Composite Higgs Models After Run 2

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Composite Higgs models after Run 2

Jack Setford

University of Sussex

10th May 2017

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 1 / 24 Outline of this talk

1 Motivation

2 Composite Higgs

3 Higgs couplings and Recent Results

4 Conclusions

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 2 / 24 Outline of this talk

1 Motivation

2 Composite Higgs

3 Higgs couplings and Recent Results

4 Conclusions

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 3 / 24 Motivation

Hierarchy problem – loop corrections to the Higgs mass are quadratically divergent. Unless loops are naturally cut oﬀ, Higgs mass has a sensitive dependence on high energy scales. Extreme ﬁne tuning between bare Higgs mass and loop contributions.

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 4 / 24 Natural loop cutoffs

Supersymmetry oﬀers one solution to the hierarchy problem. Superpartners cancel out quadratic divergences:

+ = 0

Generally speaking, the hierarchy problem points to TeV-scale new physics.

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 5 / 24 Outline of this talk

1 Motivation

2 Composite Higgs

3 Higgs couplings and Recent Results

4 Conclusions

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 6 / 24 Loops are cut oﬀ at conﬁnement scale ∼ ΛQCD.

ΛQCD is generated dynamically when QCD becomes strongly interacting. QCD condensate breaks chiral symmetry:

hqLqRi

→ pions are pseudo-Goldstone bosons, natural “little” hierarchy between mπ and ΛQCD.

Pions in QCD

Pions – which are also scalars – have no hierarchy problem.

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 7 / 24 ΛQCD is generated dynamically when QCD becomes strongly interacting. QCD condensate breaks chiral symmetry:

hqLqRi

→ pions are pseudo-Goldstone bosons, natural “little” hierarchy between mπ and ΛQCD.

Pions in QCD

Pions – which are also scalars – have no hierarchy problem.

Loops are cut oﬀ at conﬁnement scale ∼ ΛQCD.

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 7 / 24 QCD condensate breaks chiral symmetry:

hqLqRi

→ pions are pseudo-Goldstone bosons, natural “little” hierarchy between mπ and ΛQCD.

Pions in QCD

Pions – which are also scalars – have no hierarchy problem.

Loops are cut oﬀ at conﬁnement scale ∼ ΛQCD.

ΛQCD is generated dynamically when QCD becomes strongly interacting.

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 7 / 24 Pions in QCD

Pions – which are also scalars – have no hierarchy problem.

Loops are cut oﬀ at conﬁnement scale ∼ ΛQCD.

ΛQCD is generated dynamically when QCD becomes strongly interacting. QCD condensate breaks chiral symmetry:

hqLqRi

→ pions are pseudo-Goldstone bosons, natural “little” hierarchy between mπ and ΛQCD.

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 7 / 24 Composite Higgs

Higgs is a composite boson, arising from strong dynamics that conﬁnes at a scale f. The scale f is natural – it is generated dynamically. The Higgs is a Nambu-Goldstone boson, to keep a natural hierarchy between mH and f.

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 8 / 24 Comparison to QCD

QCD Composite Higgs

pNGBs: π0, π± H (+ φi ... ) fermionic resonances: p, n T, T˜ 0 hπi = 0 hHi = v → EWSB

no pion-fermion couplings Yukawa terms: ψLHψR

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 9 / 24 Partial compositeness

SM fermions couple to the strong sector via mixing with composite partner fermions.

Lmix ⊃ yLftLTR + yRftRT˜L + h.c.

t˜ = cos θ |ti + sin θ |T i Partial compositeness mechanism – allows one to generate large top Yukawa coupling, plus a natural quark mass hierarchy.

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 10 / 24 Breaking symmetries

Partner fermions must come in representations of the global symmetry G. SM fermions do not. Partial compositeness breaks the symmetry explicitly.

