Elizabeth H. Simmons Michigan State University

Nagoya University March 6, 2015

- Introduction

- Coloron Discovery and Properties

- Color Discriminant Variable

- Including Flavor

- Beyond Vector Resonances

- Conclusions

Separating Di-jet Resonances using the

Color Discriminant Variable

If Any New State Is Seen at LHC:

New State Decaying to Dijets:

How can we quickly tell different dijet resonances apart using straightforward measurements of the dijet state?

u

h1 h2

SU(3)1 SU(3)2

Coloron Models: Gauge Sector

SU(3)1 x SU(3)2 color sector with

unbroken subgroup: SU(3)1+2 = SU(3)QCD

M2 =u2

4

✓h2

1 �h1h2

�h1h2 h22

◆

h1 =

gs

cos ✓h2 =

gs

sin ✓

CAµ = � sin ✓ AA

1µ + cos ✓ AA2µ

GAµ = cos ✓ AA

1µ + sin ✓ AA2µgluon state:

coloron state:

couples to:

couples to:

gSJµG ⌘ gS(Jµ

1 + Jµ2 )

gSJµC ⌘ gS(�Jµ

1 tan ✓ + Jµ2 cot ✓)

MC =up2

qh2

1 + h22

MG = 0

Quarks’ SU(3)1 x SU(3)2 charges impact phenomenology

Quark Charges -> Coloron Phenomenology

SU(3)1 SU(3)2 model pheno.

(t,b)L qL tR,bR qR coloron dijet

qR (t,b)L qL tR,bR

tR,bR (t,b)L qL qR

qL (t,b)L tR,bR qR

qL tR,bR (t,b)L qR new axigluon dijet, AtFB, FCNC

qL qR (t,b)L tR,bR topgluon dijet, tt, bb, FCNC, Rb...

tR,bR qR (t,b)L qL classic axigluon dijet, AtFB

qL tR,bR qR (t,b)L

q = u,d,c,s

Coloron Discovery and Properties

LHC Limits on New Dijet Resonances

Resonance mass (GeV)1000 2000 3000 4000 5000

(pb)

A × B × σ

-510

-410

-310

-210

-110

1

10

210

310

410CMS

(8 TeV) -119.7 fb

95% CL upper limits

gluon-gluon

quark-gluon

quark-quark

StringExcited quarkAxigluon/coloronScalar diquarkS8W' SSMZ' SSMRS graviton (k/M=0.1)

CMS arXiv:1501.04198ATLAS arXiv:1407.1376

[TeV]8sm1 2 3 4

[pb]

A × σ

-210

-110

1

10

210

310

ATLAS

8sObserved 95% CL upper limitExpected 95% CL upper limit68% and 95% bands

-1L dt = 20.3 fb∫=8 TeVs

[TeV]*qm1 2 3 4 5

[pb]

A × σ

-310

-210

-110

1

10

210

310

ATLAS

*qObserved 95% CL upper limitExpected 95% CL upper limit68% and 95% bands

-1L dt = 20.3 fb∫=8 TeVs

Coloron Production

C

q̄

q

q

q̄C

q̄

q

q

q̄

C

q̄

q

q

q̄LO vs NLO production impacts

• cross-section value• scale-dependence• pT of produced coloron

R.S. Chivukula, A. Farzinnia, R. Foadi, EHS arXiv:1111.7261R.S. Chivukula, A. Farzinnia, J. Ren, EHS arXiv:1303.1120

W+Ca probes Coloron’s Chiral Couplings

q̄

q j

j

W (Z)l (l+)

ν̄ (l−)

C

q̄

q j

j

W (Z)

l (l+)

ν̄ (l−)

C

q̄′

q j

j

W (Z)

l (l+)

ν̄ (l−)

C

q̄′

q j

j

W (Z)

l (l+)

ν̄ (l−)

C

FIG. 2: Representative Feynman diagrams for associated production of a W,Z gauge boson with acolor-octet resonance, C. Both s and t channel diagrams along with leptonic decays of the associated

gauge boson are shown.

We present the the monte-carlo simulation details in Sec.IIIA and in Sec.III B and Sec.IIICwe study the modes of associated production with a W and a Z boson respectively.

The color-octet states (C) are produced and decay to two jets via the process

ppC−→ j j. (8)

They can also be produced in association with a gauge boson via the process

ppC−→ j j W±, (9)

ppC−→ j j Z, (10)

where j = u, d, s, c, b. We will refer to the process in Eq.(9) and Eq.(10) as the CW and CZchannels respectively. The diagrams of interest for the associated production which includes and t channel diagrams with the emission of the gauge bosons in either the initial or finalstate are shown in Fig. 2. The final state channels of our current interest are

pp → ℓ±E/T 2j, ℓ+ℓ− 2j, (11)

coming from W±(→ ℓ±ν) or Z(→ ℓ+ℓ−), respectively and ℓ = e, µ. Although the inclusionof the τ lepton in the final state could increase signal statistics, for simplicity we ignore thisexperimentally more challenging channel.

The relevant backgrounds to the signal processes in Eq.(11) are

• W+ jets, Z+ jets with W, Z leptonic decays;

• top pair production with fully leptonic, semi-leptonic and hadronic decays;

• single top production leading to W±b q;

• W+W−, W±Z and ZZ with W, Z leptonic decays;

Next, we present some details about the monte-carlo simulation.

5

Wjj

Zjj

Dije

t

− 3 − 2 − 1 0 1 2 3gL

− 3

− 2

− 1

0

1

2

3

gR

FIG. 1: A cartoon illustration of the constraints on chiral couplings from the di-jet channel (dashedblack line with red band), the channel with associated production of a W boson (solid black line

with green band) and the channel with associated production of a Z boson (dotted black line withblue band).

with the di-jet measurement is shown in Fig. 1. Notice that there remains an ambiguity inextracting the sign of the couplings. This method of using the associated production of thegauge boson was studied earlier in the context of the measurement of Z ′ couplings [27, 28].

In this article we study the sensitivity of the LHC with c.m. energy of 14 TeV to probe thechiral structure of the couplings for colored resonances with 10fb−1 and 100fb−1 integratedluminosity by the method proposed above. We study colored resonances with masses inthe range 2.5 TeV to 4.5 TeV and various couplings and widths. The rest of the paperis organized as follows. In Sec.II we present a simple parameterization for the coloredresonances and our notation. In Sec.III we discuss the signal and associated backgrounds,the monte-carlo simulation details in Sec.IIIA and the channels with charged and neutralgauge bosons in Sec. III B and Sec.IIIC respectively. We present a discussion of our resultsin Sec.IV and conclusions in Sec.V.

