Beyond the Higgs - Istituto Nazionale di Fisica...

Beyond the Higgs new ideas on electroweak

symmetry breakingE = mc

2

Rµ! ! 12Rgµ! = 16!G Tµ!

E = h!

( [email protected] )

Ch!"ophe GrojeanCERN-TH & CEA-Saclay/SPhT

Higgs mechanism. The Higgs as a UV moderator of EW interactions. Needs for New Physics beyond the Higgs. Dynamics of EW symmetry breaking

Review of possible scenarios :Gauge-Higgs Unification, Little Higgs, Composite Higgs, (5D) Higgsless models.

Ch!"ophe Grojean Beyond the Higgs To!no, January‘08

what is unitarizing the WW scattering amplitude?

Weakly coupled models Strongly coupled models

prototype: Susy

TeVQCD

prototype: Technicolorsusy partners ~ 100 GeV rho meson ~ 1 TeV

A = g2

!

E

MW

"2

other ways?

L

L

L

L

!l =

!

|"k|

M,

E

M

"k

|"k|

"

WL & ZL part of EWSB sector (we have already discovered

75% of the Higgs doublet!) ➲ WW scattering is a probe of Higgs sector interactions

Unitarization of scattering amplitude


Strongly coupled models

The resonance that unitarizes the WW scattering amplitudes

generates a tree-level effect on the SM gauge bosons self-energy

S parameter of order 1. Not seen at LEP

a technical challenge: how to evade EW precision data

+ ...=TC

a theoretical challenge: need to develop tools to do computation


“AdS/CFT” correspondence for model-builder

Warped gravity with fermions and gauge field in the bulk

and Higgs on the brane

Strongly coupled theorywith slowly-running couplings in 4D

UVIR

HH

H0

Holographic Approach to Strong Sector

StrongBSM

SM

g!gSMproto-Yukawa

gauge

g2

SM/g!

G

5D

motion along 5th dim

UV brane

IR brane

bulk local sym.

4D

RG flow

UV cutoff

break. of conformal inv.

global sym.

KK modes vector resonances (ρmesons in QCD)


Fermionic sector in AdS


Holographic Models of EWSB

cutoff ~ 1 TeV

conflict with EW precision data

problems with flavour

UV

IR

All SM fieldson the IR brane

Gravity inthe bulk

Original Randall-Sundrum proposal: ‘99


Holographic Models of EWSBBulk gauge fields: Pomarol, ‘00Holographic technicolor=Higgsless: Csaki et al., ‘03Holographic composite Higgs: Agashe et al., ‘04

UV

IR

Higgson the IR brane

Gauge fields + fermions in the bulk

UV completion: log running of gauge couplings

Custodial symmetry from bulk SU(2)R

Dynamical ‘explanation’ of fermion masses

Built-in flavour structure

SU(2)LxSU(2)R

xU(1)B-L

SU(2)RxU(1)B-L

U(1)y


Fermions in AdS: Partial Compositeness

5D fermion = no chirality

! =

!

!!

"!

" 4D LH chirality

4D RH chirality

Chirality in 4D KK theorythanks to

orbifold projection/boundary condition

ψ Dirichlet bc on IR and UV branes➲ zero mode for χ

S =

!

d5xR4

z4

"

!i!"µ#µ! ! i$"µ#µ$ + 1

2($

"##5 ! ! !

"##5 $) +

c

z($! + !$)

#

AdS wavefunction

5D mass term in AdS unit: c ~ O(1)

c > 1/2: the zero is normalizable when zIR is sent to infinity (no IR brane): UV localized

c < 1/2: the zero is normalizable when zUV is sent to 0 (no UV brane): IR localized

Elementary fermion Composite fermion

fermion zero mode:

! = a0

!

z

zUV

"2!c

!4D

! zUV

zIR

dz a2

0

"

z

zUV

#2!c

= 1with

Grossman and Neubert, ’00Gherghetta and Pomarol, ‘00


Masses from IR overlaps

light fermion exponentially localized on the UV brane➲ overlap with Higgs vev on the IR tiny

➲ exponentially small 4D mass

UV IR


Partial Compositeness: Dual Picture

SM sectorstrong sector

EWSB

elementary fermions: χ Higgs

heavy fermions: ψ vector resonances: ρ

linear mixing

mass eigenstate is a mixture of elementary and composite

!L,R("/ + g!#/ )!L,R ! M!!L!R!L"/!L

! !L"R

|light!L = cos !|"L! + sin!|#L!|heavy!L = " sin!|"L! + cos !|#L!

|heavy!R = |!R!

massless massive

tan! =!

