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New Physics Models Facing Lepton Flavor Violating Higgs Decays Nejc Ko nik with Ilja Dor ner, Svjetlana Fajfer, Admir Greljo, Jernej F. Kamenik, I. Ni and i Based

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SLIDE 1

New Physics Models Facing Lepton Flavor Violating Higgs Decays

Nejc Košnik with Ilja Doršner, Svjetlana Fajfer, Admir Greljo, Jernej F. Kamenik, I. Nišandžić Based on arXiv:1502.07784

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SLIDE 2

Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Introduction

  • Hint of huge Lepton Flavor

Violation in Higgs decay

2

B(h → τµ) =

  • 0.84+0.39

−0.37

  • %

(null hypothesis 2.4σ excluded)

[CMS,1502.07400]

  • Clearly beyond the SM (or SM with Dirac neutrinos)
  • What kind of NP model could accommodate this result and be

consistent with numerous (negative) tests of LFV?

τ → µγ τ → 3µ µ → eγ µN → eN

< 10-7 < 10-13 branching fraction LFV process

Z → `i`j

< 10-5

h → τµ ≈ 10-2

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)
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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Outline

  • 1. Constraints on effective Higgs couplings
  • 2. Effective theory approach
  • 3. Extended scalar sector
  • 4. Extended fermionic sector or loop-induced LFV
  • 5. Summary and outlook

4

Motivation:

  • Find complementary LFV observables
  • Identify viable scenarios
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SLIDE 5

Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)
  • 1. Constraints on effective Higgs

couplings from h→τμ

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SLIDE 6

Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Effective Higgs couplings

6

  • Assuming New Physics only in h→μτ then CMS result gives

B(h → τµ) =

  • 0.84+0.39

−0.37

  • %

0.0019(0.0008) < q |yτµ|2 + |yµτ|2 < 0.0032(0.0036) at 68% (95%) C.L. Leff.

Y` = −miij ¯

`i

L`j R − yij

⇣ ¯ `i

L`j R

⌘ h + . . . + h.c. B(h → τµ) = mh 8πΓh

  • |yτµ|2 + |yµτ|2
  • General parameterisation of the off-diagonal

Yukawa couplings

ySM

ij

= δij mi v

CMS 1σ

0.000 0.001 0.002 0.003 0.004 0.0 0.5 1.0 1.5 2.0 (τμ+μτ)/ ℬ(→τμ) [%]

yµτ h µ τ

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SLIDE 7

Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Effective Higgs couplings

7

  • Testing robustness of the lower bound of LFV

Yukawas: allowing for non- SM Higgs production rate and total decay width

Nh→τµ ∼ σh Γh→τµ Γh

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SLIDE 8

Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Effective Higgs couplings

8

Higgs data fit

() () τμ

0.000 0.002 0.004 0.006 0.008 1 2 3 4 5 6 7 (τμ+μτ)/ χ2

0.0017(0.0007) < q |yτµ|2 + |yµτ|2 < 0.0036(0.0047) at 68% (95%) C.L. Nh→τµ ∼ σh Γh→τµ Γh

  • Well known Higgs production
  • Strong lower bound on Γh

Robust lower bound on the LFV Yukawas

  • Testing robustness of the lower bound of LFV

Yukawas: allowing for non- SM Higgs production rate and total decay width

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)
  • 2. Effective theory approach
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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Effective Theory Framework

10

  • Integrate out heavy Higgses, fermions, scalars. Keep terms up to dim-6:

LY` = −λα

ij ¯

LiHαEj − λ0αβγ

ij

1 Λ2 ¯ LiHαEj(H†

βHγ) + h.c.

yij = mi v ij + ✏ij

Dim-6 operator creates mismatch between mass and Yukawa matrices

✏ = VL  α¯ vα ✓xα ¯ vα − 1 ◆ + 0αβγ v2 Λ2 ¯ vα¯ vβ¯ vγ ✓xα ¯ vα + xβ ¯ vβ + xγ ¯ vγ − 1 ◆ V †

