M. Serone, The Composite Higgs Paradigm

The Composite Higgs Paradigm
Marco Serone, SISSA, Trieste
1
Vrnjacka Banja, April 25-28 2013
Based mostly on 1205.0770, with D. Marzocca and J. Shu
(and 1211.7290, with F. Caracciolo and A. Parolini)
Saturday, April 27, 2013

Plan
Introduction on Composite Higgs Models
Generalized Weinberg Sum Rules and Higgs Mass
Conclusions
2
A Possible Issue for Partial Compositeness

But is this the SM Higgs or not ?
Naturalness disfavour a SM Higgs, but a non-SM Higgs should
come together with new physics particles, yet to be seen
Broadly speaking, there are two ways to go
for naturally motivated new physics:
3
Strongly coupled (technicolor, little Higgs, composite Higgs)
Weakly coupled (Supersymmetry)
The Higgs, the missing piece of the Standard
Model (SM), is finally a reality
For decades theorists have been thinking to extensions
of the SM, motivated mostly by the so called
hierarchy or naturalness problem
GF GNWhy ?

Technicolor, already in trouble for tensions with LEP
electroweak bounds, is essentially ruled out by a 125 GeV
Higgs (techni-dilaton too heavy)
Little Higgs are also Composite Higgs Models (CHM)
4
Little Higgs: thanks to an ingenious symmetry breaking mechanism,
the Higgs mass is radiatively generated, while the quartic is not
Composite Higgs: the entire Higgs potential is radiatively generated
In principle little-Higgs models are better, because allow
for a natural separation of scales between the Higgs
VEV and the Higgs compositeness scale
In practice they are not, because the above ingenious mechanism
becomes very cumbersome when fermions are included

Fundamental difference between Technicolor and CHM:
• Technicolor: the EW group is broken by the strongly coupled
sector (techni-quark condensates), no Higgs at all is necessary
• Composite Higgs: the EW group is unbroken by the strongly
coupled sector, but a Higgs-like particle appears in the
spectrum and breaks the EW group via its VEV, as in the SM
5

A composite Higgs coming from some strongly coupled theory can
solve the hierarchy problem. At some scale the Higgs compositeness
appears and the quadratic divergence is naturally cut-off
6
The Higgs field might or might not be a pseudo Nambu-Goldstone
boson (pNGb) of a spontaneously broken global symmetry.
Models where the Higgs is a pNGB are the most promising
The spontaneously broken global symmetry has also to be explicitly broken
(by SM gauge and Yukawa couplings), otherwise the Higgs remains massless
Whole Higgs potential is radiatively generated
The symmetry breaking pattern is closely related to the QCD case
The SU(2)L × SU(2)R global symmetry is replaced by
Gf ⊃ SU(2)L × U(1)Y
The SM gauge group arises as a weak gauging of Gf
The SM gauge fields are the analogue of the photon.
The Higgs field is the analogue of the pions

7
Not only relatively weakly coupled description of CHM, Higgs
potential fully calculable, but the key points of how to go in
model building have been established in higher dimensions
Important difference: fermion fields must now be added (no QCD analogue)
Implementations in concrete models hard (calculability, flavour problems)
Recent breakthrough: the composite Higgs paradigm is
holographically related to theories in extra dimensions!
Extra-dimensional models have allowed a tremendous progress
The Higgs becomes the fifth component of a gauge field, leading to
Gauge-Higgs-Unification (GHU) models also known as
Holographic Composite Higgs models
Connection particularly clear in Randall-Sundrum warped models
thanks to the celebrated AdS/CFT duality

UV Brane IR Brane
Elementary fields
Composite fields
Red-shift effect/dimensional transmutation
8
Bulk

Dual 4D interpretation:
Flavour hierarchies nicely explained by large RG effects (geography in
extra dimensions)
partial compositeness
Old idea, revived and finally realized within 5D models
Standard Model fields get a mass by mixing with composite fermions
The more they mix the heavier they are
m ∝ LRvH
Light generations are automatically screened by new physics effects
9
Natural mechanism to suppress dangerous FCNC

Main lesson learned from extra dimensions reinterpreted in 4D
Ltot = Lel + Lcomp + Lmix
Elementary sector: SM particles but Higgs (and possibly top quark)
Composite sector: unspecified strongly coupled theory with
unbroken global symmetry G ⊃ GSM
Mixing sector: mass mixing between SM fermion and gauge
fields and spin 1 or 1/2 bound states of the composite sector
10
Independently of the nature of composite sector, the pNGB Higgs dynamics
can be parametrized by using the Callan-Coleman-Wess-Zumino (CCWZ)
construction

11
Contrary to what happens in 5D models, the Higgs
potential is generally incalculable in 4D models
One can impose a collective symmetry breaking mechanism on
moose-type models, deconstructed versions of 5D models or
impose generalized Weinberg sum rules
The composite sector might be intrinsically strongly coupled, with no small
expansion parameter (e.g. some CFT), or admit some weakly coupled
description in terms of free fields (e.g. mesons in large N)
We assume the second case, where simple parametrizations are possible