M!

the smaller is the angle, the more elementary is the light fermionthe 5D picture gives a rationale for hierarchical angles

amount of compositeness in the light dof


Partial Compositeness: Yukawa Couplings

Higgs part of the strong sector: it couples only to composite fermions

when the Higgs gets a vev, the light dof will acquire a mass prop. to

y = y! sin!L sin!R

Yukawa hierarchy comes from the hierarchy of compositeness

H

|light!R|light!L

sin!L sin!R

Yukawa coupling in the strong sector


Partial Compositeness with 3 Families

Neglecting brane kinetic terms, we can diagonalize simultaneously the mixing and the composite masses

sin!d,s,bL sin!

d,s,bR are diagonal matrices&

flavour mixings arise through non-diagonal (anarchic) Yukawa in the strong sector

yij

= yij!

sin!iL sin!

jR

For hierarchical angles, we can easily diagonalize the mass matrices

(VCKM )ij =sin!i

L

sin!jL


FCNC from KK gluons/rho meson

|light!iL

|light!jL |light!kL

|light!lL

rho meson

g! g!

sin!iL

sin!jL sin!

kL

sin!lL1

M2!

AijklLL !

g2!

M2!

sin!iL sin!j

L sin!kL sin!l

L

Built-in GIM supressionthe smaller the mass ➲ the smaller the angle ➲ the smaller coefficient

Agashe, Perez, Soni ’04Contino, Kramer, Son, Sundrum ‘06


Composite Higgs Models


≠ susy: no naturalness pb ➲ no need for new particles to cancel Λ2 divergences

≠ technicolor: heavier rho ➲ smaller oblique corrections; one tunable parameter: v/f.

Higgs = composite object (part of the strong sector too) its couplings deviate from a point-like scalar

+ ...=strong +

light Higgs partial unitarization

heavy rho

Unitarity with Composite HiggsTechnicolor: WL and ZL are part of the strong sector

unitarization halfway between weak and strong unitarizations!

Georgi, Kaplan ‘84

SUV !

g2N

96!2

v2

f2


usual resonances of the strong sector

How to obtain a light composite Higgs?Higgs=Pseudo-Goldstone boson of the strong sector

⇔

UV completion

Higgs = light resonance of the strong sector

10 TeV4!f

m! = g!f

246 GeV

strong sector broadly characterized by 2 parametersm! = mass of the resonances

StrongBSM

SM

g!gSMproto-Yukawa

gauge

g2

SM/g!

global symmetry G/H residual

global symmetry

SO(5)/SO(4), 4PGB=Doublet of SU(2)L=Higgs

example:

mHiggs=0 when gSM=0

g! = coupling of the strong sector or decay cst of strong sector f =

m!

g!

G SU(2)LxU(1)Y

H U(1)em

⊂⊂

➲ WL & ZLv

f


SO(5)/SO(4) modelSM Higgs: a SO(4) global symmetry.

Higgs=Goldstone ➾ need to extend the symmetry, e.g. SO(5)

φ = 5 of SO(5) with the constraint | φ |2 = f2

weakly gauge SU(2)LxU(1)Y of SO(4)⊂SO(5)

the dynamics will determine the alignement of the two SO(4)! = ("!, !5) !" 2 + "2

5 = f2

V = f4!("2 ! f2)!Af2#" 2 + Bf3"5

SO(5) inv. potential

Most general soft breaking potential dim≤2

A SO(5) breaking potential is generated, e.g., by interaction with gauge bosons or quarks and leptons

v2 = !!" 2" = f2

!1 # B

2A

".

v/f determined by the dynamics


Model-dependent: production of resonances at mρ

Model-independent: study of Higgs properties & W scattering

Higgs anomalous couplingstrong WW scatteringstrong HH productiongauge bosons self-couplings

Testing the composite nature of the Higgs?if LHC sees a Higgs and nothing else*:

* a likely possibility that precision data seems to point to, at least in strongly coupled models

evidence for string landscape???

it will be more important then ever to figure out

whether the Higgs is composite!


What distinguishes a composite Higgs?

L !cH

2f2!µ

!

|H|2"

!µ

!

|H|2"

cH ! O(1)

H =

!

