concha gonzalez-garcia · effective lagrangian for higgs interactions concha gonzalez-garcia (yitp...

EFFECTIVE LAGRANGIAN FOR

HIGGS INTERACTIONS

Concha Gonzalez-Garcia(YITP Stony Brook & ICREA U. Barcelona )

MPIK Heidelberg, July 24th 2013

T. Corbett, O. Eboli and J. Gonzalez-Fraile

arXiv:1207.1344, 1211.4580, 1304.1151

http://hep.if.usp.br/Higgs

EFFECTIVE LAGRANGIAN FOR

HIGGS INTERACTIONS

Concha Gonzalez-Garcia(ICREA-U Barcelona & YITP-Stony Brook)

MPKI Heidelberg, July 24th, 2013

OUTLINE

Introduction: the SM Higgs Boson

Effective Lagrangian for SM-like Higgs Boson

Data Driven Choice of Operator Basis

Application to Present Analysis of Higgs Data

Summary

Introduction: the Standard Model

Introduction: the Standard Model• The SM is a gauge theory based on the symmetry group

SU(3)C × SU(2)L × U(1)Y


SU(3)C × SU(2)L × U(1)Y

With matter made of3 fermion generationswith quantum numbers

(1, 2)− 12

(3, 2) 16

(1, 1)−1 (3, 1) 23

(3, 1)− 13

(

νe

e

)

L

(

ui

di

)

LeR ui

R diR

(

νµ

µ

)

L

(

ci

si

)

LµR ci

R siR

(

ντ

τ

)

L

(

ti

bi

)

LτR tiR bi

R

And the gauge bosonscarriersof thestrong, weakandelectromagneticinteractions

g W± Z0 γ


SU(3)C × SU(2)L × U(1)Y

With matter made of3 fermion generationswith quantum numbers

(1, 2)− 12

(3, 2) 16

(1, 1)−1 (3, 1) 23

(3, 1)− 13

(

νe

e

)

L

(

ui

di

)

LeR ui

R diR

(

νµ

µ

)

L

(

ci

si

)

LµR ci

R siR

(

ντ

τ

)

L

(

ti

bi

)

LτR tiR bi

R

And the gauge bosonscarriersof thestrong, weakandelectromagneticinteractions

g W± Z0 γ

• In a gauge theory the Lagrangian is fully determined by symmetry• In 90’s we tested fermion-GB interactions to better than 1%• Also we have tested GB self-interactions to 5-10%

Introduction: SM• Plus: Gauge Theories are renormalizable (theoretically sound)

• Minus: GS forbids mass for gauge-bosons (for SM group also for fermions)

VµV µ or fRfL are not Gauge Invariant

• But we know that many particles have mass:

Most fermionshave masses

W± andZ0 have mass (weak interaction is short range)







• To give mass to these states without spoiling renormalizability:

⇒ Spontaneous Symmetry Breaking

≡ It is the ground state (vacuum) which breaks the symmetry

≡ Vacuum is invariant only under a subgroup of the GS

⇒ There will be massless excitations

⇒ In presence of long range forces massless excitations disappear

and the force becomes short ranged

≡ Generation of mass for the Gauge Bosons







• To give mass to these states without spoiling renormalizability:

⇒ Spontaneous Symmetry Breaking

≡ It is the ground state (vacuum) which breaks the symmetry

≡ Vacuum is invariant only under a subgroup of the GS

⇒ There will be massless excitations

⇒ In presence of long range forces massless excitations disappear

and the force becomes short ranged

≡ Generation of mass for the Gauge Bosons

• In SM EWSSB: SU(3)C × SU(2)L × U(1)Y ⇒ SU(3)C × U(1)EM

Introduction: Higgs Mechanism of EWSB

• To allow for EWSB we need to addsomethingto parametrize this non-trivial vacuum

Lorentz Invariance⇒ somethingcannot have spin≡ scalar

EWSB⇒ somethingmust benon-singletSU(2)L but colorlessandelec neutral





• Most minimal choice:

something≡ fundamental scalarSU(2) doublet: Φ(1, 2) 12

=

(

φ+

φ0

)

With particular form of the potential[Englert& Brout;Higgs:Guralnik&Hagen&Kibble]

LΦ = (DµΦ)(DµΦ)† − (µ2|Φ|2 + λ|Φ|4)with µ2 < 0





• Most minimal choice:

something≡ fundamental scalarSU(2) doublet: Φ(1, 2) 12

=

(

φ+

φ0

)

With particular form of the potential[Englert& Brout;Higgs:Guralnik&Hagen&Kibble]

LΦ = (DµΦ)(DµΦ)† − (µ2|Φ|2 + λ|Φ|4)with µ2 < 0

• SSB≡ choice of vacuum:Φ0 = 1√2

(

0

v

)

About this vacuum

⇒ W andZ become massive

⇒ fermionscan acquire a mass via Yukawa interactionsλf ffΦ

⇒ Physical scalar excitationh(x): Φ(x) = 1√2

(

0

v + h(x)

)