R

Hα = (h+

α, vα + xαh + . . .)T

Multiple higgses

X

α

v2

α ∼ v2/2

X

α

|xα|2 ∼ 1/2

vanishing in single Higgs scenarios

m v = VL ✓ λα¯ vα + λ0αβγ v2 Λ2 ¯ vα¯ vβ¯ vγ ◆ V †

R

Λ ' 4 TeV ✓ 0.84% B(h ! τµ) ◆ ⇣ |VLλ0111V †

R|2 τµ + |VLλ0111V † R|2 µτ

⌘1/4

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Naturalness

11

  • Naturalness criterium for effective Higgs couplings (to avoid cancellations

in the mass matrix)

q |yτµyµτ| . √mµmτ v = 0.0018

CMS hÆtm

68% C.L. 95% C.L.

»ytmymt» > mtmmêv2 0.000 0.001 0.002 0.003 0.004 0.005 0.000 0.001 0.002 0.003 0.004 0.005 »ytm» »ymt»

[Cheng,Sher, Phys.Rev. D35, 3484] [Branco et al,, Phys.Rept. 516, 1]

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Tau LFV radiative decay

12

  • Constraint from τ→μγ

Comparable 1-loop and Barr-Zee contributions

τ τ µ t

τ τ µ

yτµ yτµ

[Harnik, Kopp, Zupan, JHEP 1303, 026] [Goudelis, Lebedev, Park, Phys.Lett. B707, 369 ]

[Blankenburg, Ellis, Isidori, Phys.Lett. B712, 386]

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Additional LFV correlations

13

µ τ e

µ → eγ µN → eN h → τµ h → τe

Suppose that hτe is nonzero.

}

B(µ ! eγ) ' 185

  • |yµτyτe|2 + |yτµyeτ|2

B(µ ! e)Au ' 4.67 ⇥ 10−4 |yeτyµτ|2 + |yτeyτµ|2 B(h → τµ) × B(h → τe) = 7.95 × 10−10 B(µ → eγ) 10−13

  • + 3.15 × 10−4

B(µ → e)Au 10−13

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

h→μτ

  • Vs. h→eτ

14

SINDRUM II, μe conv. on Au < 7×10-13

[Eur.Phys.J. C47, 337 (2006)]

projected Mu2e limit on μe < 6×10-17 τ→eγ < 3.3×10-8

[BaBar. PRL104, 021802 (2010)]

0.19

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)
  • 3. Two Higgs doublet mode (type III)
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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Framework

16

Hd = ✓H0

d

H−

d

◆ , Hu = ✓H+

u

H0

u

◆ H0

u =

1 √ 2

  • H0 sin α + h0 cos α + iA0 cos β
  • H0

d =

1 √ 2

  • H0 cos α − h0 sin α + iA0 sin β
  • H1

u = H+ cos β

H2

u = H− sin β

tan β = vu vd , tan 2α = tan 2β m2

A + m2 Z

m2

A − m2 Z

, m2

H± = m2 A + m2 W

m2

H = m2 A + m2 Z − m2 h

5 physical scalars: h, H0, H±, A

[Crivellin et al, PRD,87,094031 (2013)]

2 parameters: tan β, mA

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Flavor couplings

17

yHk

fi = xk d

m`i vd fi − ✏`

fi

  • xk

d tan − xk∗ u

  • yH±

fi

= √ 2

3

X

j=1

sin V PMNS

fj

✓m`i vd ji − ✏`

ji tan

◆

L = yHk

fi

√ 2 Hk¯ `L,f`R,i + yH+

fi

√ 2 H+¯ ⌫L,f`R,i + h.c.

