16
Z’ VBF at the LHC Peisi Huang Texas A&M University Nov 23, 2016 1
Z’VBFattheLHC
PeisiHuangTexasA&MUniversity
Nov23,2016
1
Z’
• ArethereanynewgaugebosonsbeyondtheonesassociatedwiththeSU(3)×SU(2)×U(1)gaugegroup?• Inmanybeyondstandardmodeltheories,newgaugebosonsarepredicted• simplestway,includeasecondU(1)group.newgaugebosonZ’• Z’mixeswiththeZboson,Z’WWcoupling~sinφ• Z’alsocouplestofermions,
�(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 2
currentLHCZ’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.easytocomparenotgaugeinvariant
OnlysensitivetoZ’ff couplings3
VBF• VBFissensitivetoZ’WWcoupling.• VBFprocesshasdistinctivekinematics-- easytosuppressbackgrounds• energeticjetsintheforwarddirection,becauseofthet-channelkinematics• largerapidityseparationandlargeinvariantmassofthetwojets
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
4
VBFZ’crosssection
Fora1TeV Z’,assumingitscouplingtoapairofWisthesameasaZboson,
MadGraph
�(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
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 = 62fb (15)
1
�(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
5
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
6
�(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
�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
�(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 ) =
g2 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
7
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 8
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
9
VBFZ’vsHiggsFortheHiggs,onlylongitudinalmodecontributes
�(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
10
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,
Fora1TeV heavyHiggs
UsingeffectiveWapproximation,
�(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
CorrectionsofeffectiveWapproximationareO(mW2/mZ’
2),andO(mZ’2/s)
InmodelswhereZ’WWisgeneratedthroughZ-Z’mixing,thecrosssectionscalesas~gWWZ’
2 ~sin2 θZ-Z
11
ConstraintsonZ-Z’mixing
• AZ’mixeswithSMZdistortstheZproperties.• StrongconstraintsfromLEP,frome+e- ->ffmeasurements.• Incanonicalmodels,VBFZ’crosssectionissmall,notthemostsensitivechannel.• Incaseofdiscovery(fromDrell-Yanprocess),VBFisimportanttoestablishmodels,andcouplings.
4 Paul Langacker
-0.004 -0.002 0 0.002 0.0040
1
2
3
4
5
6
x
0.6 0.2
CDFD0LEP 2
MZ’ [TeV]
Zχ
sin θzz’
0.4 00.81
-0.004 -0.002 0 0.002 0.0040
1
2
3
4
5
6
x
CDF
MZ’ [TeV]
Z ψ
sin θzz’
00.50.751 0.25
D0LEP 2
Figure 2. Experimental constraints on the mass and mixing angle for the Z� and Z , from [17]. Thesolid lines show the regions allowed by precision electroweak data at 95% C.L. assuming Higgs doubletsand singlets, while the dashed regions allow arbitrary Higgs. The labeled curves assume specific ratios ofHiggs doublet VEVs.
and a variety of laboratory and collider experi-ments [61,62,63,64,65,66,67,68,69,70,71,72,73].
4. The LHC
4.1. discoveryThe LHC should ultimately have a discov-
ery reach for Z 0s with electroweak-strength cou-plings to u, d, e, and µ up to MZ0 ⇠ 4 � 5TeV [29,30,32,37]. This is based on decays into`+`� where ` = e or µ, and assumes
ps = 14
TeV and LI =RLdt = 100 fb�1. The reach for
a number of models is shown for various energiesand integrated luminosities in Figure 3. A recentdetailed study emphasized the Z 0 discovery po-tential in early LHC running at lower energy andluminosity for couplings to B � L and Y [74].