II. GENERAL PARAMETERIZATION

The color-octet resonance of interest to our study may be motivated in many BSM sce-narios as explained in the introduction. Hence we explore a phenomenological model ofcolor-octet resonances independent of the underlying theory. The interaction of the color-octet resonance with the SM quarks has the form

L = igsq̄iCµγµ

!

giV + gi

Aγ5

"

qi = igsq̄iCµγµ

!

giLPL + gi

RPR

"

qi, (1)

where Cµ = Caµta with ta an SU(3) generator, gi

V and giA (or gi

L and giR) denote coupling

strengths relative to the QCD coupling gs, PL,R = (1∓γ5)/2 and i = u, c, d, s, b, t. We denote

3

pp ! Ca +W [Z] ! jj`⌫[``]

Associated production probes a coloron’s couplings to RH and LH fermions:

A. Atre, R.S.Chivukula, P. Ittisamai, EHSarXiv:1206.1661

Jet Energy Profile

Gluons radiate more than Quarks

R.S. Chivukula, EHS, N. Vignaroli arXiv:1412.3094

Expect quarks to form “tighter” jets than gluons, for fixed pT

Relative fraction of qq, qg, gg jet pairs in event sample can suggest the nature of any new resonance

Color Discriminant Variable: Basics

A. Atre, R.S. Chivukula, P. Ittisamai, EHS arXiv:1306.4715

Identifying Dijet Resonances

Suppose a new dijet resonance of mass M and cross-section is found. Is it a coloron or a leptophobic Z’? Assume its quark couplings are flavor universal to start.

�jj

A. Review of the flavor universal scenario

We briefly review how the color discriminant variable helps distinguish between the twotypes of resonances in the scenario that we either have clues from experiments or assumethat the resonance have flavor universal couplings.

The color discriminant variable defined in (??) is independent of the overall strength ofcouplings and can emphasize the di↵erence in color structures between a coloron and a Z

0.To illustrate how it works first recall that in a narrow-width approximation the dijet crosssection for a process involving a vector resonance V can be written as

�

Vjj ⌘ �(pp

V�! jj) ' �(pp ! V )Br(V ! jj), (10)

where �(pp ! V ) is the cross section for producing the resonance and Br(V ! jj) is itsdijet branching fraction. Note that jet consists of quarks from the first two families.

Recall that the total decay width for a coloron and a leptophobic Z

0 are

�C =↵s

2MC

�g

2

CL+ g

2

CR

�, (11)

and�Z0 = 3↵wMZ0

�g

2

Z0L+ g

2

Z0R

�, (12)

respectively. The dijet cross sections for the coloron is

�

Cjj =

4

9↵s

�g

2

CL+ g

2

CR

� 1

M

2

C

X

q

Wq(Mc)Br(C ! jj)

=8

9

�C

M

3

C

X

q

Wq(MC)Br(C ! jj), (13)

while for the leptophobic Z

0,

�

Z0

jj =1

3↵w

�g

2

Z0L+ g

2

Z0R

� 1

M

2

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj)

=1

9

�Z0

M

3

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj), (14)

where Wq, the parton luminosity for the production of the resonance having mass M fromthe qq̄ annihilation at the center-of-mass energy squared s, is defined by

Wq(MV ) = 2⇡2

M

2

V

s

Z1

M2V /s

dx

x

fq

�x,Q

2

�fq̄

✓M

2

V

sx

,Q

2

◆+ fq̄

�x,Q

2

�fq

✓M

2

V

sx

,Q

2

◆�. (15)

where fq (x,Q2) is the parton distribution function at the factorization scale Q2. Throughoutthis article, we set Q

2 = M

2. The color discriminant variables for the two particles aretherefore,

D

Ccol

=M

3

C

�C�

Cjj =

8

9

"X

q

Wq(MC)Br(C ! jj)

#(16)

D

Z0

col

=M

3

Z0

�Z0�

Z0

jj =1

9

"X

q

Wq(MZ0)Br(Z 0 ! jj)

#(17)

4

must be equal

A. Review of the flavor universal scenario

We briefly review how the color discriminant variable helps distinguish between the twotypes of resonances in the scenario that we either have clues from experiments or assumethat the resonance have flavor universal couplings.

The color discriminant variable defined in (??) is independent of the overall strength ofcouplings and can emphasize the di↵erence in color structures between a coloron and a Z

0.To illustrate how it works first recall that in a narrow-width approximation the dijet crosssection for a process involving a vector resonance V can be written as

�

Vjj ⌘ �(pp

V�! jj) ' �(pp ! V )Br(V ! jj), (10)

where �(pp ! V ) is the cross section for producing the resonance and Br(V ! jj) is itsdijet branching fraction. Note that jet consists of quarks from the first two families.

Recall that the total decay width for a coloron and a leptophobic Z

0 are

�C =↵s

2MC

�g

2

CL+ g

2

CR

�, (11)

and�Z0 = 3↵wMZ0

�g

2

Z0L+ g

2

Z0R

�, (12)

respectively. The dijet cross sections for the coloron is

�

Cjj =

4

9↵s

�g

2

CL+ g

2

CR

� 1

M

2

C

X

q

Wq(Mc)Br(C ! jj)

=8

9

�C

M

3

C

X

q

Wq(MC)Br(C ! jj), (13)

while for the leptophobic Z

0,

�

Z0

jj =1

3↵w

�g

2

Z0L+ g

2

Z0R

� 1

M

2

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj)

=1

9

�Z0

M

3

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj), (14)

where Wq, the parton luminosity for the production of the resonance having mass M fromthe qq̄ annihilation at the center-of-mass energy squared s, is defined by

Wq(MV ) = 2⇡2

M

2

V

s

Z1

M2V /s

dx

x

fq

�x,Q

2

�fq̄

✓M

2

V

sx

,Q

2

◆+ fq̄

�x,Q

2

�fq

✓M

2

V

sx

,Q

2

◆�. (15)

where fq (x,Q2) is the parton distribution function at the factorization scale Q2. Throughoutthis article, we set Q

2 = M

2. The color discriminant variables for the two particles aretherefore,

D

Ccol

=M

3

C

�C�

Cjj =

8

9

"X

q

Wq(MC)Br(C ! jj)

#(16)

D

Z0

col

=M

3

Z0

�Z0�

Z0

jj =1

9

"X

q

Wq(MZ0)Br(Z 0 ! jj)

#(17)

4

A. Review of the flavor universal scenario

We briefly review how the color discriminant variable helps distinguish between the twotypes of resonances in the scenario that we either have clues from experiments or assumethat the resonance have flavor universal couplings.

