Z’jj attheLHC

PeisiHuangTexasA&MUniversity

Nov8,2016

Z’

• ArethereanynewgaugebosonsbeyondtheonesassociatedwiththeSU(3)×SU(2)×U(1)gaugegroup?• Inmanybeyondstandardmodeltheories,newgaugebosonsarepredicted• simplestway,includeasecondU(1)group.newgaugebosonZ’• Z’mixeswiththeZboson,Z’WWcoupling~sin2φ• Z’alsocoupletofermions,

�(W

+W

� ! Z

0) (1)

LW+W�|pp(s) (2)

�(W

+W

� ! Z

0 ! W

+W

�) =

16⇡

3

m

2Z0

m

2Z0 � 4m

2W

(�(Z

0 ! WW ))

2

((sWW �m

2Z0)

2+ �

2totm

2Z0)

(3)

�(Z

0 ! WW ) =

g

4cos

2✓w

192⇡

m

5Z0

m

4W

(4)

�(Z

0 ! ff) =

5

8

↵m

2Z0

cos

2✓w

(5)

�(W

+W

� ! Z

0) ' �(W

+W

� ! Z

0 ! W

+W

�) (6)

dF (x,k) =(E + E

0+ !)

2

(64⇡

3EE

0!)

h|M |2i(2p · k �m

2W )

2|p|dxkdkd� (7)

M = u(p

0)�"(gV + gA�5)u(p) (8)

dF (x)dx =

1

12⇡

2(g

2V+g

2A){1+

(1� x)

2

x

)Log(p

2+(1�x)m

2W )

1

(1� x)m

2W

+

(1� x)p

2

x(p

2+ (1� x)m

2W )

}dx

(9)

dL

d⌧

|qq/WW =

Z 1

⌧

f(q/W )(x)f(⌧/x)

dx

x

(10)

dL

d⌧

|pp/WW =

Z 1

⌧

d⌧

0

⌧

0

Z 01

⌧

dx

x

fi(x)fj(⌧

0

x

)

dL

d⇠

|qq/WW (11)

� =

Z 1

m2Z0/s

d⌧

dL

d⌧

|pp/WW�WW�>Z0(12)

�pp!WWjj!Z0jj = 5.3pb (13)

�pp!WWjj!Z0jj = 6.8pb (14)

�pp!WWjj!Hjj = 62fb (15)

(

mZ0

mW

)

8(16)

�WW�>H =

↵⇡

2

sin

2✓w

m

2H

m

2W s

(17)

(

mH

mW

)

2(18)

dL

d⌧

|qq/V lV l = (

g

2V + g

2A

4⇡

2)

2 1

⌧

[(1 + ⌧)Log(1/⌧) + 2(⌧ � 1)] (19)

dL

d⌧

|qq/V TV T = (

g

2V + g

2A

8⇡

2)

2 1

⌧

Log(

s

m

2W

)

2[(2 + ⌧)

2Log(1/⌧)� 2(1� ⌧)(3 + ⌧)] (20)

� = 7.8 pb (21)

L =

X

f

zfgZZ0µ¯

f�

µf (22)

1

fermioncharges coupling

currentZ’searches

• qq ->Z’->l+l-

5.2 Limits 9

M [GeV]500 1000 1500 2000 2500 3000 3500

] ZΒ.σ

] Z' /

[Β.σ[

7−10

6−10

5−10

(LOx1.3)ψZ' (LOx1.3)SSMZ'

Obs. 95% CL limit, width = 0.0%Obs. 95% CL limit, width = 0.6%Obs. 95% CL limit, width = 3.0%Exp. 95% CL limit, width = 0.0%Exp. 95% CL limit, width = 0.6%Exp. 95% CL limit, width = 3.0%

CMSCMSdielectron

(13 TeV)-12.7 fb

M [GeV]500 1000 1500 2000 2500 3000 3500

] ZΒ.σ

] Z' /

[Β.σ[

7−10

6−10

5−10

(LOx1.3)ψZ' (LOx1.3)SSMZ'

Obs. 95% CL limit, width = 0.0%Obs. 95% CL limit, width = 0.6%Obs. 95% CL limit, width = 3.0%Exp. 95% CL limit, width = 0.0%Exp. 95% CL limit, width = 0.6%Exp. 95% CL limit, width = 3.0%

CMSCMSdimuon

(13 TeV)-12.9 fb

Figure 3: The 95% CL upper limits on the product of production cross section and branchingfraction for a spin-1 resonance for widths equal to 0, 0.6, and 3.0% of the resonance mass,relative to the product of production cross section and branching fraction for a Z boson, for the(left) dielectron and (right) dimuon channels in the 13 TeV data. Theoretical predictions for thespin-1 Z0

SSM and Z0y resonances are also shown.

The cross section as a function of mass is calculated at LO using the PYTHIA 8.2 program withthe NNPDF2.3 PDFs. As the limits in this Letter are obtained on the on-shell cross section andthe PYTHIA event generator includes off-shell effects, the cross section is calculated in a masswindow of ±5%

ps centred on the resonance mass, following the advice of Ref. [31]. To account

for NLO effects, the cross sections are multiplied by a K-factor of 1.3 for Z0 models and 1.6for RS graviton models [33], with the K-factor for Z0 models obtained by comparing POWHEGand PYTHIA cross sections for SM Drell–Yan production. These same comments apply for thetheoretical predictions shown in Figs. 2–6. For the Z0

SSM and Z0y bosons, we obtain lower mass

limits of 3.37 and 2.82 TeV, respectively. The lower mass limit obtained for the RS graviton is1.46 (3.11) TeV for a coupling parameter of 0.01 (0.10).

