phenomenology of the general two-higgs doublet...

Phenomenology of the general two-higgs doubletmodel

Xing-Bo Yuan

Yonsei University

Yonsei HEP Seminar 10 Mar 2015

Outline

1. Introduction

2. Flavor Processcharged current: B → D(∗)τν

neutral current: B → Xsγ, t→ cV , Bs − Bs mixing

3. Two-Higgs Doublet Model

4. 2HDM Effects On The Flavor Processescollaboration with Prof. C.S.Kim and Y.W.Yoon

5. Conclusion

2 / 50

Standard Model

3 / 50

Flavor Physics and Standard Model

β decayKL → µ+µ−

K0 − K0

KL → π+π−

B0 − B0

4 / 50

Higgs discovery

(GeV)Hm110 115 120 125 130 135 140 145

Loca

l p-v

alue

-1210

-1010

-810

-610

-410

-210

1σ1σ2

σ3

σ4

σ5

σ6

σ7

Combined obs.Exp. for SM H

γγ →H ZZ→H WW→H ττ →H

bb→H

Combined obs.Exp. for SM H

γγ →H ZZ→H WW→H ττ →H

bb→H

CMS -1 = 8 TeV, L = 5.3 fbs -1 = 7 TeV, L = 5.1 fbs

[GeV]Hm110 115 120 125 130 135 140 145 150

0Lo

cal p

-1110

-1010

-910

-810

-710

-610

-510-410

-310

-210

-1101

Obs. Exp.

!1 ±-1Ldt = 5.8-5.9 fb" = 8 TeV: s

-1Ldt = 4.6-4.8 fb" = 7 TeV: sATLAS 2011 - 2012

!0!1!2!3

!4

!5

!6

I mass: mh = 126 GeV ,

I spin ,

I party ,

I Yukawa coupling ,

I gauge coupling ,

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Higgs After the Discovery

Question 1This boson is the only one fundamental scalar just as the SM, orbelongs to an extended scalar sector responsible to the electroweaksymmetry breaking ?

Possible AnswerTwo-Higgs Doublet Model (2HDM)

6 / 50

Outline

1. Introduction





5. Conclusion

7 / 50

B → Xsγ

I Xs stands for the hadronic system with a s quark

e.g. K0S , K+π0, ...

I b→ sγ process at quark level

I Flavor-changing neutral current (FCNC) decay

I Forbidden at the tree level and highly suppressed at one-looplevel due to GIM

I The effects of many NP scenarios may enhance these FCNCprocesses through introducing new mediators within the loop.Therefore, B → Xsγ plays an important role in testing theSM and constraining its possible extensions.

I Exclusive decay B → K∗γ: non-perturbative parameters

8 / 50

B → Xsγ: decay width

I Decay Width (quark-hadron duality)

Γ(B → Xsγ)Eγ>E0 ≈ Γ(b→ Xps γ)Eγ>E0

B Xps stands for s, sg, sgg, sqq, etc.

B This approximation works well only in the rangemb/2 ∼ E0 � (mb − ΛQCD)/2. It has become customary touse E0 = 1.6 GeV ≈ mb/3 for comparing theory with exp.

I Feynman Diagram@LO

b W

t

s

t

γ

b t

W

s

W

γ

I Effective Operator

O7 = − e

8π2mbsσ

µν(1 + γ5)bFµν

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B → Xsγ: decay width

I Analytical Expression

Γ(b→ Xps γ)Eγ>E0

Γ(b→ Xueν)=

∣∣∣∣V ∗tsVtbVub

∣∣∣∣2 6αeπ

8∑i,j=1

Ceffi (µb)C

effj (µb)Kij(µb, E0)

B NNLO QCD corrections completed Misiak, et al.

B Γ(B → Xsγ) ∝ |C7|2

I Current status

B(B → Xsγ)theoEγ>1.6 GeV = (3.15± 0.23)× 10−4

B(B → Xsγ)exptEγ>1.6 GeV = (3.43± 0.22)× 10−4

B The SM prediction and the current experimentalmeasurements are consistent at about 1σ level.

B The SM uncertainty (7%) is dominated by O(αsΛQCD/mb)non-perturbative effects (5%).

B Difficulty in the experimental side is the measurements onabout 40 Xs decays modes.

