Heavy vector-like quarks
Constraints and phenomenology at the LHC
Luca Panizzi
University of Southampton, UK
Outline
1
Motivations and Current Status
2
The effective lagrangian
3
Constraints on model parameters
4
Signatures at LHC
Outline
1
Motivations and Current Status
2
The effective lagrangian
3
Constraints on model parameters
4
Signatures at LHC
What are vector-like fermions?
and where do they appear?
The left-handed and right-handed chiralities of a vector-like fermion ψ
transform in the same way under the SM gauge groups SU (3)c × SU (2)L × U (1)Y
What are vector-like fermions?
and where do they appear?
The left-handed and right-handed chiralities of a vector-like fermion ψ
transform in the same way under the SM gauge groups SU (3)c × SU (2)L × U (1)Y
Why are they called “vector-like”?
What are vector-like fermions?
and where do they appear?
The left-handed and right-handed chiralities of a vector-like fermion ψ
transform in the same way under the SM gauge groups SU (3)c × SU (2)L × U (1)Y
Why are they called “vector-like”?
g LW = √ J µ+ Wµ+ + J µ− Wµ−
2
Charged current Lagrangian
What are vector-like fermions?
and where do they appear?
The left-handed and right-handed chiralities of a vector-like fermion ψ
transform in the same way under the SM gauge groups SU (3)c × SU (2)L × U (1)Y
Why are they called “vector-like”?
g LW = √ J µ+ Wµ+ + J µ− Wµ−
2
Charged current Lagrangian
SM chiral quarks: ONLY left-handed charged currents
(
µ+
JL = ūL γ µ dL = ūγ µ (1 − γ5 )d = V − A
µ+
µ+
J µ+ = JL + JR
with
µ+
JR = 0
What are vector-like fermions?
and where do they appear?
The left-handed and right-handed chiralities of a vector-like fermion ψ
transform in the same way under the SM gauge groups SU (3)c × SU (2)L × U (1)Y
Why are they called “vector-like”?
g LW = √ J µ+ Wµ+ + J µ− Wµ−
2
Charged current Lagrangian
SM chiral quarks: ONLY left-handed charged currents
(
µ+
JL = ūL γ µ dL = ūγ µ (1 − γ5 )d = V − A
µ+
µ+
J µ+ = JL + JR
with
µ+
JR = 0
vector-like quarks: BOTH left-handed and right-handed charged currents
µ+
µ+
J µ+ = JL + JR = ūL γ µ dL + ūR γ µ dR = ūγ µ d = V
What are vector-like fermions?
and where do they appear?
The left-handed and right-handed chiralities of a vector-like fermion ψ
transform in the same way under the SM gauge groups SU (3)c × SU (2)L × U (1)Y
Vector-like quarks in many models of New Physics
Warped or universal extra-dimensions
KK excitations of bulk fields
Composite Higgs models
VLQ appear as excited resonances of the bounded states which form SM particles
Little Higgs models
partners of SM fermions in larger group representations which ensure the cancellation of
divergent loops
Gauged flavour group with low scale gauge flavour bosons
required to cancel anomalies in the gauged flavour symmetry
Non-minimal SUSY extensions
VLQs increase corrections to Higgs mass without affecting EWPT
SM and a vector-like quark
LM = −Mψ̄ψ
Gauge invariant mass term without the Higgs
SM and a vector-like quark
LM = −Mψ̄ψ
Gauge invariant mass term without the Higgs
Charged currents both in the left and right sector
ψL
ψR
W
ψL′
W
ψR′
SM and a vector-like quark
LM = −Mψ̄ψ
Gauge invariant mass term without the Higgs
Charged currents both in the left and right sector
ψL
ψR
W
ψL′
W
ψR′
They can mix with SM quarks
t′
×
ui
b′
×
di
Dangerous FCNCs −→ strong bounds on mixing parameters
BUT
Many open channels for production and decay of heavy fermions
Rich phenomenology to explore at LHC
Searches at the LHC
Overview of ATLAS searches
from ATLAS Twiki page
https://twiki.cern.ch/twiki/bin/view/AtlasPublic/CombinedSummaryPlots
Overview of CMS searches
from CMS Twiki page
https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsEXO
But look at the hypotheses . . .
Example: b′ pair production
P
b′
b
t
W−
W+
P
b̄′
t̄
W+
Common assumption
BR(b′ → tW ) = 100%
W−
Searches in the
same-sign dilepton channel
(possibly with b-tagging)
b̄
Example: b′ pair production
P
b
t
b′
W−
W+
P
b̄′
t̄
W+
Common assumption
BR(b′ → tW ) = 100%
W−
Searches in the
same-sign dilepton channel
(possibly with b-tagging)
b̄
If the b′ decays both into Wt and Wq
P
P
b′
b
t
W−
W+
b̄′
jet
W+
P
P
b′
jet
W−
W+
b̄′
jet
There can be less events in the same-sign dilepton channel!
Representations and lagrangian terms
Assumption: vector-like quarks couple with SM quarks through Yukawa interactions
Representations and lagrangian terms
Assumption: vector-like quarks couple with SM quarks through Yukawa interactions
SM
uc t d
s
b
SU(2)L
2 and 1
U (1)Y
qL = 1/6
uR = 2/3
dR = −1/3
LY
−yiu q̄iL Hc uiR
i,j
j
−yid q̄iL VCKM HdR
Singlets
(U)
(D)
Doublets
X
U U
D D
Y
1
2/3
2
-1/3
− λiu q̄iL Hc UR
− λid q̄iL HDR
7/6
1/6
Triplets
 
