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Effective Lagrangian approach to the EWSBsector

Juan González Fraile

Universitat de Barcelona

Tyler Corbett, O. J. P. Éboli, J. G–F and M. C. Gonzalez–Garcia

arXiv:1207.1344, 1211.4580, 1304.1151

Juan González Fraile (UB) HEFT 2014 Madrid, September 2014 1 / 19
Introduction

Effective Lagrangian approach to the EWSB sector

The common idea during ∼ O(30) years: the SM remarkable success (lack of unexpectedparticles) motivates a model independent parametrization to look for NP→ Leff

Two main routes have been followed during these last decades:

� Assume there is no light Higgs→ Non–linear or chiral effective Lagrangian (Stronginteracting EWSB sector).

� Assume there is a light Higgs→ linear Effective Lagrangian.

The talk is focused on the linear:

Leff = LSM0 +∞∑m=1

∑n

f(4+m)n

ΛmO(4+m)n

Let me start with a brief historical review1...

1

Apologies for the ones unintentionally missed.

Introduction








∑n

f(4+m)n

ΛmO(4+m)n


1


Introduction








∑n

f(4+m)n

ΛmO(4+m)n


1


Introduction








∑n

f(4+m)n

ΛmO(4+m)n


1Apologies for the ones unintentionally missed.

Introduction

pre-HEFT: a biased review. Part I.

The common idea remains (model independent parametrization to look for NP), but the contextchanges:

� First lists→ motivation from flavor!Burguess and Schnitzer (1983), Leung, Love and Rao (1986) (hγZ, hγγ),Buchmuller and Wyler (1986) (dim–6 list reduced to 109).

� After first LEP EWPD, what could happen with LEP2 (and TGV)?De Rújula, Gavela, Hernández and Massó (1992) (EWPD–TGV, EOM’s, blind directions...),Hernández and Vegas (1993), Hagiwara, Ishihara, Szalapski and Zeppenfeld (1992 and 1993).

� EWPD and other aspects of Leff :Artz, Einhorn and Wudka (1992), Wudka (1994),Politzer (1980), Georgi (1991), Arzt (1994) and Simma (1994) (S-matrix equivalence),Gounaris and Renard (1996) idem plus Layssac (1996) (gauge boson scatterings),Gounaris, Layssac and Renard (1994, 1995) idem plus Paschalis (1995) (unitarity),Hagiwara, Matsumoto and Szalapski (1995) (EWPD revisited),and Alam, Dawson and Szalapski (1998) (EWPD revisited),Éboli, Lietti, Gonzalez–Garcia and Novaes (1998) (EWPD bounds on aTGV),

Introduction






Introduction






Introduction






Introduction

pre-HEFT: a biased review. Part II.

The focus moved from flavor, to EWPD, to TGV... but the SM standed... so...

� First Higgs analysis (considering the open space from EWPD):Hagiwara, Szalapski and Zeppenfeld (1993)

Followed by many interesting LEP-pheno Higgs studies (kinematics, observables, differentchannels/operators, TGV, SM tree vrs. loop...)

Hagiwara and Stong (1994), Grzadkowski and Wudka (1995), Hagiwara, Hatsukano, Ishiharaand Szalapski (1996) Killian, Kramer and Zerwas (1996), Lietti, Novaes and Rosenfeld (1996),idem plus De Campos (1996 and 1997), Lietti and Novaes (1997),Éboli, Gonzalez–Garcia, Lietti and Novaes (1998) (LEP data to bound TGV)

� then Tevatron-pheno:De Campos, Gonzalez–Garcia and Novaes (1997) (1st study using experiment (Tevatron) toanalyze open space on TGV),Gonzalez-Garcia, Lietti and Novaes (1998), idem plus de Campos and Rosenfeld (1998).