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B → Xsγ: direct CP violation

I Direct CP violation

ACP(B → Xsγ)Eγ>E0 =Γ(B → Xsγ)− Γ(B → Xsγ)

Γ(B → Xsγ) + Γ(B → Xsγ)

∣∣∣∣Eγ>E0

I Feynman Diagram

(a) (b) (c)

2 28

B one-loop diagrams with insertions of the operators O2 and O8

B gluon bremsstrahlung diagrams with a charm loopB tree-level diagram containing an insertion of the operator O7

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B → Xsγ: direct CP violation

I Analytical expression@NLO

Ab→sγCP =αs(mb)

|C7|2{

+40

81Im[C2C

∗7 ]− 8z

9

[v(z) + b(z, δ)

]Im[(1 + εs)C2C

∗7 ]

− 4

9Im[C8C

∗7 ] +

8z

27b(z, δ) Im[(1 + εs)C2C

∗8 ]

}I Weak phases

Im[(1 + εs)C∗7 ] = −ImC7 +O(λ2)

Im[(1 + εd)C∗7 ] = −ReC7 · η

I ACP(B → Xsγ) is sensitive to the phase of C7

I Current status

A(B → Xsγ)theoEγ>1.6GeV = +2.6+0.8−3.3

A(B → Xsγ)exptEγ>1.6GeV = −0.8+2.9−2.9

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εq =V ∗uqVub

V ∗tqVtb

Outline

1. Introduction





5. Conclusion

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Bs − Bs mixingI Feynman Diagram

b

b

s

W−

u, c, t

W+

u, c, ts

I Mass eigenstate

|BHs 〉 =

|Bs〉+ ε|Bs〉√1 + |ε|2

|BLs 〉 =

ε|Bs〉+ |Bs〉√1 + |ε|2

I Time evolution

idψ(t)

dt= Hψ(t) ψ(t) =

(|Bs〉|Bs〉

)I Hamiltonian

H = M − i

2Γ =

(M11 − i

2Γ11 M12 − i2Γ12

M21 − i2Γ21 M22 − i

2Γ22

)I Mass difference ∆Ms ≡M s

H −M sL = 2|M12|

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Bs − Bs mixing: basic formalism

I Effective Hamiltonian in the SM

Heff =GF

16π2MW (V ∗tbVts)

2CVLL1 (µ)QVLL

1 + h.c.

I Four-quark operators

QVLL1 = (bαγµPLs

α)(bβγµPLsβ)

I Wilson coefficientB calculated perturbatively at the matching scale µW

CVLL1 (µW ) = C

VLL(0)1 +

αs4πC

VLL(1)1 +

(αs4π

)2C

VLL(2)1 + ...

CVLL(0)1 = S0(xt) ≡

4xt − 11x2t + x3t4(1− xt)2

− 3x3t lnxt2(1− xt)3

B xt = mt(µW )2/M2W

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Bs − Bs mixing: basic formalism

I off-diagonal matrix element

M12 =1

2MBs

〈Bs|Heff |Bs〉

=1

2MBs

GF

16π2M2W (V ∗tbVts)

2CVLL1 (µ)〈Bs|QVLL

1 |Bs〉(µ),

I contain all the physical information

I scale-independent

I hadronic matrix element 〈Bs|QVLL1 |Bs〉(µ)

B obtained from lattice calculationB at low energy scale: µL = 4.6 GeV

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Bs − Bs mixing: Evaluation of CVLL1 (µ)〈Bs|QVLL

1 |Bs〉(µ)

I initial conditionsB Wilson coefficient @matching scale

CVLL1 (µW ) = C

VLL(0)1 +

αs4πC

VLL(1)1 +

(αs4π

)2C

VLL(2)1 + ...

B hadronic matrix element @lattice scale

〈QVLL1 〉(µL)

I renormalization group evolution

CVLL1 (µ2) = U(µ2, µ1)CVLL

1 (µ1)

〈QVLL1 〉(µ2) = 〈QVLL

1 〉(µ1)U(µ1, µ2)

B evolution matrix

U(µ2, µ1) =αs4πU (0)(µ2, µ1) +

(αs4π

)2

U (1)(µ2, µ1) + ...

B ADM γ =αs4πγ(0) +

(αs4π

)2

γ(1) + ...