The Higgs Boson

Intro: The Higgs Boson

• A few properties of the Higgs Boson

∗ Neutral Scalar with CP=+10+

∗ Its mass is the only free parametermH =√

2λ v

∗ Interactions with GBand fermionsproportional to their masses

Intro: Higgs Decay Modes

Γ(h → ff) =GF m2

f (Nc)

4√

2πMh (1 − rf )

32 ri ≡ 4M2

i

M2h

Γ(h → W+W−) =GF M3

h

8π√

2

√1 − rW (1 − rW + 3

4r2

W )

Γ(h → ZZ) =GF M3

h

8π√

2

√1 − rZ(1 − rZ + 3

4r2

Z)

Γ0(h → gg) =GF α2

sM3h

64√

2π3 |X

q

F1/2(rq) |2 Γ(h → γγ) = α2GF

128√

2π3 gV M3h |

X

q,W

NciQ2i Fi(ri) |2

F1/2(rq) ≡ −2rq [1 + (1 − rq)f(rq)] f(x) =

8

>

>

>

>

>

<

>

>

>

>

>

:

sin−2(p

1/x), if x ≥ 1

− 14

2

6

6

4

log

0

B

B

@

1+√

1−x1−

√1−x

1

C

C

A

− iπ

3

7

7

5

2

, if x < 1,FW (rW ) = 2 + 3rW [1 + (2 − rW )f(rW )]

50.0 100.0 150.0 200.0Mh (GeV)

10-4

10-3

10-2

10-1

100

Hig

gs B

ranc

hing

Rat

ios

Higgs Branching Ratios to Fermion Pairs

bb

τ+τ-

cc

ss

µ+µ-

50.0 100.0 150.0 200.0Mh (GeV)

10-6

10-5

10-4

10-3

10-2

10-1

100

Hig

gs B

ranc

hing

Rat

ios

Higgs Branching Ratios to Gauge Boson Pairs

gg

γγ

ZγZZ*

WW*

50 100 200 500 100010

-3

10-2

10-1

1

10

102

Γ (H

)

(G

eV)

MH (GeV)

H→tt

140

H→ZZ

H→WW

Intro: Higgs at e+e−

σ(e+e− → Zh) =πα2λ

1/2Zh [λZh + 12

M2Z

s][1 + (1 − 4 sin2 θW )2]

192s sin4 θW cos4 θW (1 − M2Z/s)2

λZh ≡ (1 − M2h+M2

Zs

)2 − 4M2hM2

Zs2 s = (pe+ + pe−)2

180.0 190.0 200.0 210.0ECM (GeV)

0.0

0.2

0.4

0.6

σ (p

b)

Mh=90 GeVMh=100 GeVMh=110 GeV

e+e

- -> Zh

Searches at LEP (e+e−√

s = 90 − 210 GeV) ⇒ MH ≥ 114.4 GeV

Intro: Higgs at Hadron Collidersgg t H�pp (a) �pp �q0q W WH(b) �pp �qq Zf gZf gH(c) W;Zf gW;Zf gH�pp (d)Tevatron (pp

√s = 2 TeV) LHC (pp

√s = 7–14 TeV)

[GeV] HM

100 150 200 250 300

H+

X)

[pb

]

→(p

p

σ

-210

-110

1

10= 7 TeVs

LH

C H

IGG

S X

S W

G 2

01

0

H (NNLO+NNLL QCD + NLO EW)

→pp

qqH (NNLO QCD + NLO EW)

→pp

WH (NNLO QCD + NLO EW)

→pp

ZH (NNLO QCD +NLO EW)

→pp

ttH (NLO QCD)

→pp

Intro: Higgs at LHC7-8

• SM main discovery modes for a light Higgs:

pp → γγ

pp → ZZ → ℓℓℓℓ

pp → WW → ℓνℓν

Also:

pp → bb

pp → τ τ [GeV]HM

100 150 200 250

BR

[pb]

× σ

-410

-310

-210

-110

1

10

LH

C H

IGG

S X

S W

G 2

012

= 8TeVs

µl = e, τν,µν,eν = ν

q = udscb

bbν± l→WH

bb-l+ l→ZH

b ttb→ttH

-τ+τ →VBF H

-τ+τ

γγ

qqν± l→WW

ν-lν+ l→WW

qq-l+ l→ZZ

νν-l+ l→ZZ -l+l-l+ l→ZZ

Eureka!

• July 4th 2012 marks the dawning of new era


• 48 years between EWSB theory and discovery

• 1964: THEORY[Englert& Brout;Higgs:Guralnik&Hagen&Kibble]

• 2013: DATA Signal in many channelsγγ, ZZ, WW , bb , τ τ . . .