X
 
U
U
D 
D
Y
3
-5/6
− λiu ψL H (c) uiR
− λid ψL H (c) diR
2/3
-1/3
− λi q̄iL τ a H (c) ψRa
Representations and lagrangian terms
Assumption: vector-like quarks couple with SM quarks through Yukawa interactions
SM
uc t d
s
b
SU(2)L
2 and 1
U (1)Y
qL = 1/6
uR = 2/3
dR = −1/3
LY
yi v
2
i,j
j
yi v
− √d d̄iL VCKM dR
2
− √u ūiL uiR
Singlets
(t′ )
(b′ )
Doublets
X
t′ t′ b′ b′ Y
1
2/3
2
-1/3
i
− λ√u v ūiL UR
2
λi v
− √d d̄iL DR
2
7/6
1/6
 Triplets

X
 ′
 t′ 
t
 b′ 
b′
Y
3
-5/6
i
− λ√u v UL uiR
2
λi v
− √d DL diR
2
2/3
-1/3
λi v i
−√
ūL UR
2
− λi vd̄iL DR
Representations and lagrangian terms
Assumption: vector-like quarks couple with SM quarks through Yukawa interactions
SM
uc t d
s
b
SU(2)L
2 and 1
U (1)Y
qL = 1/6
uR = 2/3
dR = −1/3
LY
Lm
Free
parameters
yi v
2
i,j
j
yi v
− √d d̄iL VCKM dR
2
− √u ūiL uiR
Singlets
(t′ )
(b′ )
Doublets
X
t′ t′ b′ b′ Y
1
2/3
2
-1/3
i
− λ√u v ūiL UR
2
λi v
− √d d̄iL DR
2
7/6
1/6
 Triplets

X
 ′
 t′ 
t
 b′ 
b′
Y
3
-5/6
i
− λ√u v UL uiR
2
λi v
− √d DL diR
2
2/3
-1/3
λi v i
−√
ūL UR
2
− λi vd̄iL DR
−Mψ̄ψ (gauge invariant since vector-like)
4
M + 3 × λi
4 or 7
M + 3λiu + 3λid
4
M + 3 × λi
Outline
1
Motivations and Current Status
2
The effective lagrangian
3
Constraints on model parameters
4
Signatures at LHC
Mixing between VL and SM quarks
Flavour and mass eigenstates
 

u
ũ
 c̃ 
u  c 
 t̃  = VL,R  t 
t′
U L,R

and


 
d̃
d
 s̃ 
d  s 
  = VL,R
 b 
 b̃ 
b′
D L,R
The exotics X5/3 and Y−4/3 do not mix → no distinction between flavour and mass eigenstates
Ly+M


ũ
d̃
 s̃
c̃


= ũ¯ c̃¯ ¯t̃ Ū Mu   + d̃¯ s̃¯ b̃¯ D̄ Md 
 b̃
t̃
L
L
U R
D



 + h.c.

