M. Serone, The Composite Higgs Paradigm

The Composite Higgs Paradigm

Marco Serone, SISSA, Trieste

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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

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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:

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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 problemGF � 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)

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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

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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

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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 caseThe 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


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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

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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 ∝ �L�RvH

Light generations are automatically screened by new physics effects

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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

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Independently of the nature of composite sector, the pNGB Higgs dynamics can be parametrized by using the Callan-Coleman-Wess-Zumino (CCWZ)

construction


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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 aµ (q)V b

ν (−q)� ≡ P tµνδabΠV V (q2)

�Aaµ(q)Ab

ν(−q)� ≡ P tµνδabΠAA(q2)

In QCD, for SU(2)V × SU(2)A → SU(2)V

ΠLR = ΠV V −ΠAA is such that

limp2

E→∞ΠLR(−p2

E) = 0

limp2

E→∞p2

EΠLR(−p2E) = 0

First sum rule (I)

Second sum rule (II)

(I) consequence of symmetry restoration(II) assumes UV asymptotically free theory

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Good theoretical prediction of pion mass difference

ΠV V (p2E) = p2

E

�

n

f2ρn

p2E + m2

ρn

ΠAA(p2E) = f2

π + p2E

�

n

f2an

p2E + 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

m2π± −m2

π0 �3αem

4π

m2ρm

2a

m2a −m2

ρ

log�m2

a

m2ρ

�


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Higgs Mass

Basic question: what is its expected mass in CHM ?


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Higgs Mass


mH ∼ g

4πΛ generically


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Higgs Mass


mH ∼ g

4πΛ

mH ∼ g

4πmρ

generically

QCD analogue with Weinberg sum rules

only mass scale in the composite sectormρ = gρf > f


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Higgs Mass


mH ∼ g

4πΛ

mH ∼ g

4πmρ

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


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Let first consider the top quark.

mt ∼�2

Mf

v

f∼ v �2 ∼Mff

The top mixing largest explicit symmetry breaking terms

Higgs PotentialCalculable 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) = −γgs2h + βgs

4h Vf (h) = −γfs2

h + βfs4h

sh ≡ sinh

f� 1


s2h = ξ =

γ

2βNon-trivial minimum at

m2h =

8β

f2ξ (1− ξ) .

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β � βf ∝�4Nc

16π2

m2H∼ �4Nc

2π2f2ξ � Nc

2π2

m2tM2

ff2

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

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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 fermionMany 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

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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 ?


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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



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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

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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


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M. Serone, The Composite Higgs Paradigm

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