LHC bounds on coloured scalars: the Manohar-Wise model

LHC bounds on coloured scalars:

the Manohar-Wise model

V´ıctor Miralles(Instituto de F´ısica Corpuscular) in collaboration with A. Pich

Universitat de Val`encia

Salamanca, October 30th, 2018

Introduction

The Standard Model succeed but it has some deficiencies⇒Not the definitive theory

The Higgs boson was discovered but is it the only scalar particle in Nature?

Other possibilities should be compatible with the data

Processes involving flavour changing neutral currents gives hard constraints In order to avoid those processes some assumption can be made

Minimal Flavour Violation (MFV)⇒the dynamics of flavour violation is completely determined by the structure of the ordinary Yukawa couplings A. V. Manohar & M. B. Wise⇒only (1,2)_1/2 and (8,2)_1/2 satisfy MFV

Our Work

Many works studying extensions with more (1,2)_1/2scalars

We focussed on the (8,2)_1/2 scalar extensions

Most of the works came before the LHC

A few works concerning the direct searches of these scalars

We study the direct production finding better constraints than previous works

The Manohar-Wise Model

Scalar sector

φ= φ⁺

φ⁰

S^A= S^+A S^0A

!

Different quantum numbers than the SM Higgs doublet⇒No mixture Conservation of colour⇒Cannot acquire a vev

h0|φ|0i= 0

√1 2ve^iθ

h0|S^A|0i= 0

0

Most general potential build with these scalars (S=S^AT^A)

V = λ 4

φ^†iφi−v² 2

²

+ 2mS2

TrS^†iSi+λ1φ^†iφiTrS^†jSj+λ2φ^†iφjTrS^†jSi

+ [λ₃φ^†iφ^†jTrS_iS_j+λ₄φ^†iTrS^†jS_jS_i+λ₅φ^†iTrS^†jS_iS_j+h. c.]

+λ6TrS^†iSiS^†jSj+λ7TrS^†iSjS^†jSi+λ8TrS^†iSiTrS^†jSj

+λ9TrS^†iSjTrS^†jSi+λ10TrSiSjTrS^†iS^†j+λ11TrSiSjS^†jS^†i

The Manohar-Wise Model

The vev produces a splitting of the masses m²_H= λ

2v² m²_S0

R=m²_S+ (λ1+λ2+ 2λ3)v² 4 m²_S±=m²_S+λ₁v²

4 m²_S0 I

=m²_S+ (λ₁+λ₂−2λ₃)v² 4

The kinetic term of the colour octet is

LSKin= 2 Tr[(DµS)^†D^µS], with DµS =∂µS+igs[Gµ, S] +igWfµS+iySg⁰Bµ

The Yukawa term takes the form:

LSY =−

3

X

i,j=1

hη_UY_ij^dQ_L

iSd_Rj +η_DY_ij^uQ_L

iSue _Rj +h. c.i

Degrees of Freedom

18 degrees of freedom →

1 mass parameterm_S 11λ’s 2 of them complex 2 complex in the Yukawa sector

→

→

→ 1 13 4

CP-conserving limit →

Im(λ4,5) = 0

Im(ηU,D) = 0 → 14

Custodial Symmetry →

2λ₃=λ₂ 2λ₆= 2λ₇=λ₁₁

λ₉=λ₁₀ λ₄=λ₅

→ 9

Avoid 4 point

interactions →

λ6= 0 λ8= 0 λ₉= 0

→ 6

Higgs processes

irrelevant → λ1= 0 → 5

Kinematic Suppresion

With the previous assumptions the final parameters are mS λ2 λ4 ηU ηD

The mass splitting is totally determined byλ₂

∆m²_S =m²_S0

R−m²_S± =m²_S0 R−m²_S0

I =λ2

v² 2

It is convenient to avoid the decay of one scalar particle to another

While studyingS_R⁰ processes we will chooseλ2<0

While studyingS^± processes we will chooseλ2>0

Production channels

At tree level the colour scalars are produced by pairs

The single production of the neutral colour scalars is only possible at loop level via gluon fusion

Decay channels

Suppressing kinematically the decay to colour scalar the only possible decay at tree lever is the decay to quarks

The decay to gluons although being a loop process can be dominant for neutral scalars

Effective Lagrangian

For the generation of the events it is convenient to work only at tree level Condense the physics of the decay to gluons in a dimension six effective Lagrangian

L6d=F_RG^A_µνG^Bµνd^ABCS_R^0C+F_I Ge^A_µνG^Bµνd^ABCS_I^0C

F_R→(η_U, η_D,Re(λ₄+λ₅)) FI →(ηU, ηD,Im(λ4+λ5))