Intro: H → γγ

100 110 120 130 140 150 160

Eve

nts

/ 2 G

eV

2000

4000

6000

8000

10000

γγ→H

-1Ldt = 4.8 fb∫ = 7 TeV s

-1Ldt = 20.7 fb∫ = 8 TeV s

ATLAS

Data 2011+2012=126.8 GeV (fit)

HSM Higgs boson mBkg (4th order polynomial)

[GeV]γγm100 110 120 130 140 150 160E

vent

s -

Fitt

ed b

kg

-200-100

0100200300400500

[GeV]Hm

110 115 120 125 130 135 140 145 150

0Lo

cal p

-1410-1310-1210-1110-1010-910

-810-710-610-510-410-310-210-1101

10210

3100

expected pγγ →SM H

0Observed p

Obs. 2011Exp. 2011Obs. 2012Exp. 2012

= 7 TeVsData 2011

-1Ldt = 4.8 fb∫

= 8 TeVsData 2012 -1

Ldt = 20.7 fb∫

ATLAS

σ1σ2σ3σ4

σ5

σ6

σ7

Intro: H → ZZ∗ → 4l

[GeV]4lm100 150 200 250

Eve

nts/

5 G

eV

0

5

10

15

20

25

30

35

40

-1Ldt = 4.6 fb∫ = 7 TeV s-1Ldt = 20.7 fb∫ = 8 TeV s

4l→ZZ*→HData 2011+ 2012

SM Higgs Boson

=124.3 GeV (fit)H m

Background Z, ZZ*

tBackground Z+jets, tSyst.Unc.

ATLAS

[GeV]Hm110 120 130 140 150 160 170 180

0Lo

cal p

-1310

-1110

-910

-710

-510

-310

-110

10

310

510 Obs 2012Exp 2012Obs 2011Exp 2011Obs CombinationExp Combination

PreliminaryATLAS

4l→(*) ZZ→H-1Ldt =4.6 fb∫=7 TeV: s

-1Ldt =20.7 fb∫=8 TeV: s

σ2

σ3

σ1

σ4

σ5

σ6

σ7

[GeV]4lm110 120 130 140 150 160 170 180

Eve

nts

/ 3 G

eV

0

2

4

6

8

10

12

14

16

18

20Data

Z+X

,ZZ*γZ

=126 GeVHm

CMS Preliminary -1 = 8 TeV, L = 19.6 fbs ; -1 = 7 TeV, L = 5.1 fbs

[GeV]Hm110 120 130 140 150 160 170 180

loca

l p-v

alue

-1610

-1510

-1410

-1310

-1210

-1110

-1010

-910

-810

-710

-610

-510

-410

-310

-210

-1101

CMS Preliminary

-1 = 7 TeV, L = 5.1 fbs -1 = 8 TeV, L = 19.6 fbs

4l→ ZZ →H

σ5

σ7

Observed 7 TeV

Observed 8 TeV

Observed 7+8 TeV

Expected

Intro: MassATLAS

[GeV]Hm122 123 124 125 126 127 128 129

)µS

igna

l str

engt

h (

0

0.5

1

1.5

2

2.5

3

3.5

4 ATLAS-1Ldt = 4.6-4.8 fb∫ = 7 TeV s

-1Ldt = 20.7 fb∫ = 8 TeV s

+ZZ*+WW* combinedγγγγ →H

l 4→ ZZ* →H

νlνl → WW* →H

Best fit

68% CL

95% CL

MH = 125.5 ± 0.2stat ± 0.6sys GeV

CMS

(GeV)Xm124 126 128

ln L

∆-

2 0

1

2

3

4

5

6

7

8

9

10Combined

γγ →H

ZZ→H

Combinedγγ →H

ZZ→H

CMS Preliminary -1 19.6 fb≤ = 8 TeV, L s -1 5.1 fb≤ = 7 TeV, L s

ZZ→ + H γγ →H (ggH,ttH),

γγµ,

ZZµ

(VBF,VH)γγ

µ

MH = 125.5 ± 0.3stat ± 0.3sys GeV

Intro: Summary of Other Channels

• Signal Strengths:µ = σobs

σSM

ATLAS

)µSignal strength ( -1 0 +1

Combined

4l→ (*) ZZ→H

γγ →H

νlν l→ (*) WW→H

ττ →H

bb→W,Z H

-1Ldt = 4.6 - 4.8 fb∫ = 7 TeV: s-1Ldt = 13 - 20.7 fb∫ = 8 TeV: s

-1Ldt = 4.6 fb∫ = 7 TeV: s-1Ldt = 20.7 fb∫ = 8 TeV: s



-1Ldt = 4.6 fb∫ = 7 TeV: s-1Ldt = 13 fb∫ = 8 TeV: s

-1Ldt = 4.7 fb∫ = 7 TeV: s-1Ldt = 13 fb∫ = 8 TeV: s

= 125.5 GeVHm

0.20± = 1.30 µ

ATLAS Preliminary

CMS

*|θ|cos

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Events

/ 0

.1

0

50

100

150

200

250 Expected

+ = 2PJ

Data+

= 2PJ

Bkg. syst. uncertainty

ATLAS1

L dt = 20.7 fb∫ = 8 TeV s

γγ →H

=0%)qq

(f

=$C/N!9"C*O(@%*%"IC/9&#/(

;/9:Ou%A(G+9//%:'M(

•  K!(γγ(A%G9O(9/F:%(G#'`θfa(C/(2#::C/'N=#$$%"()"9I%('%/'C&J%(*#(t(

•  K(!(eef(!(lνlν((=%J%"9:(J9"C98:%'('%/'C&J%(*#(t!((–  ∆φ

l(l((>(?l(l((>(11(

–  2#I8C/%A(-C*+(.##'*%AN@%GC'C#/N<"%%(`.@<a(

(

•  K(!(ggf(!clM(03::(W/9:('*9*%("%G#/'*"3G&#/('%/'C&J%(*#(t!((–  Y(I9''%'(`?gZ>?gYa((9/A(X(