Charged Higgs couplings Neutral Higges couplings

  • LFV parameters are εlij
  • Type-III THDM: no restrictions on the Higgs couplings to fermions
  • Tree-level Higgs couplings exhibit

➡

Charged and FCN currents in the quark sector (K, D, B meson mixing, rare decays)

➡

Lepton Flavor Violation

  • Decoupling limit of MSSM
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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

h→τμ

18

yµ⌧ (⌧µ) = ✏`

µ⌧ (⌧µ)

√ 2 (sin ↵ tan + cos ↵) B(h → ⌧µ) = mh 16⇡Γh (sin ↵ tan + cos ↵)2 |✏`

µ⌧|2 + |✏` ⌧µ|2

sin α tan β + cos α ' 2m2

Z

m2

A

τ/

ℬ(→τμ)=% β= β=

200 300 400 500 600 700 0.00 0.02 0.04 0.06 0.08 0.10

mA.(GeV)

(ϵτμ

ℓ +ϵμτ ℓ )/

yµτ h µ τ

Effect decouples for large mA

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SLIDE 19

Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Tau LFV decays

19

τ H+ ν µ H+

τ H0

k

τ µ H0

k

yττ yτµ

A1-loop ~ (LFV Yukawa) * (tiny LFC Yukawa) ABarr-Zee ~ (LFV Yukawa) * (loop suppression)

[Chang et al, PRD48, 217(1993)] *Missing contributions at 2-loops with H+ mediator

Dominant Barr-Zee contributions

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

LFV correlations

20

ε

τ μ , μ τ

f r e e d

  • m

ε

τ μ , μ τ , τ τ

f r e e d

  • m

µ

τ τ

= 1 . 2

+ . 2 1 − . 2

[CMS ’14, ATLAS ‘15]

Works up to mA ~ 0.5 TeV

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Two Higgs Doublet Model

21

µ τ e

µ → eγ µN → eN h → τµ h → τe

Correlation with h→τe decay!

B(µ ! e) ' Bµ→eγ (tβ, mA)

  • |✏µτ✏τe|2 + |✏eτyτµ|2

, B(µ ! e)Au ' Bµe

0 (tβ, mA)

  • |✏eτ✏µτ|2 + |✏τe✏τµ|2

B(h → τµ) × B(h → τe) ∼ B(µ → eγ) Bµ→eγ (tβ, mA) + B(µ → e)Au Bµe

0 (tβ, mA)

}

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

22

B(h → τe) < 6 × 10−6

(taking central value for h→τμ)

h→μτ

  • Vs. h→eτ

SINDRUM II, μe conv. on Au < 7×10-13 and MEG μ→eγ <5.7×10-13

[Eur.Phys.J. C47, 337 (2006)]

[PRL110, 201801 (2013)]

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)
  • 4. Extended fermionic sector or loop-induced LFV
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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Vector-like leptons

24

  • Chiral leptons get additional Higgs couplings through mixing with

VL leptons:

−LV LL = λΨ ¯ ΨEH(1 − γ5)ΨL + ˜ λΨ ¯ ΨEH(1 + γ5)ΨL + MΨ

  • λe ¯

EΨE + λl ¯ LΨL + CL ¯ ΨLΨL + CR ¯ ΨEΨE + h.c.

mass terms of VL leptons mixings VL Yukawas

ΨL transforms as (1, 2)1/2 ⊕ (1, 2)−1/2 ΨE transforms as (1, 1)1 ⊕ (1, 1)−1

  • Yukawas with chiral leptons are obtained when

VL leptons are integrated out: A single LFV Yukawa matrix:

✏ = 8v2 M 2

Ψ

lC−1

L ΨC−1 R ˜

ΨC−1

L ΨC−1 R e

[Falkowski et al, JHEP1405, 092 (2014)]

B(h → τµ) B(τ → µγ) = 4π 3α B(h → τ +τ −)SM B(τ → µ¯ νν)SM ≈ 2 × 102

  • ne-to-one correlation:
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SLIDE 25

Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Vector-like leptons

25

B(h → τµ) B(τ → µγ) = 4π 3α B(h → τ +τ −)SM B(τ → µ¯ νν)SM ≈ 2 × 102

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SLIDE 26

Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Scalar leptoquarks

26

t h t Μ Τ

  • h

Τ Μ Μ t

  • h

Τ Μ t

  • Τ

h t Μ Τ

  • ~ portal coupling

~ top Yukawa * (LFV Yukawas)

  • Loop induced LFV
  • Need top-quark mass chiral enhancemet:

⇒ non-chiral LQ ⇒ τ→μγ enhanced in the same way as h→τμ

  • λ decouples the two observables

λv h LQLQ

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

27

L∆1 = yL

ij ¯

ui

L`C j L ∆1 − (V † CKMyL ijVPMNS) ¯

di

L⌫C j L ∆1 + yR ij ¯

ui

R`C j R ∆1 + h.c.