M [GeV]500 1000 1500 2000 2500 3000 3500

] ZΒ.σ

] Z' /

[Β.σ[

7−10

6−10

5−10

Observed 95% CL limit

Expected 95% CL limit, median

Expected 95% CL limit, 1 s.d.

Expected 95% CL limit, 2 s.d.

(LOx1.3)ΨZ'

(LOx1.3)SSMZ'

CMS Observed 95% CL limit

Expected 95% CL limit, median

Expected 95% CL limit, 1 s.d.

Expected 95% CL limit, 2 s.d.

(LOx1.3)ΨZ'

(LOx1.3)SSMZ'

CMSµµee +

)µµ (13 TeV, -1 (13 TeV, ee) + 2.9 fb-12.7 fb

M [GeV]500 1000 1500 2000 2500 3000 3500

] ZΒ.σ

] Z' /

[Β.σ[

7−10

6−10

5−10

(LOx1.3)ψZ' (LOx1.3)SSMZ'

Obs. 95% CL limit, width = 0.0%Obs. 95% CL limit, width = 0.6%Obs. 95% CL limit, width = 3.0%Exp. 95% CL limit, width = 0.0%Exp. 95% CL limit, width = 0.6%Exp. 95% CL limit, width = 3.0%

CMSCMSµµee +

)µµ (13 TeV, -1 (13 TeV, ee) + 2.9 fb-12.7 fb

Figure 4: The 95% CL upper limits on the product of production cross section and branchingfraction for a spin-1 resonance, relative to the product of production cross section and branch-ing fraction for a Z boson, for the combined dielectron and dimuon channels in the 13 TeVdata, (left) for a resonance width equal to 0.6% of the resonance mass and (right) for resonancewidths equal to 0, 0.6, and 3.0% of the resonance mass. The shaded bands correspond to the 68and 95% quantiles for the expected limits. Theoretical predictions for the spin-1 Z0

SSM and Z0y

resonances are also shown.

L =

X

f

zfgZZ0µ¯f�µf (22)

E6 ! SO(10)⌦ U(1) (23)

2

L =

X

f

zfgZZ0µ¯f�µf (22)

E6 ! SO(10)⌦ U(1) (23)

! SU(5)⌦ U(1)� ⌦ U(1) (24)

2

sequentialSM:Z’hasSMZcouplings.easytocompare,scale

VBF

• VBFprocesshasdistinctivekinematics-- easytosuppressbackgrounds• energeticjetsintheforwarddirection,becauseofthet-channelkinematics• largerapidityseparationandlargeinvariantmassofthetwojets

• Alsoconsiderleptonic decayoftheZ’

L =!f

zfgZZ′µfγ

µf (22)

E6 → SO(10)⊗ U(1)ψ (23)

→ SU(5)⊗ U(1)χ ⊗ U(1)ψ (24)

q

q

W

W

Z ′

2

Zprime VBFcrosssection,effectiveWapproximation

• AttheLHC,√s>>mW,onecanconsidertheinitialbeamsofquarksas

sourceswhichemitWs.ThenWinteracttoproducenewstates.Or

equivalently,givingWs structurefunction.(Kane,Repko,andRolnick,

1984.Dawson1985)

• WhenusingtheeffectiveWapproximation,

• Firstcalculate

• ThencalculatetheWluminosity

�(W+W� ! Z 0) (1)

LW+W�|pp(s) (2)

1

�(W+W� ! Z 0) (1)

LW+W�|pp(s) (2)

1

�(W+W� ! Z 0) (1)

LW+W�|pp(s) (2)

1

�(W+W� ! Z 0) (1)

LW

+W

�|pp(s) (2)

� =

16⇡

3

m2Z

0

m2Z

0 � 4m2W

(�(Z 0 ! WW ))

2

(sWW

� �

2tot

m2Z

0)(3)

�(Z 0 ! WW ) =

g4 cos2 ✓w

sin

2 �

192⇡

m5Z

0

m4W

(4)

�(Z 0 ! ff) =5

8

↵m2Z

0

cos

2 ✓w

(5)

1

DuttaandNandi,1993

largeenhancementfactorforheavyZ’

AssumeZ’WWcouplingisthesameasZWW

�(W+W� ! Z 0) (1)

LW

+W

�|pp(s) (2)

�(W+W� ! Z 0 ! W+W�) =

16⇡

3

m2Z

0

m2Z

0 � 4m2W

(�(Z 0 ! WW ))

2

(sWW

� �

2tot

m2Z

0)(3)

�(Z 0 ! WW ) =

g4 cos2 ✓w

192⇡

m5Z

0

m4W

(4)

�(Z 0 ! ff) =5

8

↵m2Z

0

cos

2 ✓w

(5)

1

�(W+W� ! Z 0) (1)

LW

+W

�|pp(s) (2)

�(W+W� ! Z 0 ! W+W�) =

16⇡

3

m2Z

0

m2Z

0 � 4m2W

(�(Z 0 ! WW ))

2

((sWW

�m2Z

0)2+ �

2tot

m2Z

0)(3)

�(Z 0 ! WW ) =

g4 cos2 ✓w

192⇡

m5Z

0

m4W

(4)

�(Z 0 ! ff) =5

8

↵m2Z

0

cos

2 ✓w

(5)

1

Small,comparedtoZ’->WW

�(W+W� ! Z 0) (1)

LW

+W

�|pp(s) (2)

�(W+W� ! Z 0 ! W+W�) =

16⇡

3

m2Z

0

m2Z

0 � 4m2W

(�(Z 0 ! WW ))

