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Extensions of the Standard Model scalar sector
Ana Penuelas Martınezin collaboration with A. Pich
Instituto de Fısica Corpuscular (IFIC)
Taller de Altas Energıas 2016, Benasque
September 7, 2016
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Contents
1 IntroductionStandard ModelMotivation
2 Higgs singlet extensionThe modelPhenomenology and fits
Heavy scenarioLight scenario
3 The Aligned Two Higgs doublets
Scalar potential and symmetrybreakingYukawa sectorPhenomenology and Higgs signalstrengthsGlobal fits in the A2HDM
Light CP-even Higgs with H± loopLight CP-odd Higgs
4 Conclusions
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Overview
1 IntroductionStandard ModelMotivation
2 Higgs singlet extensionThe modelPhenomenology and fits
Heavy scenarioLight scenario
3 The Aligned Two Higgs doublets
Scalar potential and symmetrybreakingYukawa sectorPhenomenology and Higgs signalstrengthsGlobal fits in the A2HDM
Light CP-even Higgs with H± loopLight CP-odd Higgs
4 Conclusions
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016
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Introduction. Standard Model
The SM is the theory better describing elementary particles and theirinteractions
Local gauge invariance underSU(3)C ⌦ SU(2)L ⌦ U(1)Y )massless particles
To generate masses )spontaneously symmetry breaking
We introduce the complex doublet
�(x) =
�(+)(x)�(0)(x)
�
Minimum of the potential for"0q�µ2
2h
#=
0vp2
�
! �(x) = 1p2
0
v + H(x)
�
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Introduction. Motivation
The Higgs mechanism is the simplest to generate masses in the SM
Di↵erent alternatives would both reproduce the content of the SM as well asincluding some new ingredients
⇢ =M2
W
M2Z cos2 ✓w
=X
i
v2i [Ti (Ti + 1)� Y 2
i ]
2P
i v2i Y
2i
= 1 ,
The experimental data will be connected through µ
µ =�(pp ! h2Y )
�(pp ! HY )SM
BR(h2 ! X )
BR(H ! X )SM
The �2 function will be minimized
�2('0i ) =
X
k
⇣µ'0
i
k � µk
⌘2
�2k
,
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Introduction. Motivation
The Higgs mechanism is the simplest to generate masses in the SM
Di↵erent alternatives would both reproduce the content of the SM as well asincluding some new ingredients
⇢ =M2
W
M2Z cos2 ✓w
=X
i
v2i [Ti (Ti + 1)� Y 2
i ]
2P
i v2i Y
2i
= 1 ,
The experimental data will be connected through µ
µ =�(pp ! h2Y )
�(pp ! HY )SM
BR(h2 ! X )
BR(H ! X )SM
The �2 function will be minimized
�2('0i ) =
X
k
⇣µ'0
i
k � µk
⌘2
�2k
,
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Introduction. Motivation
The Higgs mechanism is the simplest to generate masses in the SM
Di↵erent alternatives would both reproduce the content of the SM as well asincluding some new ingredients
⇢ =M2
W
M2Z cos2 ✓w
=X
i
v2i [Ti (Ti + 1)� Y 2
i ]
2P
i v2i Y
2i
= 1 ,
The experimental data will be connected through µ
µ =�(pp ! h2Y )
�(pp ! HY )SM
BR(h2 ! X )
BR(H ! X )SM
The �2 function will be minimized
�2('0i ) =
X
k
⇣µ'0
i
k � µk
⌘2
�2k
,
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Overview
1 IntroductionStandard ModelMotivation
2 Higgs singlet extensionThe modelPhenomenology and fits
Heavy scenarioLight scenario
3 The Aligned Two Higgs doublets
Scalar potential and symmetrybreakingYukawa sectorPhenomenology and Higgs signalstrengthsGlobal fits in the A2HDM
Light CP-even Higgs with H± loopLight CP-odd Higgs
4 Conclusions
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016
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Higgs singlet extension. The model
Simplest extension of the SM: A real bosonic singlet invariant under all thequantum numbers of the SM is added (')
doing ' ! '+ h'i
V (�,') = µ2(�†�) + h(�†�)2 + (a'+ b'2 + c'3 + d'4)
+(�†�)(A'+ B'2) + V0
with h > 0, d > 0,B > 0 (increasing), detH > 0 (bounded) i µ2 < 0
h0|� |0i =0vp2
�, h0|' |0i = 0 .
�(x) = e i�i2 ✓i (x) 1p
2
0
v + H(x)
�unitary gauge���������! 1p
2
0
v + H(x)
�,
'(x)unitary gauge���������! '(x) .