R
Mixing between VL and SM quarks
Flavour and mass eigenstates
 

u
ũ
 c̃ 
u  c 
 t̃  = VL,R  t 
t′
U L,R



 
d̃
d
 s̃ 
d  s 
  = VL,R
 b 
 b̃ 
b′
D L,R
and
The exotics X5/3 and Y−4/3 do not mix → no distinction between flavour and mass eigenstates
Ly+M


ũ
d̃
 s̃
c̃


= ũ¯ c̃¯ ¯t̃ Ū Mu   + d̃¯ s̃¯ b̃¯ D̄ Md 
 b̃
t̃
L
L
U R
D

Mixing matrices depend on representations
Singlets and triplets:


m̃u
x1

m̃c
x2 

Mu = 

m̃t x3 
M
I4
Doublets: M4I
u,d ↔ Mu,d


Md = 

ṼLCKM


m̃d


 + h.c.

R


x1
CKM

x2 
m̃s
ṼR

x3 
m̃b
M
Mixing matrices
 
d
u
 
 
Lm = ū c̄ t̄ t¯′ L (VLu ) † Mu (VRu )  ct  + d̄ s̄ b̄ b̄′ L (VLd ) † Md (VRd )  sb  + h.c.
b′ R
t′ R


(VLu ) † Mu (VRu ) = diag (mu , mc , mt , mt′ )
(VLd ) † Md (VRd ) = diag (md , ms, mb , mb′ )
Mixing matrices
 
d
u
 
 
Lm = ū c̄ t̄ t¯′ L (VLu ) † Mu (VRu )  ct  + d̄ s̄ b̄ b̄′ L (VLd ) † Md (VRd )  sb  + h.c.
b′ R
t′ R


(VLu ) † Mu (VRu ) = diag (mu , mc , mt , mt′ )
(VLd ) † Md (VRd ) = diag (md , ms, mb , mb′ )
Mixing in left- and right-handed sectors behave differently
q †
q
(VL ) (MM† )(VL ) = diag
I
q
q
qL,R
(VR ) † (M† M)(VR ) = diag
q
VL,R
×
J
qL,R
Mixing matrices
 
d
u
 
 
Lm = ū c̄ t̄ t¯′ L (VLu ) † Mu (VRu )  ct  + d̄ s̄ b̄ b̄′ L (VLd ) † Md (VRd )  sb  + h.c.
b′ R
t′ R


(VLu ) † Mu (VRu ) = diag (mu , mc , mt , mt′ )
(VLd ) † Md (VRd ) = diag (md , ms, mb , mb′ )
Mixing in left- and right-handed sectors behave differently
q †
q
(VL ) (MM† )(VL ) = diag
I
q
q
qL,R
(VR ) † (M† M)(VR ) = diag
q
VL,R
×
J
qL,R
Singlets and triplets (case of up-type quarks)
VLu
VRu
=⇒ Mu ·
=⇒
Mu†
Mu†


=

m̃2u


· Mu = 


mixing in the left sector
x1∗ M
present also for m̃q → 0
x2∗ M 

x3 M  flavour constraints for qL
M2
are relevant

x1∗ m̃2u
mq ∝ m̃q

m̃2c
x2∗ m̃2c

mixing is suppressed

m̃2t
x3 m̃2t
by quark masses
x2 m̃c x3 m̃t ∑3i=1 |xi |2 + M2
m̃2u + |x1 |2
x1∗ x2
x1∗ x3
x2∗ x1
m̃2c + |x2 |2 x2∗ x3
x3 x1
x3 x2
m̃2t + x23
x1 M
x2 M
x3 M
x1 m̃u
Doublets: other way round
Now let’s check how couplings are modified
this will allow us to identify which observables
can constrain masses and mixing parameters
Couplings
With Z
 





q1
0
1
′
g
q  q2 
q
q
q  0  µ
q †
q 2  1 
′
γ ( VL )   Z µ
+ T3 − T3 
LZ =
(q̄1 q̄2 q̄3 q̄1 )L (VL )  T3 − Q sw 



q3
0
1
cW
q′ L
1
1
 





q1
0
1
 1 
g

q q 
q′  0   µ
q
+
γ ( VR )  2  Z µ
+ T3 
(q̄1 q̄2 q̄3 q̄1′ )R (VR ) †  −Qq s2w 



q3
0
1
cW
q′ R
1
1
Couplings
With Z
 





q1
0
1
′
g
q  q2 
q
q
q  0  µ
q †
q 2  1 
′
γ ( VL )   Z µ
+ T3 − T3 
LZ =
(q̄1 q̄2 q̄3 q̄1 )L (VL )  T3 − Q sw 