2

((sWW

�m2Z

0)2+ �

2tot

m2Z

0)(3)

�(Z 0 ! WW ) =

g4 cos2 ✓w

192⇡

m5Z

0

m4W

(4)

�(Z 0 ! ff) =5

8

↵m2Z

0

cos

2 ✓w

(5)

�(W+W� ! Z 0) ' �(W+W� ! Z 0 ! W+W�

) (6)

1

Rizzo,1995

EffectiveWapproximationDistributionofaWinsideaquarkisgivenby

�(W

+W

� ! Z

0) (1)

L

W

+W

�|pp(s) (2)

�(W

+W

� ! Z

0 ! W

+W

�) =

16⇡

3

m

2Z

0

m

2Z

0 � 4m

2W

(�(Z

0 ! WW ))

2

((s

WW

�m

2Z

0)2+ �

2tot

m

2Z

0)(3)

�(Z

0 ! WW ) =

g

4cos

2✓

w

192⇡

m

5Z

0

m

4W

(4)

�(Z

0 ! ff) =

5

8

↵m

2Z

0

cos

2✓

w

(5)

�(W

+W

� ! Z

0) ' �(W

+W

� ! Z

0 ! W

+W

�) (6)

dF (x,k) =(E + E

0+ !)

2

(64⇡

3EE

0!)

h|M |2i(2p · k �m

2W

)

2|p|dxkdkd� (7)

M = u(p

0)�"(gV + g

A

�5)u(p) (8)

dF (x)dx =

1

12⇡

2(g

2V

+g

2A

)((1+

(1� x)

2

x

)Log(p

2+(1�x)m

2W

)

1

(1� x)m

2W

+

(1� x)p

2

x(p

2+ (1� x)m

2W

)

)dx

(9)

1

averageoverinitialquarkspins,andthepolarizationsofWs

�(W

+W

� ! Z

0) (1)

L

W

+W

�|pp(s) (2)

�(W

+W

� ! Z

0 ! W

+W

�) =

16⇡

3

m

2Z

0

m

2Z

0 � 4m

2W

(�(Z

0 ! WW ))

2

((s

WW

�m

2Z

0)2+ �

2tot

m

2Z

0)(3)

�(Z

0 ! WW ) =

g

4cos

2✓

w

192⇡

m

5Z

0

m

4W

(4)

�(Z

0 ! ff) =

5

8

↵m

2Z

0

cos

2✓

w

(5)

�(W

+W

� ! Z

0) ' �(W

+W

� ! Z

0 ! W

+W

�) (6)

dF (x,k) =(E + E

0+ !)

2

(64⇡

3EE

0!)

h|M |2i(2p · k �m

2W

)

2|p|dxkdkd� (7)

M = u(p

0)�"(gV + g

A

�5)u(p) (8)

dF (x)dx =

1

12⇡

2(g

2V

+g

2A

)((1+

(1� x)

2

x

)Log(p

2+(1�x)m

2W

)

1

(1� x)m

2W

+

(1� x)p

2

x(p

2+ (1� x)m

2W

)

)dx

(9)

1

�(W

+W

� ! Z

0) (1)

L

W

+W

�|pp(s) (2)

�(W

+W

� ! Z

0 ! W

+W

�) =

16⇡

3

m

2Z

0

m

2Z

0 � 4m

2W

(�(Z

0 ! WW ))

2

((s

WW

�m

2Z

0)2+ �

2tot

m

2Z

0)(3)

�(Z

0 ! WW ) =

g

4cos

2✓

w

192⇡

m

5Z

0

m

4W

(4)

�(Z

0 ! ff) =

5

8

↵m

2Z

0

cos

2✓

w

(5)

�(W

+W

� ! Z

0) ' �(W

+W

� ! Z

0 ! W

+W

�) (6)

dF (x,k) =(E + E

0+ !)

2

(64⇡

3EE

0!)

h|M |2i(2p · k �m

2W

)

2|p|dxkdkd� (7)

M = u(p

0)�"(gV + g

A

�5)u(p) (8)

dF (x)dx =

1

12⇡

2(g

2V

+g

2A

){1+(1� x)

2

x

)Log(p

2+(1�x)m

2W

)

1

(1� x)m

2W

+

(1� x)p

2

x(p

2+ (1� x)m

2W

)

}dx

(9)

1

Kane,Repko,andRolnick,1984.Dawson1985

transverse Longitudinal

EffectiveWapproximationWWluminosityinatwo-quarksystem

�(W

+W

� ! Z

0) (1)

L

W

+W

�|pp(s) (2)

�(W

+W

� ! Z

0 ! W

+W

�) =

16⇡

3

m

2Z

0

m

2Z

0 � 4m

2W

(�(Z

0 ! WW ))

2

((s

WW

�m

2Z

0)2+ �

2tot

m

2Z

0)(3)

�(Z

0 ! WW ) =

g

4cos

2✓

w

192⇡

m

5Z

0

m

4W

(4)

�(Z

0 ! ff) =

5

8

↵m

2Z

0

cos

2✓

w

(5)

�(W

+W

� ! Z

0) ' �(W

+W

� ! Z

0 ! W

+W

�) (6)

dF (x,k) =(E + E

0+ !)

