Vector and Axial-vector Resonances from a Fundamental Composite Higgs Model

Planck 2016, 23-27 May, Valencia, Spain

Vector and Axial-vector Resonances from a Fundamental Composite Higgs Model

Haiying Cai

IPNL, Universite Lyon 1

D.Buarque Franzosi, G.Cacciapaglia, H.Cai,

A.Deandra, M.Frandsen arXiv:1605.1363

Outline

• A brief review of Composite Higgs Models

• Model implementation of Spin-1 resonances in SU(4)/Sp(4)

• Phenomenology at LHC and 100 TeV Collider

• Conclusion and future outlooks

Composite Higgs Model

Top quark mass can be generated via partial compositeness

[Contino, Nomura, Pomarol 2003; Agashe, Contino, Pomarol, 2004]

[Georgi, Kaplan 1984]

Minimal CHM based on fundamental dynamics requires SU(4)/Sp(4) Give rise to one Higgs doublet plus one singlet

Original one: SU(5)/SO(5) gives 14 pNGBs; Higgs mass protected by “shift symmetry”;

EWSB triggered by vacuum misalignment.

What is Composite Higgs? > PNGB from strong dynamics

SM O CF T

SM fermion couples to strong sector:

Global symmetry broken at TeV scale with f >> v, EWPT vs “Naturalness”

Fundamental Theory

How to implement vector resonances in EFT ?

[Galloway, Evans, Luty, Tacchi, 2010 ;

Cacciapaglia, Sannino, 2014]

[Barnard, Gherghetta, Ray, 2014; Ferretti, 2014; Cacciapaglia, Cai, Deandra, Flacke, Lee, Parolini, 2015]

h QQ i = 6 SU (4) ! 5 Sp(4) 1 Sp(4) compsoite scalars

h Q ¯ µ Q i = 15 SU (4) ! 10 Sp(4) 5 Sp(4) composite vectors For N c 2, add 6 techni-quarks j ) coloured pNGBs plus top partners . (⇡ a , ) :

(⇢ i µ , a k µ ) :

Underlying dynamics is Sp(2N c ) T C gauge theory with 4 Weyl techni-quarks:

L = 1

4 F

F

+ ¯ Q

(i

D

)Q

M

Q

Q

+ h.c.

M

=

✓ µ

i

0 0 µ

i

◆

, techni-quark mass Sp(2) ⇠ SU (2)

[Belyaeav, Cacciapaglia, Cai, Flacke, Parolini, Serodio, 2015]

Bound states will form in the IR:

Minimal choice :

Hidden Symmetry

K = e ik i V i /f K

⇡ 0 a , W , B ˜

SU (4) 0 ⇥ SU (4) 1 ! Sp(4)

elementary sector strong sector

⇡ 0 a , ⇡ 1 a , k i : 20 Nambu-Goldstone bosons, 15 eaten by V i , A a 3 eaten by W, Z , two physical scalars remain: h, ⌘.

⇡ 1 a , ⇢ i µ , a k µ

Composite fermions?

SM fermions

Using Hidden symmetry techniques, one can extend the global symmetry to be:

Model Setup

[Coleman, Wess, Zumino, 1969; Callan, Coleman,

Wess, Zumino, 1969; Bando, Kugo, Yamawaki, 1988]

We adopt the CCWZ formalism and define 2 sets of pions for enhanced global symmetry:

U

= exp

"

i p 2 f

X

a=1

(⇡

Y

)

#

U

= exp

"

i p 2 f

X

a=1

(⇡

Y

)

#

Project Maurer-Cartan forms into:

broken direction ) p µ i = 2 X

a

T r(Y a U i † D µ U i ) Y a

unbroken direction ) v µ i = 2 X

a

T r(V a U i † D µ U i ) V a

Thus v µ,i transform like gauge bosons and p µ,i transform homogeneously.

Effective Lagrangian

pion kinetic terms Vector partial compositeness Axial partial compositeness

L = 1

2g 2 Tr W µ⌫ W µ⌫ 1

2g 0 2 Tr B µ⌫ B µ⌫ 1

2˜ g 2 Tr F µ⌫ F µ⌫

+ 1

2  G

( )f 0 2 Trp 0µ p µ 0 + 1

2  G

( )f 1 2 Trp 1µ p µ 1 + r[ ]f 1 2 Trp 0µ Kp µ 1 K †

+ 1

2  K ( )f K 2 Tr D µ K D µ K † + 1

2 @ µ @ µ V ( )

composite vectors: F µ =

X 10

a=1

V µ a V a +

X 5

a=1

A a µ Y a .

