Low scale seesaw mechanisms and lepton flavour violating ...€¦ · Cedric Weiland (IPPP Durham)´...

Low scale seesaw mechanisms and lepton flavourviolating Higgs decays

Cedric Weiland

Institute for Particle Physics Phenomenology, Durham University, UK

International Workshop on Baryon & Lepton Number Violation 2017Case Western Reserve University

15 May 2017

E. Arganda, M.J. Herrero, X. Marcano and C. W., PRD91(2015)015001 and PRD93(2016)055010

E. Arganda, M.J. Herrero, X. Marcano and C. W., work in progress

N. Haba, C.W. and T. Yamada, work in progress

Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 1 / 20

Massive Neutrinos

Neutrino phenomena

Neutrino oscillations (best fit from nu-fit.org):solar θ12 » 340 ∆m2

21 » 7.5ˆ 10´5eV2

atmospheric θ23 » 420 |∆m223| » 2.5ˆ 10´3eV2

reactor θ13 » 8.50

Absolute mass scale:cosmology Σmνi ă 0.23 eV [Planck, 2016]

β decays mνe ă 2.05 eV [Mainz, 2005; Troitsk, 2011]

Neutrino oscillations “ Neutral lepton flavour violationWhat about charged lepton flavour violation (cLFV) ?

SM: no ν mass term, lepton flavour is conservedñ need new Physics

- Radiative models- Extra dimensions- R-parity violation in supersymmetry- Seesaw mechanisms Ñ ν mass at tree-level

Seesaw mechanisms Ñ+ BAU through leptogenesis


Massive Neutrinos

Charged lepton flavour violation

In the Standard Model: cLFV from higher order processesñ negligible

If cLFV observed:Clear evidence of physics at a higher scaleProbe the origin of lepton mixingProbe the origin of New Physics

Searched for in numerous channels:Radiative decays BrpµÑ eγq ă 4.2ˆ 10´13 [MEG, 2016]

3-body decays Brpτ Ñ 3µq ă 2.1ˆ 10´8 [Belle, 2010]

Meson decays BrpB0d Ñ eµq ă 2.8ˆ 10´9 [LHCb, 2013]

Z decays BrpZ0Ñ eµq ă 1.7ˆ 10´6 [OPAL, 1995]

Neutrinoless muon conversion µ´,Au Ñ e´,Au ă 7ˆ 10´13 [SINDRUM II, 2006]


Massive Neutrinos

A new opportunity

Huge effort to measure Higgs properties: mass, width, couplings

Use the Higgs sector to probe neutrino mass models

Low-scale seesaw: TeV-scale neutrinos + Large Yukawa couplingsñ Possibly large deviations from SM properties in the Higgs sector

To probe diagonal Yukawa couplings: HHH [J.Baglio and C.W., 2017]

To proble off-diagonal components: LFV Higgs decays, e.g.H Ñ τµ: Br ă 1.51% [CMS, PLB749(2015)337]

H Ñ τµ: Br ă 1.43% [ATLAS, EPJC77(2017)70]


Inverse Seesaw

The inverse seesaw mechanism

Lower seesaw scale from approximately conserved lepton numberAdd fermionic gauge singlets νR (L “ `1) and X (L “ ´1)[Mohapatra and Valle, 1986]

Linverse “ ´YνLHνR ´MRνcRX ´

12µXXcX ` h.c.

with mD “ Yνv ,Mν“

¨

˝

0 mD 0mT

D 0 MR

0 MTR µX

˛

‚

mν «m2

D

M2RµX

mN1,N2 « ¯MR `µX

2

X X

νR νR

H

L

H

L

2 scales: µX and MR

Decouple neutrino mass generation from active-sterile mixingInverse seesaw: Yν „ Op1q and MR „ 1 TeVñ within reach of the LHC and low energy experiments


Inverse Seesaw

Diagrams for the ISS (PRD91(2015)015001)

In the Feynman-’t Hooft gauge, sameas [Arganda et al., 2005]:

Formulas adaptedfrom [Arganda et al., 2005]

