Probing Two Higgs Doublet Models with LHC andEDMs

Satoru Inoue, w/ M. Ramsey-Musolf and Y. Zhang (Caltech)

ACFI LHC Lunch, March 13, 2014

Outline

1 Motivation for 2HDM w/ CPV

2 Introduction to 2HDM

3 LHC bounds

4 EDM bounds

5 Conclusions

Motivations for 2HDM

We now know that there is a scalar sector

Are there more scalars? Can the scalar sector really beminimal?

2 Higgs doublets appear in SUSY extension of SM and somePeccei-Quinn models2HDM is the EFT when other particles are very heavy

BaryogenesisRicher scalar potential can violate CP, allow 1st order EWphase transition

Basics of 2HDM

2HDM = SM + one more Higgs doublet

�i !

H+i

1p2

�

vi + H0i + iA0

i

�

!

, i = 1, 2,

with v =q

v21 + v22 = 246 GeV

8 degrees of freedom ! 3 Goldstones + 5 physical:H01 ,H

02 ,A

0,H±

Pseudoscalar A0 important for CPV

Flavor-changing neutral current

2HDM Yukawa interaction

�(y1,ij ̄i j�1 + y2,ij ̄i j�2)

gives fermion mass matrix

Mij = y1,ijv1p2+ y2,ij

v2p2

In general, M cannot be diagonalized simultaneously with y ’s.

! tree level FC Yukawa interaction, e.g. d̄s� term (bad!)

Z2 symmetry (type II 2HDM)

Introduce symmetry: �1 ! ��1, dR ! �dR

Each type of fermions couples to only one doublet

LY = �YUQL(i⌧2)�⇤2uR � YDQL�1dR � YLL�1eR + h.c.

Mass matrix and Yukawa can both be diagonalized.Same structure as SUSY.

Other schemes exist (type I, aligned, etc.), but ignore for this talk

Higgs potential

V =�12|�1|4 +

�22|�2|4 + �3|�1|2|�2|2 + �4|�†1�2|

2+

+1

2

h

�5(�†1�2)

2 + h.c.i

� 1

2

n

m211|�1|2 +

h

m212(�

†1�2) + h.c.

i

+m222|�2|2

o

Quartic terms respect Z2, and we break it softly with m212 term.

Red parameters are complexOnly one CPV invariant - Im(�5m⇤4

12)

Mass eigenbasis

After EWSB, there is a 3⇥ 3 mass matrix for the neutral Higgs.Diagonalization involves rotation in 3D.

0

@

h1h2h3

1

A = R

0

@

H01

H02

A0

1

A

With CPV in the scalar potential, all 3 states mix to form masseigenstates, e.g.

h1 = �s↵c↵bH01 + c↵c↵b

H02 + s↵b

A0 (1)

Roughly - ↵ gives how much of each doublet is in h1↵b gives how much pseudoscalar is in h1Another angle ↵c a↵ects heavy Higgs

Higgs interactions in mass basis

Finally, we can write the lightest Higgs interactions to fermionsand gauge bosons:

Lh1 = �mf

vh1�

cf f̄ f + c̃f f̄ i�5f�

+ah1

✓

2m2W

vWµW

µ +m2

Z

vZµZ

µ

◆

cf and a are CP-even, 1 in SM, mostly a↵ected by angle ↵c̃f is CP-odd, 0 in SM, mostly a↵ected by angle ↵b

Recap

Type-II 2HDM w/ softly broken Z2:

There are 3 neutral Higgs, h1,2,3, and a charged Higgs, H+

FCNC is suppressed by symmetry

Potential can have 1 new CPV phase

CP even mixing angle ↵ shifts scalar Yukawa and gauge-Higgscouplings for h1

CP odd ↵b introduces scalar-pseudoscalar mixing, andpseudoscalar Yukawa coupling for h1

Higgs production and decay

There are heavy/charged Higgs searches (for another LHC lunch?)but (lightest) Higgs phenomenology can already probe 2HDM.