q3
0
1
cW
q′ L
1
1
 





q1
0
1
 1 
g

q q 
q′  0   µ
q
+
γ ( VR )  2  Z µ
+ T3 
(q̄1 q̄2 q̄3 q̄1′ )R (VR ) †  −Qq s2w 



q3
0
1
cW
q′ R
1
1
FCNC, are induced by the mixing with vector-like quarks!
g
cW
gIJZR =
g
cW
′
q
q′
q
q′ J
g
T3 − Qq s2w δIJ + c (T3 − T3 )(VL∗ )q I VL
Z
Z
W
−Qq s2w δIJ
q′
′
q′ J
+ c g T3 (VR∗ )q I VR
W
u
×
=
t′
′
c
′
∗ )t u V t c
∝ (VL,R
L,R
u
×
gIJZL =
c
Couplings
With W ±
LW ±

CKM matrices for left and right handed sector:


gWL

 
d
 µ ds 
 γ VL   Wµ+

b
b′ L
1
 


d
0
g
0


+
µ d  s 
γ
V
+ √ (ū c̄ t̄ |t¯′ )R (VRu ) † 
R  b  Wµ + h.c.
0 
2
1
b′ R
 Ṽ CKM
g
L
= √ (ū c̄ t̄ |t¯′ )L (VLu ) † 

2
 ṼCKM
g
= √ (VLu ) † 

2
1
 d
 VL ≡ √g VLCKM

2
gWR


0
g
g
 d
u † 0
V ≡ √ VRCKM
= √ ( VR ) 
0  R
2
2
1
If BOTH t′ and b′ are present −→ CC between right-handed quarks
W
uR
tR′
×
W
′
= uR
bR′
×
dR
′
∝ (VRu∗ )t I (VRd )b J
dR
Couplings
With Higgs



 
0
q1
1
0
q


  q  q2 
Lh = (q̄1 q̄2 q̄3 q̄1′ )L (VL ) † Mq − M 
(
V
)
h + h.c.
0   R  q3 
v
1
q′ R
The coupling is:

0
1
M q † 0  q
1 q †
q
(V ) =
( VL ) 
C = ( VL ) M q ( VR ) −
0  R
v
v
v
1





mq1
mq2



0
 M q † 0  q
−
(V )
( VL ) 

mq3
0  R
v
1
mq′
FCNC induced by vector-like quarks are present in the Higgs sector too!
H
CIJ =
1
M
′
q′ J
mI δIJ − (VL∗ )q I VR
v
v
qIR
×
H
′
= qIR
qJL
q′ J
∝ (VL∗ )q I VR
×
q′
qJL
Outline
1
Motivations and Current Status
2
The effective lagrangian
3
Constraints on model parameters
4
Signatures at LHC
Rare FCNC top decays
Suppressed in the SM, tree-level with t′
u, c
u, c
W
t
b
t
b
b
Z
BR(t → Zq) = O(10−14 )
SM prediction
u, c
t
W
W
Z
Z
BR(t → Zq) < 0.24%
measured at CMS @ 5 fb−1
Rare FCNC top decays
Suppressed in the SM, tree-level with t′
u, c
u, c
W
b
t
t
b
u, c
t
W
b
W
Z
BR(t → Zq) = O(10−14 )
SM prediction
Z
Z
BR(t → Zq) < 0.24%
measured at CMS @ 5 fb−1
Loop decays with both SM and vector-like quarks
u, c
u, c
W
t
Z
di , X5/3
di , X5/3
g
t
ui
ui
g
BR(t → Zq) = O(10−12 )
SM prediction
BR(t → gu) < 5.7 × 10−5
ATLAS @ 2.5 fb−1
BR(t → gc) < 2.7 × 10−4
Rare FCNC top decays
Suppressed in the SM, tree-level with t′
u, c
u, c
W
b
t
u, c
t
b
t
W
b
W
Z
BR(t → Zq) = O(10−14 )
SM prediction
Z
Z
BR(t → Zq) < 0.24%
measured at CMS @ 5 fb−1
Loop decays with both SM and vector-like quarks
u, c
u, c
W
t
Z
di , X5/3
di , X5/3
g
t
ui
Bound on mixing parameters
ui
g
=⇒
BR(t → Zq) = O(10−12 )
SM prediction
BR(t → gu) < 5.7 × 10−5
ATLAS @ 2.5 fb−1
BR(t → gc) < 2.7 × 10−4
q′ u
q′ c
q′ t
BR(t → Zq, gq) = f (VL,R , VL,R , VL,R ) ≤ BRexp
Zcc̄ and Zbb̄ couplings
Coupling measurements
q
q
gcZL = 0.3453 ± 0.0036
gcZR = −0.1580 ± 0.0051
gbZL = −0.4182 ± 0.00315
gbZR =
0.0962 ± 0.0063
data from LEP EWWG
q
gZL,ZR = (gZL,ZR )SM (1 + δgZL,ZR )
gcZL = 0.34674 ± 0.00017
gcZR = −0.15470 ± 0.00011
0.00045
gbZL = −0.42114+
−0.00024
+0.000052
b
gZR = 0.077420−0.000061
SM prediction
Asymmetry parameters
q
q
(g )2 − (gZR )2
Aq = ZL
= ASM
q (1 + δAq )
q
q
(gZL )2 + (gZR )2
Ac = 0.670 ± 0.027
Ab = 0.923 ± 0.020
PDG fit
Rc =
0.1721 ± 0.0030
Rb = 0.21629 ± 0.00066
PDG fit
Ac = 0.66798 ± 0.00055
0.00016
Ab =
0.93462+
−0.00020
SM prediction
Decay ratios
Γ (Z → qq̄)
Rq =
= RSM
q (1 + δRq )
Γ (Z → hadrons)
0.00016
Rc = 0.17225+
−0.00012
+0.00033
Rb = 0.21583−0.00045
SM prediction
Atomic Parity Violation
Atomic parity is violated through exchange of Z between nucleus and atomic electrons
Weak charge of the nucleus
QW =
i
2cW h
VL
(2Z + N )(guZL + guZR ) + (Z + 2N )(gdZL + gdZR ) = QSM
W + δQW
g
From Z couplings