H H

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 11 / 24 Outline of this talk

1 Motivation

2 Composite Higgs

3 Higgs couplings and Recent Results

4 Conclusions

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 12 / 24 Lots of models

To mention but a few: SO(5)/SO(4) SO(6)/SO(4) × SO(2) SU(4)/Sp(4) SO(8)/SO(7) SU(5)/SO(5) SO(9)/SO(8) SU(4) × SU(4)/SU(4)

Given one coset there are still many options for the partner fermion representations. In SO(5)/SO(4) alone the options 4, 5, 10, 14 have been studied. Correct choice would depend on UV completion.

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 13 / 24 Effective theory for the pNGBs

CCWZ formalism – toolkit for writing down pNGB eﬀective theory Parameterise pNGBs with the matrix:

U = exp(iφaXa/f)

where Xa are the broken generators and f is the breaking scale. Non-linear transformations

U → g U h−1(φa, g).

Can form an object Σ out of contractions of U which has linear transformations.

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 14 / 24 Effective theory for the pNGBs

Must construct an eﬀective Lagrangian as a function of Σ and the fermion spurions, all of which are representations of the group G. SO(5)/SO(4) Σ = (0, 0, 0, sin(h/f), cos(h/f))T SU(4)/Sp(4)

 0 cos(h/f) − sin(h/f) 0  − cos(h/f) 0 0 sin(h/f) Σ =    sin(h/f) 0 0 cos(h/f) 0 − sin(h/f) − cos(h/f) 0

SU(5)/SO(5)

1 0 0 0 0  0 1 0 0 0    Σ = 0 0 1 0 0    0 0 0 cos(h/f) i sin(h/f) 0 0 0 i sin(h/f) cos(h/f)

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 15 / 24 which leads generically to pNGB gauge couplings of the form

2 2 µ 2 g f AµA sin (h/f).

If we expand around the Higgs VEV: h → hhi + h, we ﬁnd

1 L = g2v2W aW aµ gauge 8 µ 1 1 + g2vp1 − ξW aW aµh + g2(1 − 2ξ)W aW aµh2 4 µ 8 µ where ξ = v2/f 2.

Effective theory for the pNGBS

Gauge interactions come from kinetic term:

f 2 h i L = Tr D Σ†DµΣ eﬀ 4 µ

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 16 / 24 If we expand around the Higgs VEV: h → hhi + h, we ﬁnd

1 L = g2v2W aW aµ gauge 8 µ 1 1 + g2vp1 − ξW aW aµh + g2(1 − 2ξ)W aW aµh2 4 µ 8 µ where ξ = v2/f 2.

Effective theory for the pNGBS

Gauge interactions come from kinetic term:

f 2 h i L = Tr D Σ†DµΣ eﬀ 4 µ which leads generically to pNGB gauge couplings of the form

2 2 µ 2 g f AµA sin (h/f).

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 16 / 24 Effective theory for the pNGBS

Gauge interactions come from kinetic term:

f 2 h i L = Tr D Σ†DµΣ eﬀ 4 µ which leads generically to pNGB gauge couplings of the form

2 2 µ 2 g f AµA sin (h/f).

If we expand around the Higgs VEV: h → hhi + h, we ﬁnd

1 L = g2v2W aW aµ gauge 8 µ 1 1 + g2vp1 − ξW aW aµh + g2(1 − 2ξ)W aW aµh2 4 µ 8 µ where ξ = v2/f 2.

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 16 / 24 Effective theory for the pNGBS

Gauge interactions come from kinetic term:

f 2 h i L = Tr D Σ†DµΣ eﬀ 4 µ which leads generically to pNGB gauge couplings of the form

2 2 µ 2 g f AµA sin (h/f).

If we expand around the Higgs VEV: h → hhi + h, we ﬁnd

1 L = g2v2W aW aµ gauge 8 µ 1 1 + g2vp1 − ξW aW aµh + g2(1 − 2ξ)W aW aµh2 4 µ 8 µ where ξ = v2/f 2.

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 17 / 24 κ formalism

κ-factors describe the deviation from a Standard Model cross-section:

2 SM κi = σi/σi

For instance decays of the Higgs to gauge bosons are modiﬁed by a 2 factor of κV . In Composite Higgs κV is generically given by p κV = 1 − ξ.