Diagrams 1, 8, 10dominate at large MR

Enhancement from:-Op1q Yν couplings-TeV scale ni


Inverse Seesaw

Most relevant constraints

Neutrino data Ñ Use specific parametrization(modified Casas-Ibarra (C-I) [Casas and Ibarra, 2001] or µX parametrization)

vYTν “ V:diagp

?M1 ,

?M2 ,

a

M3q R diagp?

m1 ,?

m2 ,?

m3qU:

PMNS

M “ MRµ´1X MT

R

or

µX “ MTR Y´1

ν U˚PMNSdiagp?

m1 ,?

m2 ,?

m3qU:

PMNS YTν´1

MRv2

Charged lepton flavour violationÑ For example: BrpµÑ eγq ă 4.2ˆ 10´13 [MEG, 2016]

Lepton universality violation: less constraining than µÑ eγ

Electric dipole moment: 0 with real PMNS and mass matrices

Invisible Higgs decays: MR ą mH, does not apply

Yukawa perturbativity: | Y2ν

4π | ă 1.5


Inverse Seesaw

Predictions using the modified C-I parametrization

-20

-19

-18-18

-17

-17

-16

-16

-15

-15

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

R = ImΝ1=0.1 eV

MR1=900 GeVMR2=1000 GeV

103 104 105 10610-9

10-8

10-7

10-6

10-5

10-4

MR3 HGeVL

ΜXHG

eVL

Log10BR HH ® ΜΤL

Grows with MR3 and µ´1X due to Yν

growth in C-I parametrization

Similar behaviour with degenerateheavy neutrinos

Excluded by µÑ eγNon-perturbative Yν

BrpH Ñ τµq ď 10´9

Conclusion left (mostly)unchanged from varying R


Inverse Seesaw

Large LFV Higgs decay rates from textures I

Would the LHC observation of LFV Higgs decays exclude the ISS ?Ñ Look for the largest possible BrpH Ñ τµq

Possibility to evade the µÑ eγ constraint ?

Approximate formulas for large Yν :

BrapproxµÑeγ “8ˆ 10´17GeV´4 m5

µ

Γµ|

v2

2M2RpYνY:νq12|

2

BrapproxHÑµτ “10´7 v4

M4R|pYνY:νq23 ´ 5.7pYνY:νYνY:νq23|

2

“pYνY:νq12“0

10´7 v4

M4R|1´ 5.7rpYνY:νq22 ` pYνY:νq33s|

2|pYνY:νq23|2

Ñ Different dependence on the seesaw parameters

Solution: Textures with pYνY:νq12 “ 0 and |Y ijν |

2

4π ă 1.5


Inverse Seesaw

Large LFV Higgs decay rates from textures II

Textures with pYνY:νq12 “ 0 and |Y ijν |

2

4π ă 1.5

Yp1qτµ “ f

¨

˝

0 1 ´10.9 1 11 1 1

˛

‚ , Yp2qτµ “ f

¨

˝

0 1 11 1 ´1´1 1 ´1

˛

‚ , Yp3qτµ “ f

¨

˝

0 ´1 1´1 1 10.8 0.5 0.5

˛

‚

Flavour composition of the heavy neutrinos:

3 very different flavour patterns

Heavy neutrino mixing of τ ´ µ type is always present


Inverse Seesaw

Producing large H Ñ τµ rates

YΤΜH1L

YΤΜH2L

YΤΜH3L

1 5 10 15

10-8

10-7

10-6

10-5

10-4

10-3

MR HTeVL

BR

HH®

ΜΤL

Numerics done with the fullone-loop formulas

Dotted: excluded by τ Ñ µγSolid: allowed by LFV, LUV,Solid: etc

BrmaxpH Ñ µτq „ 10´5

Same maximum branching ratiowith hierarchical heavy N

Similarly, BrmaxpH Ñ eτq „ 10´5 for Ypiqτe (=Ypiqτµ with rows 1 and 2exchanged)

Out of LHC reach, within the reach of future colliders


SUSY inverse seesaw

The supersymmetric inverse seesaw model

MSSM extended by singlet chiral superfields pN and pX with L “ ´1 andL “ `1

Defined by the superpotential:

W “ WMSSM ``Yν pNpLpHu `MRpNpX `12µXpXpX

New couplings, e.g.AYν Yν rNrLHu ` h.c.

