λ

αβL meβ

∑i

Log

(M2

hi

m2eβ

)× V5i

[(Y†3 )


]+ α↔ γ ,

(MRν)

αγ=

14π2 λ

αβR meβ

∑i

Log

(M2

hi

m2eβ

)× V5i

[(Y3)


]+ α↔ γ .





− + h.c.

νL/R νL/Re e

δ+

H0L H0

R

φ0i

φ+j

(MLν)

αγ=

14π2 λ

αβL meβ

∑i

Log

(M2

hi

m2eβ

)× V5i

[(Y†3 )


]+ α↔ γ ,

(MRν)

αγ=

14π2 λ

αβR meβ

∑i

Log

(M2

hi

m2eβ

)× V5i

[(Y3)


]+ α↔ γ .

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

(νL (νR)c

)(MLν mD

ν

mDν MR

ν

)(νL

(νR)c

)

Mαγν ' − [(mD

ν )αγ ]2

(MRν )αγ

MαγN ' (MR

ν )αγ

=1

4π2λαβR meβ

∑i

Log

(M2

hi

m2eβ

)V5i

[Yβγ3 V∗1i −

meβδβγ

v∗1V∗2i

]+ α↔ γ


(νL (νR)c

)(MLν mD

ν

mDν MR

ν

)(νL

(νR)c

)

Mαγν ' − [(mD

ν )αγ ]2

(MRν )αγ

MαγN ' (MR

ν )αγ

=1

4π2λαβR meβ

∑i

Log

(M2

hi

m2eβ

)V5i

[Yβγ3 V∗1i −

meβδβγ

v∗1V∗2i

]+ α↔ γ


(νL (νR)c

)(MLν mD

ν

mDν MR

ν

)(νL

(νR)c

)

Mαγν ' − [(mD

ν )αγ ]2

(MRν )αγ

MαγN ' (MR

ν )αγ

=1

4π2λαβR meβ

∑i

Log

(M2

hi

m2eβ

)V5i

[Yβγ3 V∗1i −

meβδβγ

v∗1V∗2i

]+ α↔ γ

Simple LR: Neutrino hierarchy

[P. Fileviez Perez and C. Murgui, arXiv:1701.06801]

MαγN ' 1

4π2λαβR meβ

∑i

Log

(M2

hi

m2eβ

)V5i

[Yβγ3 V∗1i −

meβδβγ

v∗1V∗2i

]+ α↔ γ

Limit v2 � v1 and Y3 � Y4, (MN)αβ ≈ ∆

4π2v∗1λαβR (m2

eα − m2eβ )



MαγN ' 1

4π2λαβR meβ

∑i

Log

(M2

hi

m2eβ

)V5i

[Yβγ3 V∗1i −

meβδβγ

v∗1V∗2i

]+ α↔ γ

Limit v2 � v1 and Y3 � Y4,

(MN)αβ ≈ ∆


eα − m2eβ )



MαγN ' 1

4π2λαβR meβ

∑i

Log

(M2

hi

m2eβ

)V5i

[Yβγ3 V∗1i −

meβδβγ

v∗1V∗2i

]+ α↔ γ



eα − m2eβ )



MαγN ' 1

4π2λαβR meβ

∑i

Log

(M2

hi

m2eβ

)V5i

[Yβγ3 V∗1i −

meβδβγ

v∗1V∗2i

]+ α↔ γ



eα − m2eβ )

So far...

X� 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...


• with usual properties of a LR theory,

• with simplest higgs sector to generate Majorana neutrinos,• which predicts light sterile neutrinos.


So far...


• with usual properties of a LR theory,• with simplest higgs sector to generate Majorana neutrinos,

• which predicts light sterile neutrinos.


So far...




So far...




Lepton Flavor Violation

Current Status CLFV

LFV process Current limit Projected limitµ→ eγ 4,2× 10−13 MEG, 2016 6× 10−14 MEG-IIτ → eγ 3,3× 10−8 BaBar, 2010 3× 10−9 Super KEKBτ → µγ 4,4× 10−8 BaBar, 2010 ∼ 10−9 Super KEKBµ→ eee 1× 10−12 SINDRUM, 1988 ∼ 10−16 Mu3e

µAl→ eAl ∼ 10−16 COMET6× 10−17 Mu2e

µTi→ eTi 4,3× 10−12 SINDRUM II, 1993 ?µAu→ eAu 7× 10−13 SINDRUM II, 2006µPb→ 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]

• ì → `jγ:

µ νi/Ni e

γW+

R/Lγ

µ νi/Ni e

δ+j

(a) (b)

LFV in simple LR: µ→ eγ


AWRL ≈ g2

Re mµ

64π2M2WR

∑i

(VN)ei(V∗N)µiF

(m2

Ni

m2WR

),

AWLR ≈ g2

Le mµ

64π2M2WL

∑i

(Vν)ei(V∗ν )µiF

(m2νi

m2WL

),

F(x) =1

6(1− x)4

(10− 43 x + 78 x2 − 49 x3 + 18 x3 Log(x) + 4 x4) ,

F(x)x→∞ ∼23

+3Log(x)

x, F(x)x→0 ∼

53−1

2x, F(x)x→1 ∼

1712

+3

20(1−x).