The color discriminant variable defined in (??) is independent of the overall strength ofcouplings and can emphasize the di↵erence in color structures between a coloron and a Z

0.To illustrate how it works first recall that in a narrow-width approximation the dijet crosssection for a process involving a vector resonance V can be written as

�

Vjj ⌘ �(pp

V�! jj) ' �(pp ! V )Br(V ! jj), (10)

where �(pp ! V ) is the cross section for producing the resonance and Br(V ! jj) is itsdijet branching fraction. Note that jet consists of quarks from the first two families.

Recall that the total decay width for a coloron and a leptophobic Z

0 are

�C =↵s

2MC

�g

2

CL+ g

2

CR

�, (11)

and�Z0 = 3↵wMZ0

�g

2

Z0L+ g

2

Z0R

�, (12)

respectively. The dijet cross sections for the coloron is

�

Cjj =

4

9↵s

�g

2

CL+ g

2

CR

� 1

M

2

C

X

q

Wq(Mc)Br(C ! jj)

=8

9

�C

M

3

C

X

q

Wq(MC)Br(C ! jj), (13)

while for the leptophobic Z

0,

�

Z0

jj =1

3↵w

�g

2

Z0L+ g

2

Z0R

� 1

M

2

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj)

=1

9

�Z0

M

3

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj), (14)

where Wq, the parton luminosity for the production of the resonance having mass M fromthe qq̄ annihilation at the center-of-mass energy squared s, is defined by

Wq(MV ) = 2⇡2

M

2

V

s

Z1

M2V /s

dx

x

fq

�x,Q

2

�fq̄

✓M

2

V

sx

,Q

2

◆+ fq̄

�x,Q

2

�fq

✓M

2

V

sx

,Q

2

◆�. (15)

where fq (x,Q2) is the parton distribution function at the factorization scale Q2. Throughoutthis article, we set Q

2 = M

2. The color discriminant variables for the two particles aretherefore,

D

Ccol

=M

3

C

�C�

Cjj =

8

9

"X

q

Wq(MC)Br(C ! jj)

#(16)

D

Z0

col

=M

3

Z0

�Z0�

Z0

jj =1

9

"X

q

Wq(MZ0)Br(Z 0 ! jj)

#(17)

4

A. Review of the flavor universal scenario

We briefly review how the color discriminant variable helps distinguish between the twotypes of resonances in the scenario that we either have clues from experiments or assumethat the resonance have flavor universal couplings.

The color discriminant variable defined in (??) is independent of the overall strength ofcouplings and can emphasize the di↵erence in color structures between a coloron and a Z

0.To illustrate how it works first recall that in a narrow-width approximation the dijet crosssection for a process involving a vector resonance V can be written as

�

Vjj ⌘ �(pp

V�! jj) ' �(pp ! V )Br(V ! jj), (10)

where �(pp ! V ) is the cross section for producing the resonance and Br(V ! jj) is itsdijet branching fraction. Note that jet consists of quarks from the first two families.

Recall that the total decay width for a coloron and a leptophobic Z

0 are

�C =↵s

2MC

�g

2

CL+ g

2

CR

�, (11)

and�Z0 = 3↵wMZ0

�g

2

Z0L+ g

2

Z0R

�, (12)

respectively. The dijet cross sections for the coloron is

�

Cjj =

4

9↵s

�g

2

CL+ g

2

CR

� 1

M

2

C

X

q

Wq(Mc)Br(C ! jj)

=8

9

�C

M

3

C

X

q

Wq(MC)Br(C ! jj), (13)

while for the leptophobic Z

0,

�

Z0

jj =1

3↵w

�g

2

Z0L+ g

2

Z0R

� 1

M

2

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj)

=1

9

�Z0

M

3

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj), (14)

where Wq, the parton luminosity for the production of the resonance having mass M fromthe qq̄ annihilation at the center-of-mass energy squared s, is defined by

Wq(MV ) = 2⇡2

M

2

V

s

Z1

M2V /s

dx

x

fq

�x,Q

2

�fq̄

✓M

2

V

sx

,Q

2

◆+ fq̄

�x,Q

2

�fq

✓M

2

V

sx

,Q

2

◆�. (15)

where fq (x,Q2) is the parton distribution function at the factorization scale Q2. Throughoutthis article, we set Q

2 = M

2. The color discriminant variables for the two particles aretherefore,

D

Ccol

=M

3

C

�C�

Cjj =

8

9

"X

q

Wq(MC)Br(C ! jj)

#(16)

D

Z0

col

=M

3

Z0

�Z0�

Z0

jj =1

9

"X

q

Wq(MZ0)Br(Z 0 ! jj)

#(17)

4

A. Review of the flavor universal scenario

We briefly review how the color discriminant variable helps distinguish between the twotypes of resonances in the scenario that we either have clues from experiments or assumethat the resonance have flavor universal couplings.

The color discriminant variable defined in (??) is independent of the overall strength ofcouplings and can emphasize the di↵erence in color structures between a coloron and a Z

0.To illustrate how it works first recall that in a narrow-width approximation the dijet crosssection for a process involving a vector resonance V can be written as

�

Vjj ⌘ �(pp

V�! jj) ' �(pp ! V )Br(V ! jj), (10)

where �(pp ! V ) is the cross section for producing the resonance and Br(V ! jj) is itsdijet branching fraction. Note that jet consists of quarks from the first two families.

Recall that the total decay width for a coloron and a leptophobic Z

0 are

�C =↵s

2MC

�g

2

CL+ g

2

CR

�, (11)

and�Z0 = 3↵wMZ0

�g

2

Z0L+ g

2

Z0R

�, (12)

respectively. The dijet cross sections for the coloron is

�

Cjj =

4

9↵s

�g

2

CL+ g

2

CR

� 1

M

2

C

X

q

Wq(Mc)Br(C ! jj)

=8

9

�C

M

3

C

X

q

Wq(MC)Br(C ! jj), (13)

while for the leptophobic Z

0,

�

Z0

jj =1

3↵w

�g

2

Z0L+ g

2

Z0R

� 1

M

2

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj)

=1

9

�Z0

M

3

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj), (14)

where Wq, the parton luminosity for the production of the resonance having mass M fromthe qq̄ annihilation at the center-of-mass energy squared s, is defined by

Wq(MV ) = 2⇡2

M

2

V

s

Z1

M2V /s

dx

x

fq

�x,Q

2

�fq̄

✓M

2

V

sx

,Q

2

◆+ fq̄

�x,Q

2

�fq

✓M

2

V

sx

,Q

2

◆�. (15)

where fq (x,Q2) is the parton distribution function at the factorization scale Q2. Throughoutthis article, we set Q

2 = M

2. The color discriminant variables for the two particles aretherefore,

D

Ccol

=M

3

C

�C�

Cjj =

8

9

"X

q

Wq(MC)Br(C ! jj)

#(16)

D

Z0

col

=M

3

Z0

�Z0�

Z0

jj =1

9

"X

q

Wq(MZ0)Br(Z 0 ! jj)

#(17)

4

Color Discriminant Variable

must be equal

A. Review of the flavor universal scenario

We briefly review how the color discriminant variable helps distinguish between the twotypes of resonances in the scenario that we either have clues from experiments or assumethat the resonance have flavor universal couplings.