0v+h!

2

"

L =1

2

!

1 + cHv2

f2

"

(!µh)2 + . . .

Modified Higgs propagator

Higgs couplings

rescaled by 1

!

1 + cHv2

f2

! 1 " cHv2

2f2~

= !

!

1 ! cH

v2

f2

"

g2E2

M2

W

no exact cancellation of the growing amplitudes

Giudice, Grojean, Pomarol, Rattazzi ‘07

unitarization restored by heavy resonancesFalkowski, Pokorski, Roberts ‘07

Strong W scattering below mρ ?


SILH Effective LagrangianGiudice, Grojean, Pomarol, Rattazzi ‘07

extra derivative: !/m!H/fextra Higgs leg:

(strongly-interacting light Higgs)

cH

2f2

!

!µ

!

|H|2""2 cT

2f2

!

H†!"DµH"2

custodial breaking

cyyf

f2|H|2fLHfR + h.c.

c6!

f2|H|6

loop-suppressed strong dynamics

icW

2m2!

!

H†!

i!"D

µH

"

(D"Wµ")i icB

2m2!

!

H†!"D

µH

"

(!"Bµ")

icHW

m2!

g2!

16!2(DµH)†"i(D"H)W i

µ"

icHB

m2!

g2!

16!2(DµH)†(D"H)Bµ"

minimal coupling: h ! !Z

c!

m2"

g2"

16!2

g2

g2"

H†HBµ#Bµ#cg

m2!

g2!

16!2

y2t

g2!

H†HGaµ"Gaµ"

Goldstone sym.

Genuine strong operators (sensitive to the scale f)

Form factor operators (sensitive to the scale mρ)


cH and cT are fully fixed by the σ-model structure (up to the overall normalization of f)

(independent of the physics at the scale mρ)

Coset Structure

U = ei

0

@

H/fH†/f

1

A

U0

f2tr

!

!µU†!µU"

= |!µH|2 +"

f2

!

!|H|2"2

+"

f2|H|2 |!H|2 +

"

f2

#

#H†!H#

#

2

can be removed by field redefinitionH ! H + !|H|2H/f2

SO(5)/SO(4): cH=1/2, cT=0 SU(3)/SU(2)xU(1): cH=cT=1/36

!|H|4 !"

f2!|H|6 yfLHfR !

!

f2y|H|2fLHfR

c6 and cy receive contributions both from the σ-model structure and from the resonance at mρ


SO(5)/SO(4)

! = exp

!

"""#if

!

"""#

0 h1

. . ....

0 h4

!h1 . . . !h4 0

$

%%%&

$

%%%&"!#!!" =

!

""""#

0000f

$

%%%%&.

L = f2Tr!!µ!t!µ!

"= |!µH|2 ! 1

3f2|H|2|!µH|2 +

112f2

!!µ|H|2

"2

H =

!

"h1 + ih2

h3 + ih4

#

$ .with

H ! H " 16f2

|H|2H

L = |!µH|2 +!

112

+16

"1f2

#!µ|H|2

$2

cH=1/2

exercise


SU(3)/SU(2)xU(1)

!!" =

!

"1

1#2

#

$ .

!! U!U†

! = ei!/f !!"e!i!/f i! =!

0 H/3!

2"H†/3

!2 0

".

L = f2Tr!!µ!†!µ!

"= |!µH|2 ! 1

54f2|H|2|!µH|2 ! 1

18f2|H†!H|2 +

154f2

!!µ|H|2

"2

H ! H " 1108f2

|H|2H

L = |!µH|2 +1

72f2

!!µ|H|2

"2 +1

72f2

#H†!"!µH

$2

cH=cT=1/36

exercise


EWPT constraints

T = cT

v2

f2

removed by custodial symmetry

|cT

v2

f2| < 2 ! 10

!3

S = (cW + cB)m2

W

m2!

m! ! (cW + cB)1/2 2.5 TeV

LEPII, for mh~115 GeV:

IR effects can be cancelled by heavy fermions (model dependent)

There are also some 1-loop IR effectsBarbieri, Bellazzini, Rychkov, Varagnolo ‘07

S, T = a log mh + b

S, T = a ((1 ! cH!) log mh + cH! log! ) + b

modified Higgs couplings to matter

effective Higgs mass

me!h = mh

!!

mh

"cHv2/f2

> mh

cHv2/f2 < 1/3 ! 1/2


Higgs anomalous couplings

!!

h ! ff"

SILH= !

