Higgs to PhotonsBeyond the Standard

Model

G.CacciapagliaIPN, Lyon

ULB, 27 feb. 2009

G.C.,A.Deandrea,J.Llodra-Perez 0901.0927

An old friend: the Higgs Boson

• The Higgs Boson is the most valuable game at the LHC

• New Physics motivated by the radiative instability of the Brout-Englert-Higgs mechanism

• If we detect New Physics, how can we test if it has anything to do with the Higgs?

• Higgs properties

102

103

104

105

100 200 300 400 500

qq ! Wh

qq ! Zh

gg ! h

bb ! h

qb ! qth

gg,qq ! tth

qq ! qqh

mh [GeV]

! [fb]

SM Higgs production

LHC

TeV4LHC Higgs working group

The main production channelis via gluon fusion (loop induced!)

Followed by Vector Boson Fusion.

Sizable photon decay for 100<mH<150.

• H to photons and gluons couplings are loop induced

• sensitive to massive particles that play a role in the EWSB (top and W)

• most sensitive to New Physics (in the EWSB sector)!

• what can we learn from measuring them?

Definitions:

!x =m2

H

4m2x

!!! =GF !2m3

H

128!

2"3

!!!!!AW (#W ) +"

fermions

Nc,fQ2fAF (#f ) +

"

NP

Nc,NP Q2NP ANP (#NP )

!!!!!

2

!gg =GF !2

sm3H

16!

2"3

!!!!!!12

"

quarks

AF (#f ) +"

NP

C(rNP )ANP (#NP )

!!!!!!

2

AF (0) =43

, AW (0) = !7 , AS(0) =13

.

Non decoupling because the Higgs couplingsare proportional to the mass!

ANP =v

mNP

!mNP

!vAF,W,SFor New Physics loops:

A(!)" 0

Simple parameterization:

!!! =GF !2m3

H

128!

2"3

!!!!!AW (#W ) + 3"

23

#2

At(#t) [1 + $!! ] + . . .

!!!!!

2

!gg =GF !2

sm3H

16!

2"3

!!!!12At(#t) [1 + $gg] + . . .

!!!!2

!!! =!

NP

34Nc,NP Q2

NPv

mNP

"mNP

"v

AF,W,S(mNP )At

!gg =!

NP

2C(rNP )v

mNP

"mNP

"v

AF,W,S(mNP )At

where

Simple parameterization:

!!! =GF !2m3

H

128!

2"3

!!!!!AW (#W ) + 3"

23

#2

At(#t) [1 + $!! ] + . . .

!!!!!

2

!gg =GF !2

sm3H

16!

2"3

!!!!12At(#t) [1 + $gg] + . . .

!!!!2

!!! =!

NP

34Nc,NP Q2

NPv

mNP

"mNP

"v

AF,W,S(mNP )At

!gg =!

NP

2C(rNP )v

mNP

"mNP

"v

AF,W,S(mNP )At

where

ANP

At=

!"

#

1 for fermions! 21

4 for vectors14 for scalars

For heavy new physics:

Simple parameterization:

!!! =GF !2m3

H

128!

2"3

!!!!!AW (#W ) + 3"

23

#2

At(#t) [1 + $!! ] + . . .

!!!!!

2

!gg =GF !2

sm3H

16!

2"3

!!!!12At(#t) [1 + $gg] + . . .

!!!!2

!!! =!

NP

34Nc,NP Q2

NPv

mNP

"mNP

"v

AF,W,S(mNP )At

!gg =!

NP

2C(rNP )v

mNP

"mNP

"v

AF,W,S(mNP )At

where

v

mNP

!mNP

!v! v2

m2NP

Decoupling:

Simple parameterization:

!!! =GF !2m3

H

128!

2"3

!!!!!AW (#W ) + 3"

23

#2

At(#t) [1 + $!! ] + . . .

!!!!!

2

!gg =GF !2

sm3H

16!

2"3

!!!!12At(#t) [1 + $gg] + . . .