K = exp ⇥

ik i V i /f K ⇤

, D µ K = @ µ K iv 0µ K + iKv 1µ

The K field is to break Sp(4) 0 ⇥ Sp(4) 1 into the diagonal final Sp(4).

Physical Pions

Due to the r term, we need to rotate 2 sets of pions into orthogonal unitary basis,

⇡ 0 a = ⇡ P a 1 q

1 r 2 f 1 2 /f 0 2

⇡ 1 a = ⇡ U a ⇡ P a rf 1 /f 0 q

1 r 2 f 1 2 /f 0 2

⇡ P is associated with physical scalars and ⇡ U is NG boson eaten by x µ 0 and x e µ 0 .

Since v 2 = (f 0 2 r 2 f 1 2 ) sin 2 ✓, with EWSB, there is no divergence in the pion rotation.

Unitary basis ) no bilinear mixing in terms of @ µ h x µ 0 and @ µ ⌘ x e µ 0

Model Spectrum

One charged state of exact mass M V does not mix with ˜ W and ˜ B; Neutral Sector gives a massless photon.

There are additional no mixing states s e

, e v

, x

and x e

, with masses:

M

= M

= M

and M

= M

= M

.

2M 2 2M 2

Typical HVV couplings:

M_W^{2 +} = 1

4g²v² +O

✓g e g

◆4

, M_S⁺ = M_V²

M_A²+ = M_A² 0

B@1 + r²⇣

g e g

⌘2

s_✓² 2

1 CA+O

✓g e g

◆4

MV⁺ = 1 4MV²

✓g²(cos(2✓) + 3) e

g² + 4

◆ +O

✓g e g

◆4

Haiying Cai (Planck, 2016) Vector and Axial-vector Resoannces 10 / 20

MZ² = 1

4(g² + g⁰²)v² +O

✓g e g

◆4

M_A²⁰ = M_A² 0

@1 + r²⇣

g²+g⁰² e g²

⌘s_✓² 2

1 A+O

✓g e g

◆4

M_V⁰_,S⁰ = MV²



1 + g² +g⁰² 4eg²

⇣1 +c_✓²⌘

+O

✓g e g

◆4

Haiying Cai (Planck, 2016) Vector and Axial-vector Resoannces 11 / 21

Electroweak Precision Tests

r=0.1 r=0.6 r=0.9 r=1.1

2 4 6 8 10

0.0 0.2 0.4 0.6 0.8 1.0

�

θ

S-T exclusion

stronger than Higgs coupling constraint !

S = 4s

↵

g

r

1 s

2˜ g

+ g

⇥

2 + (r

1)s

⇤

+ 1

6⇡ s

log

✓ ⇤ m

◆

T = 3

8⇡ cos

✓

s

ln ⇤ m

r ' 1: a partial cancellation occurs in S parameter, in certain range of ˜ g , there is no bound for the ✓ angle.

r < 1: EWPT typically requires ✓ < 0.2.

The S-T is exploited to exclude the unfavored region in the parameter space.

Haiying CAI (Planck 2016)

Fermion Currents

11

Field Fermion currents P C G GP

Massive spin-1 Vµ (unbroken generators)