!

h ! ff"

SM

#

1 " (2cy + cH) v2/f2$

! (h ! gg)SILH

= !(h ! gg)SM

!

1 " (2cy + cH) v2/f2"

observable @ LHC?

Duhrssen ‘03

LHC can measure

cHv2

f2, cy

v2

f2

up to 20-40%

(ILC could go to few % ie test composite Higgs up to

)4!f ! 30 TeV

(composite scale 5-7 TeV)

ATLAS!Ldt = 300 fb

!1

cHv2/f2 = 1/4cyv2/f2 = 1/4


Strong W scattering

A!

Z0LZ0

L ! W+L

W!

L

"

= A!

W+L

W!

L! Z0

LZ0L

"

= "A!

W±

LW±

L! W±

LW±

L

"

=

cHs

f2

A!

W±Z0L ! W±Z0

L

"

=cHt

f2, A

!

W+L

W!

L! W+

LW!

L

"

=cH(s + t)

f2

Even with a light Higgs, growing amplitudes (at least up to )m!

A!

Z0

LZ0

L ! Z0

LZ0

L

"

= 0

q

q

leptonic and semileptonicvector decay channels

with 300 fb-1

Bagger et al ’95Butterworth et al. ‘02

LHC is sensitive to

bigger than0.5 ~ 0.7

cH

v2

f2

W

W

! (pp! VLV !LX)cH

=!

cHv2

f2

"2

! (pp! VLV !LX)"H


Strong Higgs productionO(4) symmetry between WL, ZL and the physical Higgs

strong boson scattering ⇔ strong Higgs production

A!

Z0LZ0

L ! hh"

= A!

W+L

W!

L! hh

"

=

cHs

f2

2!!,M (pp ! hhX)cH= !!,M

!

pp ! W+L W!

L X"

cH

+1

6

#

9 " tanh2 "

2

$

!!,M

!

pp ! Z0LZ0

LX"

cH

Sum rule (with cuts and )|!!| < " s < M2

signal: hh → bbbb

hh → 4W → l±l±ννjets

q

q

h

h

WW


Gauge boson self-couplingsLV = !ig cos !W gZ

1 Zµ!

W+!W!

µ! ! W!!W+µ!

"

!ig (cos !W "ZZµ! + sin !W ""Aµ!) W+µ W!

!

gZ1 =

m2

Z

m2!

cW !" =m2

W

m2!

! g!

4"

"2

(cHW + cHB) !Z = gZ1 ! tan2 #W !"

TGC are sensitive to the form factor operators

@ LHC 100fb-1 gZ1 ! 1% !! ! !Z ! 5%

sensitive to resonance up to mρ~800 GeV

not competitive with the measure of S at LEPII

T. Abe et al, Snowmass ‘01

sensitive to resonance up to mρ~8TeV

@ ILC


Direct vs. indirect signalsdirect production of (TeV) resonances

for larger gρ, the resonances are increasingly harder to see as 1/ they are broader and heavier2/ they couple more and more weakly to fermions

LHC could reach a resonance around 4 TeV

=

g2

SM

g!

= g!

!!

pp ! "±H + X"

=

#

4#

g!

$2 #

3 TeV

m!

$6

0.5 fb


Usefulness of SILH effective theory

halfway between model-dependent and blind operator analysis

dominant effects are associated from strong self-Higgs interactions

operator analysis: h → γγ dominated by cH and not loop-suppressed

SILHdirect resonances

gρ > 4π

4πf

(indirect evidence of strong interactions)

mρ

7 TeV

2 TeV

1 TeV

4 TeV

LEPIR contributions to S and T

|H|2B2

µ!

cannot apply the analysis Manohar, Wise ‘06

v2/f2 = 0.6


Minimal Composite Higgs ModelAgashe, Contino, Pomarol ‘04

S0(5)xU(1)B-L

SU(2)LxU(1)y SO(4)xU(1)B-L ! =RIR

RUV

! 1016

GeV

z = RUV ~ 1/MPl z = RIR ~ 1/TeV

UV braneIR brane

ds2=

!