Light right-handed sneutrinos:

M2rN “ m2

rN `M2R ` YνY:νv2

u „ p1TeVq2

ñ Natural Yukawa couplings with a TeV new Physics scale


SUSY inverse seesaw

LFV in supersymmetric seesaw models

Typically in SUSY, LFV through RGE-induced slepton mixing p∆m2Lqij

[Borzumati and Masiero, 1986, Hisano et al., 1996, Hisano and Nomura, 1999]

ñ p∆m2Lqij9pY:νYνqijln MGUT

MR

Contribute to all LFV observablesÑ Dominant in most SUSY seesaw models

Type I seesaw (Yν „ 1, MR „ 1014GeV) Ñ p∆m2Lqij95

Inverse seesaw (Yν „ 1, MR „ 1TeV) Ñ p∆m2Lqij930

Ñ one-loop rN-mediated processes are no longer suppressed[Deppisch and Valle, 2005, Hirsch et al., 2010, Abada et al., 2012, Ilakovac et al., 2012,

Krauss et al., 2014, Abada et al., 2014]


SUSY inverse seesaw

LFV Higgs decays from SUSY loops (PRD93(2016)055010)

In the Feynman-’t Hooft gauge, same as [Arganda et al., 2005]:

Formulas adapted from [Arganda et al., 2005]

Enhancement from: -Op1q Yν couplingsEnhancement from: -TeV scale ν


SUSY inverse seesaw

Dependence on MR

ò

ò

ò

ò

ò

ò

ò

ò

ò

òò ò ò ò

ò

ò

ò

ò

ò

ò

ò

ò

òò ò ò ò ò ò ò

ò

ò

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ò

òò

òò ò ò ò ò ò ò ò ò

òò

òò ò ò ò ò ò ò ò ò ò ò ò ò

òò

òò ò ò ò ò ò ò ò ò ò ò ò ò

� �

YΤΜH3L

f = 6 Π

f = 4Π

f = 1

f = 0.1

f = 0.01

AΝ = 0

mL� = mΝ

�R

= mX� = 1 TeV

Μ = 2 TeV

M2 = 750 GeV

2 4 6 8 10 12 1410

-21

10-19

10-17

10-15

10-13

10-11

10-9

10-7

10-5

10-3

MR HTeVL

BR

Hh®

ΤΜ

L

ò

ò

ò

ò

ò

ò

ò

òò

ò

ò

ò

ò

ò

ò

ò

ò

òò ò ò ò

ò

ò

ò

� ��

�

�

�

� �

�

�

�

�

�

��

f = 6 Π

YΤΜH1L

YΤΜH2L

YΤΜH3L

AΝ = 2.5 TeV

mL� = mΝ

�R

= mX� = 1 TeV

Μ = 500 GeV

M2 = 500 GeV

2 4 6 8 10 12 1410

-8

10-7

10-6

10-5

10-4

10-3

10-2

MR HTeVL

BR

Hh®

ΤΜ

L

MR degenerate and real, mA “ 800 GeV,squark parameters safe from LHC (direct searches, Higgs mass)

N: allowed by LFV radiative decays, ˆ: excluded

At low MR: dominated by chargino-sneutrino loopsAt large MR / small f : dominated by neutralino-slepton loops