� and LHC–pheno:

Éboli, Gonzalez–Garcia, Lietti and Novaes (1999)

Introduction









Introduction









Introduction









Introduction









Introduction

HEFT: back to the present.Together with many other aspects of Leff

D’Ambrosio, Giudice, Isidori and Strumia (2002)(MFV), Barger, Han, Langacker, McElrath andZerwas (2003) (future machines), Horejsi and Kampf (2004) (hγγ), Barbieri, Pomarol, Rattazziand Strumia (2004), Han and Skiba (2004), Han (2005), Manohar and Wise (2006)(LHC–pheno), Hamkele, Klamke, Zeppenfeld and Figy (2006), Pierce, Thaler and Wang (2006),Giudice, Grojean, Pomarol and Rattazzi (2007) (SILH), Kanemura and Tsumura (2008), Qi,Kuang, Liu and Zhang (2008), Del Aguila, De Blas and Perez–Victoria (2008, 2010), idem plusLangacker (2011), Low, Rattazzi and Vichi (2009), Grzadkowski, Iskrzynski, Misiak andRosiek (2010) (59!), Bonnet, Gavela, Ota and Winter (2011), Domenech, Pomarol and Serra(2012), Blankenburg and Ellis (2012), Degrande, Gerard, Grojean, Maltoni and Servant (2012)and many more...

The Higgs discovery

First Leff analysis using Higgs experimental results:

Corbett, Éboli, G–F and Gonzalez–Garcia (2012) (arXiv:1207.1344)

Updated and extended in 1211.4580 and 1304.1151.

Introduction



The Higgs discovery




Introduction



The Higgs discovery




Introduction

Outline: accessing the EWSB mechanism

• Higgs boson discovery→ A particle directly related to the EWSB.Its study is an alternative to the direct seek for new resonances.

• Huge variety of data→ Higgs analysis, TGV, EWPD...

• Main ingredients of Leff studied during the last O(30) years

• Apply to decipher the nature of the observed state→ deviations, (de)correlations betweeninteractions, special kinematics, new signals

Studying the Higgs interactions may be the fastest track to understand the origin of EWSB.

Indirect approach

Model independentparametrization

→ EFFECTIVE LAGRANGIANAPPROACH!Juan González Fraile (UB) HEFT 2014 Madrid, September 2014 6 / 19
Effective Lagrangian for Higgs Interactions

Effective Lagrangian: the linear realization

Bottom-up model-independent effective Lagrangian approach:


∑n

f(4+m)n

ΛmO(4+m)n

• Particle content: There is no undiscovered low energy particle.Observed state: scalar, SU(2) doublet, CP-even, narrow and no overlapping resonances.

• Symmetries: SU(3)c ⊗ SU(2)L ⊗ U(1)Y SM local symmetry (linearly realized).Global symmetries: lepton and baryon number conservation.

59 dimension-6 operators are enough...

� Reduced set considering only C and P even2.� EOM to eliminate/choose the basis.� Huge variety of data to make the choice and reduce the LHC studied set: DATA–DRIVEN.

2Non–linear CP–odd→arxiv:1406.6367.





∑n

f(4+m)n

ΛmO(4+m)n → Ld=6 =

∑n

fn

Λ2On










∑n

f(4+m)n

ΛmO(4+m)n → Ld=6 =

∑n

fn

Λ2On







The right of choiceHiggs interactions with gauge bosons3:

OGG = Φ†Φ GaµνGaµν , OWW = Φ†ŴµνŴµνΦ , OBB = Φ†B̂µν B̂µνΦ ,

OBW = Φ†B̂µνŴµνΦ , OW = (DµΦ)†Ŵµν(DνΦ) , OB = (DµΦ)†B̂µν(DνΦ) ,

OΦ,1 =(DµΦ

)† Φ Φ† (DµΦ) , OΦ,2 = 12 ∂µ (Φ†Φ) ∂µ (Φ†Φ) , OΦ,4 = (DµΦ)† (DµΦ) (Φ†Φ) ,Higgs interactions with fermions:

OeΦ,ij = (Φ†Φ)(L̄iΦeRj ) O(1)ΦL,ij

= Φ†(i↔DµΦ)(L̄iγ

µLj) O(3)ΦL,ij

= Φ†(i↔DaµΦ)(L̄iγ

µσaLj)

OuΦ,ij = (Φ†Φ)(Q̄iΦ̃uRj ) O(1)ΦQ,ij

= Φ†(i↔DµΦ)(Q̄iγ

µQj) O(3)ΦQ,ij

= Φ†(i↔DaµΦ)(Q̄iγ

µσaQj)

OdΦ,ij = (Φ†Φ)(Q̄iΦdRj) O(1)Φe,ij = Φ

†(i↔DµΦ)(ēRiγ

µeRj )

O(1)Φu,ij = Φ†(i

↔DµΦ)(ūRiγ

µuRj )

O(1)Φd,ij

= Φ†(i↔DµΦ)(d̄Riγ

µdRj )

O(1)Φud,ij

= Φ̃†(i↔DµΦ)(ūRiγ

µdRj )

In the absence of theoretical prejudice chose a basis where the operators are more directly related to the existing data

TGV, Z properties, W decays, low energy ν scattering, atomic P , FCNC, Moller scattering P and e+e− → ff̄ at LEP2 and

tree level contribution to the oblique parameters: must avoid blind directions.