The color discriminant variable defined in (??) is independent of the overall strength ofcouplings and can emphasize the di↵erence in color structures between a coloron and a Z

0.To illustrate how it works first recall that in a narrow-width approximation the dijet crosssection for a process involving a vector resonance V can be written as

�

Vjj ⌘ �(pp

V�! jj) ' �(pp ! V )Br(V ! jj), (10)

where �(pp ! V ) is the cross section for producing the resonance and Br(V ! jj) is itsdijet branching fraction. Note that jet consists of quarks from the first two families.

Recall that the total decay width for a coloron and a leptophobic Z

0 are

�C =↵s

2MC

�g

2

CL+ g

2

CR

�, (11)

and�Z0 = 3↵wMZ0

�g

2

Z0L+ g

2

Z0R

�, (12)

respectively. The dijet cross sections for the coloron is

�

Cjj =

4

9↵s

�g

2

CL+ g

2

CR

� 1

M

2

C

X

q

Wq(Mc)Br(C ! jj)

=8

9

�C

M

3

C

X

q

Wq(MC)Br(C ! jj), (13)

while for the leptophobic Z

0,

�

Z0

jj =1

3↵w

�g

2

Z0L+ g

2

Z0R

� 1

M

2

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj)

=1

9

�Z0

M

3

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj), (14)

where Wq, the parton luminosity for the production of the resonance having mass M fromthe qq̄ annihilation at the center-of-mass energy squared s, is defined by

Wq(MV ) = 2⇡2

M

2

V

s

Z1

M2V /s

dx

x

fq

�x,Q

2

�fq̄

✓M

2

V

sx

,Q

2

◆+ fq̄

�x,Q

2

�fq

✓M

2

V

sx

,Q

2

◆�. (15)

where fq (x,Q2) is the parton distribution function at the factorization scale Q2. Throughoutthis article, we set Q

2 = M

2. The color discriminant variables for the two particles aretherefore,

D

Ccol

=M

3

C

�C�

Cjj =

8

9

"X

q

Wq(MC)Br(C ! jj)

#(16)

D

Z0

col

=M

3

Z0

�Z0�

Z0

jj =1

9

"X

q

Wq(MZ0)Br(Z 0 ! jj)

#(17)

4

A. Review of the flavor universal scenario

We briefly review how the color discriminant variable helps distinguish between the twotypes of resonances in the scenario that we either have clues from experiments or assumethat the resonance have flavor universal couplings.

The color discriminant variable defined in (??) is independent of the overall strength ofcouplings and can emphasize the di↵erence in color structures between a coloron and a Z

0.To illustrate how it works first recall that in a narrow-width approximation the dijet crosssection for a process involving a vector resonance V can be written as

�

Vjj ⌘ �(pp

V�! jj) ' �(pp ! V )Br(V ! jj), (10)

where �(pp ! V ) is the cross section for producing the resonance and Br(V ! jj) is itsdijet branching fraction. Note that jet consists of quarks from the first two families.

Recall that the total decay width for a coloron and a leptophobic Z

0 are

�C =↵s

2MC

�g

2

CL+ g

2

CR

�, (11)

and�Z0 = 3↵wMZ0

�g

2

Z0L+ g

2

Z0R

�, (12)

respectively. The dijet cross sections for the coloron is

�

Cjj =

4

9↵s

�g

2

CL+ g

2

CR

� 1

M

2

C

X

q

Wq(Mc)Br(C ! jj)

=8

9

�C

M

3

C

X

q

Wq(MC)Br(C ! jj), (13)

while for the leptophobic Z

0,

�

Z0

jj =1

3↵w

�g

2

Z0L+ g

2

Z0R

� 1

M

2

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj)

=1

9

�Z0

M

3

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj), (14)

where Wq, the parton luminosity for the production of the resonance having mass M fromthe qq̄ annihilation at the center-of-mass energy squared s, is defined by

Wq(MV ) = 2⇡2

M

2

V

s

Z1

M2V /s

dx

x

fq

�x,Q

2

�fq̄

✓M

2

V

sx

,Q

2

◆+ fq̄

�x,Q

2

�fq

✓M

2

V

sx

,Q

2

◆�. (15)

where fq (x,Q2) is the parton distribution function at the factorization scale Q2. Throughoutthis article, we set Q

2 = M

2. The color discriminant variables for the two particles aretherefore,

D

Ccol

=M

3

C

�C�

Cjj =

8

9

"X

q

Wq(MC)Br(C ! jj)

#(16)

D

Z0

col

=M

3

Z0

�Z0�

Z0

jj =1

9

"X

q

Wq(MZ0)Br(Z 0 ! jj)

#(17)

4

A. Review of the flavor universal scenario

We briefly review how the color discriminant variable helps distinguish between the twotypes of resonances in the scenario that we either have clues from experiments or assumethat the resonance have flavor universal couplings.

The color discriminant variable defined in (??) is independent of the overall strength ofcouplings and can emphasize the di↵erence in color structures between a coloron and a Z

0.To illustrate how it works first recall that in a narrow-width approximation the dijet crosssection for a process involving a vector resonance V can be written as

�

Vjj ⌘ �(pp

V�! jj) ' �(pp ! V )Br(V ! jj), (10)

where �(pp ! V ) is the cross section for producing the resonance and Br(V ! jj) is itsdijet branching fraction. Note that jet consists of quarks from the first two families.