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Higgs singlet extension. The model
V =�1
4hv4 + V 0
0| {z }
V0
+ (hvH3 +h
4H4)
| {z }Higgs self-interactions
+ (c'3 + d'4)| {z }' self-interactions
+1
2M2
HH2 +
1
2M2
''2 + Av'H
| {z }mass terms
+Bv'2H +1
2AH2'+
1
2BH2'2
| {z }H-' interactions
,
h1h2
�=
cos ✓ sin ✓� sin ✓ cos ✓
� H'
�, m2
h1,2 =M2
H +M2'
2±
|M2H �M2
'|2
p1 + tan2 2✓ .
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Phenomenology and fits
LY = � 1p2
⇣1 +
h1 cos ✓ � h2 sin ✓
v
⌘⇣c2dd + c2uu + c3ee
⌘.
Reduction of the couplings with respect to the SM
h1V ⌘ gh1VV /g
SMHVV = cos ✓ , h1
f ⌘ yh1↵ /ySMH↵ = cos ✓ ,
h2V ⌘ gh2VV /g
SMHVV = � sin ✓ , h2
f ⌘ yh2↵ /ySMH↵ = � sin ✓ .
�h1 = �SM cos2 ✓ + �h1!h2h2| {z }if allowed
,
�h2 = �SM sin2 ✓ .
�h1!h2h2 =|eµ|2
8⇡mh1
s
1�4m2
h2
m2h1
,
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Phenomenology and fits. Heavy scenario
The cross sections�(pp ! h2Y )
�(pp ! HY )SM= sin2 ✓ .
For the branching ratios
BR(h2 ! X )
BR(H ! X )SM=
�(h2 ! X )
�h2
�H,SM
�(H ! X )SM=
sin2 ✓
1
1
sin2 ✓= 1 .
All the strengths are identical
µ = sin2 ✓
Results of the fit (�2)
sin ✓ = 0.99± 0.01 , �2/d.o.f. = 0.55
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Phenomenology and fits. Heavy scenario
bb bbVWWWWjjZZ ZZjj γγ γγjj ττ ττV0
1
2
Channels
μ
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Phenomenology and fits. Light scenario
The cross sections
�(pp ! h1Y )
�(pp ! HY )SM= cos2 ✓ .
For the branching ratios, with the additional decay
BR(h1 ! X )
BR(H ! X )SM=
�h1!X
�h1
�H,SM
�H!X ,SM
=cos2 ✓�H,SM
cos2 ✓�H,SM + �h1!h2h2
=1
1 +�h1!h2h2
cos2 ✓�H,SM
.
All the strengths are identical
µ = cos2 ✓ ⇥ 1
1 +�h1!h2h2
cos2 ✓�H,SM
=cos4 ✓
cos2 ✓ +�h1!h2h2
�H,SM
.
Results of the fit (�2)
cos ✓ = 0.99± 0.01 , �h1!h2h2 = 0 , �2/d.o.f. = 0.55
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Overview
1 IntroductionStandard ModelMotivation
2 Higgs singlet extensionThe modelPhenomenology and fits
Heavy scenarioLight scenario
3 The Aligned Two Higgs doublets
Scalar potential and symmetrybreakingYukawa sectorPhenomenology and Higgs signalstrengthsGlobal fits in the A2HDM
Light CP-even Higgs with H± loopLight CP-odd Higgs
4 Conclusions
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016
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A2HDM. Scalar potential and symmetry breaking
A doublet with the same quantum numbers of the SM one is added
�1 =
"�(+)1
�(0)1
#, �2 =
"�(+)2
�(0)2
#.
General form of the vev
h0|�1 |0i =1p2
0
v1ei✓1
�, h0|�2 |0i =
1p2
0
v2ei✓2
�.
U(1) transformation to eliminate one of the phases
h0|�1 |0i =1p2
0v1
�, h0|�2 |0i =
1p2
0
v2ei✓2�✓1
�=
1p2
0
v2ei"
�.
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A2HDM. Scalar potential and symmetry breaking
SU(2) transformation in the scalar space (�1,�2) ! just one of the doubletsacquire a vev
�1
��2
�=
1
v
v1 v2v2 �v1
� �1
e�i"�2
�=
1
v
v1�1 + e�i"v2�2
v2�1 � e�i"v1�2
�,
with v2 = v21 + v2
2 .
Excitations over the vacuum
�1 =
G+
1p2(v + S1 + iG 0)
�, �2 =
H+
1p2(S2 + iS3)
�.
V = µ21(�
†1�1) + µ2
2(�†2�2) + [µ3�
†1�2 + µ⇤
3�†2�1]
+�1(�†1�1)
2 + �2(�†2�2)
2 + �3(�†1�1)(�
†2�2) + �4(�
†1�2)(�
†2�1)
+h(�5�
†1�2 + �6�
†1�1 + �7�
†2�2)(�
†1�2) + h.c.
i.