2cW
g
2cW
g
qq
q
q′
q
q′
q′ q
q′ q
gZL = 2(T3 − Qq s2W ) +2(T3 − T3 )|VL |2
qq
gZR = 2(−Qq s2W )
+2(T3 )|VR |2
Atomic Parity Violation
Atomic parity is violated through exchange of Z between nucleus and atomic electrons
Weak charge of the nucleus
QW =
i
2cW h
VL
(2Z + N )(guZL + guZR ) + (Z + 2N )(gdZL + gdZR ) = QSM
W + δQW
g
From Z couplings



2cW
g
2cW
g
qq
q
q′
q
q′
q′ q
q′ q
gZL = 2(T3 − Qq s2W ) +2(T3 − T3 )|VL |2
qq
gZR = 2(−Qq s2W )
+2(T3 )|VR |2
′
1
1
′
′
′
t′
t′ u 2
t′
t′ u 2
+ (Z + 2N ) (T3b + )|VLb d |2 + T3b |VRb d |2
δQVL
W = 2 ( 2Z + N ) ( T3 − )|VL | + T3 |VR |
2
2
Atomic Parity Violation
Atomic parity is violated through exchange of Z between nucleus and atomic electrons
Weak charge of the nucleus
QW =
i
2cW h
VL
(2Z + N )(guZL + guZR ) + (Z + 2N )(gdZL + gdZR ) = QSM
W + δQW
g
From Z couplings