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Bs − Bs mixing: New Physics

I all possible four-quark operators (5 sectors)

QVLL1 = (bαγµPLs

α)(bβγµPLsβ) QLR

1 = (bαγµPLsα)(bβγµPRs

β)

QVRR1 = (bαγµPRs

α)(bβγµPRsβ) QLR

2 = (bαPLsα)(bβPRs

β)

QSLL1 = (bαPLs

α)(bβPLsβ) QSLL

2 = (bασµνPLsα)(bβσµνPLs

β)

QSRR1 = (bαPRs

α)(bβPRsβ) QSRR

2 = (bασµνPRsα)(bβσµνPRs

β)

I RG evolution (operator mixing)(CLR

1 (µ2)

CLR2 (µ2)

)= U(µ2, µ1)

(CLR

1 (µ1)

CLR2 (µ1)

)(〈QLR

1 (µ2)〉, 〈QLR2 (µ2)〉

)=(〈QLR

1 (µ1)〉, 〈QLR2 (µ1)〉

)U(µ1, µ2)

I ADM: NLO Buras, et al.

I hadronic matrix element: lattice

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Outline

1. Introduction





5. Conclusion

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Possible AnswerTwo-Higgs Doublet Model

Question 2Hierarchy problem

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Hierarchy Problem

I If SM is an effective theory below Λ

I Higgs mass receives quadratically divergent radiative corrections

δm2h =

t

+ . . . =c

16π2Λ2

I Large cancellation regularization independent

m2h = m2

h,0 +c

16π2Λ2 = 126 GeV2

fine-tuning

Possible AnswerTop quark physics

δm2h =

t

+

NP

+ . . .

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Top quark physics: FCNC decays

I Top quark: spin, QCD and EW charge, couplings

I Top quark FCNC decaysB t→ cZ, t→ cγ, t→ cg, t→ chB t→ uZ, t→ uγ, t→ ug, t→ uh

I Highly suppressed by the GIM mechanism (d, s, b in loop)

I SM/BSM predictions and experimental status

B(t→ qZ) B(t→ qγ) B(t→ qg) B(t→ qh)

SM 1× 10−13 5× 10−13 5× 10−11 8× 10−14

SUSY ∼ 10−4 ∼ 10−5 ∼ 10−3

Exp < 5.0× 10−4 < 3.2× 10−2 < 1.6× 10−4 < 8.3× 10−3

LHC 3 ab−1 < 4.1× 10−5 < 1.3× 10−5

I Sensitive to New Physics

As will be shown later, there may exist correlation between thet→ cg and B → D(∗)τν processes in the general 2HDM.

22 / 50

Outline

1. Introduction





5. Conclusion

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B → D(∗)τν

ν

b

cW−

τ−R(D) ≡ B(B → Dτν)/B(B → Dlν)

Rexp(D) = 0.440± 0.058± 0.042 BaBar, 2013

RSM(D) = 0.297± 0.017 2.2σ

R(D∗) ≡ B(B → D∗τν)/B(B → D∗lν)

Rexp(D∗) = 0.332± 0.024± 0.018 BaBar, 2013

RSM(D∗) = 0.252± 0.003 2.7σ

I tree-level process

I SM: hadronic matrix elements

24 / 50

Outline

1. Introduction

2. Flavor Processcharged current:B → D(∗)τν




5. Conclusion

25 / 50



Possible AnswerTwo-Higgs Doublet Model (2HDM)

26 / 50

27 / 50

2HDM

NFC 2HDM

Natural Flavour Conservation

other 2HDMs MFV 2HDM

Minimal Flavour Violation

type-I

type-II

type-X

type-Y

type-III H2

type-C Ha2

A2HDM

other 2HDMs

LARGEFCNC

Z2

char

ge

ass

ign

men

t

tree-level FCNCtree-level FCNC

controlled by CKM

General 2HDM

I Lagrangian (interaction basis)

−LY = QL(Y d1 Φ1 + Y d

2 Φ2)dR + QL(Y u1 Φ1 + Y u

2 Φ2)uR + LL(Y `1 Φ1 + Y `

2 Φ2)eR

I Higgs basis

Φ1 =

(G+

1√2(v + η1 + iG0)

)Φ2 =

(H+

1√2(η2 + iA0)

)

I Mass eigenstate(η1

η2

)=

(cosα − sinαsinα cosα

)(H0

h0

)I Higgs spectrum: H0, h0, A0, H±

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General 2HDM: Yukawa interaction

I Lagrangian (mass basis)