!!!!2

!!! =!

NP

34Nc,NP Q2

NPv

mNP

"mNP

"v

AF,W,S(mNP )At

!gg =!

NP

2C(rNP )v

mNP

"mNP

"v

AF,W,S(mNP )At

where

Given the spectrum as a function of he Higgs VEV,the contribution can be easily calculated!

Simple parameterization:

!!! =GF !2m3

H

128!

2"3

!!!!!AW (#W ) + 3"

23

#2

At(#t) [1 + $!! ] + . . .

!!!!!

2

!gg =GF !2

sm3H

16!

2"3

!!!!12At(#t) [1 + $gg] + . . .

!!!!2

Anomalous W and top to Higgs couplings can also becast in the kappa parameters:

!!!(top) = !gg(top) =v

mt

"mt

"v! 1

!!!(W ) =34

!v

mW

"mW

"v! 1

"AW (#W )AF (#top)

!gg(W ) = 0

Top:

W:

Formalism easily extendable to non-minimal Higgs sectors!

Simple parameterization:

!!! =GF !2m3

H

128!

2"3

!!!!!AW (#W ) + 3"

23

#2

At(#t) [1 + $!! ] + . . .

!!!!!

2

!gg =GF !2

sm3H

16!

2"3

!!!!12At(#t) [1 + $gg] + . . .

!!!!2

Normalizing with the top contribution has many advantages:

New physics likely to be linked to top physics;

for a top partner ;

same sign for a single new particle;

positive kappas reduce photon and enhance gluon widths.

!!! = !gg

Now, we can write observables in terms of those parameters:

!̄(H) =

!!NP

gg + !SMV BF + !SM

V H,t̄tH

!SMgg + !SM

V BF + !SMV H,t̄tH

"!

!(1 + "gg)2!SM

gg + !SMV BF + !SM

V H,t̄tH

!SMgg + !SM

V BF + !SMV H,t̄tH

"

The total Higgs production cross section (normalized with the SM one) is

Corrections to the bottom Yukawa will invalidate our analysis (see SUSY)

Marginal effects from the W couplings: VBF or total width

Possible to extend the analysis with more parameters!

Note that we neglected corrections to the couplings of the Higgs:especially to the bottom and W!

Now, we can write observables in terms of those parameters:

The photon Branching Ratio (normalized with the SM one) is

Corrections to the bottom Yukawa will invalidate our analysis (see SUSY)

Marginal effects from the W couplings: VBF or total width

Possible to extend the analysis with more parameters!

Note that we neglected corrections to the couplings of the Higgs:especially to the bottom and W!

BR(H ! !!) =!NP

!!

!SM!!

!SMtot

!NPgg + !NP

!! + !SMothers

!!

1 +!!!

916AW ("W ) + 1

"2 !SMtot

(1 + !gg)2!SMgg + (!SM

tot " !SMgg )

Example 1:4th generation.

Add a full chiral 4th generation:190 GeV < mQ < 2 TeV100 GeV < mL < 2 TeV

The gluon loop counts number of color triplets:

The photon loop depends on charges:

All in all, like two tops!

!gg = 2

!!! =34

!3

"23

#2

+ 3"!1

3

#2

+ 1

$= 2

Example 2:models of flavour in extra dimension

gauge bosons

light fermions

top

KK modes

Higgs

Fermion mass hierarchy generated by exponential localization:Order(1) masses in the bulk, Order(1) Yukawas on the brane!

Do the light fermion KK modes contribute?

Gauge boson (W): negligible!

!!5W+

µ (y1) = 0!5W+

µ (y2) + g25V 2

4 W+µ (y2) = 0

W+(y, x) =!

n

fn(mny) Wn(x)+ mnf !(mny2)f(mny2)

+g25V 2

4= 0

Spectrum fixed by the Boundary Conditions:

The function f is determined by the geometry.

Gauge boson (W): negligible!

