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Flavor Violating Higgs Yukawa Couplings in Minimal Flavor Violation - - PowerPoint PPT Presentation

May 18, 2023 232 likes •500 views

Flavor Violating Higgs Yukawa Couplings in Minimal Flavor Violation Xing-Bo Yuan Central China Normal University based on arXiv: 1807.00921, in collaboration with Min He, Xiao-Gang He, XY, Jin-Jun Zhang CLHCP 2018, CCNU, Wuhan 20 Dec 2018

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SLIDE 1

Flavor Violating Higgs Yukawa Couplings in Minimal Flavor Violation

Xing-Bo Yuan

Central China Normal University

based on arXiv: 1807.00921, in collaboration with Min He, Xiao-Gang He, XY, Jin-Jun Zhang CLHCP 2018, CCNU, Wuhan 20 Dec 2018

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SLIDE 2

Higgs Discovery

(GeV)

H

m

110 115 120 125 130 135 140 145

Local p-value

  • 12
10
  • 10
10
  • 8
10
  • 6
10
  • 4
10
  • 2
10 1 σ 1 σ 2 σ 3 σ 4 σ 5 σ 6 σ 7 Combined obs.
  • Exp. for SM H
γ γ → H ZZ → H WW → H τ τ → H bb → H Combined obs.
  • Exp. for SM H
γ γ → H ZZ → H WW → H τ τ → H bb → H CMS
  • 1
= 8 TeV, L = 5.3 fb s
  • 1
= 7 TeV, L = 5.1 fb s

[GeV]

H

m 110 115 120 125 130 135 140 145 150 Local p

  • 11
10
  • 10
10
  • 9
10
  • 8
10
  • 7
10
  • 6
10
  • 5
10
  • 4
10
  • 3
10
  • 2
10
  • 1
10 1 Obs. Exp. ! 1 ±
  • 1
Ldt = 5.8-5.9 fb

"

= 8 TeV: s
  • 1
Ldt = 4.6-4.8 fb

"

= 7 TeV: s

ATLAS 2011 - 2012

! ! 1 ! 2 ! 3 ! 4 ! 5 ! 6

LHC Run I ◮ mass: mh ≈ 125 GeV

  • ◮ spin
  • ◮ parity
  • ◮ Yukawa coupling
  • ◮ gauge coupling
  • ◮ self coupling

? LHC Run II/HL/CEPC/ILC

2 / 17
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SLIDE 3

Higgs After the Discovery

3 / 17

t

+ . . . = c 16π2 Λ2 m2

h,0 +

c 16π2 Λ2 = 125 GeV2

fine-tuning

Hierarchy Problem

Instability 107 1010 1012 115 120 125 130 135 165 170 175 180 Higgs mass Mh in GeV Pole top mass Mt in GeV 1,2,3 Σ Instability Stability Metastability

Vacuum Stability

∆LH =+µ2Φ†Φ−λ

  • Φ†Φ

2 + (2m2

W W + µ W −µ + m2 ZZµZµ)h

v − mi ¯ fifi h v +h · XNP− 1 √ 2 ¯ fi(λij + iγ5¯ λij)fjh + . . .

µeV meV eV keV MeV GeV TeV ν1 ν2 ν3 e µ τ u c t d s b

Many Parameters

S.Baek, XY, PLB, 2017
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SLIDE 4

Higgs FCNC: exp

e µ τ e µ τ B < 0.035% B < 0.61% B < 0.25% e+e−collider µ < 2.1 µ = 1.09+0.27

−0.26

B < 0.12% B < 0.11% µtth = 1.3+0.3

−0.3

u c t u c t µ = 1.01+0.20

−0.20

d s b d s b

◭ direct search indirect study

McWilliams, Li 1981 Shanker 1982 Barr, Zee 1990 Kanemura, Ota, Tsumura 2006 Davidson, Grenier 2010 Golowich et al 2011 Buras, Girrbach 2012 Blankenburg, Ellis, Isidori 2012 Harnik, Kopp, Zupan 2013 Gorbahn, Haisch 2014 Celis, Cirigliano, Passemar 2014 Chiang, He, Ye, XY 2017 . . . . . .