3DµΦ =

(∂µ + i

12g′Bµ + ig

σa2Waµ

)Φ, B̂µν = i

g′2Bµν , Ŵµν = i

g2σaWaµν





OΦ,1 =(DµΦ

)† Φ Φ† (DµΦ) , OΦ,2 = 12 ∂µ (Φ†Φ) ∂µ (Φ†Φ) , OΦ,4 = (DµΦ)† (DµΦ) (Φ†Φ) ,

Also to HV V andOBW to ∆S and V V V .

3DµΦ =

(∂µ + i

12g′Bµ + ig

σa2Waµ

)Φ, B̂µν = i


g2σaWaµν





OΦ,1 =(DµΦ


Also to HV V andOBW to ∆S and V V V .

3DµΦ =

(∂µ + i

12g′Bµ + ig

σa2Waµ

)Φ, B̂µν = i


g2σaWaµν





OΦ,1 =(DµΦ


� Contribute to HV V , V V V and V V V V

� Redefine Scalar field:

H = h

[1 +

v2

2Λ2

(fΦ,1 + 2fΦ,2 + fΦ,4)

)]

⇒ Rescale of all the Couplings of the Higgs.

� In additionOφ,1 contributes to ∆T

3DµΦ =

(∂µ + i

12g′Bµ + ig

σa2Waµ

)Φ, B̂µν = i


g2σaWaµν





OΦ,1 =(DµΦ


� Contribute to HV V , V V V and V V V V

� Redefine Scalar field:

H = h

[1 +

v2

2Λ2

(fΦ,1 + 2fΦ,2 + fΦ,4)

)]

⇒ Rescale of all the Couplings of the Higgs.

� In additionOφ,1 contributes to ∆T

3DµΦ =

(∂µ + i

12g′Bµ + ig

σa2Waµ

)Φ, B̂µν = i


g2σaWaµν





OΦ,1 =(DµΦ




µLj) O(3)ΦL,ij


µσaLj)



µQj) O(3)ΦQ,ij


µσaQj)



µeRj )


↔DµΦ)(ūRiγ

µuRj )

O(1)Φd,ij


µdRj )

O(1)Φud,ij


µdRj )




3DµΦ =

(∂µ + i

12g′Bµ + ig

σa2Waµ

)Φ, B̂µν = i


g2σaWaµν





OΦ,1 =(DµΦ




µLj) O(3)ΦL,ij


µσaLj)



µQj) O(3)ΦQ,ij


µσaQj)



µeRj )


↔DµΦ)(ūRiγ

µuRj )

O(1)Φd,ij


µdRj )

O(1)Φud,ij


µdRj )




3DµΦ =

(∂µ + i

12g′Bµ + ig

σa2Waµ

)Φ, B̂µν = i


g2σaWaµν





OΦ,1 =(DµΦ




µLj) O(3)ΦL,ij


µσaLj)



µQj) O(3)ΦQ,ij


µσaQj)



µeRj )


↔DµΦ)(ūRiγ

µuRj )

O(1)Φd,ij


µdRj )

O(1)Φud,ij


µdRj )


TGV,

Z properties, W decays, low energy ν scattering, atomic P , FCNC, Moller scattering P and e+e− → ff̄ at LEP2 and


3DµΦ =

(∂µ + i

12g′Bµ + ig

σa2Waµ

)Φ, B̂µν = i


g2σaWaµν





OΦ,1 =(DµΦ




µLj) O(3)ΦL,ij


µσaLj)



µQj) O(3)ΦQ,ij


µσaQj)



µeRj )


↔DµΦ)(ūRiγ

µuRj )

O(1)Φd,ij


µdRj )

O(1)Φud,ij


µdRj )