Recall that the total decay width for a coloron and a leptophobic Z

0 are

�C =↵s

2MC

�g

2

CL+ g

2

CR

�, (11)

and�Z0 = 3↵wMZ0

�g

2

Z0L+ g

2

Z0R

�, (12)

respectively. The dijet cross sections for the coloron is

�

Cjj =

4

9↵s

�g

2

CL+ g

2

CR

� 1

M

2

C

X

q

Wq(Mc)Br(C ! jj)

=8

9

�C

M

3

C

X

q

Wq(MC)Br(C ! jj), (13)

while for the leptophobic Z

0,

�

Z0

jj =1

3↵w

�g

2

Z0L+ g

2

Z0R

� 1

M

2

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj)

=1

9

�Z0

M

3

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj), (14)

where Wq, the parton luminosity for the production of the resonance having mass M fromthe qq̄ annihilation at the center-of-mass energy squared s, is defined by

Wq(MV ) = 2⇡2

M

2

V

s

Z1

M2V /s

dx

x

fq

�x,Q

2

�fq̄

✓M

2

V

sx

,Q

2

◆+ fq̄

�x,Q

2

�fq

✓M

2

V

sx

,Q

2

◆�. (15)

where fq (x,Q2) is the parton distribution function at the factorization scale Q2. Throughoutthis article, we set Q

2 = M

2. The color discriminant variables for the two particles aretherefore,

D

Ccol

=M

3

C

�C�

Cjj =

8

9

"X

q

Wq(MC)Br(C ! jj)

#(16)

D

Z0

col

=M

3

Z0

�Z0�

Z0

jj =1

9

"X

q

Wq(MZ0)Br(Z 0 ! jj)

#(17)

4

A. Review of the flavor universal scenario

We briefly review how the color discriminant variable helps distinguish between the twotypes of resonances in the scenario that we either have clues from experiments or assumethat the resonance have flavor universal couplings.

The color discriminant variable defined in (??) is independent of the overall strength ofcouplings and can emphasize the di↵erence in color structures between a coloron and a Z

0.To illustrate how it works first recall that in a narrow-width approximation the dijet crosssection for a process involving a vector resonance V can be written as

�

Vjj ⌘ �(pp

V�! jj) ' �(pp ! V )Br(V ! jj), (10)

where �(pp ! V ) is the cross section for producing the resonance and Br(V ! jj) is itsdijet branching fraction. Note that jet consists of quarks from the first two families.

Recall that the total decay width for a coloron and a leptophobic Z

0 are

�C =↵s

2MC

�g

2

CL+ g

2

CR

�, (11)

and�Z0 = 3↵wMZ0

�g

2

Z0L+ g

2

Z0R

�, (12)

respectively. The dijet cross sections for the coloron is

�

Cjj =

4

9↵s

�g

2

CL+ g

2

CR

� 1

M

2

C

X

q

Wq(Mc)Br(C ! jj)

=8

9

�C

M

3

C

X

q

Wq(MC)Br(C ! jj), (13)

while for the leptophobic Z

0,

�

Z0

jj =1

3↵w

�g

2

Z0L+ g

2

Z0R

� 1

M

2

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj)

=1

9

�Z0

M

3

Z0

X

q

Wq(MZ0)Br(Z 0 ! jj), (14)

where Wq, the parton luminosity for the production of the resonance having mass M fromthe qq̄ annihilation at the center-of-mass energy squared s, is defined by

Wq(MV ) = 2⇡2

M

2

V

s

Z1

M2V /s

dx

x

fq

�x,Q

2

�fq̄

✓M

2

V

sx

,Q

2

◆+ fq̄

�x,Q

2

�fq

✓M

2

V

sx

,Q

2

◆�. (15)

where fq (x,Q2) is the parton distribution function at the factorization scale Q2. Throughoutthis article, we set Q

2 = M

2. The color discriminant variables for the two particles aretherefore,

D

Ccol

=M

3

C

�C�

Cjj =

8

9

"X

q

Wq(MC)Br(C ! jj)

#(16)

D

Z0

col

=M

3

Z0

�Z0�

Z0

jj =1

9

"X

q

Wq(MZ0)Br(Z 0 ! jj)

#(17)

4

Define a color discriminant variable:

• based on standard observables

• useful whenever width is measurable

• distinguishes color structure of resonance

Dcol

⌘ M3

��jj

Establish Detection Range

Un-shadowed colored area shows the observable region at LHC• width is above detector resolution, yet still narrow• cross-section allows detection, yet is not already excluded

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0M [TeV]

0

2

4

6

8

� g2 u+

g2 d

� /g2 Q

CD

1000fb

�1

No reach

300 fb

�1100 f

b�1

30fb

�1

Exc

lude

d

� Mres

� � 0.15MColoron

⇢u =0.5 ⇢t + ⇢b =1.0

3.7⇥10�1 1.6⇥10�1 5.1⇥10�2 1.4⇥10�2Dcol

20%

50%

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0M [TeV]

0

1

2

3

� g2 u+

g2 d

� /g2 w

1000

fb�1

Noreac

h

300fb

�1

100 f

b�1

30fb

�1

Exc

lude

d

� Mres

� � 0.15MLeptophobicZ0

⇢u =0.5 ⇢t + ⇢b =1.0

4.6⇥10�2 1.9⇥10�2 6.4⇥10�3 1.7⇥10�3Dcol

20%

50%

log(Dcol) Separates Coloron from Z’

log(Dcol)

M (TeV)FIG. 2: (a) Top left: Sensitivity at the LHC withp

s = 14 TeV and integrated luminosity of30 fb�1 for distinguishing a coloron from a leptophobic Z 0 in the plane of the log of the colordiscriminant variable

⇣D

col

= M3

�

�jj

⌘and mass (in TeV) for the flavor universal scneario. The

central value of Dcol

for each particle is shown as a black dashed line. The uncertainty in themeasurement of D

col

due to the uncertainties in the measurement of the cross section, mass andwidth of the resonance is indicated by gray bands. The outer (darker gray) band corresponds tothe uncertainty in D

col

when the width is equal to the experimental mass resolution i.e. � = Mres

.The inner (lighter gray) band corresponds to the case where the width � = 0.15M . Resonanceswith width M

res

� 0.15M will have bands that extend between the outer and inner gray bands.The blue (green) colored region indicates the region in parameter space of the coloron (leptophobicZ 0) that has not been excluded by current searches [47] and has the potential to be discovered at a5� level at the LHC with

ps = 14 TeV after statistical and systematic uncertainties are taken in

to account. (b) Top right: Same as (a) but for an integrated luminosity of 100 fb�1. (c) Bottomleft: Same as (a) but for an integrated luminosity of 300 fb�1 (d) Bottom right: Same as (a) butfor an integrated luminosity of 1000 fb�1. Note that the colored regions in all panels correspond tothe same colored regions in the mass and coupling plane used in Fig. 1 for di↵erent luminosities.

15

Color Discriminant Variable: Including Flavor

R.S. Chivukula, P. Ittisamai, EHS arXiv:1406.2003

Generalize Flavor Structure

Most models of new vector resonances allow different couplings to different fermion flavors

(though 1st and 2nd generations experimentally constrained to behave alike).

Can Dcol still yield information about such models?