9/F:%'((

–  2#I8C/%A(-C*+(.@<(#"(?9*"CHN\:%I%/*N89'%A(AC'G"CIC/9/*(BCD'

XUYYUZ[( 01(2%"34(6.,6(N(\!=NK\!(=*#GD#:I((YBZ[( ^(

*|θ|cos

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Events

/ 0

.1

0

50

100

150

200

250 Expected

+ = 0PJ

Data+

= 0PJ

Bkg. syst. uncertainty

ATLAS1

L dt = 20.7 fb∫ = 8 TeV s

γγ →H

- = 0 PJ + = 1 PJ - = 1 PJ m + = 2 PJ

ATLAS

4l→ ZZ* →H -1Ldt = 4.6 fb∫ = 7 TeV s

-1Ldt = 20.7 fb∫ = 8 TeV s

γγ →H -1Ldt = 20.7 fb∫ = 8 TeV s

νeνµ/νµν e→ WW* →H -1Ldt = 20.7 fb∫ = 8 TeV s

σ1

σ2

σ3

σ4

Data

expectedsCL + = 0 Passuming J

σ 1 ±

) a

lt

P (

Js

CL

-610

-510

-410

-310

-210

-110

1

(

(

(

(

(

(

;<6;=(9/A(2?=M((N6#&#+1>O(A%G9O(I#A%'(

(

G#%*-S'U()"V*%(WX(K(2I(GH(m39/*3I(/3I8%"'(

(

N''("'#$%-"CV$(WX(!*6$'/(#$/#$6P((

((((((((((((4+,'56$6(7(R8B<(=>(

=$C/N!9"C*O(;<6;=(N(2?=(7J%"JC%-(

XUYYUZ[( 01(2%"34(6.,6(N(\!=NK\!(=*#GD#:I((YBZ[( ZZ(

2?=(ggf`cla(

(

(

2#3$:C/F'(7J%"JC%-(

•  @CV%"%/*(;$>,#"&(#)(*+%(,%-(.#'#/(2#3$:C/F'(*%'*%AM(!=?|ZYs(

N''(,*!."CD'$(E&#F(GH(^&SS/($+.$,#"C*-/(

XUYYUZ[( 01(2%"34(6.,6(N(\!=NK\!(=*#GD#:I((YBZ[( YB(

parameter value0 0.5 1 1.5 2 2.5

BSMBR

γκ

gκ

lqλ

duλ

WZλ

fκ

Vκ

= 0.37 SM

p

= 0.41 SM

p

= 0.39 SM

p

= 0.49 SM

p

= 0.23 SM

p

= 0.41 SM

p

68% CL

95% CL

-1 19.6 fb≤ = 8 TeV, L s

-1 5.1 fb≤ = 7 TeV, L s

CMS Preliminary 68% CL

95% CL

Parameter value

-1 0 1

ATLAS

-1Ldt = 4.6-4.8 fb = 7 TeV s

-1Ldt = 20.7 fb = 8 TeV s

= 125.5 GeVHm

, ZZ*, WW* Combined H

V

1

2

F

1

2

Model:

F, V

FV

1

2 Model:

VV,

FV

WZ

1

2 Model:

,Z

, WZ

ZZ,

FZ

g

1

2

1

2

Model:, g

Total uncertainty

1! 2!

!=?(P(ZYs(

!=?(P(ZYs(

!=?(P(YBs(

!=?(P(Zcs(

WZλ

duλ

lqλWZ

Model:,

Z,

WZ

ZZ,

FZ

FVModel:

VV,

FV

=?=?=?=?=?

Model:

Ass

umpt

ion

only

one

ortw

oco

uplin

gsva

ried

ata

time

Intro: Couplings

• Several phenomenological multi-coupling analysis

• In general assumed re-scaled/shifted SM couplings:

SFitter-Higgs (Dursssen),Klute,Lafaye,Plhen,Rauch, Zerwas


• 48 years between EWSB theory and discovery

• 1964: THEORY[Englert& Brout;Higgs:Guralnik&Hagen&Kibble]

• 2013: DATA Signal in many channelsγγ, ZZ, WW , bb , τ τ . . .

[GeV]tm140 150 160 170 180 190 200

[G

eV]

WM

80.25

80.3

80.35

80.4

80.45

80.5

=50 GeV

HM=125.7

HM=300 G

eV

HM=600 G

eV

HM

σ 1± Tevatron average kintm

σ 1± world average WM

=50 GeV

HM=125.7

HM=300 G

eV

HM=600 G

eV

HM

68% and 95% CL fit contours measurementst and mWw/o M

68% and 95% CL fit contours measurementsH and M

t, mWw/o M

G fitter SM

Sep 12

New state fits the global SM picture[Gfitter arXiv:1209.2716]

Courtesy of O. Eboli

Effective Lagrangian for a SM-like Higgs Boson

• Someconservative/realistic/agnosticassumptions

• There is a mass gapbetween SM and NP




• OneNew State:CP EvenandSpin 0

• New State belongs toSU(2) doublet:Φ

• SU(2) × U(1) is realized linearly as in the SM




• OneNew State:CP EvenandSpin 0

• New State belongs toSU(2) doublet:Φ

• SU(2) × U(1) is realized linearly as in the SM

• Building Blocks ofLeff :

Φ DµΦ

Bµν = i g′

2 Bµν Wµν = i g2σaW a

µν Gaµν

. . . . . . . . .