3DµΦ =

(∂µ + i

12g′Bµ + ig

σa2Waµ

)Φ, B̂µν = i


g2σaWaµν




OBW = Φ†B̂µνŴµνΦ ,

OW = (DµΦ)†Ŵµν(DνΦ) , OB = (DµΦ)†B̂µν(DνΦ) ,

OΦ,1 =(DµΦ

)† Φ Φ† (DµΦ) ,

OΦ,2 = 12 ∂µ(Φ†Φ

)∂µ

(Φ†Φ

),

OΦ,4 =(DµΦ

)† (DµΦ) (Φ†Φ) ,

Higgs interactions with fermions:

OeΦ,33 = (Φ†Φ)(L̄3ΦeR3 )

O(1)ΦL,ij


µLj) O(3)ΦL,ij


µσaLj)



µQj) O(3)ΦQ,ij


µσaQj)

OdΦ,33 = (Φ†Φ)(Q̄3ΦdR3)

O(1)Φe,ij = Φ†(i

↔DµΦ)(ēRiγ

µeRj )


↔DµΦ)(ūRiγ

µuRj )

O(1)Φd,ij


µdRj )

O(1)Φud,ij


µdRj )




3DµΦ =

(∂µ + i

12g′Bµ + ig

σa2Waµ

)Φ, B̂µν = i


g2σaWaµν



Leff = −αsv

8π

fg

Λ2OGG+

fΦ,2

Λ2OΦ,2+

fBB

Λ2OBB+

fWW

Λ2OWW+

fB

Λ2OB +

fW

Λ2OW+

fτ

Λ2OeΦ,33 +

fbot

Λ2OdΦ,33

Unitary gauge:

LHVVeff = gHgg HGaµνG

aµν+ gHγγ HAµνA

µν+ g

(1)HZγ

AµνZµ∂νH + g

(2)HZγ

HAµνZµν

+ g(1)HZZ

ZµνZµ∂νH + g

(2)HZZ

HZµνZµν

+ g(3)HZZ

HZµZµ

+ +g(1)HWW

(W

+µνW

−µ∂νH + h.c.

)+ g

(2)HWW

HW+µνW

−µν+ g

(3)HWW

HW+µ W

−µ

LHffeff

= gfHij

f̄′Lf′RH + h.c.

gHgg = −αs

8π

fgv

Λ2, gHγγ = −

(g2vs2

2Λ2

)fWW + fBB

2,

g(1)HZγ

=

(g2v

2Λ2

)s(fW − fB)

2c, g

(2)HZγ

=

(g2v

2Λ2

)s[2s2fBB − 2c2fWW ]

2c,

g(1)HZZ

=

(g2v

2Λ2

)c2fW + s

2fB

2c2, g

(2)HZZ

= −(g2v

2Λ2

)s4fBB + c

4fWW

2c2,

g(1)HWW

=

(g2v

2Λ2

)fW

2, g

(2)HWW

= −(g2v

2Λ2

)fWW ,

gfHij

= −mfi

vδij +

v2

√2Λ2

f′fΦ,ij , g

Φ,2Hxx

= gSMHxx

(1−

v2

2

fΦ,2

Λ2

)Juan González Fraile (UB) HEFT 2014 Madrid, September 2014 9 / 19


Leff = −αsv

8π

fg

Λ2OGG+

fΦ,2

Λ2OΦ,2+

fBB

Λ2OBB+

fWW

Λ2OWW+

fB

Λ2OB +

fW

Λ2OW+

fτ

Λ2OeΦ,33 +

fbot

Λ2OdΦ,33

Unitary gauge:



µν+ g

(1)HZγ

AµνZµ∂νH + g

(2)HZγ

HAµνZµν

+ g(1)HZZ

ZµνZµ∂νH + g

(2)HZZ

HZµνZµν

+ g(3)HZZ

HZµZµ

+ +g(1)HWW

(W

+µνW

−µ∂νH + h.c.