AWRL ≈ g2

Re mµ

64π2M2WR

∑i

(VN)ei(V∗N)µiF

(m2

Ni

m2WR

),

AWLR ≈ g2

Le mµ

64π2M2WL

∑i


(m2νi

m2WL

),

F(x) =1

6(1− x)4

(10− 43 x + 78 x2 − 49 x3 + 18 x3 Log(x) + 4 x4) ,

F(x)x→∞ ∼23

+3Log(x)

x,

F(x)x→0 ∼53−1

2x, F(x)x→1 ∼

1712

+3

20(1−x).



AWRL ≈ g2

Re mµ

64π2M2WR

∑i

(VN)ei(V∗N)µiF

(m2

Ni

m2WR

),

AWLR ≈ g2

Le mµ

64π2M2WL

∑i


(m2νi

m2WL

),

F(x) =1

6(1− x)4

(10− 43 x + 78 x2 − 49 x3 + 18 x3 Log(x) + 4 x4) ,

F(x)x→∞ ∼23

+3Log(x)

x, F(x)x→0 ∼

53−1

2x,

F(x)x→1 ∼1712

+3

20(1−x).



AWRL ≈ g2

Re mµ

64π2M2WR

∑i

(VN)ei(V∗N)µiF

(m2

Ni

m2WR

),

AWLR ≈ g2

Le mµ

64π2M2WL

∑i


(m2νi

m2WL

),

F(x) =1

6(1− x)4

(10− 43 x + 78 x2 − 49 x3 + 18 x3 Log(x) + 4 x4) ,

F(x)x→∞ ∼23

+3Log(x)

x, F(x)x→0 ∼

53−1

2x, F(x)x→1 ∼

1712

+3

20(1−x).


Limit AWRL

mNi � MWR −g2R

e128π2

mµ

M4WR

∑i(VN)ei(V∗N)µim2

Ni

mNi � MWR g2Rmµ

3e64π2

∑i Log

(m2

NiM2

WR

)(VN)ie(V∗N)iµ

1m2

Ni

mNi ∼ MWR g2R

31280π2

mµ

M2WR

∑i(VN)ei(V∗N)µi

M2WR−m2

NiM2

WR



• ì → `jγ:

Aδ+

L =e

4π2

mµm2δ+

∑i

∑c,d

(λ∗R)ceλdµR Vci

N (V∗N)di G

(m2

Ni

m2δ+

)

G(x) =1− 6x + 3x2 + 2x3 − 6x2Log(x)

12(1− x)4



• ì → `jγ:

Aδ+

L =e

4π2

mµm2δ+

∑i

∑c,d


N (V∗N)di G

(m2

Ni

m2δ+

)

G(x) =1− 6x + 3x2 + 2x3 − 6x2Log(x)

12(1− x)4


• ì → `jγ:

Aδ+

L =e

4π2

mµm2δ+

∑i

∑c,d


N (V∗N)di G

(m2

Ni

m2δ+

)(1)

Simple LR: LFV predictions[P. Fileviez Perez and C. Murgui, arXiv:1701.06801]

• µ→ e conversion:

Mu2e, COMET

DeeMe

Ti

0.2 0.5 1 2

10-20

10-17

10-14

10-11

10-8

Mδ+ (TeV)

BR(μ

→e)

Au

0.2 0.5 1 2

10-26

10-22

10-18

10-14

10-10

Mδ+ (TeV)

BR(μ

→e)

Pb

0.2 0.5 1 2

10-23

10-19

10-15

10-11

Mδ+ (TeV)

BR(μ

→e)

DeeMe

Mu2e, COMET

Al

0.2 0.5 1 2

10-20

10-17

10-14

10-11

10-8

Mδ+ (TeV)

BR(μ

→e)

Conclusions

• New left-right model with the simplest scalar sector to generateMajorana neutrinos.

• The model predics light right-handed neutrinos with a peculiarhierarchy.

• Predictions for lepton flavor violating processes testable in the currentand new generation of experiments.

Conclusions




Conclusions




Thanks for your attention!

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