Flavor Problem = ⇒ MFV

4 / 17

see also Xin Chen’s talk

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SLIDE 5

Higgs FCNC in EFT

◮ Effective Field Theory Lfull = LSM +

  • i

ci Λ2 Od=6

i

+ . . . ◮ Dim-4 operator in the SM ( ¯ QLHYddR), ( ¯ QL ˜ HYuuR), ( ¯ QLHYeeR), ◮ Dim-6 operator in the EFT (Warsaw)

Grzadkowski, Iskrzynski, Misiak, Rosiek, 2010

OdH = (H†H)( ¯ QLHCdHdR), OuH = (H†H)( ¯ QL ˜ HCuHuR), OeH = (H†H)( ¯ QLHCeHeR), ◮ Yukawa interaction

Harnik, Kopp, Zupan, 2013

Lf

Y = − 1

√ 2 ¯ fL ¯ YffRv − 1 √ 2 ¯ fL

  • ¯

Yf − v2 Λ2 CfH

  • fRh + h.c. .

¯ Yf = Yf − 1 2 v2 Λ2 CfH,

◮ FCNCs arise in the mass eigenstate

5 / 17
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SLIDE 6

Higgs FCNC in EFT with MFV

Quark Sector

◮ Flavor symmetry without Yukawa some U(1)′s GQF = SU(3)QL ⊗ SU(3)uR ⊗ SU(3)dR ◮ Flavor symmetry breaking −LY = ¯ QLHYddR + ¯ QL ˜ HYuuR + h.c. ◮ Flavor symmetry recovering: Yukawa coupling ⇒ spurion field Yu ∼ (3, ¯ 3, 1) and Yd ∼ (3, 1, ¯ 3). ◮ EFT with Minimal Flavor Violation: dim-6 operators, constructed from SM and Yukawa spurion fields, are invariant under CP and GQF. OdH = (H†H)( ¯ QLHCdHdR), A = YuY †

u ,

B = YdY †

d

CdH = fd(A, B)Yd ≡ (ξ01 + ξ1A + ξ2B + ξ3A2 + ξ4B2 + ξ5AB + ξ6BA + . . . . . . )Yd

6 / 17

D’Ambrosio, Giudice, G.Isidori, Strumia, 2009 (8 + 1, 1, 1) (8 + 1, 1, 1)

slide-7
SLIDE 7

Higgs FCNC in EFT with MFV

Quark Sector

◮ Higgs FCNC coupling

CdH = fd(A, B)Yd ≡ (ξ01 + ξ1A + ξ2B + ξ3A2 + ξ4B2 + ξ5AB + ξ6BA + . . . . . .)Yd

◮ Cayley-Hamilton identity for 3 × 3 invertible matrix X X3 = DetX · 1 + 1 2[TrX2 − (TrX)2] · X + TrX · X2 ◮ Higgs FCNC coupling after resummation

fd(A, B) = κ11+κ2A + κ5B2 + κ6AB + κ8ABA + κ11AB2 + κ13A2B2 + κ15B2AB + κ16AB2A2 +κ3B + κ4A2 + κ7BA + κ10BAB + κ9BA2 + κ14B2A2 + κ12ABA2 + κ17B2A2B

◮ Approximation #1: neglect tiny imaginary parts of κi ◮ Approximation #2: B ≈ 0 due to highly suppressed down-type Yukawa couplings fu(A, B) ≈ ǫu

0 1 + ǫu 1A + ǫu 2A2

fd(A, B) ≈ ǫd

0 1 + ǫd 1A + ǫd 2A2 .

7 / 17
  • G. Colangelo, E. Nikolidakis, C. Smith, 2009
  • L. Mercolli, C. Smith, 2009
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SLIDE 8

Higgs FCNC in EFT with MFV

Quark Sector

◮ Higgs Yukawa interaction in the interaction eigenstate Ld

Y = − 1

√ 2 ¯ dL ¯ YddRv − 1 √ 2 ¯ dL

  • ¯

Yd − v2 Λ2 CdH

  • dRh + h.c.