v⁺ D ^µU

v⁰ p¹

2 U ^µU D ^µD +

v U ^µD

˜

v⁰ p

2 cos✓= U^TC ^µD + p¹

2sin✓ U ^µU +D ^µD +

s⁺ cos✓ D ^{µ 5}U + ₂ⁱ sin✓ ⇣

U^TC ^{µ 5}U D ^µC ⁵D^T⌘ s⁰ p¹

2cos✓ U ^{µ 5}U D ^{µ 5}D p

2 sin✓= U^TC ^{µ 5}D + + + + s cos✓ U ^{µ 5}D + ₂ⁱ sin✓ ⇣

U ^µC ⁵U^T D^TC ^{µ 5}D⌘

˜

s⁺ ₂ⁱ ⇣

U^TC ^{µ 5}U +D ^µC ⁵D^T⌘

˜

s⁰ p

2< U^TC ^{µ 5}D +

˜

s ₂ⁱ ⇣

U ^µC ⁵U^T +D^TC ^{µ 5}D⌘

Massive spin-1 Aµ (broken generators) a⁺ ₂ⁱ cos✓ ⇣

U^TC ^{µ 5}U D ^µC ⁵D^T⌘

sin✓ D ^{µ 5}U a⁰ p

2 cos✓= U^TC ^{µ 5}D + p¹

2sin✓ U ^{µ 5}U D ^{µ 5}D + + + + a ₂ⁱ cos✓ ⇣

U ^µC ⁵U^T D^TC ^{µ 5}D⌘

sin✓ U ^{µ 5}D

x⁰ p

2< U^TC ^µD + +

˜

x⁰ p¹

2cos✓ U ^µU +D ^µD p

2 sin✓= U^TC ^µD +

TABLE II: Classification of composite vectors in terms of the underlying fermionic currents, using a notation C = ^{0 2}. We quote transformation properties in terms of spacial parity P, charge conjugation C, and pion parity G defined from listed currents.

The combination GP is a good symmetry from the strong dynamics. In our notation, P-parity is defined in spacial direction, i.e. ( 1)^µ is “ ” parity.

Under CP, the bound state fields transform as

M ^CP!M^†, F^{µ CP}! ( 1)^µ(F^µ)^T , (74)

P-Parity : U

! i

U, D

! i

D

C-Parity : U

! i

U

, D

! i

D

G-Parity : U

!

D

, D

!

U

The GP is a good symmetry and being selection rule for decays. Only the tilded fields and ⌘ are odd under this parity.

Under the parity operation: a vector fermion-

current has CP = +; and a pseudo-vector

fermion-current has CP = .

Cross Section @ LHC Run II

The benchmark point: M

= 3 TeV,

˜

g = 3.0, r = 0.6 and ✓ = 0.2.

No S

state can be directly produced since it is purely composite.

For M

= M

, cross sections of axial

resonances turn out to be zero.

Scenario

θ

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

X X')→0 BR(V

−4

10

−3

10

−2

10

−1

10 1

Leptons Neutrinos Light quarks Top W-

W+ hZ

θ

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

X X')→0 BR(A

−4

10

−3

10

−2

10

−1

10 1

Leptons_± Neutrinos Light quarks Top

± W

V S^± W^± V⁰h S⁰h

W-

W+ hZ S~⁰

η

M V < M A

Scenario M A < M V

θ

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

X X')→0 BR(A

−4

10

−3

10

−2

10

−1

10 1

Leptons Neutrinos Light quarks Top W-

W+ hZ

θ

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

X X')→0 BR(V

−4

10

−3

10

−2

10

−1

10 1

Leptons_± Neutrinos Light quarks Top

± W

A A⁰h X⁰Z W⁺W^-

hZ

A 0 mainly decays into SM fermions and dibosons and Higgs.

Direct Bounds - LHC Run II

�=���

�=���

�=���

1600 1800 2000 2200 2400 2600 2800 3000 2

3 4 5 6 7 8

�_� (���)

�

l⁺l^-/WZ exclusion

θ=0.2

�=���

�=���

�=���

1600 1800 2000 2200 2400 2600 2800 3000 0.1

0.2 0.3 0.4 0.5 0.6

�_� (���)

θ

l⁺l^-/WZ exclusion

g˜

=3.0

W Z

l

l

W Z

l

l

Recasted from ATLAS measurement, with dilepton bound in solid line and WZ bound in dashed line.

+

Future100 TeV Collider

θ

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

X X')→0 BR(A

−4

10

−3

10

−2

10

−1

10 1

Leptons_± Neutrinos Light quarks Top

± W

V S^± W ^± V⁰h S⁰h

W-

W+ hZ S~⁰

η

[Arthur, Drach, Hansen, Pica, Sannino 2016]

R .O (1) fb for ✓ ⇠ 0.2, with an integrated luminosity 3 30ab 1 per year.

[Richter, 2014; Rizzo, 2015]

- The branching ratio into W

W , hZ is sensitive to r.

- A

state mainly decays into heavy resonances, in particular ⌘ S ˜

.

- Cascade decay: A

! ⌘ S ˜

! 2⌘ + Z ,

⌘ ! t ¯ t, will give rise to interesting multi-tops events .

Using Lattice benchmark point: M V = 3.2/ sin ✓ TeV, M A = 3.5/ sin ✓ TeV.

Conclusion and Outlook

Spin-1 resonances are implemented in a SU(4)/Sp(4) CHM using Hidden symmetry techniques; Composite fermions not included yet.

S parameter can be well protected due to a partial cancellation.

At LHC Run-II, the Drell-Yan process imposes a stringent bound.

Searching for signatures related to such resonances is possible to unveil

EWSB mechanism.