�gg!h1

�SMgg!h1

=�h1!gg

�SMh!gg

⇡ (1.03ct � 0.06cb)2 + (1.57c̃t � 0.06c̃b)2

(1.03� 0.06)2

�h1!��

�SMh!��

⇡ (0.23ct � 1.04a)2 + (0.35c̃t)2

(0.23� 1.04)2

�VV!h1

�SMVV!h

=�V ⇤!Vh1

�SMV ⇤!Vh

=�h1!WW

�SMh!WW

=�h1!ZZ

�SMh!ZZ

⇡ a2

�h1!bb̄

�SMh!bb̄

=�h1!⌧+⌧�

�SMh!⌧+⌧�

⇡ cb2 + c̃b

2

Fit to LHC Higgs data

Fit to Higgs decay signal strengths (⇠ 25 fb�1)�� WW ZZ Vbb ⌧⌧

ATLAS 1.6± 0.3 1.0± 0.3 1.5± 0.4 �0.4± 1.0 0.8± 0.7CMS 0.8± 0.3 0.8± 0.2 0.9± 0.2 1.3± 0.6 1.1± 0.4

SM

-1.5-1.0-0.5 0.0 0.5 1.0 1.5-1.0

-0.5

0.0

0.5

1.0

a

a b

Combined, tan b=0.6

SM

-1.5-1.0-0.5 0.0 0.5 1.0 1.5-1.0

-0.5

0.0

0.5

1.0

a

Combined, tan b=1.0

SM

-1.5-1.0-0.5 0.0 0.5 1.0 1.5-1.0

-0.5

0.0

0.5

1.0

a

Combined, tan b=5

↵ mostly constrained near SM value (� � ⇡/2)↵b not well constrained

EDMs - very short review

BSM CPV sources induce d = 6 CPV operatorsMain ones generated by 2HDM:

EDMs - �f⇤2mf ef̄ �µ⌫�5fFµ⌫

chromo-EDMs - �̃q⇤2mqgs q̄�µ⌫�5T aqG aµ⌫

Weinberg operator -CG̃2⇤2 gs f

abc✏µ⌫⇢�G aµ�G

b �⌫ G c

⇢�

�f , �̃q,CG̃ are dimensionless Wilson coe�cients

These operators need to be run down to ⇤QCD and matched toEDMs by evaluating matrix elements

2-loop diagrams

In 2HDM, 1-loop EDM/CEDM for e, u, d are tiny (Yukawas)

hi

g

g g

t

f f f

g

t

g hi

f f f

�

t,H+

W+, G+

�,Z hi

2-loop diagrams dominate

EDM experimental summary

90% C.L. limits:eEDM: |de | < 8.7⇥ 10�28e cmACME experiment on ThO molecule, 2013.

nEDM: |dn| < 2.9⇥ 10�26e cmGrenoble, 2006. Many groups aiming for order of magnitude ormore improvement.

HgEDM: |dHg| < 2.6⇥ 10�29e cmSeattle, 2009. Taking more data.

Plans for Ra and Xe - more sensitive due to nuclear enhancement

EDM current bounds

Exclusion plots on tan� � sin↵b plane:electron, neutron, Hg(magenta - theoretically inaccessible)

eEDM places strongest constraints: sin↵b . .01nEDM and HgEDM have large theory uncertainties

EDM future bounds

electron, neutron, Hg, Ra

Left - currentCenter - 10x improvement for neutron and HgRight - 100x improvement for neutronRa limit taken to be order of magnitude short of target

Conclusions

2HDM is a theoretically motivated model to probe a richerscalar sector

LHC Higgs data is constraining CP-even e↵ects of 2HDM

EDM constrains CPV e↵ects - complementarity

Current CPV bounds come from eEDM, but otherexperiments can become competitive

Hadronic/nuclear uncertainties are problematic

Backup slides

Higgs mass matrix

The Higgs mass matrix in (H01 ,H

02 ,A

0) basis is

M2 = v2

0

@

�1c2� + ⌫s2� (�345 � ⌫)c�s� �12 Im�5 s�

(�345 � ⌫)c�s� �2s2� + ⌫c2� �12 Im�5 c�

�12 Im�5 s� �1

2 Im�5 c� �Re�5 + ⌫

1

A ,

�345 ⌘ �3 + �4 + Re�5, ⌫ ⌘ Re�5 csc� sec�/2v2

Scalar-pseudoscalar mixing from Im�5, as expected.