◮ Interaction eigenstate = ⇒ mass eigenstate CdH =

  • ǫd

0 1 + ǫd 1YuY † u + ǫd 2(YuY † u )2

Yd ¯ Yf = Yf − 1 2 v2 Λ2 CfH =

  • ǫd

0 1 + ǫd 1 ¯

Yu ¯ Y †

u + ǫd 2( ¯

Yu ¯ Y †

u )2 ¯

Yd + O(v2/Λ2) . ◮ Higgs Yukawa interaction in the mass eigenstate ˆ ǫd

i ≡ (v2/Λ2)ǫd i

Ld

Y = − 1

√ 2 ¯ dL

  • (1 − ˆ

ǫd

0)λd − ˆ

ǫd

1V †λ2 uV λd − ˆ

ǫd

2V †λ4 uV λd

  • dRh + h.c.

≈ − 1 √ 2 ¯ dL

  • (1 − ˆ

ǫd

0)λd − ˆ

ǫd

1V †λ2 uV λd

  • dRh + h.c. ,

◮ Approximation: (ˆ ǫd

1 + λ2 t ˆ

ǫd

2) → ˆ

ǫd

1

8 / 17
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SLIDE 9

Higgs FCNC in EFT with MFV

Lepton Sector

◮ Lepton MFV depends on the underlying mechanism for neutrino mass

2005 V. Cirigliano, B. Grinstein, G. Isidori, M. B. Wise 2006 V. Cirigliano, B. Grinstein 2009 M. B. Gavela, T. Hambye, D. Hernandez, and P. Hernandez 2011 R. Alonso, G. Isidori, L. Merlo, L. A. Munoz, and E. Nardi . . . . . .

◮ Type-I Seesaw

O : complex orthogonal matrix, ˆ mν = diag(m1, m2, m3)

mν = −v2 2 YνM −1

N Y T ν = U ˆ

mνU T , Yν = i √ 2 v U ˆ m1/2

ν

OM 1/2

N

◮ Lepton MFV in Type-I Seesaw

Casas, Ibarra, 2001

Aℓ = 2M v2 U ˆ m1/2

ν

OO† ˆ m1/2

ν

U † ◮ Higgs Yukawa interaction Lℓ

Y = − 1

√ 2 ¯ ℓL

  • (1 − ˆ

ǫℓ

0)λℓ − ˆ

ǫℓ

1Aℓλℓ − ˆ

ǫℓ

2A2 ℓλℓ

  • ℓRh ,

In numerical analysis, M = 1015 GeV, m1(3) = 0, and real matrix O

9 / 17
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SLIDE 10

Higgs FCNC in EFT with MFV

◮ Higgs Yukawa interaction YL = Y †

R

LY = − 1 √ 2 ¯ f(YLPL + YRPR)fh Y d

R = (1 − ˆ

ǫd

0)λd − ˆ

ǫd

1V †λ2 uV λd

Y u

R = (1 − ˆ

ǫu

0)λu

Y ℓ

R = (1 − ˆ

ǫℓ

0)λℓ − ˆ

ǫℓ

1Aℓλℓ − ˆ

ǫℓ

2A2 ℓλℓ

◮ Higgs FCNC in up-sector is highly suppressed by λ2

d

◮ 6 free real parameter:

  • ǫu

0, ǫd 0, ǫd 1, ǫℓ 0, ǫℓ 1, ǫℓ 2

  • hat suppressed

Constraints: ◮ Bs − ¯ Bs, Bd − ¯ Bd, K0 − ¯ K0 mixing (ǫd

1)

◮ h → ℓiℓj ℓi → ℓjγ, ℓi → ℓjℓk¯ ℓl, µ → e conversion in nuclei (ǫu

0, ǫd 0, ǫℓ 0, ǫℓ 1, ǫℓ 2)

◮ Higgs data@LHC Run I (ǫu

0, ǫd 0, ǫℓ 0)

◮ Bs → ℓiℓj (ǫd

1, ǫℓ 1, ǫℓ 2)

10 / 17
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SLIDE 11

Constraints from Bs − ¯ Bs mixing

◮ Observables: ∆md, ∆ms, φs, ∆mK, ǫK ∆mSM

s

= 19.196+1.377

−1.341,

∆mexp

s

= 17.757 ± 0.021, in unit of ps−1 ◮ Bound @95% CL |ǫd

1| < 0.59

◮ Prediction @95% CL Γ(h → sd) < 7.4 × 10−11 MeV Γ(h → sb) < 2.0 × 10−3 MeV Γ(h → db) < 9.4 × 10−5 MeV ◮ Discovery sensitivity@500GeV ILC with 4000 fb−1 D.Barducci, A.J.Helmboldt, 2017 B(h → bj) 0.5% with j a light quark