2

(64⇡

3EE

0!)

h|M |2i(2p · k �m

2W

)

2|p|dxkdkd� (7)

M = u(p

0)�"(gV + g

A

�5)u(p) (8)

dF (x)dx =

1

12⇡

2(g

2V

+g

2A

){1+(1� x)

2

x

)Log(p

2+(1�x)m

2W

)

1

(1� x)m

2W

+

(1� x)p

2

x(p

2+ (1� x)m

2W

)

}dx

(9)

dL

d⌧

|qq/WW

=

Z 1

⌧

f(q/W )(x)f(⌧/x)

dx

x

(10)

dL

d⌧

|pp/WW

=

Z 1

⌧

d⌧

0

⌧

0

Z 01

⌧

dx

x

f

i

(x)f

j

(

⌧

0

x

)

dL

d⇠

|qq/WW (11)

� =

Z 2

m

2Z0/s

d⌧

dL

d⌧

|pp/WW

�

WW�>Z

0(12)

1

WWluminosityinaproton-protonsystem

�(W

+W

� ! Z

0) (1)

L

W

+W

�|pp(s) (2)

�(W

+W

� ! Z

0 ! W

+W

�) =

16⇡

3

m

2Z

0

m

2Z

0 � 4m

2W

(�(Z

0 ! WW ))

2

((s

WW

�m

2Z

0)2+ �

2tot

m

2Z

0)(3)

�(Z

0 ! WW ) =

g

4cos

2✓

w

192⇡

m

5Z

0

m

4W

(4)

�(Z

0 ! ff) =

5

8

↵m

2Z

0

cos

2✓

w

(5)

�(W

+W

� ! Z

0) ' �(W

+W

� ! Z

0 ! W

+W

�) (6)

dF (x,k) =(E + E

0+ !)

2

(64⇡

3EE

0!)

h|M |2i(2p · k �m

2W

)

2|p|dxkdkd� (7)

M = u(p

0)�"(gV + g

A

�5)u(p) (8)

dF (x)dx =

1

12⇡

2(g

2V

+g

2A

){1+(1� x)

2

x

)Log(p

2+(1�x)m

2W

)

1

(1� x)m

2W

+

(1� x)p

2

x(p

2+ (1� x)m

2W

)

}dx

(9)

dL

d⌧

|qq/WW

=

Z 1

⌧

f(q/W )(x)f(⌧/x)

dx

x

(10)

dL

d⌧

|pp/WW

=

Z 1

⌧

d⌧

0

⌧

0

Z 01

⌧

dx

x

f

i

(x)f

j

(

⌧

0

x

)

dL

d⇠

|qq/WW (11)

� =

Z 2

m

2Z0/s

d⌧

dL

d⌧

|pp/WW

�

WW�>Z

0(12)

1

Z’productioncrosssectionthroughVBF

�(W

+W

� ! Z

0) (1)

L

W

+W

�|pp(s) (2)

�(W

+W

� ! Z

0 ! W

+W

�) =

16⇡

3

m

2Z

0

m

2Z

0 � 4m

2W

(�(Z

0 ! WW ))

2

((s

WW

�m

2Z

0)2+ �

2tot

m

2Z

0)(3)

�(Z

0 ! WW ) =

g

4cos

2✓

w

192⇡

m

5Z

0

m

4W

(4)

�(Z

0 ! ff) =

5

8

↵m

2Z

0

cos

2✓

w

(5)

�(W

+W

� ! Z

0) ' �(W

+W

� ! Z

0 ! W

+W

�) (6)

dF (x,k) =(E + E

0+ !)

2

(64⇡

3EE

0!)

h|M |2i(2p · k �m

2W

)

2|p|dxkdkd� (7)

M = u(p

0)�"(gV + g

A

�5)u(p) (8)

dF (x)dx =

1

12⇡

2(g

2V

+g

2A

){1+(1� x)

2

x

)Log(p

2+(1�x)m

2W

)

1

(1� x)m

2W

+

(1� x)p

2

x(p

2+ (1� x)m

2W

)

}dx

(9)

dL

d⌧

|qq/WW

=

Z 1

⌧

f(q/W )(x)f(⌧/x)

dx

x

(10)

dL

d⌧

|pp/WW

=

Z 1

⌧

d⌧

0

⌧

0

Z 01

⌧

dx

x

f

i

(x)f

j

(

⌧

0

x

)

dL

d⇠

|qq/WW (11)

� =

Z 1

m

2Z0/s

d⌧

dL

d⌧

|pp/WW

�

WW�>Z

0(12)

1

VBFZ’crosssection

Fora1TeV Z’,assumingitscouplingtoapairofWisthesameasaZboson

�(W

+W

� ! Z

0) (1)

L

W

+W

�|pp(s) (2)

�(W

+W

� ! Z

0 ! W

+W

�) =

16⇡

3

m

2Z

0

m

2Z

0 � 4m

2W

(�(Z

0 ! WW ))

2

((s

WW

�m

2Z

0)2+ �

2tot

m

2Z

0)(3)

�(Z

0 ! WW ) =

g

4cos

2✓

w

192⇡

m

5Z

0

m

4W

(4)

�(Z

0 ! ff) =

5

8

↵m

2Z

0

cos

2✓

w

(5)

�(W

+W

� ! Z

0) ' �(W

+W

� ! Z

0 ! W

+W

�) (6)

dF (x,k) =(E + E

0+ !)