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A2HDM. Scalar potential and symmetry breaking
Mass terms
V2 = M2H±H+H� +
1
2
⇥S1, S2, S3
⇤M
2
4S1S2S3
3
5 ,
Mass matrix �Ii ⌘ =(�i ),�
Ri ⌘ <(�i )
M =
2
642�1v
2 v2�R6 �v2�I
6
v2�R6 M2
H± + v2(�4
2 + �R5 ) �v2�I
5
�v2�I6 �v2�I
5 M2H± + v2
⇣�4
2 � �R5
⌘
3
75 .
2
4hHA
3
5 = R
2
4S1S2S3
3
5 CP-conserving limit�����������!�Ii=0
hH
�=
cos ↵ sin ↵� sin ↵ cos ↵
� S1S2
�,
A = S3 .
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A2HDM. Yukawa sector
The new doublet has the same quantum numbers as the one of the SM )more terms in the Yukawa Lagrangian
LY = �¯
Q
0L(�1�1 + �2�2)d
0R � ¯
Q
0L(�1�1 +�2�2)u
0R
� ¯
L
0L(⇧1�1 +⇧2�2)l
0R + h.c.
In the Higgs basis
LY = �p2
v
⇣¯
Q
0L(M
0d�1 + Y
0d�2)d
0R � ¯
Q
0L(M
0u�1 + Y
0u�2)u
0R
�¯
L
0L(M
0l�1 + Y
0l�2)l
0R + h.c
⌘
M
0a can be diagonalized by performing transformations in the fields and
introducing the CKM matrix
Nothing guarantees us that the matrices Y0a will be diagonal ) it can give
flavour changing neutral currents (FCNC)
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A2HDM. Yukawa sector
To avoid FCNC we require that Y0a and M
0a are aligned in flavour space
�2 = "de�i"�1 , �2 = "⇤ue
i"�1 , ⇧2 = "le�i"⇧1 .
And we have
Y
0a = &(⇤)a M
0a ,
Yukawa Lagrangian
LY = �p2
vH+
�u(x)[&dVMdPR � &uM
†uVPL]d(x) + &l ⌫(x)MlPR l(x)
� 1
v
X
'0i ,f
y'0
i
f '0i [f (x)MfPR f (x)] + h.c. .
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A2HDM. Yukawa Sector
Consequences of the alignment
All the couplingsscalars-fermions are proportionalto the masses
The Yukawas are diagonal inflavour
The only contribution tointeractions changing flavour isgiven by the CKM matrix
There is only three new parameters,&f (in general complex)
The couplings satisfy universalityamong generations
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A2HDM. Phenomenology and Higgs signal strengths
'0i (~p1)
f (~p2), r2
f (~p3), r3SM : � imf
v
A2HDM : � imf y'0i
f (�5)
v
'0i (~p1)
V (~p2), r2,µ
V (~p3), r3,µSM :2m2
V
v
A2HDM :2m2
V
v Ri1
'0i (~p1)
�(~p2), µ
�(~p3), ⌫
�iv�
�e(k � p)µ
�e(k � p0)⌫
~k
H±
H±
H±
'0i (~p1)
�(~p2), µ
�(~p3), ⌫
�iv�ie2gµ⌫
~k
H±
H±
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A2HDM. Fit of light CP-even Higgs with H± loop
With the signs of yu and cos ↵ chosen as in the SM and in the CP-conservinglimit
Results of the fit
cos ↵ = 0.98+0.02�0.05 , Ch
H± = (�0.03+0.70�0.61 [ 12.68+0.70
�0.67) ,
yhu = 0.98± 0.08 , |yh
d | = 0.84+0.08�0.09 , |yh
l | = 0.97+0.14�0.16 .
with �2/d.o.f = 0.59
C'0i
H± =v2
2M2H±
�'0i H
+H�A(xH±) .
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A2HDM. Fit of light CP-even Higgs with H± loop
bb bbV WW WWjj ZZ ZZjj γγ γγjj ττ ττV0
1
2
Channels
μ
H±h = -0.03 ± 1σ
0 10 20 30 40 50100
200
300
400
500
600
700
|λhH+ H- |
MH±(GeV
)
Perturbativity
H±h = 12.68 ± 1σ
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A2HDM. Fit of light CP-even Higgs with H± loop
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4-2
-1
0
1
2
yuh
y dh
0.6 0.8 1.0 1.2 1.4-2
-1
0
1
2
yuh
y lh
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A2HDM. Fit of light CP-odd Higgs
R31 = 0 so A does not couple to bosons at tree level
µAbbV = µA
⌧⌧V = µA��jj = µA
VV = µAVVjj = 0
Results of the fit
|yAu | = 0.84± 0.07 , |yA
d | = 0.34+0.10�0.08 , |yh
l | = 0.35+0.09�0.12 .
