Extensions of the Standard Model scalar sectorbenasque.org/2016tae/talks_contr/078_Penuelas.pdf ·...
Transcript of Extensions of the Standard Model scalar sectorbenasque.org/2016tae/talks_contr/078_Penuelas.pdf ·...
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
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 1 / 22
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
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 2 / 22
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
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)
�
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 3 / 22
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
,
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 4 / 22
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
,
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 4 / 22
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
,
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 4 / 22
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
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) .
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 5 / 22
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✓ .
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 6 / 22
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
,
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 7 / 22
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
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 8 / 22
Phenomenology and fits. Heavy scenario
bb bbVWWWWjjZZ ZZjj γγ γγjj ττ ττV0
1
2
Channels
μ
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 9 / 22
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
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 10 / 22
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
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"
�.
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 11 / 22
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.
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 12 / 22
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 .
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 13 / 22
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)
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 14 / 22
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. .
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 15 / 22
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
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 16 / 22
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±
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 17 / 22
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±) .
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 18 / 22
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
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 19 / 22
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
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 20 / 22
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
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 21 / 22
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
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...
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 22 / 22
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 1 / 8
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 .
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 2 / 8
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 ,
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 3 / 8
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)
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 4 / 8
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.
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 5 / 8
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
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 6 / 8
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
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 7 / 8
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
Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 8 / 8