11 / 17 ¯ b b ¯ s W − u, c, t W + u, c, t s ¯ b b ¯ s h s
slide-12
SLIDE 12

Constraints from Higgs data

0.6 0.4 0.2 0.0 0.2 0.4 0.6

Ε0

d

0.6 0.4 0.2 0.0 0.2 0.4 0.6

Ε0

u

0.6 0.4 0.2 0.0 0.2 0.4 0.6

Ε0

  • 0.6

0.4 0.2 0.0 0.2 0.4 0.6

Ε0

u

◮ 90% CL allowed regions of (ǫu

0, ǫd 0, ǫℓ 0)

◮ LHC Run I data and Tevatron ◮ By Lilith package

12 / 17
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SLIDE 13

Constraints from µ → eγ and µ → e in nuclei

S.I combined S.II combined S.I Μe in AlMu2e S.II Μe in AlMu2e

Normal Ordering

0.10 0.05 0.00 0.05 0.10

Ε2

  • 0.10

0.05 0.00 0.05 0.10

Ε1

  • S.I combined
S.II combined S.I Μe in AlMu2e S.II Μe in AlMu2e

Inverted Ordering

1.0 0.5 0.0 0.5 1.0

Ε2

  • 1.0

0.5 0.0 0.5 1.0

Ε1

  • τ
h τ τ γ µ Y ∗ ττPL + YττPR Y ∗ τµPL + YµτPR + µ h µ τ γ µ Y ∗ τµPL + YµτPR Y ∗ µµPL + YµµPR µ h γ, Z t t τ γ µ µ h γ, Z W W τ γ µ µ h γ, Z W W τ γ µ µ h µ Z µ τ γ µ h N µ N e Y ∗ µePL + YeµPR + µ h µ γ N µ N e Y ∗ µµPL + YµµPR Y ∗ µePL + YeµPR + e h e γ N µ N e Y ∗ µePL + YeµPR Y ∗ eePL + YeePR

◮ dominated by

13 / 17

τ → µγ (ǫu

0, ǫℓ 0, ǫℓ 1, ǫℓ 2) D.Chang, W.S.Hou, Y.Okada, 1993

µ → e in nuclei (ǫu

0, ǫd 0, ǫℓ 0, ǫℓ 1, ǫℓ 2) R.Harnik,J.Kopp, J.Zupan, 2012

µ → eγ at present µ → e in Al in future S.I: (ǫℓ

0, ǫℓ 1, ǫℓ 2),

S.II: (ǫu

0, ǫd 0, ǫℓ 0, ǫℓ 1, ǫℓ 2)

slide-14
SLIDE 14

Predictions on µ → eγ and µ → e in nuclei

sensitivityMu2e sensitivityMEG II S.I S.II

Normal Ordering

1017 1016 1015 1014 1013 1012

ΜAleAl

1015 1014 1013 1012

ΜeΓ

sensitivityMu2e sensitivityMEG II S.I S.II

Inverted Ordering

1017 1016 1015 1014 1013 1012

ΜAleAl

1015 1014 1013 1012

ΜeΓ

◮ strong and similar correlations in NO and IO cases ◮ scenario I: Y eµ

R

vs Y eµ

R

◮ scenario II: (Y tt

L , Y eµ R ) vs (Y qq R , Y eµ R )

14 / 17
slide-15
SLIDE 15

Predictions on h → ℓiℓj and Bs → ℓiℓj

◮ h → ℓiℓj and Bs → ℓiℓj B(Bs → ℓ1ℓ2) B(h → ℓ1ℓ2) ≈ 2.1| ¯ Ysb|2 ◮ Predicted upper bounds on Γ(h → ℓiℓj) [MeV] and B(Bs → ℓiℓj)