• To parametrize departures from the SM predictions we write

Leff = LSM +∑

i

fi

Λ2Oi + . . .

Dimension-6 operators

Summarizing NP effects

of scaleΛ

• To parametrize departures from the SM predictions we write

Leff = LSM +∑

i

fi

Λ2Oi + . . .

Dimension-6 operators

Summarizing NP effects

of scaleΛ

• There are 59independentdimension-6 operators

[Buchmuller&Wyler;Gradzkowski et al arXiv:1008.4884]

⇒ There is freedom in choosing the operator basis

⇒ Possible to choose a basis to make best use of all available data

Application to Higgs pheno: Hagiwara, Szalapski, Zeppenfeld, hep-ph/9308347;de Camposetalhep-ph/9707511,9806307; MCG-G hep-ph/9902321; Ebolietalhep-ph/9802408,0001030

• A partial list of operators involving the scalar and SM gaugebosons

OGG = Φ†Φ GaµνGaµν OWW = Φ†WµνW µνΦ OBB = Φ†BµνBµνΦ

OBW = Φ†BµνW µνΦ OW = (DµΦ)†W µν(DνΦ) OB = (DµΦ)†Bµν(DνΦ)

OΦ,1 = (DµΦ)† Φ Φ† (DµΦ) OΦ,2 = 12∂µ

`

Φ†Φ´

∂µ

`

Φ†Φ´

OΦ,4 = (DµΦ)† (DµΦ)`

Φ†Φ´

• In Unitary Gauge Φ(x) =1√2

0

v + h(x)




OΦ,1 = (DµΦ)† Φ Φ† (DµΦ) OΦ,2 = 12∂µ

`

Φ†Φ´

∂µ

`

Φ†Φ´


Φ†Φ´

(a) Operators with Higgs and its Derivatives[ DµΦ =`

∂µ + i 12g′Bµ + ig σa

2Wa

µ

´

Φ ]

∗ Scalar Field Redefinition Required

H = h

[

1 +v2

2Λ2(fΦ,1 + 2fΦ,2 + fΦ,4))

]

⇒ Rescale of all the Couplings of the Higgs

∗ OΦ,1:Z Z

× ⇒ ∆T ∝ fΦ,1




OΦ,1 = (DµΦ)† Φ Φ† (DµΦ) OΦ,2 = 12∂µ

`

Φ†Φ´

∂µ

`

Φ†Φ´


Φ†Φ´

(b) Operators Inducing Higgs-Gauge Boson Couplings which are 1-loop in SM

∗ Coupling to Gluons:OGG In SM

∗ Coupling to Photons:OBW OWW OBB In SM




OΦ,1 = (DµΦ)† Φ Φ† (DµΦ) OΦ,2 = 12∂µ

`

Φ†Φ´

∂µ

`

Φ†Φ´


Φ†Φ´




⇒ Also HVV VVV VVVVRemoved byW, Z andg, g′

redefinitions




OΦ,1 = (DµΦ)† Φ Φ† (DµΦ) OΦ,2 = 12∂µ

`

Φ†Φ´

∂µ

`

Φ†Φ´


Φ†Φ´




⇒ Also HVV VVV VVVVRemoved byW, Z andg, g′

redefinitions

∗ OBW :Z γ

× ⇒ ∆S ∝ fBW




OΦ,1 = (DµΦ)† Φ Φ† (DµΦ) OΦ,2 = 12∂µ

`

Φ†Φ´

∂µ

`

Φ†Φ´

, OΦ,4 = (DµΦ)† (DµΦ)`

Φ†Φ´

(c) Operators with GB Stress Tensors andDµΦ [ DµΦ =`


2Wa

µ

´

Φ ]

OB OW

⇒ HVV VVV VVVV

• Higgs Coupl to Fermions are Modified by: [DµΦ =`


2Wa

µ

´

Φ ]

OeΦ,ij = (Φ†Φ)(LiΦeRj) O(1)

ΦL,ij = Φ†(i↔

DµΦ)(LiγµLj) O(3)

ΦL,ij = Φ†(i↔

DaµΦ)(Liγ

µσaLj)

OuΦ,ij = (Φ†Φ)(QiΦuRj) O(1)

ΦQ,ij = Φ†(i↔

DµΦ)(QiγµQj) O(3)

ΦQ,ij = Φ†(i↔

DaµΦ)(Qiγ

µσaQj)

OdΦ,ij = (Φ†Φ)(QiΦdRj) O(1)Φe,ij = Φ†(i

↔

DµΦ)(eRiγµeRj

)