Flavor Non-universal Couplings

Flavor non-universal coloron has 6 distinct quark couplings:

Flavor non-universal Z’ has 8 distinct quark couplings:

gu,cCL= gd,sCL

and gu,cCR, gd,sCR

gtCL= gbCL

and gtCR, gbCR

gu,cZ0L, gd,sZ0

Land gu,cZ0

R, gd,sZ0

R

gtZ0L, gbZ0

Land gtZ0

R, gbZ0

R

gu 2V = gc 2V , gd 2

V = gs 2V , gt 2V , gb 2V

Our observables , M, Dcol don’t distinguish chirality, reducing the number to 4 for either vector resonance:

�jj

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0M [TeV]

10�5

10�4

10�3

10�2

10�1

100

Wd+WsWu+Wc

WbWu+Wc

Flavor Implications

Measurements sensitive to? • chirality of quark couplings - NO• 1st vs 2nd family quarks - NO• b contribution to production - NO• b, t contribution to width - YES

where they have been written using parametrization to which we will often refer. Theexpressions for leptophobic Z

0 are similar

�(pp ! Z

0) =1

3

↵w

M

2

Z0

�g

u 2

Z0 + g

d 2Z0�"

g

u 2

Z0

g

u 2

Z0 + g

d 2Z0

(Wu +Wc)

+

✓1� g

u 2

Z0

g

u 2

Z0 + g

d 2Z0

◆(Wd +Ws) +

g

b 2Z0

g

u 2

Z0 + g

d 2Z0

Wb

#(22)

�Z0 =↵w

2MZ0

�g

u 2

Z0 + g

d 2Z0�

2 +g

t 2Z0

g

u 2

Z0 + g

d 2Z0

+g

b 2Z0

g

u 2

Z0 + g

d 2Z0

�. (23)

The color discriminant variables are, for the coloron,

D

Ccol

=16

3(Wu +Wc)

"g

u 2

C

g

u 2

C + g

d 2C

+

✓1� g

u 2

C

g

u 2

C + g

d 2C

◆✓Wd +Ws

Wu +Wc

◆

+g

b 2C

g

u 2

C + g

d 2C

✓Wb

Wu +Wc

◆#⇥ 2

⇣2 +

gt 2Cgu 2C +gd 2

C+

gb 2C

gu 2C +gd 2

C

⌘2

(24)

and for the Z

0,

D

Z0

col

=2

3(Wu +Wc)

"g

u 2

Z0

g

u 2

Z0 + g

d 2Z0

+

✓1� g

u 2

Z0

g

u 2

Z0 + g

d 2Z0

◆✓Wd +Ws

Wu +Wc

◆

+g

b 2Z0

g

u 2

Z0 + g

d 2Z0

✓Wb

Wu +Wc

◆#⇥ 2

⇣2 +

gt 2Z0

gu 2Z0 +gd 2

Z0+

gb 2Z0

gu 2Z0 +gd 2

Z0

⌘2

(25)

where parts related relevant to the production are grouped within the brackets in eachexpression. While the relative strength of couplings between u� and d�type quarks ofthe light family, g2u/ (g

2

u + g

2

d), is not well-accessible by experiments available shortly after adiscovery in the dijet channel, those for quarks in the third families are

g

2

t

g

2

u + g

2

d

=�(pp ! tt̄)

�(pp ! jj)(26)

and

g

2

b

g

2

u + g

2

d

=�(pp ! bb̄)

�(pp ! jj). (27)

Supplementary measurements on these ratios of cross sections will help pinpoint the structureof couplings of the resonance.

To illustrate the roles of the relative strength of couplings in the production part, we listthe range of values for the ratios of the parton density functions Wd+Ws

Wu+Wcand Wb

Wu+Wc. We plot

these functions in figure 1 for mass range of 2.5� 6TeV at a pp collider with center-of-massenergy 14TeV, where the values have been calculated using CTEQ6L1 parton distribution

6

Generalize Flavor Structure

Consider color discriminant variable: Dcol

⌘ M3

��jj

DC

col

=16

3(W

u

+Wc

)

"gu 2C

gu 2C

+ gd 2C

+

✓1� gu 2

C

gu 2C

+ gd 2C

◆✓W

d

+Ws

Wu

+Wc

◆

+gb 2C

gu 2C

+ gd 2C

✓W

b

Wu

+Wc

◆#⇥

8><

>:2

⇣2 +

g

t 2C

g

u 2C +g

d 2C

+g

b 2C

g

u 2C +g

d 2C

⌘2

9>=

>;

Depends on “up”, “bottom”, “top” coupling ratios:

g2tg2u + g2d

= 2�Vtt̄

�Vjj

g2bg2u + g2d

= 2�Vbb̄

�Vjj

g2ug2u + g2d

Measurable:

Invisible:

Is the Invisible “up ratio” a problem?

Could the unknown “up ratio” blur the distinction between coloron and Z’ in Dcol?

g2ug2u + g2d

DZ

0

col

/ 2

3

gu 2Z

0

gu 2Z

0 + gd 2Z

0+

✓1� gu 2

Z

0

gu 2Z

0 + gd 2Z

0

◆✓W

d

+Ws

Wu

+Wc

◆�! 2

3

DC

col

/ 16

3

gu 2C

gu 2C

+ gd 2C

+

✓1� gu 2

C

gu 2C

+ gd 2C

◆✓W

d

+Ws

Wu

+Wc

◆�! 16

3

W

d

+Ws

Wu

+Wc

�

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0M [TeV]

10�5

10�4

10�3

10�2

10�1

100

Wd+WsWu+Wc

WbWu+Wc

C : if up ratio = 0

Z’ : if up ratio = 1

Only at large M is confusion possible

Can this = [1/8] ?