with �2/d.o.f. = 11.6
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Overview
1 IntroductionStandard ModelMotivation
2 Higgs singlet extensionThe modelPhenomenology and fits
Heavy scenarioLight scenario
3 The Aligned Two Higgs doublets
Scalar potential and symmetrybreakingYukawa sectorPhenomenology and Higgs signalstrengthsGlobal fits in the A2HDM
Light CP-even Higgs with H± loopLight CP-odd Higgs
4 Conclusions
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Conclusions
Motivation for the study of extensions ! aspects of nature not explainedonly by the SM + freedom to extend the scalar sector
Singlet extension: A real bosonic singlet invariant under all the SM quantumnumber ! 2 scalars (Higgs-like)
A2HDM: Two doublets with the same quantum numbers as the Higgsdoublet! 3 scalar neutral particles ({Si}i=1,2,3) + 2 charged particles H±
Statistical analysis of the models with the LHC data. Best fit A2HDM,CP-even
Interesting aspects of the models: CP-violation, dark matter...
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A2HDM. Yukawa sector
y'0
f are the couplings for the physical fields
y'0
i
d,l = Ri1 + (Ri2 + iRi3)&d,l , y'0
iu = Ri1 + (Ri2 � iRi3)&
⇤u .
With the relations
3X
i=1
(y'0
i
f )2 = 1 ,3X
i=1
|y'0i
f |2 = 1 + 2|&f |2 ,3X
i=1
y'0
i
f Ri1 = 1 ,
3X
i=1
y'0
i
d,lRi2 = &d,l ,3X
i=1
y'0
iu Ri2 = &⇤u ,
3X
i=1
y'0
i
d,lRi3 = i&d,l ,3X
i=1
y'0
iu Ri3 = �i&⇤u .
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A2HDM. Phenomenology and Higgs signal strengths
µ'0
i
bb = C'0
igg
h<(y'0
i
d )2 + =(y'0i
d )2��2b
i⇢('0
i )�1,
µ'0
i�� = C
'0i
gg C'0
i��⇢('0
i )�1 ,
µ'0
i⌧⌧ = C
'0i
gg
h<(y'0
i
l )2 + =(y'0i
l )2��2⌧
i⇢('0
i )�1,
µ'0
i
��jj = (Ri1)2C
'0i
��⇢('0i )
�1 ,
µ'0
i
bbV = (Ri1)2h<(y'0
i
d )2 + =(y'0i
d )2��2b
i⇢('0
i )�1,
µ'0
i
VV = C'0
igg (Ri1)
2⇢('0i )
�1 ,
µ'0
i
⌧⌧V = (Ri1)2h<(y'0
i
l )2 + =(y'0i
l )2��2⌧
i⇢('0
i )�1 ,
µ'0
i
VVjj = (Ri1)4⇢('0
i )�1 ,
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Phenomenology and fits. Heavy scenario
4.0 4.5 5.0 5.5 6.0 6.5 7.00
2000
4000
6000
8000
10000
X
μ(GeV
)
μ (GeV) perturbativeΓh1→h2 h2 = (100) (GeV)
Γh1→h2 h2 = (101) (GeV)
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A2HDM. Fit light CP-even Higgs without H± loop
Fit results yu > 0 and cos ↵ > 0
cos ↵ = 0.98+0.02�0.06 , y
hu = 0.98± 0.08 , |yh
d | = 0.84+0.08�0.09 , |yh
l | = 0.97+0.14�0.16 ,
amb �2/d.o.f = 0.47.
Fit results yu < 0 i cos ↵ > 0
cos ↵ = 0.83± 0.06 , yhu = �0.83± 0.06 , |yh
d | = 0.87+0.08�0.09 , |yh
l | = 1.12+0.15�0.18 ,
amb �2/d.o.f = 2.96.
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A2HDM. Fit light CP-even Higgs without H± loop
bb bbV WW WWjj ZZ ZZjj γγ γγjj ττ ττV0
1
2
Channels
μ
bb bbV WW WWjj ZZ ZZjj γγ γγjj ττ ττV0
1
2
Channelsμ
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A2HDM. Fit light CP-even Higgs without H± loop
-2 -1 0 1 2-2
-1
0
1
2
yuh
y dh
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-2
-1
0
1
2
yuh
y lh
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A2HDM. Discrete Z2 symmetries
Model &d &u &lType I cot� cot� cot�Type II � tan� cot� � tan�Type X cot� cot� � tan�Type Y � tan� cot� cot�Inert 0 0 0
Table : CP-conserving 2HDMs based on discrete Z2 symmetries, being tan� ⌘ v2/v1
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