Γ(h → eµ) Γ(h → eτ) Γ(h → µτ) B(Bs → eµ) B(Bs → eτ) B(Bs → µτ) NO S.I 1.2 × 10−8 1.3 × 10−5 9.0 × 10−5 2.4 × 10−16 2.6 × 10−13 1.8 × 10−12 NO S.II 2.2 × 10−8 2.4 × 10−5 1.7 × 10−4 4.6 × 10−16 5.0 × 10−13 3.5 × 10−12 IO S.I 1.2 × 10−8 4.7 × 10−6 7.1 × 10−5 2.4 × 10−16 9.6 × 10−14 1.4 × 10−12 IO S.II 2.2 × 10−8 8.7 × 10−6 1.3 × 10−4 4.5 × 10−16 1.8 × 10−13 2.6 × 10−12

◮ B(Bs → µ+µ−) can’t deviate from the SM prediction by more than 1% ◮ Experimental upper limits @ 95% CL,

LHCb 2018, CMS 2016, 2017

B(Bd → eµ) < 1.3 × 10−9 , B(Bs → eµ) < 6.3 × 10−9 , B(h → eµ) < 3.5 × 10−4 , B(h → eτ) < 6.1 × 10−3 , B(h → µτ) < 2.5 × 10−3 ,

15 / 17
slide-16
SLIDE 16

Summary

◮ Higgs FCNC Yukawa couplings in the EFT + type-I seesaw with MFV ◮ All the Yukawa couplings are described by 6 parameter (ǫu

0, ǫd 0, ǫd 1, ǫℓ 0, ǫℓ 1, ǫℓ 2)

◮ Constraints ǫu

0, ǫd 0, ǫℓ 0 : constrained by Higgs data

ǫℓ

1, ǫℓ 2 : constrained by µ → eγ

(µ → e in Al in future) ǫd

1 : constrained by Bs − ¯

Bs mixing ◮ Using these constraints, predicted upper limints for B(h → didj), B(h → uiuj), B(h → ℓ1ℓ2), and B(Bs → ℓ1ℓ2) are much lower than the current experimental bounds. ◮ B(Bs → µ+µ−) can’t deviate from the SM prediction by more than 1% ◮ However, with the improved measurements at the future MEG II and Mu2e experiments, searches for the LFV Higgs couplings in the µ → eγ decay and µ → e conversion in Al are very promising.

16 / 17
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SLIDE 17

Thank You !

17 / 17
slide-18
SLIDE 18

Backup

1 / 9
slide-19
SLIDE 19

Higgs After the Discovery: 1. Hierarchy Problem

◮ If SM is an effective theory below Λ ◮ Higgs mass receives quadratically divergent radiative corrections δm2

h =

t + . . . = c 16π2 Λ2 ◮ Large cancellation

regularization independent

m2

h = m2 h,0 +

c 16π2 Λ2 = 126 GeV2

fine-tuning

◮ Possible answer: New Physics

⊲ SUSY ⊲ Extra Dimensions ⊲ Dynamical Symmetry Breaking ⊲ Compositeness ⊲ . . . . . .

2 / 9
slide-20
SLIDE 20

Higgs After the Discovery: 2. Vacuum Stability

Instability 107 1010 1012 115 120 125 130 135 165 170 175 180 Higgs mass Mh in GeV Pole top mass Mt in GeV 1,2,3 Σ Instability Stability Metastability

“While λ (Higgs quartic coupling) at the Planck scale is remarkably close to zero, absolute stability of the Higgs potential is excluded at 98% C.L. for Mh < 126 GeV. ”

  • G. Degrassi, et. al. JHEP 12

Why λ ≈ 0 @ ΛPlanck ?

3 / 9
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SLIDE 21

Bs → µ+µ− decay: SM and exp

◮ SM prediction

Bobeth et al. 2013, with updated inputs

B(Bs → µ+µ−)SM =

  • 3.44 ± 0.19
  • × 10−9

◮ Exp data B(Bs → µ+µ−)LHCb2017 =

  • 3.0 ± 0.6+0.3

−0.2

  • × 10−9

B(Bs → µ+µ−)CMS2013 =

  • 3.0+1.0

−0.9

  • × 10−9

B(Bs → µ+µ−)avg. =

  • 3.0 ± 0.5
  • × 10−9

◮ Consistent within 1σ. We can use it to constrain possible NP effects. ◮ However, experimental central value is ∼ 13% lower than the SM one. NP effects may address such a discrepancy, though the error bars are still too large to call for such a solution.