The cross section for pp ! ff (or pp ! ff)for a specific final fermion f is just
�fZ0 ⌘ �Z0Bf = Nf/LI , (18)
where Bf = �f/�Z0 is the branching ratio intoff , �Z0 =
R d�Z0dy dy, and Nf is the number of
produced ff pairs for integrated luminosity LI .For given couplings to the SM particles, �f
Z0 andtherefore the discovery reach depend on the to-tal width �Z0 . For example, in the E
6
mod-els �Z0/MZ0 can vary from ⇠ 0.01 � 0.05 de-pending on whether the important open channelsinclude light (compared to MZ0) superpartnersand exotics in addition to the SM fermions [32].The consequences for the discovery reaches at theTevatron and LHC are illustrated in Figure 4,where it is seen, e.g., that the LHC reach can
ArbitraryHiggs
SpecificratiosofHiggsvevsLangacker,200912
fermiophobic Z’
• Allconstraints(directsearches,electroweakprecisions)arestronglyweakenedforfermiophobic models,wherethereisnodirectcouplingofZ’toSMfermions.(TheconstraintsarealsoweakforleptophobicZ’,orZ’doesnotcoupletofirstgenerationleptons)• Oneexample,considerahiddenU(1),whichcanonlycoupletoSMthroughamixedanomaly.ThegaugeanomalyiscancelledbyGreen-Schwarzmechanism. Kumar,Rajaraman andWells,2007.
• Infermiophobic models,Z’canonlybeproducedthroughVBF.• possibledecaymodes,Z’->WW,ZZ,Z𝛾
13
fermiophobic Z’
0.01
0.1
1
10
100
1000
10000
500 600 700 800 900 1000
MX (GeV)
(pp
X) (
fb)
1000 GeV
500 GeV
250 GeV
150 GeV
100 GeV
Figure 2: Plot of σ(pp → X) at√
spp = 14 TeV LHC as a function of MX for variousΛX . The dashed line corresponds to the cross-section required for detection at LHC in theX → ZZ → 4l decay channel using the standard leptonic and jet cuts associated with thisgold-plated vector boson fusion channel, discussed in text.
In our analysis we integrate over the phase space of pp → X → ZZ → 4l events to
determine the total kinematic and geometric acceptance rate of these cuts. This is defined
to be the fraction of pp → X → ZZ → 4l events that satisfy the imposed jet and leptonic
kinematic and geometric cuts. The results are plotted in fig. 1, which shows that about
5% − 10% of the signal events passes these cuts in the interesting range of X boson mass.
For the background, after imposing these cuts, one finds that in the mass range of interest
(MX ∼ 500 − 1000 GeV), less than one background event survives in each 50 GeV bin with
100 fb−1 of integrated luminosity [13]. Detection of this process can therefore be achieved
with 10 signal events in a 50 GeV bin centered on MZZ .
In fig. 2 we plot the total cross section σ(pp → X) at the LHC as a function of the X
boson mass, MX . The various solid lines in the plot correspond to different choices of ΛX .
The dashed line in fig. 2 shows the required pp → X production cross-section in order to
find a 10 event signal in a 50 GeV bin centered on MZZ in 100 fb−1 in the 4l channel. For
MX in the range 500 − 1000 GeV, discovery can be made if ΛX ∼ 100 − 150 GeV.
For any viable model, the fermion which run in the loop must be massive (to avoid the
appearance of SM chiral exotics). This implies that U(1)X gauge symmetry must be broken
[8]. The symmetry breaking effects may provide additional signals for the U(1)X gauge
11
• Z’->ZZ->4l
• crosssectioncanbesizable
• worthstudyingotherchannels
Kumar,Rajaraman andWells,2007. 14
Z’->WW
15Preliminary,A.Gurrola
Thisyeardata,exclude~1.4- 1.6TeVLongterm,excludeupto3TeV
Conclusion
• AnewgaugebosonispredictedinmanybeyondStandardModeltheories.• CurrentLHCsearchesarefocusedonDrell-Yanmode.• Forcanonicalmodels(E6,B-L),VBFprocessisimportantforestablishingmodels.• Forfermiophobic models(andbaryophobic models),Z’canonlybeproducedthroughVBF,anddecaytotwobosons(notapairofphotons).• withthisyearsdataatCMS(~40-1fb),emu canexcludeup to~1.6TeV.Similarly,mumu canexcludeupto~1.4TeV.with thisyear'sdata.• Longterm-->exclusionscanbecloserto3TeV.
16