Can adjust other parameters (Aν , mνR ) to reach Brph Ñ τ µq „ 1%


SUSY inverse seesaw

Dependence on Aν

ò

ò

ò

ò

ò

ò

ò

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�

YΤΜH1L

YΤΜH2L

YΤΜH3L

f = 6 Π

M2 = 750 GeV

Μ = 2 TeV

MR = 1 TeV

mL� = mΝ

�R

= mX� = 1 TeV

-3 -2 -1 0 1 2 310

-6

10-5

10-4

10-3

10-2

10-1

AΝ HTeVL

BR

Hh®

ΤΜ

L

ò

ò

ò

ò

ò

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YΤΜH1L

YΤΜH2L

YΤΜH3L

MR = 1 TeV

mL� = mΝ

�R

= mX� = 1 TeV

M2 = 500 GeV

Μ = 500 GeV

f = 6 Π

-3 -2 -1 0 1 2 310

-6

10-5

10-4

10-3

10-2

10-1

AΝ HTeVL

BR

Hh®

ΤΜ

LMR degenerate and real, mA “ 800 GeV, MR “ mL “ mνR “ mX “ 1 TeV

N: allowed by LFV radiative decays, ˆ: excluded

Aν in both h0 ´ νL ´ νR coupling and νL ´ νR mixingÑ Dips when dominated by chargino loops

Dips in BR(h Ñ τ µ) and BR(τ Ñ µγ) do not exactly coincide


2HDM

2HDM contributions (work in progress)

Goal: complete SUSY calculation

Missing piece: charged Higgs contributions in 2HDM type II + ISS

L “ ´Y`LHd`R ´ YνLHuνR ´MRνcRX ´

12µXXcX ` h.c.

Status: analytical formulas validated through 2 independent calculations


2HDM

Numerical results


2HDM

An alternative low-scale seesaw model

Type 1 seesaw: mν “ ´mTDM´1

R mD

MR „ TeV ñ mD „ MeV ñ Yν „ 10´6 ñ Signals are suppressed

What if mD ď MeV but Yν „ 1 ? Ñ Neutrinophilic 2HDM [Ma, 2001,

Wang et al., 2006, Gabriel and Nandi, 2007, Davidson and Logan, 2009, Haba and Hirotsu, 2010]

L “ ´Y`LH`R ´ YνLHννR ´MRνcRνR ` h.c.

Taking vν ! v leads to tanβ ! 1 and α ď 5β [Machado et al., 2015]

Ñ h0 is SM-like while H0/A0/H˘ couple mostly to neutrinos

Expect different LFV patterns that could be used to distinguish models


Conclusion

Conclusion

cLFV Higgs decays: complementary to other cLFV searches

Enhancement from the inverse seesawbut largest values excluded by τ Ñ µγ / τ Ñ eγ

non-SUSY ISS: BrpH Ñ τµq ď 10´5

non-SUSY ISS: BrpH Ñ τeq ď 10´5

SUSY loops give Brph Ñ τ µq ď Op1%q

SUSY contributions are within the current LHC reach

τµ and τe will be probed at future LHC runs and future colliders

2HDM calculation is done and will be applied to different models tohighlight similarities and differences


Backup

Backup slides


Backup

Constraints: focus on µ Ñ eγ

ΜX = 10-8 GeVΜX = 10-6 GeVΜX = 10-4 GeVΜX = 10-2 GeV

mΝ1 = 0.1 eVR = I

102 103 104 105 106 107

10-35

10-30

10-25

10-20

10-15

10-10

MR HGeVL

BRHΜ®

eΓL

BRl m®l k Γ

approx= 8�10-17GeV-4

ml m

5

Gl m

v2

2 MR2IYΝ YΝ

†Mkm

2

BR HΤ ® ΜΓLBR HΜ ® eΓLBR HΤ ® eΓL

ΜX = 10-7 GeVmΝ1= 0.1 eV

R = I

102 103 104 105 106 10710-16

10-15

10-14

10-13

10-12

MR HGeVL

BR Hlm®lkΓL

MR and µX real and degenerate, Casas-Ibarra (C-I) parametrization

Constrains µX

Perturbativity Ñ |Y2ν

4π | ă 1.5 (Dotted line = non-perturbative couplings)