2

(64⇡

3EE

0!)

h|M |2i(2p · k �m

2W

)

2|p|dxkdkd� (7)

M = u(p

0)�"(gV + g

A

�5)u(p) (8)

dF (x)dx =

1

12⇡

2(g

2V

+g

2A

){1+(1� x)

2

x

)Log(p

2+(1�x)m

2W

)

1

(1� x)m

2W

+

(1� x)p

2

x(p

2+ (1� x)m

2W

)

}dx

(9)

dL

d⌧

|qq/WW

=

Z 1

⌧

f(q/W )(x)f(⌧/x)

dx

x

(10)

dL

d⌧

|pp/WW

=

Z 1

⌧

d⌧

0

⌧

0

Z 01

⌧

dx

x

f

i

(x)f

j

(

⌧

0

x

)

dL

d⇠

|qq/WW (11)

� =

Z 1

m

2Z0/s

d⌧

dL

d⌧

|pp/WW

�

WW�>Z

0(12)

�

pp!WWjj!Z

0jj

= 5.3pb (13)

1

UsingeffectiveWapproximation,

MadGraph,HiddenAbelianHiggsmodel

�(W

+W

� ! Z

0) (1)

L

W

+W

�|pp(s) (2)

�(W

+W

� ! Z

0 ! W

+W

�) =

16⇡

3

m

2Z

0

m

2Z

0 � 4m

2W

(�(Z

0 ! WW ))

2

((s

WW

�m

2Z

0)2+ �

2tot

m

2Z

0)(3)

�(Z

0 ! WW ) =

g

4cos

2✓

w

192⇡

m

5Z

0

m

4W

(4)

�(Z

0 ! ff) =

5

8

↵m

2Z

0

cos

2✓

w

(5)

�(W

+W

� ! Z

0) ' �(W

+W

� ! Z

0 ! W

+W

�) (6)

dF (x,k) =(E + E

0+ !)

2

(64⇡

3EE

0!)

h|M |2i(2p · k �m

2W

)

2|p|dxkdkd� (7)

M = u(p

0)�"(gV + g

A

�5)u(p) (8)

dF (x)dx =

1

12⇡

2(g

2V

+g

2A

){1+(1� x)

2

x

)Log(p

2+(1�x)m

2W

)

1

(1� x)m

2W

+

(1� x)p

2

x(p

2+ (1� x)m

2W

)

}dx

(9)

dL

d⌧

|qq/WW

=

Z 1

⌧

f(q/W )(x)f(⌧/x)

dx

x

(10)

dL

d⌧

|pp/WW

=

Z 1

⌧

d⌧

0

⌧

0

Z 01

⌧

dx

x

f

i

(x)f

j

(

⌧

0

x

)

dL

d⇠

|qq/WW (11)

� =

Z 1

m

2Z0/s

d⌧

dL

d⌧

|pp/WW

�

WW�>Z

0(12)

�

pp!WWjj!Z

0jj

= 5.3pb (13)

�

pp!WWjj!Z

0jj

= 6.8pb (14)

1

VerydifferentfromaheavyHiggs

UsingeffectiveWapproximation,

MadGraph

fullNNLOcalculation,VBFNNLO

Bothhaveweakcoupling,whyZ’crosssectionsomuchlarger?

�(W

+W

� ! Z

0) (1)

LW+W�|pp(s) (2)

�(W

+W

� ! Z

0 ! W

+W

�) =

16⇡

3

m

2Z0

m

2Z0 � 4m

2W

(�(Z

0 ! WW ))

2

((sWW �m

2Z0)

2+ �

2totm

2Z0)

(3)

�(Z

0 ! WW ) =

g

4cos

2✓w

192⇡

m

5Z0

m

4W

(4)

�(Z

0 ! ff) =

5

8

↵m

2Z0

cos

2✓w

(5)

�(W

+W

� ! Z

0) ' �(W

+W

� ! Z

0 ! W

+W

�) (6)

dF (x,k) =(E + E

0+ !)

2

(64⇡

3EE

0!)

h|M |2i(2p · k �m

2W )

2|p|dxkdkd� (7)

M = u(p

0)�"(gV + gA�5)u(p) (8)

dF (x)dx =

1

12⇡

2(g

2V+g

2A){1+

(1� x)

2

x

)Log(p

2+(1�x)m

2W )

1

(1� x)m

2W

+

(1� x)p

2

x(p

2+ (1� x)m

2W )

}dx

(9)

dL

d⌧

|qq/WW =

Z 1

⌧

f(q/W )(x)f(⌧/x)

dx

x

(10)

dL

d⌧

|pp/WW =

Z 1

⌧

d⌧

0

⌧

0

Z 01

⌧

dx

x

fi(x)fj(⌧

0

x

)

dL

d⇠

|qq/WW (11)

� =

Z 1

m2Z0/s

d⌧

dL

d⌧

|pp/WW�WW�>Z0(12)

�pp!WWjj!Z0jj = 5.3pb (13)

�pp!WWjj!Z0jj = 6.8pb (14)

�pp!WWjj!Hjj = 50fb (15)

1

�(W

+W

� ! Z

0) (1)

LW+W�|pp(s) (2)

�(W

+W

� ! Z

0 ! W

+W

�) =

16⇡

3

m

2Z0

m

2Z0 � 4m

2W

(�(Z

0 ! WW ))

2

((sWW �m

2Z0)

2+ �

2totm

2Z0)

(3)

�(Z

0 ! WW ) =

g

4cos

2✓w

192⇡

m

5Z0

m

4W

(4)

�(Z

0 ! ff) =

5

8

↵m

2Z0

cos

2✓w

(5)

�(W

+W

� ! Z

0) ' �(W

+W

� ! Z

0 ! W

+W

�) (6)

dF (x,k) =(E + E

0+ !)