O(1)Φu,ij = Φ†(i

↔

DµΦ)(uRiγµuRj

)

O(1)Φd,ij = Φ†(i

↔

DµΦ)(dRiγµdRj

)

O(1)Φud,ij = Φ†(i

↔

DµΦ)(uRiγµdRj

)

These Modify the Yukawa

Couplings

These Modify the Fermion Cou-

plings to Gauge Bosons

• All the Operators Contaning the Higgs areNot IndependentRelated by the Equations of Motion

Operator Basis:The Right of Choice

• Operators related by EOM lead to the same S matrix elements[Politzer;Georgi;Artz;Simma]

• The EOM lead to the relations

2OΦ,2 − 2OΦ,4 =X

ij

“

yeijOeΦ,ij + y

uijOuΦ,ij + y

dij(OdΦ,ij)

†+ h.c.

”

2OB + OBW + OBB + g′2 “

OΦ,1 − 12OΦ,2

”

= − g′22

X

i

„

−1

2O(1)

ΦL,ii+

1

6O(1)

ΦQ,ii− O(1)

Φe,ii+

2

3O(1)

Φu,ii−

1

3O(1)

Φd,ii

«

2OW + OBW + OW W + g2“

OΦ,4 − 12OΦ,2

”

= − g2

4

X

i

„

O(3)ΦL,ii

+ O(3)ΦQ,ii

«

EOM allow to Eliminate 3 Operators

Operator Basis:The Right of Choice

• Operators related by EOM lead to the same S matrix elements[Politzer;Georgi;Artz;Simma]

• The EOM lead to the relations

2OΦ,2 − 2OΦ,4 =X

ij

“

yeijOeΦ,ij + y

uijOuΦ,ij + y

dij(OdΦ,ij)

†+ h.c.

”

2OB + OBW + OBB + g′2 “

OΦ,1 − 12OΦ,2

”

= − g′22

X

i

„

−1

2O(1)

ΦL,ii+

1

6O(1)

ΦQ,ii− O(1)

Φe,ii+

2

3O(1)

Φu,ii−

1

3O(1)

Φd,ii

«

2OW + OBW + OW W + g2“

OΦ,4 − 12OΦ,2

”

= − g2

4

X

i

„

O(3)ΦL,ii

+ O(3)ΦQ,ii

«

EOM allow to Eliminate 3 Operators

Data DrivenApproach to Choice of Basis:

⇒ Avoid Theoretical Prejudice (tree vs. loop, etc...)

⇒ Choose Operator Basis Easiest to Relate to Available Data

⇒ Keep Operators Most Directly Constrained by Existing Data

• Z-pole physics, Atomic Parity Violation . . . constrain

O(1)ΦL,ij = Φ†(i

↔


ΦL,ij = Φ†(i↔

DaµΦ)(Liγ

µσaLj)

O(1)ΦQ,ij = Φ†(i

↔


ΦQ,ij = Φ†(i↔

DaµΦ)(Qiγ

µσaQj)

O(1)Φe,ij = Φ†(i

↔

DµΦ)(eRiγµeRj

)


↔

DµΦ)(uRiγµuRj

)


↔

DµΦ)(dRiγµdRj

)


↔

DµΦ)(uRiγµdRj

)

Z

Z, W



↔


ΦL,ij = Φ†(i↔

DaµΦ)(Liγ

µσaLj)


↔


ΦQ,ij = Φ†(i↔

DaµΦ)(Qiγ

µσaQj)


↔

DµΦ)(eRiγµeRj

)


↔

DµΦ)(uRiγµuRj

)


↔

DµΦ)(dRiγµdRj

)


↔

DµΦ)(uRiγµdRj

)

Z

Z, W

• EWPD Bounds:At tree level α∆S = −e2 v2

Λ2fBW α∆T = −e2 v2

2Λ2fΦ,1



↔


ΦL,ij = Φ†(i↔

DaµΦ)(Liγ

µσaLj)


↔


ΦQ,ij = Φ†(i↔

DaµΦ)(Qiγ

µσaQj)


↔

DµΦ)(eRiγµeRj

)


↔

DµΦ)(uRiγµuRj

)


↔

DµΦ)(dRiγµdRj

)


↔

DµΦ)(uRiγµdRj

)

Z

Z, W

• EWPD Bounds:At tree level α∆S = −e2 v2

Λ2fBW α∆T = −e2 v2

2Λ2fΦ,1

• Bounds on FCNC Constrain the Off-Diagonal Elements of

OeΦ,ij = (Φ†Φ)(LiΦeRj ) OuΦ,ij = (Φ†Φ)(QiΦuRj ) OdΦ,ij = (Φ†Φ)(QiΦdRj)

⇒ LHff = gfHij fLifRjH with g

fHij = −m

fi

vδij +

v2

√2Λ2

ffΦ,ij

• OperatorsOW andOB modify Triple Gauge Boson Vertex

OW = (DµΦ)†W µν(DνΦ) OB = (DµΦ)†Bµν(DνΦ)

LWWV = −igWWV

8

<

:

gV1

„

W+µνW− µV ν − W+

µ VνW− µν

«

+ κV W+µ W−

ν V µν + . . .