Γ(h → τµ) = 9mhm2

t

213π5v2 ⇣ yL

tµyR tτ

  • 2 +
  • yL

tτyR tµ

  • 2⌘

|g1(λ, m∆1)|2

Δ1(3,1,-1/3)

Scalar leptoquarks

B(τ → µγ) = αm3

τ

212π4Γτ m2

t

m4

∆1

h1(xt)2 ⇣ yL

tµyR tτ

  • 2 +
  • yL

tτyR tµ

  • 2⌘

CMS 1σ Δ = Δ = λ = Δ2 Δ1

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.5 1.0 1.5 2.0 (μ

τ + τ μ )/

ℬ(→τμ) [%]

Δ = Δ = Δ2 Δ1

10-5 10-4 0.001 0.010 0.100 1 10-11 10-8 10-5 10-2 (μ

τ + τ μ )/

ℬ(τ→μγ)

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SLIDE 28

Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

28

Δ1(3,1,-1/3)

Scalar leptoquarks

Portal coupling has an effect on h→γγ and gg→h !

σggF σSM

ggF

= |1 + 0.24λv2 m2

∆

N∆iC(r∆)|2 Γh→γγ ΓSM

h→γγ

= |1 − 0.025λv2 m2

∆

d(r∆) X

i

Q2

∆i|2

λ τμ

0.0 0.2 0.4 0.6 0.8 1.0

  • 2
  • 1

1 2

(μ

τ +τ μ )/

λ /Δ

  • ⇒ λ is bounded from above
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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

29

Δ2(3,2,7/6)

Scalar leptoquarks

CMS 1σ Δ = Δ = λ = Δ2 Δ1

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.5 1.0 1.5 2.0 (μ

τ + τ μ )/

ℬ(→τμ) [%]

Δ = Δ = Δ2 Δ1

10-5 10-4 0.001 0.010 0.100 1 10-11 10-8 10-5 10-2 (μ

τ + τ μ )/

ℬ(τ→μγ)

L∆2 = yL

ij ¯

`i

Rdj L∆2/3 ∗ 2

+ (yLV †

CKM)ij ¯

`i

Ruj L∆5/3 ∗ 2

+ (yRVPMNS)ij ¯ ui

R⌫j L∆2/3 2

− yR

ij ¯

ui

R`j L∆5/3 2

+ h.c. Γ(h → τµ) = 9mhm2

t

213π5v2 |g1(λ, m∆2)|2 |yL

µtyR tτ|2 + |yL τtyR tµ|2

B(τ → µγ) = αm3

τ

212π4Γτ m2

t

m4

∆

h2(xt)2 |yR

tτyL µt|2 + |yR tµyL τt|2

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

30

Scalar leptoquarks

Δ2(3,2,7/6) Δ1(3,1,-1/3)

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

31

Leptoquark and vector-like quark T

Add a vector like top-partner to either of the LQ scenarios

L 3 yL

33¯

tL∆τR + yR

32¯

tR∆µL + xL

33 ¯

TL∆τR + xR

32 ¯

TR∆µL + h.c.