−LY = (u, d)Mq

(ud

)+ (ν, e)M `

(νe

)I Quark sector

M q = Mm +MdH +Mn

H +MG

MdH =

1√2

(λuη1 0

0 λdη2

)MnH =

(1√2η2(Y UPR + Y U†PL)− i√

2A0(Y UPR − Y U†PL), H+(V Y DPR − Y U†V PL)

H−(−V †Y UPR + Y D†V †PL), 1√2η2(Y DPR + Y D†PL) + i√

2A0(Y DPR − Y D†PL)

)I Lepton sector

M ` = Me +MdH +Mn

H +MG

MdH =

1√2λeη1

MnH =

(0 H+Y `

2 PRH−Y `†

2 PL1√2η2(Y `

2 PR + Y `†2 PL) + i√

2A0(Y `

2 PR − Y`†

2 PL)

)

29 / 50

General 2HDM: assumption on the Yukawa coupling

1. unitary and symmetry

ξ ≡ Y U,D,` = (Y U,D,`)† = (Y U,D,`)T

2. CKM approximation

V Y D =

Vud Vus VubVcd Vcs VcbVtd Vts Vtb

Y D ≈

Vud 0 00 Vcs 00 0 Vtb

Y D =

VudY Ddd VudY

Dds VudY

Ddb

VcsYDsd VcsY

Dss VcsY

Dsb

VtbYDbd VtbY

Dbs VtbY

Dbb

Y U†V = Y U†

Vud Vus VubVcd Vcs VcbVtd Vts Vtb

≈ Y U†

Vud 0 00 Vcs 00 0 Vtb

=

VudYU†uu VcsY

U†uc VtbY

U†ut

VudYU†cu VcsY

U†cc VtbY

U†ct

VudYU†tu VcsY

U†tc VtbY

U†tt

3. experimental constraint

Y Dsb ≈ 0⇐= Bs − Bs mixing

30 / 50

Outline

1. Introduction

2. Flavor Processcharged current:B → D(∗)τν




5. Conclusion

31 / 50

Basic Idea: B → D(∗)τν

ν

b

cW−

τ−R(D) ≡ B(B → Dτν)/B(B → Dlν)

Rexp(D) = 0.440± 0.058± 0.042 BaBar, 2013

RSM(D) = 0.297± 0.017 2.2σ

R(D∗) ≡ B(B → D∗τν)/B(B → D∗lν)

Rexp(D∗) = 0.332± 0.024± 0.018 BaBar, 2013

RSM(D∗) = 0.252± 0.003 2.7σ

I SM: hadronic matrix elements

I BSM: A widely studied possibility is 2HDM, sincethe charged Higgs couples proportionally to themasses of the fermions involved in the interaction.

B NFC 2HDM /B MFV 2HDM /B General 2HDM ,

32 / 50

Basic Idea: B → D(∗)τν in the general 2HDM

ν

b

cW−

τ−

ν

b

cH−

τ−

ξττPL

mH+ = 700 GeV

!0.3 !0.2 !0.1 0.0 0.1 0.2 0.3!10

!5

0

5

10

ΡΤΤ

Ρ !"

#0 # ΤΤ#0 # ΤΤ

$!D"$!D$"

− (V ξD)23PR + (ξU†V )23PL

=− (VcdξDdb + Vcsξ

Dsb + Vcbξ

Dbb)PR

+ (ξU†cu Vub + ξU†cc Vcb + ξU†ct Vtb)PL

K.F.Chen, W.S.Hou, C.Kao, M.Kohda, PLB, 2013

33 / 50

A. Crivellin, C.Greub, A.Kokulu, PRD, 2012

Basic Idea: Higgs FCNC in the general 2HDM

h0

uj

ui

∼ − sinαλuδij +��cosαξUij t→ ch

H0

uj

ui

∼ +��cosαλuδij + sinαξUij H → tc

A0

uj

ui

∼ +ξUij A→ tc or t→ cA

LHC Higgs data =⇒ decoupling limit α = π/2

34 / 50

Basic Idea: t→ cg in the general 2HDM

t H0, A0

t

c

t

g

t H±

b

c

b

g

∼ ξUctξUtt

1e-12

1e-11

1e-10

1e-09

1e-08

1e-07

1e-06

1e-05

200 300 400 500 600 700 800

1e-04

Ms

Br

MS = mA0 = mH0 = mH+ = 700 GeV

B(t→ cg) =

(ξUct

0.06

ξUtt0.7

)2

× 10−7

≈ (ξUtt )2 × 10−3 (ξUct = 5)

B(t→ cg)exp < 1.6× 10−4

D.Atwood, L.Reina, A.Soni, PRD,1997

35 / 50

t→ cγ

t→ cg

t→ cZ

t→ cg in G2HDM

I Feynman diagram

t H0, A0

t

c

t

g

t H±

b

c

b

g

I Relevant Yukawa interaction

−∆LY = +1√2cαξctcth+

1√2sαξctctH −

i√2ξctcγ5tA+ h.c.