9

=

;

with

∆gZ1 = gZ

1 − 1 = g2v2

8c2Λ2 fW

∆κγ = κγ − 1 = g2v2

8Λ2

(

fW + fB

)

∆κZ = κZ − 1 = g2v2

8c2Λ2

(

c2fW − s2fB

)

and we have data on TGV so we keep them

• Using the EOM we eliminate: OΦ,2, OΦ,4, OBB

and choose the basis:

OGG , OBW , OWW , OW , OB , OΦ,1 , OfΦ , O(1)fΦ , O(3)

fΦ




fΦ

• Usingpre-Higgsdata×most strongly constrained:

× × × ×




fΦ

• Usingpre-Higgsdata×most strongly constrained:

× × × ×

• After Discarding the Constrained Operators⇒ 13

∗ 4 Involving Gauge Bosons: OGG , OWW , OW , OB

∗ 9 Involving Fermions: OeΦ,ii , OuΦ,ii , OdΦ,ii

Neglecting effects of couplings to first and second generation

Due to small statistics on ttH associate production

effects ofOuΦ,33 reabsorbed in redefinitions of coefficients ofOWW ,OGG

⇒ two relevant fermion operators left:OdΦ,33 ,OeΦ,33

• In Summary

Leff = −αsv8π

fg

Λ2OGG + fW WΛ2 OWW + fW

Λ2 OW + fBΛ2 OB + fbot

Λ2 OdΦ,33 + fτ

Λ2OeΦ,33

supplemented by shifts in the Yukawa couplings of bottom andτ

• In Summary for Analysis of Higgs Data

LHeff = gHgg HGa

µνGaµν + gHγγ HAµνAµν + g(1)HZγ AµνZµ∂νH + g

(2)HZγ HAµνZµν

+g(1)HZZ ZµνZµ∂νH + g

(2)HZZ HZµνZµν + g

(0)HZZ HZµZµ

+g(1)HWW

“

W+µνW− µ∂νH + h.c.

”

+ g(2)HWW HW+

µνW− µν + g(0)HWW HW+

µ W− µ

+X

f=bot,τ

“

gfHff fLfRH + h.c.

”

with

g(0)HZZ = M2

Z(√

2GF )1/2 g(0)HWW = M2

W (√

2GF )1/2

gHgg = fGGvΛ2 ≡ −αs

8π

fgv

Λ2 gHγγ = −“

g2vs2

2Λ2

”

fW W2

= s2c

g(2)HZγ = s2

c2g(2)HZZ = s2

2g(2)HWW

g(1)HZγ =

“

g2v2Λ2

”

s(fW −fB)2c

g(1)HZZ =

“

g2v2Λ2

”

c2fW +s2fB2c2

g(1)HWW =

“

g2v2Λ2

”

fW2

gfHff = −mf

v+ v2

√2Λ2 ff

Analysis of Higgs Data

• Inputs: signal strength for the different channelsµ =σobs

σSM

Analysis of Higgs Data

• With all the data points we construct

χ2 = minξpull

∑

j

(µj − µexpj )2

σ2j

+∑

pull

(

ξpull

σpull

)2

* Where

µF =ǫFggσano

gg (1+ξg)+ǫFV BF σano

V BF (1+ξV BF )+ǫFW H σano

W H (1+ξV H )+ǫFZH σano

ZH (1+ξV H )+ǫFttH

σanottH

ǫFggσSM

gg +ǫFV BF

σSMV BF

+ǫFW H

σSMW H

+ǫFZH

σSMZH

+ǫFttH

σSMttH

⊗ Brano[h→F ]

BrSM [h→F ]

∗ Production factorsǫFProd are given by the collaborations

∗ σSMi andΓSM

j are known to one or two–loops

∗ For anomalous contributions we scale the higher-order (h-o) effects as in SM :

σanoY =

σanoY

σSMY

∣

∣

∣

∣

tree

σSMY

∣

∣

h−o

Γano(h → X) =Γano(h → X)

ΓSM (h → X)

∣

∣

∣

∣

tree

ΓSM (h → X)∣

∣

h−o

• Also combined with

TGV Bounds: fW , fB

LWWV = −igWWV

8

<

:

gV1

„

W+µνW− µV ν − W+

µ VνW− µν

«

+ κV W+µ W−

ν V µν + . . .

9

=

;

with

∆gZ1 = gZ

1 − 1 = g2v2

8c2Λ2 fW

∆κγ = κγ − 1 = g2v2

8Λ2

(

fW + fB

)

∆κZ = κZ − 1 = g2v2

8c2Λ2

(

c2fW − s2fB

)

(from LEPEWWG for this scenario)

κγ = 0.984+0.049−0.049 gZ

1 = 1.004+0.024−0.025 with ρ = 0.11

• Also combined withEWPD: (with fWW , fW , fB at 1-loop)[Hagiwara,et al; Alam, Dawson, Szalapski]

α∆S =1

6

e2

16π2

8

>

>

>

>

<

>

>

>

>

:

