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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 2 / 20
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]
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 3 / 20
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]
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 4 / 20
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 5 / 20
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 6 / 20
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 7 / 20
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 8 / 20
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
BrapproxHѵτ “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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 9 / 20
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 10 / 20
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 11 / 20
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 12 / 20
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]
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 13 / 20
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 14 / 20
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
ò
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%
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 15 / 20
SUSY inverse seesaw
Dependence on Aν
ò
ò
ò
ò
ò
ò
ò
��
��
�
�
�
��
��
��
��
��
��
�
��
�
�
� ��
��
�
�
�
�
��
�
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
�
�
�
�
�
�
�
�
��
��
� �
��
��
�
�
�
��
��
�
��
��
�
�
��
�
�
�
�
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 16 / 20
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 17 / 20
2HDM
Numerical results
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 18 / 20
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 19 / 20
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 20 / 20
Backup
Backup slides
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 1 / 7
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 2 / 7
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 3 / 7
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 4 / 7
Backup
Searching for maximal BrpH Ñ τµq
-22
-20
-20
-18
-19-20
-19
-17
-16
-17
-18
-17
-16
-14
-12
-11
-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 ?
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 5 / 7
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 6 / 7
Backup
Constraints from EWPO
æ
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
à
àà
àààààààààààààààààààààààààààààà
ì
ì
ìì
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
ô
ôô
ôôôôôôôôôôôôôôôôôôôôôôôôôôôôôô
ò
òò
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
æ
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
à
àà
àààààààààààààààààààààààààààààà
ì
ì
ìì
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
ô
ôô
ôôôôôôôôôôôôôôôôôôôôôôôôôôôôôô
ò
òò
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
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 7 / 7
Backup
Cedric Weiland (IPPP Durham) LFV Higgs decays BLV 2017 7 / 7