Analysis

We generated events with MadGraph and compare with experimental data

The Universal Feynrules Output needed for MadGraph has been generated using FEYNRULES

The channels studied wherep p→S⁰_R→t¯t,p p→S_R⁰ t¯t→t¯t t¯t and p p→S⁺t¯b→t¯b t¯b

We will assume thatm_S0

R< m_S+ for the first two processes and m_S+< m_S0

R for the last one

From perturbative unitarity bounds|λ4|<13and from Rb|ηU|<2 when m_S <1TeV

Results Single Production

Experimental data from ATLAS with 36.1 fb⁻¹ (arXiv:1804.10823) Compare with KK gluons, gravitons and Z’ bosons

No constraints found with the actual data

0.01 0.1 1 10 100

400 500 600 700 800 900 1000

σ·Br (pb)

m_SR (GeV) p p → S_R → t t_

at 13 TeV and η_U=1, η_D=1

0.01 0.1 1 10 100

400 500 600 700 800 900 1000

σ·Br (pb)

m_SR (GeV) p p → S_R → t t_

at 13 TeV and η_U=1, η_D=1

λ4,5=-10, µ=(0.5-2)µ0 λ4,5=0, µ=(0.5-2)µ0 Z' ATLAS KK Graviton ATLAS KK Gluon 15% width ATLAS KK Gluon 30% width ATLAS

0.01 0.1 1 10 100

400 500 600 700 800 900 1000

σ·Br (pb)

m_SR (GeV) p p → S_R → t t_

at 13 TeV and λ_4,5=-10, η_D=1

0.01 0.1 1 10 100

400 500 600 700 800 900 1000

σ·Br (pb)

m_SR (GeV) p p → S_R → t t_

at 13 TeV and λ_4,5=-10, η_D=1

ηU=1, µ=(0.5-2)µ0 ηU=2, µ=(0.5-2)µ0 Z' ATLAS KK Graviton ATLAS KK Gluon 15% width ATLAS KK Gluon 30% width ATLAS

Results Associated Production Neutral Scalars

Better constraints will be obtained for high values ofη_U

Experimental data from ATLAS with 36.1 fb⁻¹ (arXiv:1807.11883)

Compare with the limits obtained for Two Higgs Doublet Models (THDM)

Results Associated Production Neutral Scalars

Lower bound of 1 TeV for values ofηU of order one

0.001 0.01 0.1 1 10

400 500 600 700 800 900 1000

σ·Br (pb)

mSR (GeV) p p → t t_

SR → t t_ t t_

at 13 TeV and ηU=0.1, ηD=1

0.001 0.01 0.1 1 10

400 500 600 700 800 900 1000

σ·Br (pb)

mSR (GeV) p p → t t_

SR → t t_ t t_

at 13 TeV and ηU=0.1, ηD=1

λ4,5=-10, µ=(0.5-2)µ0 λ4,5=0, µ=(0.5-2)µ0 THDM ATLAS

0.001 0.01 0.1 1 10

400 500 600 700 800 900 1000

σ·Br (pb)

mSR (GeV) p p → t t_

SR → t t_ t t_

at 13 TeV and λ4,5=-10, ηD=5

0.001 0.01 0.1 1 10

400 500 600 700 800 900 1000

σ·Br (pb)

mSR (GeV) p p → t t_

SR → t t_ t t_

at 13 TeV and λ4,5=-10, ηD=5

ηU=0.1, µ=(0.5-2)µ0 ηU=0.2, µ=(0.5-2)µ0 ηU=0.3, µ=(0.5-2)µ0 ηU=0.5, µ=(0.5-2)µ0 ηU=1, µ=(0.5-2)µ0 THDM ATLAS

0.001 0.01 0.1 1 10

400 500 600 700 800 900 1000

σ·Br (pb)

mSR (GeV) p p → t t_

SR → t t_ t t_

at 13 TeV and ηU=0.1, ηD=3

0.001 0.01 0.1 1 10

400 500 600 700 800 900 1000

σ·Br (pb)

mSR (GeV) p p → t t_

SR → t t_ t t_

at 13 TeV and ηU=0.1, ηD=3

λ4,5=-10, µ=(0.5-2)µ0 λ4,5=0, µ=(0.5-2)µ0 THDM ATLAS

0.0001 0.001 0.01 0.1 1 10

400 500 600 700 800 900 1000

σ·Br (pb)

mSR (GeV) p p → t t_

SR → t t_ t t_

at 13 TeV and λ4,5=-10, ηD=10

0.0001 0.001 0.01 0.1 1 10

400 500 600 700 800 900 1000

σ·Br (pb)

mSR (GeV) p p → t t_

SR → t t_ t t_

at 13 TeV and λ4,5=-10, ηD=10

ηU=0.1, µ=(0.5-2)µ0 ηU=0.2, µ=(0.5-2)µ0 ηU=0.3, µ=(0.5-2)µ0 ηU=0.5, µ=(0.5-2)µ0 ηU=1, µ=(0.5-2)µ0 THDM ATLAS