)+ g

(2)HWW

HW+µνW

−µν+ g

(3)HWW

HW+µ W

−µ

LHffeff

= gfHij


gHgg = −αs

8π

fgv

Λ2, gHγγ = −

(g2vs2

2Λ2

)fWW + fBB

2,

g(1)HZγ

=

(g2v

2Λ2

)s(fW − fB)

2c, g

(2)HZγ

=

(g2v

2Λ2


2c,

g(1)HZZ

=

(g2v

2Λ2

)c2fW + s

2fB

2c2, g

(2)HZZ

= −(g2v

2Λ2

)s4fBB + c

4fWW

2c2,

g(1)HWW

=

(g2v

2Λ2

)fW

2, g

(2)HWW

= −(g2v

2Λ2

)fWW ,

gfHij

= −mfi

vδij +

v2

√2Λ2

f′fΦ,ij , g

Φ,2Hxx

= gSMHxx

(1−

v2

2

fΦ,2

Λ2



Leff = −αsv

8π

fg

Λ2OGG+

fΦ,2

Λ2OΦ,2+

fBB

Λ2OBB+

fWW

Λ2OWW+

fB

Λ2OB +

fW

Λ2OW+

fτ

Λ2OeΦ,33 +

fbot

Λ2OdΦ,33

Unitary gauge:



µν+ g

(1)HZγ

AµνZµ∂νH + g

(2)HZγ

HAµνZµν

+ g(1)HZZ

ZµνZµ∂νH + g

(2)HZZ

HZµνZµν

+ g(3)HZZ

HZµZµ

+ +g(1)HWW

(W

+µνW

−µ∂νH + h.c.

)+ g

(2)HWW

HW+µνW

−µν+ g

(3)HWW

HW+µ W

−µ

LHffeff

= gfHij


gHgg = −αs

8π

fgv

Λ2, gHγγ = −

(g2vs2

2Λ2

)fWW + fBB

2,

g(1)HZγ

=

(g2v

2Λ2

)s(fW − fB)

2c, g

(2)HZγ

=

(g2v

2Λ2


2c,

g(1)HZZ

=

(g2v

2Λ2

)c2fW + s

2fB

2c2, g

(2)HZZ

= −(g2v

2Λ2

)s4fBB + c

4fWW

2c2,

g(1)HWW

=

(g2v

2Λ2

)fW

2, g

(2)HWW

= −(g2v

2Λ2

)fWW ,

gfHij

= −mfi

vδij +

v2

√2Λ2

f′fΦ,ij , g

Φ,2Hxx

= gSMHxx

(1−

v2

2

fΦ,2

Λ2



Leff = −αsv

8π

fg

Λ2OGG+

fΦ,2

Λ2OΦ,2+

fBB

Λ2OBB+

fWW

Λ2OWW+

fB

Λ2OB +

fW

Λ2OW+

fτ

Λ2OeΦ,33 +

fbot

Λ2OdΦ,33

Unitary gauge:



µν+ g

(1)HZγ

AµνZµ∂νH + g

(2)HZγ

HAµνZµν

+ g(1)HZZ

ZµνZµ∂νH + g

(2)HZZ

HZµνZµν

+ g(3)HZZ

HZµZµ

+ +g(1)HWW

(W

+µνW

−µ∂νH + h.c.

)+ g

(2)HWW

HW+µνW

−µν+ g

(3)HWW

HW+µ W

−µ

LHffeff

= gfHij


gHgg = −αs

8π

fgv

Λ2, gHγγ = −

(g2vs2

2Λ2

)fWW + fBB

2,

g(1)HZγ

=

(g2v

2Λ2

)s(fW − fB)

2c, g

(2)HZγ

=

(g2v

2Λ2


2c,

g(1)HZZ

=

(g2v

2Λ2

)c2fW + s

2fB

2c2, g

(2)HZZ

= −(g2v

2Λ2

)s4fBB + c

4fWW

2c2,

g(1)HWW

=

(g2v

2Λ2

)fW

2, g

(2)HWW

= −(g2v

2Λ2

)fWW ,

gfHij

= −mfi

vδij +

v2

√2Λ2

f′fΦ,ij , g

Φ,2Hxx

= gSMHxx

(1−

v2

2

fΦ,2

Λ2



Leff = −αsv

8π

fg

Λ2OGG+

fΦ,2

Λ2OΦ,2+

fBB

Λ2OBB+

fWW

Λ2OWW+

fB

Λ2OB +

fW

Λ2OW+

fτ

Λ2OeΦ,33 +

fbot

Λ2OdΦ,33

Unitary gauge:



µν+ g

(1)HZγ

AµνZµ∂νH + g

(2)HZγ

HAµνZµν

+ g(1)HZZ

ZµνZµ∂νH + g

(2)HZZ

HZµνZµν

+ g(3)HZZ

HZµZµ

+ +g(1)HWW

(W

+µνW

−µ∂νH + h.c.

