A UV description of a composite Higgs
model without elementary scalars
Tony Gherghetta
University of Minnesota

SCGT14 Mini-Workshop, KMI, Nagoya, Japan, March 5, 2014
[James Barnard, TG, Tirtha Sankar Ray 1311.6562][James Barnard, TG, Anibal Medina, Tirtha Sankar Ray 1307.4778]

Wednesday, 5 March 14

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Higgs discovery - Run1PDG 2013

Higgs potential:2v =µ2hhV (h) =µ2h |H|2 +' (246 GeV)2µ2h ' (89 GeV)2

Wednesday, 5 March 14h |H|

41hHi = p (v + h)
2m2h = 2 h v 2 ' (126 GeV)2h ' 0.13

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Higgs couplings[Giardino et al 1303.3570]

Looks very much like a SM Higgs boson!
Wednesday, 5 March 14

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What is the nature of the Higgs boson?

HIGGSBOSON{Elementary?

Standard Model/
Supersymmetry

ORComposite?

New strong dynamics

How to obtain a mass ~126 GeV much below
the Planck scale?
Wednesday, 5 March 14

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Composite Higgs
Higgs as a pseudo Nambu-Goldstone boson[Georgi, Kaplan `84]

Global symmetry G spontaneously broken to subgroup H at scale fe.g. SO(5)/SO(4) = 2 of SU (2)L(n) & TeV⇢

Resonance mass:

EWPT:

h

Wednesday, 5 March 14

Higgs mass protected by global symmetry-- like pions in QCDm⇢ ⇠ g⇢ fm2WS⇠ 2m⇢

1 . g⇢ . 4⇡m⇢ & 2.5 TeV

BUT global symmetry must be explicitly broken
to generate V (h) 6= 05

Global symmetry broken by mixing with elementary sector[Kaplan `91; Agashe, Contino, Pomarol `04]

SM matter andgauge fields
i , AµLmix =L,R¯ L,R O + gV Aµ Jµstrongly-coupledHiggs sector

OihhhHiggs potential

htL,RV (h) =EWSB✓µ2h |H|2 +v
hHi = p2

◆v2 =h |H|µ2hh4

where2gSM
2µh ⇠ 16⇡2 g⇢2 f 2Tuning:

2gSM
2h ⇠ 16⇡ 2 g⇢2v
1
⇠ 2 . 10%f(v = 246 GeV, f & 750 GeV)

Wednesday, 5 March 14

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Higgs mass:

2=gT
2Ncm
m2h ' 2 m2t 2T
⇡fHtL

TtR

mT = fermion resonances (EM charges 5/3, 2/3, 1/3)

mT ⇠ m⇢ & 2.5 TeV (gT ⇠ g⇢ & 3)

But, no need for mT ⇠ m⇢mh & mt
[Marzocca, Serone, Shu 2012; Pomarol, Riva 2012]mh ⇠ 126 GeV

mT < m⇢light fermion resonances!

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mT5/3 & 770 GeV
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HOWEVER, top partners

gluon partners
gluon partner couplingwhereg32↵G 'ln4⇡

Contribution to Higgs mass:✓⇤U V⇤IR◆

gluon partner mass

⇡3

whereandGluon partner correction to Higgs
mass is negative
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[Barnard, TG, Medina, Sankar Ray 1307.4778]

mG = 3 TeV↵G = 3↵G = 3For ↵G = 3 and mG = 3 TeV obtain ⇡ 10% correction

Eases tension of having light top partners!
Wednesday, 5 March 14

10Features of Composite Higgs models:• Higgs is pseudo Nambu-Goldstone boson
G!Hat scalefwhere• Partially composite topmt ⇠L Rv

whereL,R ⇠✓HSO(4) ⇠ SU (2)L ⇥ SU (2)R

L=⇤
⇤U V

L tL O R +◆dim OL,R

R tR O L

52

dim OL,R ⇠52

What is the UV description responsible for these features?
• AdS/CFT -- D-brane engineering
Involves scalars• Supersymmetric (e.g. Seiberg duality)[Caracciolo, Parolini, Serone 1211.7290]}

