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

[email protected]

September 7, 2016

Ana Penuelas Martınez (IFIC) Extensions of the Standard Model scalar sector September 7, 2016 1 / 22

[email protected]

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


Overview







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)

�


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

,


Overview







4 Conclusions


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) .


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✓ .


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

,


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



bb bbVWWWWjjZZ ZZjj γγ γγjj ττ ττV0

1

2

Channels

μ


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


Overview







4 Conclusions


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"

�.



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.



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 .


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)



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. .


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


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±


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±) .



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



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


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


Overview







4 Conclusions


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...



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 .


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 ,



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)


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.




1

2

Channels

μ


1

2

Channelsμ



-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


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


extensions of the standard model scalar sectorbenasque.org/2016tae/talks_contr/078_penuelas.pdf ·...

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