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