4 / 9
slide-22
SLIDE 22

Bs − ¯ Bs mixing

◮ Effective Hamiltonian H∆B=2 = G2

F

16π2 m2

W (V ∗ tbVts)2 i

CiOi + h.c.. ◮ Effective operator

RGE: Buras et al. 2001

OVLL

1

= (¯ bαγµPLsα)(¯ bβγµPLsβ), OLR

1

= (¯ bαγµPLsα)(¯ bβγµPRsβ), OVRR

1

= (¯ bαγµPRsα)(¯ bβγµPRsβ), OLR

2

= (¯ bαPLsα)(¯ bβPRsβ), OSLL

1

= (¯ bαPLsα)(¯ bβPLsβ), OSLL

2

= (¯ bασµνPLsα)(¯ bβσµνPLsβ), OSRR

1

= (¯ bαPRsα)(¯ bβPRsβ), OSRR

2

= (¯ bασµνPRsα)(¯ bβσµνPRsβ).

◮ Wilson coefficients from the Higgs FCNC

CSLL,NP

1

= −1 2κ(Ybs − i ¯ Ybs)2, CSRR,NP

1

= −1 2κ(Ybs + i ¯ Ybs)2, κ = 8π2 G2

F

1 m2

hm2 W

1 (V ∗

tbVts)2 ,

CLR,NP

2

= −κ(Y 2

bs + ¯

Y 2

bs),

5 / 9 ¯ b b ¯ s W − u, c, t W + u, c, t s ¯ b b ¯ s h s
slide-23
SLIDE 23

Bs − ¯ Bs mixing

◮ Mass difference ∆ms = 2| ¯ Bs|H∆B=2|Bs| = G2

F

8π2 m2

W |V ∗ tbVts|2

Ci ¯ Bs |Oi| Bs

  • ,

◮ SM prediction ∆mSM

s

= (18.64+2.40

−2.27)ps−1

◮ Exp data ∆mexp

s

= (17.757 ± 0.021)ps−1 ◮ 95% CL bound

complex Y

0.76 <

  • 1 −
  • 0.7 Y 2

sb + 2.1 ¯

Y 2

sb

  • × 106

< 1.29

6 / 9
slide-24
SLIDE 24

Bounds from Bs − ¯ Bs mixing

1 0.5 0.5 1

Ysb 103

1 0.5 0.5 1

Ysb 103

◮ dark region: 95% CL allowed ◮ black: exp central value ◮ dashed: ∆mexp

s

/∆mtheo

s

= 0.9 ◮ dot-dashed: ∆mexp

s

/∆mtheo

s

= 0.8 ◮ dotted: ∆mexp

s

/∆mtheo

s

= 0.7 ◮ constructive: Ysb, ¯ Ysb ∼ 0 ◮ destructive: other

7 / 9
slide-25
SLIDE 25

h → f1f2 decay

◮ Decay width

S = 1 (1/2) for f1 = f2 (f1 = f2)

Γ(h → f1f2) = SNc mh 8π

  • |Yf1f2|2 +
  • ¯

Yf1f2

  • 2

◮ h → µτ

  • |Yµτ|2 + | ¯

Yµτ|2 < 1.43 × 10−3 at 95% CL

B(h → µτ)CMS15 = (0.84+0.39

−0.37)%

B(h → µτ)CMS17 < 0.25% at 95% CL B(h → µτ)ATLAS16 < 1.43% at 95% CL

8 / 9
slide-26
SLIDE 26

Constraints and Predictions

Constraints: ◮ Bs → µ+µ−

b µ t W s W νµ µ b µ t W s µ W Z b µ W t s µ t Z

b µ s h µ

◮ Bs − ¯

Bs

¯ b b ¯ s W − u, c, t W + u, c, t s ¯ b b ¯ s h s

◮ h → ττ

h τ + τ − h τ + τ −

◮ h → µτ

h τ + µ−

Predictions: B(Bs → µτ), B(Bs → ττ), ...

9 / 9