v2pYνY:νqkm

M2R

« 1µX

pUPMNS∆m2 UTPMNSqkm

2mν1


Backup

Dependence on ISS parameters: µX and MR

·······

····································

·····················

··············································

···································

································

·················································

··················

diag 1 + 8 + 10

approx

full

ΜX=10

-8 GeV

ΜX=10

-6 GeV

ΜX=10

-4 GeV

ΜX=10

-2 GeV

102 103 104 105 106 10710-30

10-25

10-20

10-15

10-10

10-5

MR HGeVL

BRHH®ΜΤL

BRH®ΜΤapprox= 10-7 Iv4 �MR

4 M IYΝ YΝÖM23 -5.7 IYΝ YΝ

ÖYΝ YΝÖM23

2

R “ 1, MR and µX degenerate andreal, C-I parametrization

Dips come from interferencesbetween diagrams

Can be understood using themass insertion approximation

v2pYνY:νqkm

M2R

« 1µX

pUPMNS∆m2 UTPMNSqkm

2mν1and v2

pYνY:νYνY:νqkm

M2R

“M2

RpUPMNS∆m2 UTPMNSqkm

v2µ2X


Backup

Dependence on Casas-Ibarra parameters: R matrix

arg Θ1 = Π4arg Θ1 = Π8arg Θ1 = 0

mΝ1= 0.1eVMR = 104 GeVΜX = 10-7 GeV

0 þ �2 þ10-13

10-11

10-9

10-7

10-5

Θ1

BRHH®ΜΤL

arg Θ1 = Π4arg Θ1 = Π8arg Θ1 = 0

mΝ1= 0.1eVMR = 104 GeVΜX = 10-7 GeV

0 þ �2 þ

10-13

10-11

10-9

10-7

Θ1

BRHΜ®

eΓL

MR and µX degenerate and real

Independent of R for real mixing angles

Increase with complex angles, but increase limited by µÑ eγñ Complex R matrix doesn’t change our results


Backup

Searching for maximal BrpH Ñ τµq

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-14

-12

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-9

-8

-6

-4

R = ImΝ1 = 0.1 eV

-15

-13

-5

-7

-10

200 103 104 105 10610-9

10-8

10-7

10-6

10-5

10-4

MR HGeVL

ΜXHG

eVL

Log10BR HH ® ΜΤL

MR and µX degenerate and real

Excluded by µÑ eγNon-perturbative Yν

BrpH Ñ τµq ď 10´10

End of the story ?


Backup

Impact of the R matrix for hierarchical N

��

BR HH® Μ ΤLBR HH® e ΤL

ΜX = 10-7 GeVmΝ1 = 0.1 eVMR1 = 0.9 TeVMR2 = 1 TeVMR3 = 30 TeV

0 þ �2 þ10-15

10-14

10-13

10-12

10-11

10-10

10-9

Θ2

BR HH ® lk lmLContrary to degenerate case, Rdependence

Varying θ1: Same conclusions asbefore

Dotted = non-perturbativecouplingsCross = Excluded by µÑ eγ

θ2 „ π{4:BrpH Ñ eτq ą BrpH Ñ µτq

Results quite insensitive to θ3


Backup

Constraints from EWPO

æ

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ìì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì

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ò

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òòòòòòòòòòòòòòòòòòòòòòòòòòòòòò

YΤΜH1L = f

0 1 -1

0.9 1 1

1 1 1

ò f= 6 Π

ô f= 4 Π

ì f= 1

à f= 0.5

æ f= 0.1

1 2 3 4 5 6 7 8 9 10

10-33

10-29

10-25

10-21

10-17

MN1HTeVL

ÈV eN1È2

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æ

ææ

ææ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ

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ò

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òòòòòòòòòòòòòòòòòòòòòòòòòòòòòò

YΤΜH1L = f

0 1 -1

0.9 1 1

1 1 1

ò f= 6 Π

ô f= 4 Π

ì f= 1

à f= 0.5

æ f= 0.1

1 2 3 4 5 6 7 8 9 10

10-8

10-6

10-4

10-2

1

MN1HTeVL

ÈV ΤN1È2

Active sterile mixing is controlledby θ „ mDM´1

R

Large mixing Ñ possible conflictwith EWPO

Limits taken from [del Aguila et al., 2008]

at 90% C.L. :

|VeN |2 ă 3.0ˆ 10´3

|VµN |2 ă 3.2ˆ 10´3

|VτN |2 ă 6.2ˆ 10´3


Backup


Low scale seesaw mechanisms and lepton flavour violating ...€¦ · Cedric Weiland (IPPP Durham)´...

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