R

z

"2#

!µ!dxµdx!! dz2

$

warped dual to composite Higgs model

mW =gf

2sin

h

f

SILH

SO(5)/SO(4)

➲

➲

➲ghWW = gmW

!1! v2

2f2

"cH = 1

ghhh =3gm2

h

2mW

!1! 3v2

2f2

"c6 = 0

ghff =gmf

2mW

!1! 3v2

2f2

"cy = 1


Littlest Higgs

Global symmetry SU(5)/SO(5)

Gauge symmetry SU(2)LxSU(2)RxU(1)/SU(2)WxU(1)Y

(14-3) PGB: 31, 21/2, 10

mass not protected when gR>>gL SILH degrees of freedom

SU(5)/SO(5) SU(3)/SU(2)gR>>gL

cH = 1/4 cT = !1/16

coset structure below the LH partner masses

If gR~gL, cT =0 and cH= 5/16 but coset structure lost and large corrections of order gL/gR


Little Higgs with Custodial Symmetry

Global symmetry S0(9)/SO(5)xSO(4)

Gauge symmetry SU(2)LxSU(2)RxSU(2)xU(1)/SU(2)WxU(1)Y

(20-6) PGB: 31,30, 21/2, 10

mass not protected when gR~gL >> g

SO(9)/SO(5)xSO(4) S0(5)/S0(4)gR~gL >> g

SILH degrees of freedom

cH = 1/2 cT = 0

coset structure below the LH partner masses


Higgsless Models


Higgsless Approach

Gauge symmetry breaking

In the gauge-Higgs unification models, we have been breaking bigger gauge groups down to SU(2)xU(1) by orbifold.

Why can’t we break directly SU(2)xU(1) to U(1)em by orbifold?

Let us try...

!R

!!R

0

⤶⤶Z2

y

!yU

2= 1

Csaki, Grojean, Murayama, Pilo, Terning ‘03Csaki, Grojean, Pilo, Terning ‘03


Rank Reduction

Non Rational Mass Ratios

How is Unitarity Restored?

First Obstacles

SU(2)xU(1) U(1) the rank is reduced by one

Aµ(!y) = UAµ(y)U† U has to be an automorphism of the algebra

inner automorphism (U belongs to the gauge group): no rank reductionouter automorphism: a rank reduction is possible but few breaking patterns allowed

Kaluza-Klein spectrum is dictated by geometry: typically Mn= n/R

How can we generate gauge boson masses that depends on the gauge couplings?

If W± and Z acquire a KK mass without a Higgs, what ensures the unitarity of W scattering above 1.2 TeV?

March-Russel, Hebecker ‘01


A SM-like Example

SU(2)

U(1)

!R0

!!A3

µ = 0

A1,2

µ = 0 !!A1,2,3

µ = 0

!4Aa

µ ! !25A

a

µ = 0

Aµ(x, y) =!

n

fn(y)An

µ(x)KK decomposition

Bulk EOM

BCs

f !!

n(y) = !m2

nfn(y)

f = 0 or f != 0 at y = 0,!R

A3µ(x, y) =

!!

k=0

"

2

2!k0!Rcos

ky

R"(k)

µ (x)

A1µ(x, y) =

!!

k=0

1!

!Rsin

(2k + 1)y

2R

"

W+ (k)µ (x) + W" (k)

µ (x)#

A2µ(x, y) =

!!

k=0

1!

!Rsin

(2k + 1)y

2R

"

W+ (k)µ (x) " W" (k)

µ (x)#

M! = 0

MW± =1

2R

MZ =1

R


Dynamical Origin of the BCs

S =

!

d4x

! !R

0

dy

"

1

2!M"!M"# $% &

!V (")

'

!

!

y=0,!R

d4x 1

2M2

0,!R"2

integration by part

!S =

!

y=0,!R

d4x !""

#5" + M20,!R"

#

BC’s

!"!

#5" + M2

0,!R""

= 0

+ Bulk Partbulk eq. of motion

!5! = !V !(!)

Dirichlet BC: ! = cst.

Mixed BC: !5"0,!R = !M2

0,!R"0,!R

M2 !

" !0,!R = 0 Dirichlet BC

M 2

!0

!5"0,!R = 0 Neumann BC


Unitarization of (Elastic) Scattering AmplitudeSame KK mode

‘in’ and ‘out’ !µ

!=

! |"p|

M,

E "p

M |"p|

"

A = A(4)

!

E

M

"4

+ A(2)

!

E

M

"2

+ . . .

n

k

n

n n

s channel exchange

contact interaction

A = A(4)

!E

M

"4

+ A(2)

!E

M

"2

+ . . .