2

(64⇡

3EE

0!)

h|M |2i(2p · k �m

2W )

2|p|dxkdkd� (7)

M = u(p

0)�"(gV + gA�5)u(p) (8)

dF (x)dx =

1

12⇡

2(g

2V+g

2A){1+

(1� x)

2

x

)Log(p

2+(1�x)m

2W )

1

(1� x)m

2W

+

(1� x)p

2

x(p

2+ (1� x)m

2W )

}dx

(9)

dL

d⌧

|qq/WW =

Z 1

⌧

f(q/W )(x)f(⌧/x)

dx

x

(10)

dL

d⌧

|pp/WW =

Z 1

⌧

d⌧

0

⌧

0

Z 01

⌧

dx

x

fi(x)fj(⌧

0

x

)

dL

d⇠

|qq/WW (11)

� =

Z 1

m2Z0/s

d⌧

dL

d⌧

|pp/WW�WW�>Z0(12)

�pp!WWjj!Z0jj = 5.3pb (13)

�pp!WWjj!Z0jj = 6.8pb (14)

�pp!WWjj!Hjj = 62fb (15)

1

CorrectionsofeffectiveWapproximationareO(mW2/mZ’

2),andO(mZ’2/s)

�(W+W� ! Z 0) (1)

LW+W�|pp(s) (2)

�(W+W� ! Z 0 ! W+W�) =

16⇡

3

m2Z0

m2Z0 � 4m2

W

(�(Z 0 ! WW ))

2

((sWW �m2Z0)

2+ �

2totm

2Z0)

(3)

�(Z 0 ! WW ) =

g4 cos2 ✓w192⇡

m5Z0

m4W

(4)

�(Z 0 ! ff) =5

8

↵m2Z0

cos

2 ✓w(5)

�(W+W� ! Z 0) ' �(W+W� ! Z 0 ! W+W�

) (6)

dF (x,k) =(E + E 0

+ !)2

(64⇡3EE 0!)

h|M |2i(2p · k �m2

W )

2|p|dxkdkd� (7)

M = u(p0)�"(gV + gA�5)u(p) (8)

dF (x)dx =

1

12⇡2(g2V+g2A){1+

(1� x)2

x)Log(p2+(1�x)m2

W )

1

(1� x)m2W

+

(1� x)p2

x(p2 + (1� x)m2W )

}dx

(9)

dL

d⌧|qq/WW =

Z 1

⌧

f(q/W )(x)f(⌧/x)dx

x(10)

dL

d⌧|pp/WW =

Z 1

⌧

d⌧ 0

⌧ 0

Z 01

⌧

dx

xfi(x)fj(

⌧ 0

x)

dL

d⇠|qq/WW (11)

� =

Z 1

m2Z0/s

d⌧dL

d⌧|pp/WW�WW�>Z0

(12)

�pp!WWjj!Z0jj = 5.3pb (13)

�pp!WWjj!Z0jj = 6.8pb (14)

�pp!WWjj!Hjj = 87fb (15)

(

mZ0

mW

)

8(16)

�WW�>H =

↵⇡2

sin

2 ✓w

m2H

m2W s

(17)

(

mH

mW

)

2(18)

dL

d⌧|qq/V lV l = (

g2V + g2A4⇡2

)

2 1

⌧[(1 + ⌧)Log(1/⌧) + 2(⌧ � 1)] (19)

dL

d⌧|qq/V TV T = (

g2V + g2A8⇡2

)

2 1

⌧Log(

s

m2W

)

2[(2 + ⌧)2Log(1/⌧)� 2(1� ⌧)(3 + ⌧)] (20)

� = 7.8 pb (21)

1

VBFZ’vsHiggsFortheHiggs,onlylongitudinalmodecontributse

�(W

+W

� ! Z

0) (1)

LW+W�|pp(s) (2)

�(W

+W

� ! Z

0 ! W

+W

�) =

16⇡

3

m

2Z0

m

2Z0 � 4m

2W

(�(Z

0 ! WW ))

2

((sWW �m

2Z0)

2+ �

2totm

2Z0)

(3)

�(Z

0 ! WW ) =

g

4cos

2✓w

192⇡

m

5Z0

m

4W

(4)

�(Z

0 ! ff) =

5

8

↵m

2Z0

cos

2✓w

(5)

�(W

+W

� ! Z

0) ' �(W

+W

� ! Z

0 ! W

+W

�) (6)

dF (x,k) =(E + E

0+ !)

2

(64⇡

3EE

0!)

h|M |2i(2p · k �m

2W )

2|p|dxkdkd� (7)

M = u(p

0)�"(gV + gA�5)u(p) (8)

dF (x)dx =

1

12⇡

2(g

2V+g

2A){1+

(1� x)

2

x

)Log(p

2+(1�x)m

2W )

1

(1� x)m

2W

+

(1� x)p

2

x(p

2+ (1� x)m

2W )

}dx

(9)

dL

d⌧

|qq/WW =

Z 1

⌧

f(q/W )(x)f(⌧/x)

dx

x

(10)

dL

d⌧

|pp/WW =

Z 1

⌧

d⌧

0

⌧

0

Z 01

⌧

dx

x

fi(x)fj(⌧

0

x

)

dL

d⇠

|qq/WW (11)

� =

Z 1

m2Z0/s

d⌧

dL

d⌧

|pp/WW�WW�>Z0(12)

�pp!WWjj!Z0jj = 5.3pb (13)

�pp!WWjj!Z0jj = 6.8pb (14)

�pp!WWjj!Hjj = 62fb (15)

(

mZ0

mW

)

8(16)

�WW�>H =

↵⇡

2

sin

2✓w

m

2H

m

2W s

(17)

(

mH

mW

)

2(18)

dL

d⌧

|qq/V lV l = (

g

2V + g

2A

4⇡

2)

2 1

⌧

[(1 + ⌧)Log(1/⌧) + 2(⌧ � 1)] (19)

dL

d⌧

|qq/V TV T = (

g

2V + g

2A

8⇡

2)

2 1

⌧

Log(

s

m

2W

)

2[(2 + ⌧)

2Log(1/⌧)� 2(1� ⌧)(3 + ⌧)] (20)

1

ForaZ’,transversemode,longitudinalmode,andtransverse-longitudinalmodecontribute.Thetransversemodedominates.