14 TeV LHC Reach for Ca and Z’

FlavorUniversal

Preferring3rd

generation

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0M [TeV]

0

2

4

6

8

� g2 u+

g2 d

� /g2 Q

CD

1000fb

�1

No reach

300 fb

�1100 f

b�1

30fb

�1

Exc

lude

d

� Mres

� � 0.15MColoron

⇢u =0.5 ⇢t + ⇢b =1.0

3.7⇥10�1 1.6⇥10�1 5.1⇥10�2 1.4⇥10�2Dcol

20%

50%

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0M [TeV]

0

1

2

3

4

� g2 u+

g2 d

� /g2 Q

CD

1000

fb�1

No

reac

h

300fb

�1

100fb

�1

30fb

�1

Exc

lude

d

� Mres

� � 0.15MColoron

⇢u =0.5 ⇢t + ⇢b =4.0

9.2⇥10�2 3.9⇥10�2 1.3⇥10�2 3.5⇥10�3Dcol

20%

50%

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0M [TeV]

0

1

2

3

� g2 u+

g2 d

� /g2 w

1000

fb�1

Noreac

h

300fb

�1

100 f

b�1

30fb

�1

Exc

lude

d

� Mres

� � 0.15MLeptophobicZ0

⇢u =0.5 ⇢t + ⇢b =1.0

4.6⇥10�2 1.9⇥10�2 6.4⇥10�3 1.7⇥10�3Dcol

20%

50%

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0M [TeV]

0

0.5

1

1.5

� g2 u+

g2 d

� /g2 w

1000

fb�1

No

reac

h

300 f

b�1

100 f

b�1

� Mres

� � 0.15MLeptophobicZ0

⇢u =0.5 ⇢t + ⇢b =4.0

1.1⇥10�2 4.9⇥10�3 1.6⇥10�3 4.3⇥10�4Dcol

20%

50%

Telling Ca and Z’ Apart: M = 3 TeV

For fixed , M, Dcol, at 14 TeV LHC with 1000 fb-1,Z’ distinct from Ca

�jj

�tt̄ /�

jj

02

46

810

� b̄b/�jj

02

46

810

g2 u/

� g2 u+

g2 d

�

0

0.5

1

M = 3.0 TeV�jj = 0.015±0.0051 pb, Dcol = 0.003 ± 0.0015

ColoronZ

0

larger tcoupling larger b

coupling

larger ucoupling

Telling Ca and Z’ Apart: M = 4 TeV

For fixed , M, Dcol, at 14 TeV LHC with 1000 fb-1,Z’ distinct from Ca

�jj

�tt̄ /�

jj

02

46

810 � b̄b

/�jj

02

46

810

g2 u/

� g2 u+

g2 d

�

0

0.5

1

M = 4.0 TeV�jj = 0.0073±0.0026 pb, Dcol = 0.003 ± 0.0015

Coloron

Z0

larger tcoupling larger b

coupling

larger ucoupling

�t̄t /�

jj.0

2

4

6

8

10

.

� b̄b/� jj

02

46

810

g2u/

�g2

u + g2d

�

M = 4.0 TeV�jj = 0.0073±0.0026 pb, Dcol = 0.003 ± 0.0015

Coloron

Z0

�t̄t /�

jj.

0

2

4

6

8

10

.

� b̄b/� jj

02

46

810

g2u/

�g2

u + g2d

�

M = 3.0 TeV�jj = 0.015±0.0051 pb, Dcol = 0.003 ± 0.0015

Coloron

Z0

3 TeV TOP VIEW 4 TeV

Looking down the “u” axis from above, we see no overlap between Z’ and Ca for either value of resonance mass

larger bcoupling

larger tcoupling

larger tcoupling

larger bcoupling

Telling Ca and Z’ Apart

For fixed values of , M, Dcol flavor measurements distinguish Z’ from Ca

even if Ca couples to u less, same, or more than Z’

�jj

0 2 4 6 8 10�tt̄/�jj

0

2

4

6

8

10

C

Z 0

g2u

g2u+g2

d= 1.0(C), 1.0(Z 0)

0 2 4 6 8 10�tt̄/�jj

0

2

4

6

8

10

�bb̄/�

jj

CZ 0

g2u

g2u+g2

d= 0(C), 1.0(Z 0)

0 2 4 6 8 10�tt̄/�jj

0

2

4

6

8

10

C

Z 0

g2u

g2u+g2

d= 0.5(C), 1.0(Z 0)

LHCp

s = 14 TeV, L =1000fb�1, M =4.0 TeV, �jj = 0.0073±0.0026 pb, Dcol = 0.003 ± 0.0015

Required Measurement Precision

For viable, fixed , M, how well must we measure Dcol and heavy flavor decays?

�jj

0 2 4 6 8 10�tt̄/�jj

0

2

4

6

8

10

�bb̄/�

jj

Dcol = 0.003

C

Z 0

Dcol = 0.003Dcol ± 20 %

Dcol ± 50 %

0 2 4 6 8 10�tt̄/�jj

Dcol = 0.007

C

Z 0

Dcol = 0.007Dcol ± 20 %

Dcol ± 50 %

0 2 4 6 8 10�tt̄/�jj

Dcol = 0.01

C

Z 0

Dcol = 0.01Dcol ± 20 %

Dcol ± 50 %

LHCp

s = 14 TeV, L =1000fb�1, M =3.5 TeV, �jj = 0.01±0.0034 pb

Beyond Vector Resonances

R.S. Chivukula, EHS, N. Vignaroli arXiv:1412.3094

Various New Colored States

Gauge bosons from extended color groups:Classic Axigluon: P.H. Frampton and S.L. Glashow, Phys. Lett. B 190, 157 (1987).

Topgluon: C.T. Hill, Phys. Lett. B 266, 419 (1991).

Flavor-universal Coloron: R.S. Chivukula, A.G. Cohen, & E.H. Simmons, Phys. Lett. B 380, 92 (1996).

Chiral Color with gL ≠ gR: M.V. Martynov and A.D. Smirnov, Mod. Phys. Lett. A 24, 1897 (2009).

New Axigluon: P.H. Frampton, J. Shu, and K. Wang, Phys. Lett. B 683, 294 (2010).

Similar color-octet states:KK gluon: H. Davoudiasl, J.L. Hewett, and T.G. Rizzo, Phys. Rev. D63, 075004 (2001) B. Lillie, L. Randall, and L.-T. Wang, JHEP 0709, 074 (2007).

Techni-rho: E. Farhi and L. Susskind, Physics Reports 74, 277 (1981).

More exotic colored states: Color sextets, colored scalars, low-scale scale string resonances...T. Han, I. Lewis, Z. Liu, JHEP 1012, 085 (2010).