+1√2

(−sαλt + cαξtt)tth−i√2ξtttγ5tA

+1√2

(+cαλt + sαξtt)ttH

+ Vtbt(ξbbPR − ξttPL)bH+ + h.c.

36 / 50

t→ cg in G2HDMI tcg form factor

L =1

16π2c

(Aγµ +Bγµγ5 + iCσµν

qνmt

+ iDσµνqνmt

γ5 −Amt

q2qµ +B

mt

q2γ5q

µ

)tgaµT

q

B The last two terms do not appear in Soni’s paper

I Decay width

Γ(t→ cg) =1

(16π2)2

1

8πmtCF (|C|2 + |D|2)

I Same expressions but different numerical results

1e-12

1e-11

1e-10

1e-09

1e-08

1e-07

1e-06

1e-05

200 300 400 500 600 700 800

1e-04

Ms

Br

200 300 400 500 600 700 80010-14

10-12

10-10

10-8

10-6

10-4

37 / 50

Soni et al Our

Parameter space: R(D) and R(D∗)

I Effective Hamiltonian

Heff = CVLLOVLL + CSRLOSRL + CSLLOSLL

I Operator

OVLL = (cγµPLb)(τ γµPLντ ) CSM

VLL =4GFVcb√

2

OSRL = (cPRb)(τPLντ ) CSMSRL = 0

OSLL = (cPLb)(τPLντ ) CSMSLL = 0

I in the case of no NP effects on OVLL

R(D) = RSM(D)

(1 + 1.5Re

[CSRL + CSLL

CSMVLL

]+ 1.0

∣∣∣∣CSRL + CSLL

CSMVLL

∣∣∣∣2)

R(D∗) = RSM(D∗)

(1 + 0.12Re

[CSRL − CSLL

CSMVLL

]+ 0.05

∣∣∣∣CSRL − CSLL

CSMVLL

∣∣∣∣2)

38 / 50


I Feynman diagram

ν

b

cW−

τ−

ν

b

cH−

τ−


−∆LY =− VtbξctcPLbH+ + ξττ ντPRτH+ + h.c.

I G2HDM contributions

CG2HDMVLL = 0 CG2HDM

SRL = 0 CG2HDMSLL =

Vtbξctξττm2H±

39 / 50


• R(D∗)• R(D)

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Parameter space: B → Xsγ

I Feynman Diagram

b W

t

s

t

γ

b t

W

s

W

γ

b H−

t

s

t

γ

b t

H−

s

H−

γ


−∆LY = +Vtbt(ξbbPR − ξttPL)bH+ + t(VtbξbsPR − VcsξtcPL)sH+


CG2HDM7,8 =

1

3

(ξtt +

V ∗csV ∗ts

ξct

)(ξtt+

VcbVtb

ξct

)F

(1)7,8 (y)

2m2t /v

2−(ξtt +

V ∗csV ∗ts

ξct

)ξbb

F(2)7,8 (y)

2mtmb/v2

B ξbb term is enhanced by spin flip factor mt/mb

B The gray terms are the subleading terms which is considered inthe W.S.Hou’s paper but neglected here. Results unchanged.

41 / 50

Parameter space: B → Xsγ

-15 -10 -5 0 5 10 15-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

Ξtt

Ξ bb

-15 -10 -5 0 5 10 15-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

Ξct

Ξ bb

-15 -10 -5 0 5 10 15-15

-10

-5

0

5

10

15

Ξct

Ξ tt

I 80 GeV < mH± < 1000 GeV

I −10 < ξct < 10

I −10 < ξtt < 10

I −0.1 < ξbb < 0.1

no constraints on ξct, ξtt

42 / 50

Parameter space: Bs − Bs mixing

I Feynman Diagram

b

b

s

W−

u, c, t

W+

u, c, ts

b

b

s

W−

u, c, t

H+

u, c, ts

b

b

s

H−

u, c, t

H+

u, c, ts


−∆LY = +Vtbt(ξbbPR − ξttPL)bH+ + t(VtbξbsPR − VcsξtcPL)sH+


CVLL1 (WH) =

4s2W ξctξttxH±

e2

VcsVts

(−4 + xW

(xH± − 1)(xW − 1)+

(xW − 4xH±) log xH±

(xH± − 1)2(xH± − xW )+

3xW log xW(xW − 1)2(xH± − xW )