�(W

+W

� ! Z

0) (1)

LW+W�|pp(s) (2)

�(W

+W

� ! Z

0 ! W

+W

�) =

16⇡

3

m

2Z0

m

2Z0 � 4m

2W

(�(Z

0 ! WW ))

2

((sWW �m

2Z0)

2+ �

2totm

2Z0)

(3)

�(Z

0 ! WW ) =

g

4cos

2✓w

192⇡

m

5Z0

m

4W

(4)

�(Z

0 ! ff) =

5

8

↵m

2Z0

cos

2✓w

(5)

�(W

+W

� ! Z

0) ' �(W

+W

� ! Z

0 ! W

+W

�) (6)

dF (x,k) =(E + E

0+ !)

2

(64⇡

3EE

0!)

h|M |2i(2p · k �m

2W )

2|p|dxkdkd� (7)

M = u(p

0)�"(gV + gA�5)u(p) (8)

dF (x)dx =

1

12⇡

2(g

2V+g

2A){1+

(1� x)

2

x

)Log(p

2+(1�x)m

2W )

1

(1� x)m

2W

+

(1� x)p

2

x(p

2+ (1� x)m

2W )

}dx

(9)

dL

d⌧

|qq/WW =

Z 1

⌧

f(q/W )(x)f(⌧/x)

dx

x

(10)

dL

d⌧

|pp/WW =

Z 1

⌧

d⌧

0

⌧

0

Z 01

⌧

dx

x

fi(x)fj(⌧

0

x

)

dL

d⇠

|qq/WW (11)

� =

Z 1

m2Z0/s

d⌧

dL

d⌧

|pp/WW�WW�>Z0(12)

�pp!WWjj!Z0jj = 5.3pb (13)

�pp!WWjj!Z0jj = 6.8pb (14)

�pp!WWjj!Hjj = 62fb (15)

(

mZ0

mW

)

8(16)

�WW�>H =

↵⇡

2

sin

2✓w

m

2H

m

2W s

(17)

(

mH

mW

)

2(18)

dL

d⌧

|qq/V lV l = (

g

2V + g

2A

4⇡

2)

2 1

⌧

[(1 + ⌧)Log(1/⌧) + 2(⌧ � 1)] (19)

dL

d⌧

|qq/V TV T = (

g

2V + g

2A

8⇡

2)

2 1

⌧

Log(

s

m

2W

)

2[(2 + ⌧)

2Log(1/⌧)� 2(1� ⌧)(3 + ⌧)] (20)

1

LargeenhancementfactorwhentheZ’isheavy

Anotherproductionmodeforthesamesignature

• Anotherproductionmodealsogivesthesamesignature,whenZ’isboosted.• alsohaslargecrosssection

�(W

+W

� ! Z

0) (1)

LW+W�|pp(s) (2)

�(W

+W

� ! Z

0 ! W

+W

�) =

16⇡

3

m

2Z0

m

2Z0 � 4m

2W

(�(Z

0 ! WW ))

2

((sWW �m

2Z0)

2+ �

2totm

2Z0)

(3)

�(Z

0 ! WW ) =

g

4cos

2✓w

192⇡

m

5Z0

m

4W

(4)

�(Z

0 ! ff) =

5

8

↵m

2Z0

cos

2✓w

(5)

�(W

+W

� ! Z

0) ' �(W

+W

� ! Z

0 ! W

+W

�) (6)

dF (x,k) =(E + E

0+ !)

2

(64⇡

3EE

0!)

h|M |2i(2p · k �m

2W )

2|p|dxkdkd� (7)

M = u(p

0)�"(gV + gA�5)u(p) (8)

dF (x)dx =

1

12⇡

2(g

2V+g

2A){1+

(1� x)

2

x

)Log(p

2+(1�x)m

2W )

1

(1� x)m

2W

+

(1� x)p

2

x(p

2+ (1� x)m

2W )

}dx

(9)

dL

d⌧

|qq/WW =

Z 1

⌧

f(q/W )(x)f(⌧/x)

dx

x

(10)

dL

d⌧

|pp/WW =

Z 1

⌧

d⌧

0

⌧

0

Z 01

⌧

dx

x

fi(x)fj(⌧

0

x

)

dL

d⇠

|qq/WW (11)

� =

Z 1

m2Z0/s

d⌧

dL

d⌧

|pp/WW�WW�>Z0(12)

�pp!WWjj!Z0jj = 5.3pb (13)

�pp!WWjj!Z0jj = 6.8pb (14)

�pp!WWjj!Hjj = 62fb (15)

(

mZ0

mW

)

8(16)

�WW�>H =

↵⇡

2

sin

2✓w

m

2H

m

2W s

(17)

(

mH

mW

)

2(18)

dL

d⌧

|qq/V lV l = (

g

2V + g

2A

4⇡

2)

2 1

⌧

[(1 + ⌧)Log(1/⌧) + 2(⌧ � 1)] (19)

dL

d⌧

|qq/V TV T = (

g

2V + g

2A

8⇡

2)

2 1

⌧

Log(

s

m

2W

)

2[(2 + ⌧)

2Log(1/⌧)� 2(1� ⌧)(3 + ⌧)] (20)

� = 7.8 pb (21)

1

L =!f

zfgZZ′µfγ

µf (22)

E6 → SO(10)⊗ U(1)ψ (23)

→ SU(5)⊗ U(1)χ ⊗ U(1)ψ (24)

q

q

W

W

Z ′

g

g

q

q

Z ′

q

q

2

Canweseparatethetwomodes?