Vector, Fermion, Scalar

Colored scalar: Han, Lewis, Liu arXiv:1010.4309

Excited quark: Baur, Spira, Zerwas: PRD 42 (1990) 815

Flavor-universal coloron: Chivukula, Cohen, EHS

Phys. Lett. B 380 (1996) 92

u

h1 h2

SU(3)1 SU(3)2

Coloron Models: Gauge Sector

SU(3)1 x SU(3)2 color sector with

unbroken subgroup: SU(3)1+2 = SU(3)QCD

M2 =u2

4

✓h2

1 �h1h2

�h1h2 h22

◆

h1 =

gs

cos ✓h2 =

gs

sin ✓

CAµ = � sin ✓ AA

1µ + cos ✓ AA2µ

GAµ = cos ✓ AA

1µ + sin ✓ AA2µgluon state:

coloron state:

couples to:

couples to:

gSJµG ⌘ gS(Jµ

1 + Jµ2 )

gSJµC ⌘ gS(�Jµ

1 tan ✓ + Jµ2 cot ✓)

MC =up2

qh2

1 + h22

MG = 0

Quarks’ SU(3)1 x SU(3)2 charges impact phenomenology

Vector, Fermion, Scalar

LHC-14 can both discover flavor-universal colorons (C),

excited quarks (q*), and color-octet scalars (S8) and

also measure Dcol

G êM ≥ 0.15

LHCEXCLUDED

G b MRES

30fb-1

100 fb-

1

300 fb-

11 ab-1

3 ab-1

2 3 4 5 6 7 80.0

0.5

1.0

1.5

2.0

2.5

mq* HTeVL

f S

EXCITED QUARK

G êM ≥ 0.15LHCEXCLUDED

G b MRES

30fb-1

100 fb-

1

300 fb-

1

1 ab-

1

3 ab-

1

2 3 4 5 6 7 80.0

0.2

0.4

0.6

0.8

1.0

1.2

mS8HTeVL

k S

SCALAR OCTET

G êM ≥ 0.15

LHCEXCLUDED

G b MRES30fb-1

100 fb-1

300 fb-1

1 ab-1

3 ab-1

2 3 4 5 6 7 80.0

0.5

1.0

1.5

mCHTeVL

tgq

COLORON

Distinguishing C, q*, S8

LHC 14 TeV , 30 fb-1

q*C

S8

3.5 4.0 4.5 5.0 5.5 6.0M @TeVD

-4

-3

-2

-1

0

1

2

Log HsjjM3êGLDcol

Hwidermass range plotLLHC 14 TeV , 3 ab-1q*C

S8

4 5 6 7 8M @TeVD

-4

-3

-2

-1

0

1

2

Log HsjjM3êGLDcol

Dcol can reveal the nature of a colored

dijet resonance

Conclusions

Conclusions

Dcol on its own• distinguishes coloron from Z’ in flavor-universal models• likewise, can separate scalar, fermion, vector

resonances discovered in dijet decays

Dcol plus heavy flavor cross-sections• reliably separates coloron and Z’ in models with

flavor non-universal resonance couplings to quarks• is not impacted by our inability to measure relative

couplings of up, down quarks to the vector resonance

Dcol

⌘ M3

��jj

When LHC reveals a new BSM resonance decaying to dijets, how will we determine what has been discovered?

Library

Uncertainty in Dcolintrinsic width of the resonance. We include these uncertainties followingthe analysis of Ref. [5]. In particular, the uncertainty on Dcol is given by

✓�D

D

◆2

=

✓��jj

�jj

◆2

+

✓3�M

M

◆2

+

✓��

�

◆2

✓��jj

�jj

◆2

=1

N+ ✏2�SY S

✓�M

M

◆2

=1

N

"✓��

M

◆2

+

✓Mres

M

◆2#+

✓�MJES

M

◆2

✓��

�

◆2

=1

2(N � 1)

"1 +

✓Mres

��

◆2#2

+

✓Mres

��

◆4 ✓�Mres

Mres

◆2

(12)

where N is the number of signal events, ✏�SY S is the systematic uncertaintyon the di-jet cross section, �� is the standard deviation corresponding tothe intrinsic width of the resonance (�� ' �/2.35 assuming a Gaussian dis-tribution), Mres is the experimental di-jet mass resolution, (�Mres/Mres) isthe uncertainty in the resolution of the di-jet mass and (�MJES/M) is theuncertainty in the mass measurement due to uncertainty in the jet energyscale.

Following [5], we estimate systematic uncertainties from actual LHC re-sults, where available, and assume that any future LHC run will be able toreach at least this level of precision. In particular we use:

✏�SY S = 0.41 (14 TeV LHC [48]) Mres/M = 0.035 (8 TeV CMS [2])

�Mres/Mres = 0.1 (8 TeV CMS [3]) (�MJES/M) = 0.013 (8 TeV CMS [3])(13)

Fig. 2 shows the log10 Dcol values, including the statistical and systematicuncertainties, for the three types of di-jet resonances q⇤, C, S8, as a functionof the di-jet resonance mass at the 14 TeV LHC for di↵erent integratedluminosities. We observe that an excited quark resonance can be e�cientlydistinguished from either a coloron or a scalar octet resonance by the colordiscriminant variable at the 14 TeV LHC. Discriminating between coloronsand scalar octets using the color discriminant variable is more challenging,

10

intrinsic width of the resonance. We include these uncertainties followingthe analysis of Ref. [5]. In particular, the uncertainty on Dcol is given by

✓�D

D

◆2

=

✓��jj

�jj

◆2

+

✓3�M

M

◆2

+

✓��

�

◆2

✓��jj

�jj

◆2

=1

N+ ✏2�SY S

✓�M

M

◆2

=1

N

"✓��

M

◆2

+

✓Mres

M

◆2#+

✓�MJES

M

◆2

✓��

�

◆2

=1

2(N � 1)

"1 +

✓Mres

��

◆2#2

+

✓Mres

��

◆4 ✓�Mres

Mres

◆2

(12)

where N is the number of signal events, ✏�SY S is the systematic uncertaintyon the di-jet cross section, �� is the standard deviation corresponding tothe intrinsic width of the resonance (�� ' �/2.35 assuming a Gaussian dis-tribution), Mres is the experimental di-jet mass resolution, (�Mres/Mres) isthe uncertainty in the resolution of the di-jet mass and (�MJES/M) is theuncertainty in the mass measurement due to uncertainty in the jet energyscale.

Following [5], we estimate systematic uncertainties from actual LHC re-sults, where available, and assume that any future LHC run will be able toreach at least this level of precision. In particular we use:

✏�SY S = 0.41 (14 TeV LHC [48]) Mres/M = 0.035 (8 TeV CMS [2])

�Mres/Mres = 0.1 (8 TeV CMS [3]) (�MJES/M) = 0.013 (8 TeV CMS [3])(13)

Fig. 2 shows the log10 Dcol values, including the statistical and systematicuncertainties, for the three types of di-jet resonances q⇤, C, S8, as a functionof the di-jet resonance mass at the 14 TeV LHC for di↵erent integratedluminosities. We observe that an excited quark resonance can be e�cientlydistinguished from either a coloron or a scalar octet resonance by the colordiscriminant variable at the 14 TeV LHC. Discriminating between coloronsand scalar octets using the color discriminant variable is more challenging,

10

Reference numbers are from:R.S. Chivukula, EHS, N. Vignaroli, arXiv:1412.3094