)CVLL

1 (HH) =4s4W ξ

2tcξ

2tt

e4

V 2cs

V 2ts

xH±

xW

(xH± + 1

(xH± − 1)2− 2xH± log xH±

(xH± − 1)3

)B The G2HDM contributions to OVRR

1 , OLR1,2 , OSLL

1 and OSRR1

can be neglected after taking ξbb = ξbs = 0.

43 / 50

Parameter space: Bs − Bs mixing

200 400 600 800 1000

-0.5

0.0

0.5

mH±

Ξ ct

Ξ tt

ξctξtt is strongly bounded./

44 / 50

Parameter space: cc→ tt

200 400 600 800 10000

2

4

6

8

10

MH=MAHGeVL

ÈΞ ctÈ

45 / 50

Parameter space: oblique parameter T

-1000 -500 0 500 1000

-1000

-500

0

500

1000

mH± - mH

mH

±-

mA

I 80 GeV < mH± < 1000 GeV

I mh < mH < 1000 GeV

I 1 GeV < mA < 1000 GeV

Higgs mass splittings are highly

bounded.

46 / 50

Parameter space: other constraints

I B → τν: Only the product ξbbξττ enters this decay.Therefore, this process is irrelevant, after considering theapproximation ξbb ≈ 0.

I t→ ch: Based on a dataset corresponding to an integratedluminosity of 19.5 fb−1, CMS recently placed a 95% CL upperlimit B(t→ ch) < 0.56%. In general 2HDM with decouplinglimit, there is no FCNC associated with h. Therefore, thisbound is irrelevant.

47 / 50

Final results

0.0 0.2 0.4 0.6 0.810-10

10-8

10-6

10-4

0.01

R HDL

BHt

®cg

L�Ξ t

t2

0.0 0.2 0.4 0.6 0.810-10

10-8

10-6

10-4

0.01

R HD*L

BHt

®cg

L�Ξ t

t2

0.0 0.2 0.4 0.6 0.810-10

10-8

10-6

10-4

0.01

R HDL

BHt

®cg

L�Ξ t

t2

0.0 0.2 0.4 0.6 0.810-10

10-8

10-6

10-4

0.01

R HD*L

BHt

®cg

L�Ξ t

t2

horizontal line: current LHC upper boundvertical line: 1σ range of the experimental measurements on R(D(∗))

48 / 50

ξττ = 0.5

ξττ = 0.1

Final results

0.0 0.2 0.4 0.6 0.810-10

10-8

10-6

10-4

0.01

R HDL

BHt

®cg

L�Ξ t

t2

0.0 0.2 0.4 0.6 0.810-10

10-8

10-6

10-4

0.01

R HD*L

BHt

®cg

L�Ξ t

t2

0.0 0.2 0.4 0.6 0.810-10

10-8

10-6

10-4

0.01

R HDL

BHt

®cg

L�Ξ t

t2

0.0 0.2 0.4 0.6 0.810-10

10-8

10-6

10-4

0.01

R HD*L

BHt

®cg

L�Ξ t

t2

horizontal line: current LHC upper boundvertical line: 1σ range of the experimental measurements on R(D(∗))

49 / 50

ξττ = 0.05

ξττ = 0.01

Thank You !

50 / 50

Backup

51 / 50

Effective Hamiltonian

52 / 50

NFC 2HDMs: introduction

I Lagrangian (interaction basis)

−LY = QL(Y d1 Φ1 + Y d

2 Φ2)dR + QL(Y u1 Φ1 + Y u

2 Φ2)uR + LL(Y `1 Φ1 + Y `

2 Φ2)eR

I NFC hypotheses: Group structure (Z2 symmetry)

I Lagrangian (mass basis)