Look for one without elementary scalars...
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Candidate:SO(6)/SO(5) model[Gripaios, Riva, Pomarol, Serra `09]
[Other possibilities classified by Ferretti, Karateev 1312.5330]

SO(6)/SO(5) ⇠ SU (4)/Sp(4)}= 2 of SU (2)L + 1 singlet
Higgs doublet

Symmetry breaking-patternf

SU (4) ! Sp(4)What is the dynamics that realizes this?

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Introduce new strong gauge group Sp(2Nc )awith 4 Weyl fermion flavors(a = 1, . . . , 4)
SU (4)

global symmetry

Gauge-invariant fermion bilinear:⌦ijaibj = 6 of SU(4)Sp(2Nc ) is asymptotically freeand confines>0SU (4) ! Sp(4)Under what conditions does this happen?

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SU(4) gauged NJL modelCan be rewritten as
Like “massiveYukawa theory”

whereWednesday, 5 March 14“auxiliary scalar field”

14One-loop effective potential⇤ = UV cutoff scale

whereMinimum conditionSolutions{m1 = m2 = 0m1 = m2 =m̄20<⇠<1⇠>1SU (4)unbroken

SU (4) ! Sp(4)⇠ = 1 is a critical point

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Treat ⇤ as a renormalization scale:
UV fixed point at ⇠ = 1
Dynamically generated fermion massNear ⇠ ⇡ 1m̄ =4⇡ 2 ⇠h2
Nc ⇤iµ0 = reference scale

Large anomalous dimension
dim(⇤ ! 1 with m̄ finite)=3[Kondo, Tanabashi,Yamawaki `92
Yamawaki `96]

m =1

Four-fermion operator has dimension 2-- model appears to be renormalisable in the UV!

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Need to include gauge interaction and solve Schwinger-Dyson equation[Bardeen, Leung, Love `86; Kondo, Mino,Yamawaki `89]

For Sp(2Nc) gauge group obtainlarge anomalousdimension[Barnard, TG, Sankar Ray 1311.6562]

Large anomalous dimension for⇠ ⇡ ⇠ ⇤ and ↵ ⌧ ↵⇤m '2↵
2↵⇤

small anomalousdimension ( m ' 1)

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Evolution of couplings: (for upper trajectory)[Barnard, TG, Sankar Ray 1311.6562]

Spontaneous breaking of global symmetry
driven mainly by 4-fermion interaction!

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Top partners
Introduce a pair of colored vector-like fermionstransform as two-index antisymmetricrepresentation of Sp(2Nc),˜}Gauge-invariant combinations:transform as}
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top partner candidates

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Recall:

L=UV description:

L tL O R +R tR O L}

OL,R $(Diquark approximation to baryons [Ball `90])= tightly boundby 4-fermion interaction,bound top↵)
by Sp(2Nc) gauge interaction (⇠⇡ dim}

dim OL,R = dim

3+35↵= + ⇤2 2↵2

Marginally irrelevant!

mAllows for order-one top Yukawa coupling!
⇠p↵Top partners are naturally lighter thanuncolored partners!
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In addition there are scalar bound states:}

Coloured bound statescannot get a VEV

Coloured scalars must be stabilised by the SU(3) gauge interactions.

Require:Wednesday, 5 March 14↵d↵⇤<↵3d↵321

Conclusion

Higgs boson could be composite• The--- Higgs
is a pseudo Nambu-Goldstone boson--- Partially composite top sector• SO(6)/SO(5) model has a simple UV description--- Only fermions and gauge bosons, no elementary scalars!
--- Large anomalous dimension implies four-fermion
interaction is renormalisable• This simple framework can be applied to othercoset groups

Wednesday, 5 March 1422