Results Associated Production Charged Scalars

Experimental data from ATLAS with 36.1 fb⁻¹ ( arXiv:1808.03599) Compare with THDM

Up to 800 GeV

1e-05 0.0001 0.001 0.01 0.1 1 10 100

400 600 800 1000 1200 1400 1600 1800 2000

σ·Br (pb)

m_S+ (GeV) p p → S⁺ t_

b → t b_ t b_

at 13 TeV and η_D=1

1e-05 0.0001 0.001 0.01 0.1 1 10 100

400 600 800 1000 1200 1400 1600 1800 2000

σ·Br (pb)

m_S+ (GeV) p p → S⁺ t_

b → t b_ t b_

at 13 TeV and η_D=1

ηU=0, µ=(0.5-2)µ0 ηU=1, µ=(0.5-2)µ0 ηU=2, µ=(0.5-2)µ0 ηU=3, µ=(0.5-2)µ0 THDM ATLAS

1e-05 0.0001 0.001 0.01 0.1 1 10 100

400 600 800 1000 1200 1400 1600 1800 2000

σ·Br (pb)

m_S+ (GeV) p p → S⁺ t_

b → t b_ t b_

at 13 TeV and η_U=0

1e-05 0.0001 0.001 0.01 0.1 1 10 100

400 600 800 1000 1200 1400 1600 1800 2000

σ·Br (pb)

m_S+ (GeV) p p → S⁺ t_

b → t b_ t b_

at 13 TeV and η_U=0

ηD=1, µ=(0.5-2)µ0 ηD=10, µ=(0.5-2)µ0 ηD=20, µ=(0.5-2)µ0 THDM ATLAS

Conclusions

From thep p→S_R⁰ →tt¯channel no constraints are found with the actual data but will probably be find in the near future

From thep p→S_R⁰ t¯t→tt t¯ t¯channel we can find a lower bound on the mass of the scalars of 1 TeV whenη_U is of order one and λ₂<0

From thep p→S⁺t¯b→t¯b t¯b channel the lower bound is of 800 GeV for any value ofηU and/orηD different from 0 andλ2>0

Combining both we conclude that the mass of the colour scalars must be higher than 800 GeV ifη_U is order one

Better constraints than previous works

Thank you!

Effective Lagrangian Explicit Formulae

L6d=F_RG^A_µνG^Bµνd^ABCS_R^0C+F_I Ge^A_µνG^Bµνd^ABCS_I^0C

FR= q√

2GF

αs

8π

"

ηUIq

m²_t m²_S

R

+ηDIq

m²_b m²_S

R

+9 4

v² m²_S

R

λ4+λ5

2

Is(1) + 1 3

Is

m²_S

I

m²_S

R

+ 2Is

m²_S±

m²_S

R

#

F_I = q√

2G_F α_s 16π

"

m²_t m²_S

I

η_UF m²_t

m²_S

I

+ m²_b

m²_S

I

η_DF m²_b

m²_S

I

#

Iq(z) = 2z+z(4z−1)f(z)

I_s(z) = (1 + 2zF(z)) F(z) = ( 1

2

h log(¹⁺

√1−4z 1−√

1−4z)−iπi²

z <1/4

−2 arcsin²(1/√

4z) z >1/4

Custodial Symmetry

SU(2)_L⊗SU(2)_R symmetry of the scalar Lagrangian in the limitg⁰ →0 before SSB

After SSBSU(2)L⊗SU(2)R broken toSU(2)L+R ⇒Three Goldstone bosons “eaten” by three gauge bosons

ρtree≡ m²_W m²_W

3

≡ m²_W m²_Zcos²θW

= 1

In the case ofN multiplets belonging to different SU(2)L⊗U(1)Y

representations(Ti,Yi) ρ_tree≡ m²_W

m²_Zcosθ_W = P

iv_i²[Ti(Ti+ 1)−Y_i²] 2P

iv²_iY_i²

Custodial symmetry can be implemented in our new scalar sector

With this symmetry guarantee that the quantum corrections to gauge bosons are zero