2cW
g
2cW
g
qq
q
q′
q
q′
q′ q
q′ q
gZL = 2(T3 − Qq s2W ) +2(T3 − T3 )|VL |2
qq
gZR = 2(−Qq s2W )
+2(T3 )|VR |2
′
1
1
′
′
′
t′
t′ u 2
t′
t′ u 2
+ (Z + 2N ) (T3b + )|VLb d |2 + T3b |VRb d |2
δQVL
W = 2 ( 2Z + N ) ( T3 − )|VL | + T3 |VR |
2
2
Bounds from experiments
Most precise test in Cesium 133 Cs:
QW (133 Cs)|exp = −73.20 ± 0.35
QW (133 Cs)|SM = −73.15 ± 0.02
Flavour constraints
example with D0 − D̄0 mixing and D0 → l+ l− decay
In the SM
Mixing (∆C = 2):
D0
c
W
di
di
u
u
xD =
∆mD
ΓD
0.0024
= 0.0100+
−0.0026
yD =
∆ΓD
2ΓD
0.0017
= 0.0076+
−0.0018
D̄0
c
W
Decay (∆C = 1):
D0
c
W
di
l+
νi
u
D0
c
u
W
di
W
di
γ
BR(D0 → e+ e− )exp < 1.2 × 10−6
l−
l+
l−
BR(D0 → µ + µ − )exp < 1.3 × 10−6
BR(D0 → µ + µ − )th,SM = 3 × 10−13
Flavour constraints
example with D0 − D̄0 mixing and D0 → l+ l− decay
Contributions at tree level
Mixing (∆C = 2):
c
D0
u
Decay (∆C = 1):
c
D0
u
Z
u
D̄0
uc
δxD = f (mD , ΓD , mc , mZ , guc
ZL , gZR )
c
Z
l+
l−
uc
δBR = g(mD , ΓD , ml , mZ , guc
ZL , gZR )
Flavour constraints
example with D0 − D̄0 mixing and D0 → l+ l− decay
Contributions at tree level
Mixing (∆C = 2):
c
D0
u
Decay (∆C = 1):
c
D0
u
u
Z
uc
δxD = f (mD , ΓD , mc , mZ , guc
ZL , gZR )
D̄0
c
l+
Z
uc
δBR = g(mD , ΓD , ml , mZ , guc
ZL , gZR )
l−
Contributions at loop level
B0d,s
d, s
W
ui , t′ , X5/3
ui , t′ , X5/3
b d, s
b
B̄0d,s B0d,s
d, s
b
W
Relevant only if tree-level contributions are absent
Possible sources of CP violation
ui , t′ , X5/3
W
W
b d, s
ui , t′ , X5/3
B̄0d,s
EW precision tests and CKM
EW precision tests
t′
W
W
b′
Contributions of new fermions
to S,T,U parameters
EW precision tests and CKM
EW precision tests
t′
W
W
Contributions of new fermions
to S,T,U parameters
b′
CKM measurements
Modifications to CKM relevant for singlets and triplets because mixing in the left
sector is NOT suppressed
The CKM matrix is not unitary anymore
If BOTH t′ and b′ are present, a CKM for the right sector emerges
Higgs coupling with gluons/photons
Production and decay of Higgs at the LHC
g
γ
q
q
g
q
f
H
f
H
f
New physics contributions mostly affect loops of heavy quarks t and q′ :
κgg = κγγ =
v
v
g +
g ′ ′ −1
mt htt̄ mq′ hq q̄
γ
Higgs coupling with gluons/photons
Production and decay of Higgs at the LHC
g
γ
q
q
g
q
f
H
f
H
f
γ
New physics contributions mostly affect loops of heavy quarks t and q′ :
κgg = κγγ =
v
v
g +
g ′ ′ −1
mt htt̄ mq′ hq q̄
The couplings of t and q′ to the higgs boson are:
ghtt̄ =
′
mt
M
′
− VL∗,t t VRt t
v
v
ghq′ q̄′ =
mq ′
v
−
M ∗,q′ q′ q′ q′
VR
V
v L
In the SM: κgg = κγγ = 0
The contribution of just one VL quark to the loops turns out to be negligibly small
Result confirmed by studies at NNLO
Outline
1
Motivations and Current Status
2
The effective lagrangian
3
Constraints on model parameters
4
Signatures at LHC
Production channels
Vector-like quarks can be produced
in the same way as SM quarks plus FCNCs channels
Pair production, dominated by QCD and sentitive to the q′ mass
independently of the representation the q′ belongs to
Single production, only EW contributions and sensitive to both
the q′ mass and its mixing parameters
Production channels
Pair production: pp → q′ q̄′
q
q′
g
q̄′
q̄
qi
g
q′
V
q̄′
q̄j
q′
g
q̄′
g
q′
qi
V
q̄j
q̄′
qi
q′
g
q′
g
H
q̄j
q′
qi
H
q̄′
q̄j
q′
g
V
q′
q
g
V
q
Purely QCD diagrams
(dominant contribution)
q̄′
q′
Purely EW diagrams
q̄′
FCNC channels, but
suppressed wrt to QCD