Rotation matrix parameterization

Neutral Higgs mass matrix is diagonalized with a rotation in 3D

0

@

h1h2h3

1

A = R

0

@

H01

H02

A0

1

A

R =R23(↵c)R13(↵b)R12(↵+ ⇡/2)

=

0

@

�s↵c↵bc↵c↵b

s↵b

s↵s↵bs↵c � c↵c↵c �s↵c↵c � c↵s↵b

s↵c c↵bs↵c

s↵s↵bc↵c + c↵s↵c s↵s↵c � c↵s↵b

c↵c c↵bc↵c

1

A

↵+ ⇡/2 = � makes Yukawa and vev proportional (SM limit)

↵b = 0 is the CP-conserving limit

Charged Higgs and Goldstones

The charged sector divides up into the physical charged Higgs H+

and charged Goldstone G+:

H+ = � sin�H+1 + cos�H+

2 , G+ = cos�H+1 + sin�H+

2

Charged Higgs mass is m2H+ = 1

2 (2⌫ � �4 � Re�5) v2

There are also neutral Goldstones, from CP-odd sector:

A0 = � sin�A01 + cos�A0

2, G 0 = cos�A01 + sin�A0

2

Physical pseudoscalar A0 can mix with scalar Higgs H01,2

Yukawa expressions

Yukawa couplings for i-th mass eigenstate of the Higgs arefunctions of � and the mass diagonalization matrix R :

ct,i cb,i c̃t,i c̃b,i

Type I Ri2/ sin� Ri2/ sin� �Ri3 cot� Ri3 cot�Type II Ri2/ sin� Ri1/ cos� �Ri3 cot� �Ri3 tan�

The gauge coupling is shifted by an overall factor a:

a = Ri2 sin� + Ri1 cos�

Type-I 2HDM

In type-I 2HDM, only the 2nd doublet couples to fermions

LY = �YUQL(i⌧2)�⇤2uR � YDQL�2dR � YLL�2eR + h.c.

The expressions for the Yukawa coupling are di↵erent from type IIct,i cb,i c̃t,i c̃b,i

Type I Ri2/ sin� Ri2/ sin� �Ri3 cot� Ri3 cot�Type II Ri2/ sin� Ri1/ cos� �Ri3 cot� �Ri3 tan�

Fit to LHC Higgs data (type-I)

Fit to Higgs decay signal strengths (⇠ 25 fb�1)�� WW ZZ Vbb ⌧⌧

ATLAS 1.6± 0.3 1.0± 0.3 1.5± 0.4 �0.4± 1.0 0.8± 0.7CMS 0.8± 0.3 0.8± 0.2 0.9± 0.2 1.3± 0.6 1.1± 0.4

SM

-1.5-1.0-0.5 0.0 0.5 1.0 1.5-1.0

-0.5

0.0

0.5

1.0

a

a b

Combined, tan b=0.6

SM

-1.5-1.0-0.5 0.0 0.5 1.0 1.5-1.0

-0.5

0.0

0.5

1.0

a

Combined, tan b=1

SM

-1.5-1.0-0.5 0.0 0.5 1.0 1.5-1.0

-0.5

0.0

0.5

1.0

a

Combined, tan b=5

↵ mostly constrained near SM value (� � ⇡/2)↵b not well constrained

EDM current bounds (type-I)

Exclusion plots on tan� � sin↵b plane:electron, neutron, Hg(magenta - theoretically inaccessible)

eEDM places strongest constraints: sin↵b . .01 for small tan�nEDM does not constrain this model

EDM future bounds (type-I)

electron, neutron, Hg, Ra

Left - currentCenter - 10x improvement for neutron and HgRight - 100x improvement for neutroneEDM is the most sensitive channel for type-I