−LY = +∑

f=u,d,`

[mf ff +

(mf

vξfh ffh+

mf

vξfH ffH − i

mf

vξfAfγ5fA

)]+

√2

vu(muV ξ

uAPL + V mdξ

dAPR

)dH+ +

√2m`ξ

`A

vνL`RH

+

ξuH ξdH ξ`H ξuA ξdA ξ`AType-I sα/sβ sα/sβ sα/sβ − cotβ + cotβ + cotβType-II sα/sβ cα/cβ cα/cβ − cotβ − tanβ − tanβType-X sα/sβ sα/sβ cα/cβ − cotβ + cotβ − tanβType-Y sα/sβ cα/cβ sα/sβ − cotβ − tanβ + cotβ

I parameter space: (mh,mH ,mA,mH± , α, β)

53 / 50

NFC 2HDMs: constraintsI direct search for Higgs bosons@LEP, Tevatron and LHC

decoupling limit: β − α = π/2

I perturbative unitarity and vacuum stability

I Bs− Bsb

b

s

W−

u, c, t

W+

u, c, ts

b

b

s

W−

u, c, t

H+

u, c, ts

b

b

s

H−

u, c, t

H+

u, c, ts

I B → Xsγ

b W

t

s

t

γ

b t

W

s

W

γ

b H−

t

s

t

γ

b t

H−

s

H−

γ

I B → τνν

b

uW−

τ−

ν

b

uH−

τ−

I Bs → µ+µ−

b

µ

W

t

s

µ

t

Z

b

µ

t

W−

s

H+

νµµ

b

µ

t

W−

s

µ

H+

h,H,A

b

µ

t s

H−

s

µ

h,H,A

I parameter space : (mh,mH ,mA,mH± , α, β)54 / 50

Bs → µ+µ−: SM

I Feynman diagram

b

µ

t

W

s

Wνµ

µ

b

µ

t

W

s

µ

W

Z

b

µ

W

t

s

µ

t

Z

I Effective Hamiltonian

Heff = − GFα√2πs2

W

VtbV∗tq(C10O10 + CSOS + CPOP ) + h.c.

O10 = (qγµPLb)(¯γµγ5`) CSM10 = −0.94

OS =m`mb

m2W

(qPRb)(¯ ) CSMS ≈ 0

OP =m`mb

m2W

(qPRb)(¯γ5`) CSMP ≈ 0

55 / 50

Bs → µ+µ−: NFC 2HDMI Feynman diagram

b

µ

t

W−

s

H+

νµµ

b

µ

t

W−

s

µ

H+

h,H,A

b

µ

t s

H−

s

µ

h,H,A...

I Wilson CoefficientB type-II 2HDM in large tanβ limit H.Logan, U.Nierste, NPB, 2000.

B full one-loop calculation in A2HDM X.Q.Li, J.Lu, A.Pich, JHEP, 2014.

I Wilson Coefficient in NFC2HDM

C10 = +x2t ξu2A

8

( 1

xH± − xt+

xH±

(xH± − xt)2(log xt − log xH±)

)CS = +

xtξ`h

2xh

(−sα−βg(a)

1 + cα−βg(a)2 +

2v2

m2W

λhH+H−g0

)+xtξ

`H

2xH

(+cα−βg

(a)1 + sα−βg

(a)2 +

2v2

m2W

λHH+H−g0

)CP =− xtξ

`A

2xAg

(a)3

56 / 50

Bs → µ+µ−: Bs − Bs mixing effects

I time-integrated branching ratio Fleischer et al, PRL 12

B(Bs → `+`−) =

(1 +A∆Γys

1− y2s

)B(Bs → `+`−)

B(Bd → `+`−) = B(Bd → `+`−)

I mass-eigenstate rate asymmetry assume S, P ∈ R

A∆Γ =|P |2 − |S|2|P |2 + |S|2

I ratio assume S, P ∈ R

R ≡ B(Bs → `+`−)

B(Bs → `+`−)SM=

( |P |21− ys

+|S|2

1 + ys

)1

|SSM|2 + |PSM|2

57 / 50

backup: Higgs potential

� scalar potential in NFC 2HDM

−LSS = V = +m21Φ†1Φ1 +m2

2Φ†2Φ2 −m23

(Φ†1Φ2 + Φ†2Φ1

)+λ1

2

(Φ†1Φ1

)2+λ2

2

(Φ†2Φ2

)2+λ3

2

(Φ†1Φ1

)(Φ†2Φ2

)+ λ4

(Φ†1Φ2

)(Φ†2Φ1

)+λ5

2

[(Φ†1Φ2

)2+(Φ†2Φ1

)2]

58 / 50

phenomenology of the general two-higgs doublet...

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