!µ! =

# |"p|M

,E "p

M |"p|

$

1

n

k

n

n n

s channel exchange

n n

n n

contact interaction

A = A(4)

!E

M

"4

+ A(2)

!E

M

"2

+ . . .

!µ! =

# |"p|M

,E "p

M |"p|

$

1

n n

k

n n

t channel exchange

n

k

n n

n

u channel exchange

M! = 0

MW± =1

2R

MZ =1

R

A3µ(x, y) =

!!

k=0

"2

2"k0!Rcos

ky

R"(k)

µ (x)

A1µ(x, y) =

!!

k=0

1!!R

sin(2k + 1)y

2R

#W+(k)

µ (x) + W" (k)µ (x)

$

2

n n

k

n n

t channel exchange

n

k

n n

n

u channel exchange

M! = 0

MW± =1

2R

MZ =1

R

A3µ(x, y) =

!!

k=0

"2

2"k0!Rcos

ky

R"(k)

µ (x)

A1µ(x, y) =

!!

k=0

1!!R

sin(2k + 1)y

2R

#W+(k)

µ (x) + W" (k)µ (x)

$

2

gnnkg2

nnnn gnnk

gnnk gnnk

gnnkgnnk

A(4) = i

!

g2nnnn !

"

k

g2nnk

#

$

fabefcde(3 + 6c! ! c2!) + 2(3 ! c2

!)facef bde

%

θ!p

!q!p

!q

A(2)= i

!

4g2nnnn ! 3

"

k

g2nnk

M2k

M2n

#

$

facef bde ! s2!/2f

abefcde%


KK Sum Rules

A(4) ! g2nnnn "

!

k

g2nnk A(2) ! 4g2

nnnn " 3!

k

g2nnk

M2k

M2n

E4 Sum Ruleg2

nnnn !

!k

g2nnk = g2

5D

" !R

0

dyf4n(y) ! g2

5D

" !R

0

dy

" !R

0

dzf2n(y)f2

n(z)!

k

fk(y)fk(z) = 0

!

k

fk(y)fk(z) = !(y ! z)

Completness of KK modesA(4)

= 0

In a KK theory, the effective couplings are given by overlap integrals of the wavefunctions

gmnp = g5D

! !R

0

dyfm(y)fn(y)fp(y)g2

mnpq = g2

5D

! !R

0

dyfm(y)fn(y)fp(y)fq(y)contact interaction

A1,2µ = 0

!!A3µ = 0

Tr (UF56(0)) ! Tr (Ug(0)F56(0)g"1(0)) = Tr (UF56(0)g"1(0)g(0)) = Tr (UF56(0))

Veff(A5) = f(Wn)

Wn = eiR 2n!R0 A5dy

fHHH , fG/H G/H H

[H, H ] " H [H, G/H ] " G/H

"AG/Hµ = 0

"AG/H5 = !5#

G/H + gfG/H G/H HAG/H5 #H

7

s channel exchange

A3µ(x, y) =

!!

k=0

"2

2!k0!Rcos

ky

R"(k)

µ (x)

A1µ(x, y) =

!!

k=0

1!!R

sin(2k + 1)y

2R

#W+(k)

µ (x) + W" (k)µ (x)

$

A2µ(x, y) =

!!

k=0

1!!R

sin(2k + 1)y

2R

#W+ (k)

µ (x) " W" (k)µ (x)

$

f = 0 or f # = 0 at y = 0, !R

f ##n(y) = "m2

nfn(y)

Aµ(x, y) =!

n

fn(y)Anµ(x)

!4Aaµ " #2

5Aaµ = 0

6

Csaki, Grojean, Murayama, Pilo, Terning ‘03


Postponing Pert. Unitarity BreakdownIs it a counter-example of the theorem by Cornwall et al.?

i.e. can we unitarize the theory without scalar field?

No! g2

nnnn =!

k

g2

nnk =!

g2

nnk

3M2

k

4M2n

E4 E2

the sum rules cannot be satisfied with a finite number of KK modes (to unitarize the scattering of massive KK modes, you always need heavier KK states)

Pushing the need for a scalar to higher scaleWith a finite number of KK modes

MW

MW !

MW !!