Single production: pp → q′ + {q, V, H }
qi
qj
qi
q̄j
V
V
q′
qi
qk
q′
qj
qi
qk
q̄j
H
H
q′
g
qk
q′
q
g
qk
q
q′
q
q′
q
q′
H
q′
H
EW+QCD diagrams
potentially relevant
FCNC channel
Production channels
Pair vs single production, example with non-SM doublet (X5/3 t′ )
ΣHp b L
10
pair production
1
0.1
single X53
single t’
0.01
0.001
200
400
600
800
1000
m q,
pair production depends only on the mass of the new particle and
decreases faster than single production due to different PDF scaling
current bounds from LHC are around the region
where (model dependent) single production dominates
Decays
SM partners
Z
H
t′
t′
ui
ui
W+
W−
t′
Z
b′
t′
di
W−
b′
X5/3
di
H
b′
Neutral currents
di
W+
b′
ui
Charged currents
Y−4/3
Exotics
W+
W−
X5/3
Y−4/3
ui
, t′
Only Charged currents
di
, b′
Not all decays may be kinematically allowed
it depends on representations and mass differences
Decays of t′
Examples with non-SM doublet (X5/3 t′ )
Mixing ONLY with top
1.0
Bounds at ∼600 GeV assuming
BR t ’
0.8
0.6
tH
0.4
tZ
0.2
bW
0.0
200
400
600
m t’
800
1000
BR(t′ → bW ) = 100%
or
BR(t′
→ tZ) = 100%
Decays of t′
Examples with non-SM doublet (X5/3 t′ )
Mixing ONLY with top
1.0
Bounds at ∼600 GeV assuming
BR t ’
0.8
0.6
BR(t′ → bW ) = 100%
tH
0.4
tZ
or
0.2
BR(t′
bW
0.0
200
400
600
800
→ tZ) = 100%
1000
m t’
Mixing ALSO with charm
Mixing ONLY with charm
1.0
bW
0.8
0.6
BR t ’
BR t ’
0.8
1.0
0.4
tH
0.2
cZ
cH
0.6
cZ
0.4
cH
tZ
0.0
200
400
600
m t’
800
1000
0.2
0.0
200
400
600
m t’
800
1000
Charge
Resonant state
tj + { ZZ, ZH, HH }
jj + { ZZ, ZH, HH }
tW − + { b, j } + { Z, H }
W + W − + {bb, bj, jj}
t′ t̄′
1/3
t′ ūi
t′ t̄
tt̄ + { Z, H }
tj + { Z, H }
jj + { Z, H }
tW − + { b, j }
W ± + { bj, jj }
t ′ di
t′ b
t + { b, j } + { Z, H }
{ bj, jj } + { Z, H }
W ± + { bb, bj, jj }
W + t̄′
2/3
1
After t′ decay
tt̄+ {ZZ, ZH, HH}
0
t′ Z
t′ H
t + { ZZ, ZH, HH }
W ± + { b, j } + { Z, H }
t′ b̄
t + { b, j } + { Z, H }
{ bj, jj } + { Z, H }
W ± + { bb, bj, jj }
t′ d̄i
tt + { ZZ, ZH, HH }
tj + { ZZ, ZH, HH }
jj + { ZZ, ZH, HH }
tW + + { b, j } + { Z, H }
W ± W ± + { bb, bj, jj }
4/3
t′ t′
t′ ui
tW − + { Z, H }
jW − + { Z, H }
W + W − + { b, j }
t′ t
tt + { Z, H }
tW + + { b, j }
tj + { Z, H }
W ± + { bj, jj }
Possible final states
from pair and single production of t′
in general mixing scenario
only 2 effectively tested since now
Signatures of X5/3
Current searches vs general mixing scenario
based on arXiv:1211.4034, accepted by JHEP
Decays of X5/3
Examples with non-SM doublet (X5/3 t′ )
Mixing ONLY with top
1.0
t W+
BR X 53
0.8
0.6
0.4
0.2
0.0
200
400
600
M X 53
800
1000
Decays of X5/3
Examples with non-SM doublet (X5/3 t′ )
Mixing ONLY with top
1.0
t W+
BR X 53
0.8
0.6
0.4
0.2
0.0
200
400
600
800
1000
M X 53
Mixing ALSO with charm
Mixing ONLY with charm
1.0
1.0
0.8
0.8
cW+
BR X 53
BR X 53
t W+
0.6
cW+
0.4
0.2
0.6
0.4
0.2
u W+
0.0
200
400
600
M X 53
800
1000
0.0
200
400
600
M X 53
800
1000
Current bounds
Direct pair X5/3 searches
P
X5/3
b
t
W+
W−
P
X̄5/3
t̄
W+
W−
b̄
ATLAS search with 4.7fb−1
Assumption
BR(X5/3 → W + t) = 100%
same-sign dilepton + ≥ 2 jets
mX5/3 ≥ 670GeV
Pair b′ searches
P
b′
b
t
W−
W+
P
b̄′
t̄
W+
W−
b̄
CMS search with 5fb−1
Assumption
BR(b′ → W − t) = 100%
same-sign dilepton + jets
mb′ ≥ 675GeV
Selection of kinematical cuts
tt
VVjets
6
Zjets
10
Wt t
5
10
tt
2
10
VVjets
Zjets
10
Wt t
1
Signal X X
Zt t
Events / 100
107
Events / 100
Events / 100