3(fW + fB)m2

H

Λ2log

0

B

B

@

Λ2

m2H

1

C

C

A

+ + 2

2

6

4(5c

2 − 2)fW − (5c2 − 3)fB

3

7

5

m2Z

Λ2log

0

B

B

@

Λ2

m2H

1

C

C

A

−

2

6

4(22c2 − 1)fW − (30c2 + 1)fB

3

7

5

m2Z

Λ2log

0

B

B

@

Λ2

m2Z

1

C

C

A

− 24c2fW W

m2Z

Λ2log

0

B

B

@

Λ2

m2H

1

C

C

A

9

>

>

>

>

=

>

>

>

>

;

,

α∆T =3

4c2

e2

16π2

8

>

>

>

>

<

>

>

>

>

:

fB

m2H

Λ2log

0

B

B

@

Λ2

m2H

1

C

C

A

+ (c2

fW + fB)m2

Z

Λ2log

0

B

B

@

Λ2

m2H

1

C

C

A

+

2

6

42c2fW + (3c2 − 1)fB

3

7

5

m2Z

Λ2log

0

B

B

@

Λ2

m2Z

1

C

C

A

9

>

>

>

>

=

>

>

>

>

;

,

α∆U = −1

3

e2s2

16π2

8

>

>

>

>

<

>

>

>

>

:

(−4fW + 5fB)m2

Z

Λ2log

0

B

B

@

Λ2

m2H

1

C

C

A

+ (2fW − 5fB)m2

Z

Λ2log

0

B

B

@

Λ2

m2Z

1

C

C

A

9

>

>

>

>

=

>

>

>

>

;

More model-dependent: tree vs one-loop?, finite part?,Λ does not factorize

• Also combined with

EWPD: (with fWW , fW , fB at 1-loop)[Hagiwara,et al; Alam, Dawson, Szalapski]

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

ρ =

1 0.89 −0.55

0.89 1 −0.8

−0.55 −0.8 1

Results

• First Scenario:fg , fWW , fW , fB , fbot = 0, , fτ = 0

• Second Scenario:fg , fWW , fW , fB , fbot , fτ

Interference with SM contribution leads to (near) degeneracy

Higgs+TGV+EWPD

strong correlationfg ⊗ fbot

Best Fit and 90% CL ranges

• From Tevatron+LHC+TGV

Fit with fbot = fτ = 0 Fit with fbot andfτ

Best fit 90% CL allowed range Best fit 90% CL allowed range

fg/Λ2 (TeV−2) 0.64, 22.1 [−1.8, 2.7] ∪ [20, 25] 0.71, 22.0 [−6.2, 4.4] ∪ [18, 29]

fW W /Λ2 (TeV−2) -0.083 [−0.35, 0.15] ∪ [2.6, 3.05] -0.095 [−0.39, 0.19]

fW /Λ2 (TeV−2) 0.35 [−6.2, 8.4] -0.46 [−7.1, 6.5]

fB/Λ2 (TeV−2) -5.9 [−22, 6.7] -0.46 [−7.1, 6.5]

fbot/Λ2 (TeV−2) —– —– 0.01, 0.89 [−0.34, 0.23] ∪ [0.67, 1.2]

fτ /Λ2 (TeV−2) —– —– -0.01, 0.34 [−0.07, 0.05] ∪ [0.28, 0.40]

SM predictions within 68% CL range for all couplings

Unitarity Violation inVLVL scattering due tofW,B at 90%CL⇒ Λ . 2 TeV

Cross Sections and Branching Ratios

• From full χ2(fi) one can derive allowed ranges forσanoi andΓano

j

90% CL ranges

Interesting Correlations

Due to diphoton channel

Constraints on TGV from Higgs Results

• Gauge Invariance⇒ TGV and Higgs couplings are related:OW , OB

• Analysis of Higgs resultsmarginalizing overfg, fWW , fbot, fτ

⇒ bounds onfW ⊗ fB ≡ ∆κγ ⊗ ∆gZ1

95% CL

∆gZ1 = gZ

1 − 1 = g2v2

8c2Λ2 fW

∆κγ = κγ − 1 = g2v2

8Λ2

„

fW + fB

«

∆κZ = κZ − 1 = g2v2

8c2Λ2

„

c2fW − s2fB

«

Comparison to constraints from TGV analysis inLEP, Tevatronand ATLAS

What Next?

• To combine full Higgs and TGV 7+8 TeV data in this framework

• To exploit the different Lorentz structure of the anomalousoperators

Analysis of full kinematical distributions not only signalstrengths

Only possible within the collaborations

• To study the most promising signals for LHC-14 still allowed

H → Zγ ? H → fifj?

. . .

Concluding Remarks

• After 5 decades we have finally observed a state which seems

the one responsible for EW SSB

• So far all observations consistent with state having quantum numbers of SM

Higgs Boson

⇒ Consistent to parametrize NP in scalar sector asSU(2)×U(1) GI Leff

• Freedom of choice of basis of operators forLeff

⇒ In absence of theoretical prejudice it pays to bedata driven

• This framework consistently accounts for

relations between Higgs couplings and GB self-couplings due to GI

⇒ interesting complementarity in experimental searches

concha gonzalez-garcia · effective lagrangian for higgs interactions concha gonzalez-garcia (yitp...

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