)+ g

(2)HWW

HW+µνW

−µν+ g

(3)HWW

HW+µ W

−µ

LHffeff

= gfHij


gHgg = −αs

8π

fgv

Λ2, gHγγ = −

(g2vs2

2Λ2

)fWW + fBB

2,

g(1)HZγ

=

(g2v

2Λ2

)s(fW − fB)

2c, g

(2)HZγ

=

(g2v

2Λ2


2c,

g(1)HZZ

=

(g2v

2Λ2

)c2fW + s

2fB

2c2, g

(2)HZZ

= −(g2v

2Λ2

)s4fBB + c

4fWW

2c2,

g(1)HWW

=

(g2v

2Λ2

)fW

2, g

(2)HWW

= −(g2v

2Λ2

)fWW ,

gfHij

= −mfi

vδij +

v2

√2Λ2

f′fΦ,ij , g

Φ,2Hxx

= gSMHxx

(1−

v2

2

fΦ,2

Λ2



Leff = −αsv

8π

fg

Λ2OGG+

fΦ,2

Λ2OΦ,2+

fBB

Λ2OBB+

fWW

Λ2OWW+

fB

Λ2OB +

fW

Λ2OW+

fτ

Λ2OeΦ,33 +

fbot

Λ2OdΦ,33

Unitary gauge:



µν+ g

(1)HZγ

AµνZµ∂νH + g

(2)HZγ

HAµνZµν

+ g(1)HZZ

ZµνZµ∂νH + g

(2)HZZ

HZµνZµν

+ g(3)HZZ

HZµZµ

+ +g(1)HWW

(W

+µνW

−µ∂νH + h.c.

)+ g

(2)HWW

HW+µνW

−µν+ g

(3)HWW

HW+µ W

−µ

LHffeff

= gfHij


gHgg = −αs

8π

fgv

Λ2, gHγγ = −

(g2vs2

2Λ2

)fWW + fBB

2,

g(1)HZγ

=

(g2v

2Λ2

)s(fW − fB)

2c, g

(2)HZγ

=

(g2v

2Λ2


2c,

g(1)HZZ

=

(g2v

2Λ2

)c2fW + s

2fB

2c2, g

(2)HZZ

= −(g2v

2Λ2

)s4fBB + c

4fWW

2c2,

g(1)HWW

=

(g2v

2Λ2

)fW

2, g

(2)HWW

= −(g2v

2Λ2

)fWW ,

gfHij

= −mfi

vδij +

v2

√2Λ2

f′fΦ,ij , g

Φ,2Hxx

= gSMHxx

(1−

v2

2

fΦ,2

Λ2

Analysis Framework

Higgs collider data

Analysis Framework

Higgs collider data

χ2 = minξpull

∑j

(µj − µexpj )2

σ2j+∑pull

(ξpull

σpull

)2Where

µF =�Fggσ

anogg + �

FV BF σ

anoV BF + �

FWHσ

anoWH + �

FZHσ

anoZH + �

Ftt̄H

σanott̄H

�FggσSMgg + �

FV BF σ

SMVBF + �

FWHσ

SMWH + �

FZHσ

SMZH + �

Ftt̄H

σSMtt̄H

⊗BRano[h→ F ]BRSM [h→ F ]

.

where σanox = σanox (1 + ξx).

For the anomalous calculations:

σanoY =σanoYσSMY

∣∣∣∣∣tree

σSMY

∣∣∣soa

and

Γano(h→ X) =Γano(h→ X)ΓSM (h→ X)

∣∣∣∣tree

ΓSM (h→ X)∣∣∣soa

Analysis Framework

TGV and EWPDTGV:

LWWV = −igWWV

{gV1

(W

+µνW

−µVν −W+µ VνW

−µν)

+ κVW+µ W

−ν V

µν+

λV

m2W

W+µνW

− νρVµρ

}

∆gZ1 = gZ1 − 1 =

g2v2

8c2Λ2fW ,

∆κγ = κγ − 1 =g2v2

8Λ2

(fW + fB

), ↔

∆κZ = κZ − 1 =g2v2

8c2Λ2

(c2fW − s2fB

).

gZ1 = 0.984+0.049−0.049 LEP

κγ = 1.004+0.024−0.025 ρ = 0.11

EWPD:

∆S = 0.00± 0.10 ∆T = 0.02± 0.11 ∆U = 0.03± 0.09

ρ =

1 0.89 −0.550.89 1 −0.8−0.55 −0.8 1

OBW and OΦ,1 can already be neglected for the LHC analysis:

α∆S = e2v2

Λ2fBW and α∆T =

1

2

v2

Λ2fΦ,1 .