Weinberg sum rules
V a
µ (q)V b
ν (−q) ≡ Pt
µνδab
ΠV V (q2
)
Aa
µ(q)Ab
ν(−q) ≡ Pt
µνδab
ΠAA(q2
)
In QCD, for SU(2)V × SU(2)A → SU(2)V
ΠLR = ΠV V − ΠAA is such that
lim
p2
E →∞
ΠLR(−p2
E) = 0
lim
p2
E →∞
p2
EΠLR(−p2
E) = 0
First sum rule (I)
Second sum rule (II)
(I) consequence of symmetry restoration
(II) assumes UV asymptotically free theory
12

13
Good theoretical prediction of pion mass difference
ΠV V (p2
E) = p2
E

n
f2
ρn
p2
E + m2
ρn
ΠAA(p2
E) = f2
π + p2
E

n
f2
an
p2
E + m2
an
At leading order in 1/Nc
If one assumes that only first vector and axial resonance contribute to the
form factors and impose rules I and II, the pion potential becomes calculable
SU(2)L × SU(2)R is explicitly broken by electromagnetic interactions
mass splittings among charged and neutral pions expected
m2
π± − m2
π0
3αem
4π
m2
ρm2
a
m2
a − m2
ρ
log
m2
a
m2
ρ


14
Higgs Mass
Basic question: what is its expected mass in CHM ?

14
Higgs Mass
mH ∼
g
4π
Λ generically

14
Higgs Mass
mH ∼
g
4π
Λ
mH ∼
g
4π
mρ
generically
QCD analogue with Weinberg sum rules
only mass scale in the composite sectormρ = gρf f

14
Higgs Mass
mH ∼
g
4π
Λ
mH ∼
g
4π
mρ
generically
QCD analogue with Weinberg sum rules
mH ∼ ? with partial compositeness additional states
and scales complicate the analysis
only mass scale in the composite sectormρ = gρf f

15
Let first consider the top quark.
mt ∼
2
Mf
v
f
∼ v 2
∼ Mf f
The top mixing largest explicit symmetry breaking terms
Higgs Potential
Calculable Higgs potential is a crucial portal for new physics.
The top must be semi-composite
The Higgs mass is related to new resonances masses
V (h) = Vg(h) + Vf (h)
Vg(h) = −γgs2
h + βgs4
h Vf (h) = −γf s2
h + βf s4
h
sh ≡ sin
h
f
1

s2
h = ξ =
γ
2β
Non-trivial minimum at
m2
h =
8β
f2
ξ (1 − ξ) .
16
β βf ∝
4
Nc
16π2
m2
H ∼
4
Nc
2π2f2
ξ
Nc
2π2
m2
t M2
f f2
v2f2
v2
f2
mH

Nc
2π2
mtMf
f
Direct relation between Higgs and resonance masses and
a light Higgs implies light fermion resonances
We can relax the second sum rule. In this way EWSB no
longer calculable, but Higgs mass still predicted

Collider Signatures
17
The deviations to SM couplings might be
too small to be detected at the LHC
On the other hand, the light sub-TeV fermion resonances, necessary to
explain a 125 GeV Higgs, seem a generic and clear prediction for CHM
LHC already puts significant constraints on the parameter space of CHM,
particularly when the lightest fermion resonance has Q=5/3
Roughly one has
m5/3 600
m2/3 400 GeV
GeV

Partial Compositeness for Light Fermions
Partial compositeness for light flavours is a nice and efficient
mechanism to suppress dangerous FCNC
It requires one exotic fermion excitation for each SM fermion
Many flavours. One should worry about possible Landau poles
Minimal case (bottom-up): Gf = SO(5)
Composite fermions in the fundamental of SO(5)
In total we have
Nf = (1 + 5) × 6 = 36
active flavours above the fermion mass scale f
In this case α3 blows up at the scale ΛLP ∼ 300Λ
Λ = 4πf is cut-off of the effective field theory
18

19
In vector-like gauge theories with fermion constituents
fermion bound states are typically baryon-like
But baryons are not light !
Anyhow, where do these fermions come from ?

19
One possibility is to assume they are meson-like, made by 1 fermion and 1 scalar
Scalar is unnatural Assume composite sector is supersymmetric
In this case, UV completions of CHM have recently been constructed
Most features of bottom-up models derived but the Landau problem remains

19
One possibility is to assume they are meson-like, made by 1 fermion and 1 scalar
Scalar is unnatural Assume composite sector is supersymmetric
In this case, UV completions of CHM have recently been constructed
Most features of bottom-up models derived but the Landau problem remains
SM gauge couplings develop unacceptably low Landau poles
if one assumes partial compositeness for all SM fermions

Conclusions
Generically a 125 GeV Composite Higgs seems to imply the
presence of light, sub TeV, colored fermion resonances
20
It is important that experimentalists start to perform
dedicated analysis of direct searches for top partners
In particular, understanding the UV origin of partial
compositeness for all SM fields is an important open problem
The Composite pNGB Higgs with Partial Compositeness seems a
promising natural extension of the SM, alternative to SUSY
Finding UV completions of such models is possible but non-trivial

M. Serone, The Composite Higgs Paradigm

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