• VBFissensitivetotheZ’WWcoupling,andtherefore,sensitivetothemixingbetweenZandZ’.• Z’qq productionisonlysensitivetotheZ’ffcoupling,andnotsensitivetothemixing.• TheZZ’mixingandZ’ff couplingsaremodeldependent.• Separatethetwomodes,canbesensitivetodifferentmodelparameters.

L =!f

zfgZZ′µfγ

µf (22)

E6 → SO(10)⊗ U(1)ψ (23)

→ SU(5)⊗ U(1)χ ⊗ U(1)ψ (24)

q

q

W

W

Z ′

g

g

q

q

Z ′

q

q

2

L =!f

zfgZZ′µfγ

µf (22)

E6 → SO(10)⊗ U(1)ψ (23)

→ SU(5)⊗ U(1)χ ⊗ U(1)ψ (24)

q

q

W

W

Z ′

2

Canweseparatethetwomodes?

• ForVBF,veryfewhadronicactivityinthecentralregion,becauseofthecolorlessW-exchange.• ForQCDZ’jj,therecouldbehadronicactivityinthecentralregion.• ForVBF,theZ’decayproductsbetweenthetwojets.

L =!f

zfgZZ′µfγ

µf (22)

E6 → SO(10)⊗ U(1)ψ (23)

→ SU(5)⊗ U(1)χ ⊗ U(1)ψ (24)

q

q

W

W

Z ′

g

g

q

q

Z ′

q

q

2

L =!f

zfgZZ′µfγ

µf (22)

E6 → SO(10)⊗ U(1)ψ (23)

→ SU(5)⊗ U(1)χ ⊗ U(1)ψ (24)

q

q

W

W

Z ′

2

Conclusion

• AnewgaugebosonispredictedinmanybeyondStandardModeltheories.• CurrentsearchesarefocusedonDrell-Yanmode.• VBFproductioncanhavealargeproductioncrosssection(modeldependent.)• QCDZ’jj productionalsohasalargecrosssection,andcangivesimilarsignaturesasVBFproduction.• SeparatetwoproductionmodeshelpstoresolvedifferentmodelparametersattheLHC.

VBFZ’vsHiggsPartonic crosssection

�(W+W� ! Z 0) (1)

LW

+W

�|pp(s) (2)

�(W+W� ! Z 0 ! W+W�) =

16⇡

3

m2Z

0

m2Z

0 � 4m2W

(�(Z 0 ! WW ))

2

((sWW

�m2Z

0)2+ �

2tot

m2Z

0)(3)

�(Z 0 ! WW ) =

g4 cos2 ✓w

192⇡

m5Z

0

m4W

(4)

�(Z 0 ! ff) =5

8

↵m2Z

0

cos

2 ✓w

(5)

1

�(W+W� ! Z 0) (1)

LW

+W

�|pp(s) (2)

�(W+W� ! Z 0 ! W+W�) =

16⇡

3

m2Z

0

m2Z

0 � 4m2W

(�(Z 0 ! WW ))

2

(sWW

� �

2tot

m2Z

0)(3)

�(Z 0 ! WW ) =

g4 cos2 ✓w

192⇡

m5Z

0

m4W

(4)

�(Z 0 ! ff) =5

8

↵m2Z

0

cos

2 ✓w

(5)

1

�(W

+W

� ! Z

0) (1)

LW+W�|pp(s) (2)

�(W

+W

� ! Z

0 ! W

+W

�) =

16⇡

3

m

2Z0

m

2Z0 � 4m

2W

(�(Z

0 ! WW ))

2

((sWW �m

2Z0)

2+ �

2totm

2Z0)

(3)

�(Z

0 ! WW ) =

g

4cos

2✓w

192⇡

m

5Z0

m

4W

(4)

�(Z

0 ! ff) =

5

8

↵m

2Z0

cos

2✓w

(5)

�(W

+W

� ! Z

0) ' �(W

+W

� ! Z

0 ! W

+W

�) (6)

dF (x,k) =(E + E

0+ !)

2

(64⇡

3EE

0!)

h|M |2i(2p · k �m

2W )

2|p|dxkdkd� (7)

M = u(p

0)�"(gV + gA�5)u(p) (8)

dF (x)dx =

1

12⇡

2(g

2V+g

2A){1+

(1� x)

2

x

)Log(p

2+(1�x)m

2W )

1

(1� x)m

2W

+

(1� x)p

2

x(p

2+ (1� x)m

2W )

}dx

(9)

dL

d⌧

|qq/WW =

Z 1

⌧

f(q/W )(x)f(⌧/x)

dx

x

(10)

dL

d⌧

|pp/WW =

Z 1

⌧

d⌧

0

⌧

0

Z 01

⌧

dx

x

fi(x)fj(⌧

0

x

)

dL

d⇠

|qq/WW (11)

� =

Z 1

m2Z0/s

d⌧

dL

d⌧

|pp/WW�WW�>Z0(12)

�pp!WWjj!Z0jj = 5.3pb (13)

�pp!WWjj!Z0jj = 6.8pb (14)

�pp!WWjj!Hjj = 62fb (15)

(

mZ0

mW

)

8(16)

�WW�>H =

↵⇡

2

sin

2✓w

m

2H

m

2W s

(17)

1