We add the rest of one–loop contributions in parts of the analysis.

Analysis Framework

S,T,U Parameters

α∆S =1

6

e2

16π2

{3(fW + fB)

m2H

Λ2log

(Λ2

m2H

)+

+ 2[(5c

2 − 2)fW − (5c2 − 3)fB

]m2ZΛ2

log

(Λ2

m2H

)

−[(22c

2 − 1)fW − (30c2

+ 1)fB

]m2ZΛ2

log

(Λ2

m2Z

)

− 24c2fWWm2Z

Λ2log

(Λ2

m2H

)+ 2fΦ,2

v2

Λ2log

(Λ2

m2H

)},

α∆T =3

4c2

e2

16π2

{fB

m2H

Λ2log

(Λ2

m2H

)

+ (c2fW + fB)

m2Z

Λ2log

(Λ2

m2H

)

+[2c

2fW + (3c

2 − 1)fB]m2Z

Λ2log

(Λ2

m2Z

)− fΦ,2

v2

Λ2log

(Λ2

m2H

)},

α∆U = −1

3

e2s2

16π2

{(−4fW + 5fB)

m2Z

Λ2log

(Λ2

m2H

)

+ (2fW − 5fB)m2Z

Λ2log

(Λ2

m2Z

)}

Present Status

∆χ2 vrs fX

arXiv:1207.1344, 1211.4580http://hep.if.usp.br/Higgs

OGG OWW OBB OW OB OΦ,2 Obot Oτ

Present Status

∆χ2 vrs fX

Present Status

∆χ2 vrs fX

arXiv:1207.1344, 1211.4580http://hep.if.usp.br/Higgs

OGG OWW OBB OW OB OΦ,2 Obot Oτ

Present Status

BRs and production CS

Present Status

BRs and production CS

Determining TGV from Higgs data

Determining TGV from Higgs data arxiv:1304.1151• Gauge Invariance→ TGV4 and Higgs couplings related: OW and OB• Complementarity in experimental searches: Higgs data bounds onfW ⊗ fB ≡ ∆κγ ⊗∆gZ1

∆gZ1 = g

Z1 − 1 =

g2v2

8c2Λ2fW ,

∆κγ = κγ − 1 =g2v2

8Λ2

(fW + fB

),

∆κZ = κZ − 1 =g2v2

8c2Λ2

(c2fW − s

2fB

).

(Non–linear decorrelation→ Ilaria’s talk)

4TGV = Triple Gauge boson Vertex (WWZ, WWγ)Juan González Fraile (UB) HEFT 2014 Madrid, September 2014 16 / 19
Determining TGV from Higgs data

Determining TGV from Higgs data arxiv:1304.1151• Gauge Invariance→ TGV4 and Higgs couplings related: OW and OB• Complementarity in experimental searches: Higgs data bounds onfW ⊗ fB ≡ ∆κγ ⊗∆gZ1

∆gZ1 = g

Z1 − 1 =

g2v2

8c2Λ2fW ,

∆κγ = κγ − 1 =g2v2

8Λ2

(fW + fB

),

∆κZ = κZ − 1 =g2v2

8c2Λ2

(c2fW − s

2fB

).

(Non–linear decorrelation→ Ilaria’s talk)

4TGV = Triple Gauge boson Vertex (WWZ, WWγ)Juan González Fraile (UB) HEFT 2014 Madrid, September 2014 16 / 19
Outlook

Exploiting kinematics.LWWV = −igWWV

{gV1

(W

+µνW

−µVν

−W+µ VνW−µν

)+ κVW

+µ W

−ν V

µν

}∆g

Z1 =

g2v2

8c2Λ2fW ,

∆κγ =g2v2

8Λ2

(fW + fB

),

∆κZ =g2v2

8c2Λ2

(c2fW − s

2fB

).

LHWWeff = +g(1)HWW

(W

+µνW

−µ∂νH + h.c.