MW (n)

4!MW /g4Naive cutoff

4!MW (n)/g45D

cutoff

New Physics (Higgs/strongly coupled theory?) {

weakly coupled states observable

at low energy

not directly set by the weak scale

!5D = 24!3/g25 = 12!2MW /g2

4

flat space

already a factor 10 higher than the naive cutoff


A Flat Higgsless Model

!R

SU(2)LxSU(2)R

xU(1)B-L {

U(1)em

SU(2)RxU(1)B-L

U(1)yU(1)yAR±

µ = 0

g!5Bµ ! g5AR 3µ = 0

!5(g5Bµ + g!5AR 3µ ) = 0

SU(2)LxSU(2)R

SU(2)D

AL aµ ! AR a

µ = 0

!5(AL aµ + AR a

µ ) = 0

cotan2M

Wk !R = 0

Bµ(x, y) = g a0!µ(x) + g!!"

k=1 bk cos(MZk y) Z

(k)µ (x)

AL 3µ (x, y) = g! a0!µ(x) ! g

!"

k=1 bkcos(MZ

k(y#!R))

2 cos(MZ

k!R)

Z(k)µ (x)

AR 3µ (x, y) = g!a0!µ(x) ! g

!"

k=1 bkcos(MZ

k(y+!R))

2 cos(MZ

k!R)

Z(k)µ (x)

AL±µ (x, y) =

!"

k=1 ck cos(MWk (y ! "R))W

(k)±µ (x)

AR±µ (x, y) =

!"

k=1 ck cos(MWk (y + "R))W

(k)±µ (x)

}}

tan2 MZ

k !R =g2 + 2g!2

g2

Csaki, Grojean, Murayama, Pilo, Terning ‘03


Light W and Z resonances

Rho parameter

Phenomenological Issues

γW

Z

W’, Z’

080 GeV

90 GeV

240 GeV these resonances will have a coupling to fermions of the same strenght as the SM couplings

experimentally excluded

the gauge bosons masses have a dependence on the gauge couplings, but this dependence is different from the SM one

MZ =1

!Rarctan

!

g2 + 2g!2

g2

! ! 1.10

experimentally excluded


Warped Space and Localization of Gauge FieldsWhy is rho different from 1 while we started with an SU(2)R symmetry in the bulk?

the SU(2)R symmetry is broken on the y=0 brane

we should engineer a set-up such that the wavefunctions are localized on the other side

Go to a Warped Space

! =RIR

RUV

! 1016

GeV

z = RUV ~ 1/MPl

z = RIR ~ 1/TeV

UV braneIR brane ds2

=

!

R

z

"2#

!µ!dxµdx!! dz2

$

Wavefunction of massive gauge field

fm(z) = z (aJ1(mz) + bY1(mz))

(generically) peaked on the IR brane


Warped Higgsless Model

!(A)k

(z) = z!

a(A)k

J1(qkz) + b(A)k

Y1(qkz)"

Bµ(x, z) = g5 a0!µ(x) +!!

k=1 "(B)k (z) Z

(k)µ (x)

AL 3µ (x, z) = g"5 a0!µ(x) +

!!

k=1 "(L3)k (z) Z

(k)µ (x)

AR 3µ (x, z) = g"5 a0!µ(x) +

!!

k=1 "(R3)k (z) Z

(k)µ (x)

AL±µ (x, z) =

!!

k=1 "(L±)k (z) W

(k)±µ (x)

AR±µ (x, z) =

!!

k=1 "(R±)k (z) W

(k)±µ (x)

}}

2g!25 (RUV0 ! RIR

1 )(RIR0 ! RUV

1 )

= g2

5

!

(RUV0 ! RIR

0 )(RUV1 ! RIR

1 ) + (RIR1 ! RUV

0 )(RIR0 ! RUV

1 )"

(RUV0 ! R

IR0 )(RUV

1 ! RIR1 ) + (RIR

1 ! RUV0 )(RIR

0 ! RUV1 ) = 0

RUVi !

Yi(MRUV )

Ji(MRUV ), RIR

i !

Yi(MRIR)

Ji(MRIR).

Csaki, Grojean, Pilo, Terning ‘03

SU(2)LxSU(2)R

xU(1)B-L

U(1)em

SU(2)RxU(1)B-L

U(1)yU(1)yAR±

µ = 0

g!5Bµ ! g5AR 3µ = 0

!5(g5Bµ + g!5AR 3µ ) = 0

SU(2)LxSU(2)R

SU(2)D

AL aµ ! AR a

µ = 0

!5(AL aµ + AR a

µ ) = 0{


Warped Higgsless Model: Spectrum(RUV

0 ! RIR0 )(RUV

1 ! RIR1 ) + (RIR

1 ! RUV0 )(RIR

0 ! RUV1 ) = 0

expansion of the Bessel functions around the origin...