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 18 / 24 TL and TR in 5s:

5 5 (ΨL · Σ)(Σ · ΨR) → tLtR sin(h/f) cos(h/f)

TL in 10 and TR in 5:

T 10 5 Σ ΨL ΨR → tLtR sin(h/f)

TL in 5 and TR in 1:

5 1 (ΨL · Σ)ΨR → tLtR sin(h/f)

Couplings to fermions

Many choices for fermion representations. For instance, in SO(5)/SO(4):

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 19 / 24 TL in 10 and TR in 5:

T 10 5 Σ ΨL ΨR → tLtR sin(h/f)

TL in 5 and TR in 1:

5 1 (ΨL · Σ)ΨR → tLtR sin(h/f)

Couplings to fermions

Many choices for fermion representations. For instance, in SO(5)/SO(4):

TL and TR in 5s:

5 5 (ΨL · Σ)(Σ · ΨR) → tLtR sin(h/f) cos(h/f)

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 19 / 24 TL in 5 and TR in 1:

5 1 (ΨL · Σ)ΨR → tLtR sin(h/f)

Couplings to fermions

Many choices for fermion representations. For instance, in SO(5)/SO(4):

TL and TR in 5s:

5 5 (ΨL · Σ)(Σ · ΨR) → tLtR sin(h/f) cos(h/f)

TL in 10 and TR in 5:

T 10 5 Σ ΨL ΨR → tLtR sin(h/f)

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 19 / 24 Couplings to fermions

Many choices for fermion representations. For instance, in SO(5)/SO(4):

TL and TR in 5s:

5 5 (ΨL · Σ)(Σ · ΨR) → tLtR sin(h/f) cos(h/f)

TL in 10 and TR in 5:

T 10 5 Σ ΨL ΨR → tLtR sin(h/f)

TL in 5 and TR in 1:

5 1 (ΨL · Σ)ΨR → tLtR sin(h/f)

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 19 / 24 Couplings to fermions

A p sin(h/f) → κF = 1 − ξ 1 − 2ξ sin(h/f) cos(h/f) → κB = √ F 1 − ξ

These structures are very generic. Different fermion species can be embedded in different representations, meaning that that κF for each species may be different.

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 20 / 24 Combined fit

We broadly categorise models according to the couplings of the top, A,B A,B A,B bottom, and tau: (κt , κb , κτ ).

LHC Run1 LHC Run1+2 10 10

AAA BBB AAA BAA 8 8

min 6 min 6 2 2 - χ - χ

2 4 2 4 χ χ 2 2

0 0 400 500 600 700 400 500 600 700 (GeV) (GeV)

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 21 / 24 Outline of this talk

1 Motivation

2 Composite Higgs

3 Higgs couplings and Recent Results

4 Conclusions

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 22 / 24 Couplings to SM particles are fairly generic across diﬀerent models

Robust limit on f > 500 GeV

More data → more discrimination between models

Conclusions

Composite Higgs models oﬀer a solution to the hierarchy problem

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 23 / 24 Robust limit on f > 500 GeV

More data → more discrimination between models

Conclusions

Composite Higgs models oﬀer a solution to the hierarchy problem

Couplings to SM particles are fairly generic across diﬀerent models

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 23 / 24 More data → more discrimination between models

Conclusions

Composite Higgs models oﬀer a solution to the hierarchy problem

Couplings to SM particles are fairly generic across diﬀerent models

Robust limit on f > 500 GeV

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 23 / 24 Conclusions

Composite Higgs models oﬀer a solution to the hierarchy problem

Couplings to SM particles are fairly generic across diﬀerent models

Robust limit on f > 500 GeV

More data → more discrimination between models

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 23 / 24 Thanks for listening!

Jack Setford (University of Sussex) Composite Higgs models after Run 2 10th May 2017 24 / 24