)+g

(2)HWW

HW+µνW

−µν+ g

(3)HWW

HW+µ W

−µ

g(1)HWW

=

(g2v

2Λ2

)fW

2,

g(2)HWW

= −(g2v

2Λ2

)fWW ,

g(3)HWW

= gSMHWW

(1−

v2

2

fΦ,2

Λ2

)

Assume: LHC see deviation to TGV within 95% CLbound verifying ∆κγ = ∆κZ = cos2 θW∆g

Z1

e. g.fW

Λ2= −6.5 TeV−2

Leading to the excess

σ(pp→ WH) = 1.65σSM (pp→ WH)

⇒ but with a distorted H pT spectrum!

Relaxing assumptions

Relaxing assumptions: CP–oddM.B. Gavela, J. G–F, M. C. Gonzalez–Garcia, L. Merlo, S. Rigolin and J. Yepes→ arxiv:1406.1823

• List & applications of CP–odd non–linear operators:Lchiral = LSM + ∆L/CP ,

∆L/CP = cB̃ SB̃(h) + cW̃ SW̃ (h) + cG̃ SG̃(h) + c2D S2D(h) +16∑i=1

ci Si(h) .

• Use CP–odd sensitive signals

:

Fermionic EDMs (sensitive to κ̃γ , g̃hγγ )

γ

W W

f ff ′

q

p2p1

CP–violating TGV

CP–violation on Higgs physics: h→ ZZ, e. g. CMS analysis:

A(h→ ZZ) = v−1(d1m

2Z�∗1�∗2 + d2f

∗(1)µν f

µν∗(2)+ d3f

∗(1)µν f̃

µν∗(2)),





ci Si(h) .

• Use CP–odd sensitive signals:Fermionic EDMs (sensitive to κ̃γ , g̃hγγ )

γ

W W

f ff ′

q

p2p1

CP–violating TGV


A(h→ ZZ) = v−1(d1m

2Z�∗1�∗2 + d2f

∗(1)µν f

µν∗(2)+ d3f

∗(1)µν f̃

µν∗(2)),





ci Si(h) .


γ

W W

f ff ′

q

p2p1

CP–violating TGV


A(h→ ZZ) = v−1(d1m

2Z�∗1�∗2 + d2f

∗(1)µν f

µν∗(2)+ d3f

∗(1)µν f̃

µν∗(2)),





ci Si(h) .


γ

W W

f ff ′

q

p2p1

CP–violating TGV


A(h→ ZZ) = v−1(d1m

2Z�∗1�∗2 + d2f

∗(1)µν f

µν∗(2)+ d3f

∗(1)µν f̃

µν∗(2)),

Conclusions

Conclusions

THANK YOU!

• Model independent analysis where the effects of new physics in the Higgs couplings areparametrized in Leff . If SU(2)L doublet→ SU(2)L × U(1)Y gauge symmetry linearlyrealized:

Leff =∑n

fn

Λ2On ,

• Power to the data→ operators whose coefficients are more easily related to existing data.So far→ Higgs boson SM–like.

• Exploit interesting complementarity between experimental searches: TGV and Higgsdata.

arXiv:1207.1344, 1211.4580, 1304.1151

Outlook:

� Study non–linear CP-odd operators→ Recently finished: arxiv:1406.6367� Combine the full Higgs and TGV 7+8 TeV sets of data in this framework.� Jump from signal strengths to exploit the kinematic structures

Conclusions

Conclusions THANK YOU!• Model independent analysis where the effects of new physics in the Higgs couplings are

parametrized in Leff . If SU(2)L doublet→ SU(2)L × U(1)Y gauge symmetry linearlyrealized:

Leff =∑n

fn

Λ2On ,

• Power to the data→ operators whose coefficients are more easily related to existing data.So far→ Higgs boson SM–like.

• Exploit interesting complementarity between experimental searches: TGV and Higgsdata.

arXiv:1207.1344, 1211.4580, 1304.1151

Outlook:

� Study non–linear CP-odd operators→ Recently finished: arxiv:1406.6367� Combine the full Higgs and TGV 7+8 TeV sets of data in this framework.� Jump from signal strengths to exploit the kinematic structures


IntroductionEffective Lagrangian for Higgs InteractionsAnalysis FrameworkPresent StatusDetermining TGV from Higgs dataOutlookRelaxing assumptionsConclusions

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