!!5W+

µ (y1) = 0!5W+

µ (y2) + g25V 2

4 W+µ (y2) = 0

W+(y, x) =!

n

fn(mny) Wn(x)+ mnf !(mny2)f(mny2)

+g25V 2

4= 0

Spectrum fixed by the Boundary Conditions:

Total derivate in V;solve in V as a function of mn:

v

mn

!mn

!v=

2 f !

f

f !

f + mny2

!f !!

f !"

f !

f

#2$

Gauge boson (W): negligible!

Numerically, we found that,both in flat and warped XD:

!!

n=0

v

mn

!mn

!v= 1

Probably because Higgs couples to boundary field with standard couplings:neglecting masses, we expect no correction.

=!

1! v

mW

!mW

!v

"(AW ("W )!AW (0)) " 0

!!! !!

1" v

mW

"mW

"v

"AW (#W ) +

!#

n=1

v

mn

"mn

"vAW (0) =

Fermions: it depends...Gauge-Higgs unification in flat space:

same bulk mass for left and right-handed fields ML = MR = M

ml ! 2M̃!" e!2!M̃L β contains VEV and Yukawa

Fermions: it depends...Gauge-Higgs unification in flat space:

same bulk mass for left and right-handed fields ML = MR = M

ml ! 2M̃!" e!2!M̃L

m2nL2 = M̃2L2 + n2 ± 2n2

!n2 + M̃2L2

! +n4 + 3M̃2L2n2

(n2 + M̃2L2)2!2 +O(!3)

!

n

!

mn

"mn

"!= !2!2

"!n=1

n4"3M̃2L2n2

(n2+M̃2L2)2=

! !2"2

sinh2 !M̃L

#!M̃L

tanh !M̃L! 1

$" ! m2

l

2M̃2

%#M̃L

tanh#M̃L! 1

&.

β contains VEV and Yukawa

KK masses (n>1):

Contribution proportional to the sum:

Fermions: it depends...Different bulk masses:

case ML = - MR = M

ml ! 2M̃!" e!2!M̃L β contains VEV and Yukawa

KK masses (n>1):

Contribution proportional to the sum:

m2nL2 = M̃2L2 + n2 ± 2n2

!n2 + M̃2L2

! +(1! 2"M̃L)n4 + (3! 2"M̃L)M̃2L2n2

(n2 + M̃2L2)2!2 +O(!3)

!

n

!

mn

"mn

"!= !2!2

!!

n=1

(1 + 2#M̃L)n4 ! (3! 2#M̃L)M̃2L2n2

(n2 + M̃2L2)2=

! #2!2

4 sinh3 #M̃L

"cosh(3#M̃L) + (4#M̃L! 1) cosh(#M̃L)! 4(#M̃L + 1) sinh(#M̃L)

#

" !#2!2 # !0.075$

2TeVmKK

%2 $mf

mtop

%2

.

Fermions: it depends...

For ML ≠ MR, all fermions contribute

!

n

!

mn

"mn

"!! "#2!2

!!! = !gg ! 6(""2#2) # "0.45!

2TeVmKK

"2

(we numerically checked it for generic masses)

Fermions: it depends...

The same happens in warped case, however:

each KK mode decouples from the Higgs for ML = MR: it depends on the wave functions being approx. proportional.

The result does not depend on the specific localization pattern e/o flavour structure!

It only depends on the overall KK mass...

fourth generation;

supersymmetry in the MSSM golden region: stops;

Simplest Little Higgs (mW ! = 2 TeV);

Littlest Higgs (T-parity: f = 500 GeV, without T parity f = 5 TeV);

colour octet model;

Lee-Wick Standard Model (LW Higgs mass at 1 TeV);

Universal Extra Dimension model (mKK = 500 GeV);

model of Gauge Higgs unification in flat space (first W resonance at 2TeV);

the Minimal Composite Higgs (Gauge Higgs unification in warped space)with the IR brane at 1/R! = 1 TeV;

a flat (W ! at 2 TeV) and

warped (1/R! at 1 TeV) version of brane Higgs models with flavour.