Finely tune T and t contributions to cancel τ→μγ amplitudes T does not affect the h→τμ, if the portal is turned off

B(τ → µγ) = αEMm3

τ

212π4Γτm4

∆

  • yL

33yR∗ 32 mth2(m2 t/m2 ∆) + xL 33xR∗ 32 mT h2(m2 T /m2 ∆)

  • 2
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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

32

Finely tune T and t contributions to achieve small τ→μγ

ℬ(→τμ)=%

Δ= =

*=

  • 1.0
  • 0.9
  • 0.8
  • 0.7
  • 0.6
  • 0.5
  • 0.4
  • 0.3

10-9 10-6 0.001 1

  • *
  • ℬ(τ→μγ)

CMS 1σ Δ = Δ = λ = Δ2 Δ1

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.5 1.0 1.5 2.0 (μ

τ + τ μ )/

ℬ(→τμ) [%]

B(τ → µγ) = αEMm3

τ

212π4Γτm4

∆

  • yL

33yR∗ 32 mth2(m2 t/m2 ∆) + xL 33xR∗ 32 mT h2(m2 T /m2 ∆)

  • 2

Leptoquark and vector-like quark T

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

33

Summary and Outlook

  • A positive signal of Br(h→μτ) implies a robust lower bound on the LFV Higgs

couplings.

  • This bound is robust even after allowing for deviations in other Higgs couplings
  • Higgs-EFT framework: Belle II should see τ→μγ
  • With future μe conversion measurements, Br(h→μτ) Br(h→eτ) < 10-7
  • In concrete models Br(τ→μγ) is more restrictive

★Extensions with vector like leptons or models with loop-induced h→μτ (leptoquark) imply a too large Br(τ→μγ), unless ad-hoc fine tuning is introduced (LQ + VL top) ★Two Higgs doublet model is testable by Br(τ→μγ) at Belle II ★Two Higgs doublet model is further constrained by μe conversion. Correlation Br(h→μτ) Br(h→eτ) < 10-10 (10-12 with improved limits in μe sector)

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  • N. Košnik (UL, JSI)

Thanks!

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Effective Higgs couplings

35

  • Assuming New Physics only in h→μτ then CMS result gives

B(h → τµ) =

  • 0.84+0.39

−0.37

  • %

0.0019(0.0008) < q |yτµ|2 + |yµτ|2 < 0.0032(0.0036) at 68% (95%) C.L. Leff.

Y` = −miij ¯

`i

L`j R − yij

⇣ ¯ `i

L`j R

⌘ h + . . . + h.c. B(h → τµ) = mh 8πΓh

  • |yτµ|2 + |yµτ|2

Γh = ΓSM

h /[1 − B(h → τµ)]

  • General parameterisation of the off-diagonal

Yukawa couplings

ySM

ij

= δij mi v

slide-36
SLIDE 36

Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Effective Theory Framework

36

  • Integrate out heavy Higgses, fermions, scalars. Keep terms to dim-6

LY` = −λα

ij ¯

LiHαEj − λ0αβγ

ij

1 Λ2 ¯ LiHαEj(H†

βHγ) + h.c.

yij = mi v ij + ✏ij

Dim-6 operator creates mismatch between mass and Yukawa matrices

✏ = VL  α¯ vα ✓xα ¯ vα − 1 ◆ + 0αβγ v2 Λ2 ¯ vα¯ vβ¯ vγ ✓xα ¯ vα + xβ ¯ vβ + xγ ¯ vγ − 1 ◆ V †

R

Hα = (h+

α, vα + xαh + . . .)T

Multiple higgses

X

α

v2

α ∼ v2/2

X

α

|xα|2 ∼ 1/2

vanishing in single Higgs scenarios

¯ vα = vα/v m v = VL ✓ λα¯ vα + λ0αβγ v2 Λ2 ¯ vα¯ vβ¯ vγ ◆ V †

R

Λ ' 4 TeV ✓ 0.84% B(h ! τµ) ◆ ⇣ |VLλ0111V †

R|2 τµ + |VLλ0111V † R|2 µτ

⌘1/4

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Charm ’15, WSU, Detroit, 5/19

  • N. Košnik (UL, JSI)

Tau LFV decays

37

τ H+ ν µ H+

τ H0

k

τ µ H0

k

yττ yτµ

A1-loop ~ (LFV Yukawa) * (tiny LFC Yukawa) ABarr-Zee ~ (LFV Yukawa) * (loop suppression)

[Chang et al, PRD48, 217(1993)]

Missing contributions at 2-loops with H+ mediator τ→μμμ is tree-level but less sensitive due to small muon Yukawa