same-sign dilepton
to kill most of the background
Base selection
≥ 2jets
HT > 200 GeV
Rlj > 0.5
to kill VV+jets
to reduce tt̄
tt
8
VVjets
Zjets
7
Wt t
6
Zt t
Signal X X

Zt t
Signal X X
5
104
HT
›1
10
4
3
10
3
10›2
102
2
›3
10
1
10
107
tt
VVjets
6
10
Zjets
Wt t
0
0
0
200 400 600 800 1000 1200 1400 1600 1800 2000
HT
tt
102
VVjets
Zjets
10
Wt t
Events / 1
10›4
200 400 600 800 1000 1200 1400 1600 1800 2000
HT
Events / 1
Events / 1
0
200 400 600 800 1000 1200 1400 1600 1800 2000
HT
tt
6
VVjets
Zjets
5
Wt t
4
Signal X X
5
10
Zt t
Zt t
1
Signal X X
Signal X X
Zt t
104
Njets
10›1
3
10›2
2
3
10
2
10
›3
10
10
0
2
4
6
8
10
12
14
Njets
10›4
1
0
2
4
6
8
10
12
14
Njets
0
0
2
4
6
8
10
12
14
Njets
Comparison of selections

2 same-sign leptons


≥ 4jets
CMS selection:

 HT ≥ 300GeV
Z veto: Mll ≥ 106GeV, Mll ≤ 76GeV
S/ B
Full Signal
(BRs depend on mass)
CMS selection
Fast selection
10
1
250 300 350 400 450 500 550 600 650 700 750
MX[GeV/c2]
Our bounds
observation: 561 GeV
discovery: 609 GeV

2 same-sign leptons


≥ 2jets
Our selection:

 HT ≥ 200GeV
Rlj > 0.5
Comparison of selections

2 same-sign leptons


≥ 4jets
CMS selection:

 HT ≥ 300GeV
Z veto: Mll ≥ 106GeV, Mll ≤ 76GeV
CMS selection
Only WtWc channel
S/ B
CMS selection
Only WtWt channel
S/ B
S/ B
Full Signal
(BRs depend on mass)

2 same-sign leptons


≥ 2jets
Our selection:

 HT ≥ 200GeV
Rlj > 0.5
102
CMS selection
102
Fast selection
Fast selection
10
Fast selection
10
10
1
1
250 300 350 400 450 500 550 600 650 700 750
MX[GeV/c2]
Our bounds
observation: 561 GeV
discovery: 609 GeV
1
250 300 350 400 450 500 550 600 650 700 750
MX[GeV/c2]
250 300 350 400 450 500 550 600 650 700 750
MX[GeV/c2]
Our selection is more effective for WtWc channel
not considered in CMS study
(well, it has been designed exactly for this purpose. . . )
Comparison of selections
Branching ratio as free parameter
BR(X5/3 → W + t) = b
BR(X5/3 → W + u, W + c) = 1 − b
S/ B
and
102
10
CMS search well reproduced for BR(W + t) = 1
1
›1
10
MX =300GeV/c
MX =400GeV/c
MX =500GeV/c
MX =600GeV/c
MX =700GeV/c
Search more sensitive for BR(W + t) < 1
2
2
2
2
2
10›2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
BR(X→ Wt)
1
Conclusions and Outlook
Vector-like quarks are a very promising playground for searches of new physics
Fairly rich phenomenology at the LHC and many possibile channels to explore
→ Signatures of single and pair production of VL quarks are accessible at current CM energy and
luminosity and have been explored to some extent
→ Current bounds on masses around 500-600 GeV, but searches are not fully optimized for general
scenarios.