Y0(z) ! 2 log z

!+ . . . Y1(z) ! "

2!z

+ . . .

J0(z) ! 1 + . . . J1(z) ! z

2+ . . .

log suppression⤶⤶

W around 80 GeV, KK around 1.2 TeV

Why a log? AdS/CFT

spontaneous breaking at IR scale

M2

W ! g2

4(1/R2

IR) !1

R2IR

log(RIR/RUV )

g2

5 ! RUV1

g24

=

! RIR

RUVdzR/z

g25

=RUV log(RIR/RUV )

g25

and

“light” mode: M2

W =1

R2

IRlog(RIR/RUV )

M2

Z !

g25 + 2g!25g25

+ g!21

R2IR

log(RIR/RUV )

KK tower: M2

KK =cst of order unity

R2

IR


SM Fermions in Higgsless Models

SU(2)LxSU(2)R

xU(1)B-LSU(2)Lx U(1)y SU(2)DxU(1)B-L

vector-like braneisospin invariant mass only

(same mass for the top and bottom or electron and neutrino)

Chiral braneno possible mass term

The fermions have to live in the bulk


Some SignaturesDeviations in the gauge bosons self-couplings

in usual gauge theories:

in higgsless theories, this relation is modified to take into account the exchange of KK excitations of W and Z

typically 1%-5% deviations compare to the SM self-couplings

Non-universality of the couplings gauge boson/fermions

g24 = g

23

fermion mass ⇔ wavefunction profile in the bulkcouplings ⇔ wavefunction overlap

different masses ⇔ different couplings to W and Z

First two generations Third generation

!gSM

gSM

! O

! m

TeV

"

! 0.1% at most

ZbLbLdeviations

difficult to get a small deviation

in the perturbative regime

severe constraintscL

cR0.20.10

-0.1-0.2-0.3-0.40.30 0.35 0.40 0.45 0.50

(gR/gL=5)

1%

1.5%


a narrow and light resonance

Number of events at the LHC, 300 fb-1

discovery reach @ LHC

(10 events)

W’ production

550 GeV ! 10 fb!1

1 TeV ! 60 fb!1

should be seen within one/two year

Collider Signaturesunitarity restored by vector resonances whose masses and

couplings are constrained by the unitarity sum rulesWZ elastic cross section

[Birkedal, Matchev, Perelstein ‘05]

gWW !Z !gWWZM2

Z"3MW !MW

!(W !! WZ) "

!M3W !

144s2wM2

W

q

q

Z0

W±

W’Z0

q

q

W±


Open Issues ZbLbL

How to get large top masswithout spoiling the Zbb coupling?

introduce a scale for the W, Z masses and another scale for the top mass

... like in topcolor models

multithroat construction

the top lives in one throatwhile the W, Z masses originate mostly from the other throats

prediction: a light PGB = the top-pion strongly coupled to the third generation

[Cacciapaglia, Csaki, Grojean, Reece, Terning ‘05][Cacciapaglia, Csaki, Grojean, Terning ‘06]

dual picture: fermion masses are generated from the interaction to the strongly coupled sector

cL

cR0.20.10

-0.1-0.2-0.3-0.40.30 0.35 0.40 0.45 0.50

(gR/gL=5)

1%

1.5%

or custodial symmetry


Conclusions

1/ is there a Higgs?2/ what are the Higgs mass/couplings3/ is the Higgs a SM like weak doublet?4/ is the Higgs elementary or composite?5/ is EWSB natural or fine-tuned?6/ are there new dimensions? new strong forces?

LHC ILCCLIC

✓✓ ✓

✓ ✓

✓ ✓✓

✓ ✓

✓ ✓

✓ ✓

✓?

✓/–

–

☁☁

What is the mechanism of EW symmetry breaking?

“theorists are getting cold feet”“they have done their best to predict the possible and impossible”

the ball is in experimentalists’ hands

J. Ellis

G. Giudice

“The LHC will take experiments squarely into a new energy domain where mysteries of the EW interactions will be unveiled”

Beyond the Higgs - Istituto Nazionale di Fisica...

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