!

!

!

!

!

!

!

•

!

!

!

Our survey of models:

!!""!!

##

$$ %%

&&

"" 0.51.5

0.5

1.5

##

!!

A

B

$$

%0.5 0.0 0.5 1.0 1.5 2.0

%0.5

0.0

0.5

1.0

1.5

2.0

k&&

kgg

!!""

!!$$

%%

0.90

0.95

1.05

1.10

1.05 0.95

!!

B

A

%0.05 0.00 0.05 0.10 0.15

%0.05

0.00

0.05

0.10

0.15

k&&

kgg

mH = 120 @ LHC

4 gen Susy SLH LH LeeWick Octet

UED flat GH Warped GH flat and warped flavour

! ! ! !!! ! • ! !

!A - inclusive γγB - VBF γγ

!!""!!

##

$$ %%

&&

"" 0.51.5

0.5

1.5

##

!!

A

B

$$

%0.5 0.0 0.5 1.0 1.5 2.0

%0.5

0.0

0.5

1.0

1.5

2.0

k&&

kgg

!!""

!!$$

%%

0.90

0.95

1.05

1.10

1.05 0.95

!!

B

A

%0.05 0.00 0.05 0.10 0.15

%0.05

0.00

0.05

0.10

0.15

k&&

kgg

mH = 120 @ LHC

4 gen Susy SLH LH LeeWick Octet

UED flat GH Warped GH flat and warped flavour

! ! ! !!! ! • ! !

!A - inclusive γγB - VBF γγ

!!""!!

##

$$ %%

&&

"" 0.51.5

0.5

1.5

##

!!

A

B

$$

%0.5 0.0 0.5 1.0 1.5 2.0

%0.5

0.0

0.5

1.0

1.5

2.0

k&&

kgg

!!""

!!$$

%%

0.90

0.95

1.05

1.10

1.05 0.95

!!

B

A

%0.05 0.00 0.05 0.10 0.15

%0.05

0.00

0.05

0.10

0.15

k&&

kgg

mH = 120 @ LHC

4 gen Susy SLH LH LeeWick Octet

UED flat GH Warped GH flat and warped flavour

! ! ! !!! ! • ! !

!A - inclusive γγB - VBF γγ

mH = 150 @ LHC

4 gen Susy SLH LH LeeWick Octet

UED flat GH Warped GH flat and warped flavour

! ! ! !!! ! • ! !

!A - inclusive γγB - WW & ZZ

!!""

##

$$ %%

&&!!

0.5

2

1.5

0.5

1.5""

!!

A

B

##

$0.5 0.0 0.5 1.0 1.5 2.0

$0.5

0.0

0.5

1.0

1.5

2.0

k%%

kgg

!!""$$

%%

0.90

0.95

1.05

1.10

0.90

0.95

1.05

1.10

!!B

A

$0.05 0.00 0.05 0.10 0.15

$0.05

0.00

0.05

0.10

0.15

k%%kgg

mH = 120 @ ILC

4 gen Susy SLH LH LeeWick Octet

UED flat GH Warped GH flat and warped flavour

! ! ! !!! ! • ! !

!A - photon BRB - gluon BR

!!""!!

##

$$%%

&&""

0.5

2

1.5

0.51.5

##

!!

A

B

$$

%0.5 0.0 0.5 1.0 1.5 2.0

%0.5

0.0

0.5

1.0

1.5

2.0

k&&

kgg

!!""

!!$$

%%0.90

0.95

1.05

1.10

1.05 0.95

!!

A

B

%0.05 0.00 0.05 0.10 0.15

%0.05

0.00

0.05

0.10

0.15

k&&kgg

Conclusions

• H → γγ and g g → H are very sensitive to New Physics in the EWSB sector.

• A simple mod-ind parameterization allows easy calculation and exp. analysis.

• Many models give robust predictions, and point in a specific direction of the par. space: discrimination

• Probe new particles not directly accessible.

• Further study in collab. with experimentalists!