Top Quark Physics in the Vector Color-Octet Model Mukesh Kumar University of the Witwatersrand September 2, 2014 A. Goyal, S. Dutta (Physicsl Review D 87, 094016 (2013)) Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 1 / 34
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Top Quark Physics in the Vector Color-Octet Model
Mukesh Kumar
University of the Witwatersrand
September 2, 2014
A. Goyal, S. Dutta (Physicsl Review D 87, 094016 (2013))
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 1 / 34
Outline
1 IntroductionTop QuarkAFB
AFB vs AC
2 Vector Color-Octet ModelModelObservables and Processes at TevatronConsistency at LHCConclusion
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 2 / 34
Top mass and issues/anomaly in SM
its heavy mass
strong coupling to EWSB mechanism (λt =√2mtv
≈ 1)
good for pQCD, no hadronization (mt > mW +mb, τhad ∼ 10−24s)spin information preserved due to rapid decay (τtop ∼ 10−25s)
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 3 / 34
Top mass and issues/anomaly in SM
its heavy mass
strong coupling to EWSB mechanism (λt =√2mtv
≈ 1)
good for pQCD, no hadronization (mt > mW +mb, τhad ∼ 10−24s)spin information preserved due to rapid decay (τtop ∼ 10−25s)
|Vtb| measurement (t → Wb)
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 3 / 34
Top mass and issues/anomaly in SM
its heavy mass
strong coupling to EWSB mechanism (λt =√2mtv
≈ 1)
good for pQCD, no hadronization (mt > mW +mb, τhad ∼ 10−24s)spin information preserved due to rapid decay (τtop ∼ 10−25s)
|Vtb| measurement (t → Wb)
Hierarchy problem in the Higgs mass stabilization (affected due to large top mass)
m2H =
(
m0H
)2+
3Λ2UV
8π2v2
(
−4m2t + 2m2
W +m2Z +m2
H
)
→ New Physics Models → Vector-Like Quarks (?? in experiments . . . )
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 3 / 34
Top mass and issues/anomaly in SM
its heavy mass
strong coupling to EWSB mechanism (λt =√2mtv
≈ 1)
good for pQCD, no hadronization (mt > mW +mb, τhad ∼ 10−24s)spin information preserved due to rapid decay (τtop ∼ 10−25s)
|Vtb| measurement (t → Wb)
Hierarchy problem in the Higgs mass stabilization (affected due to large top mass)
m2H =
(
m0H
)2+
3Λ2UV
8π2v2
(
−4m2t + 2m2
W +m2Z +m2
H
)
→ New Physics Models → Vector-Like Quarks (?? in experiments . . . )
Forward-backward asymmetry in tt production at Tevatron→ Coloron Model→ Axigluon→ Z ′ etc . . .
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 3 / 34
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 5 / 34
Forward-Backward Asymmetry vs Charge-Asymmetry
tt
Tevat ron
- 2 -1 0 1 2
y
d�d
y
AFB = N(∆y>0)−N(∆y<0)N(∆y>0)+N(∆y<0)
,∆y = yt − yt
CDF: 16.2± 4.7%
SM: 6± 1%
Inconsistent
t
tLHC
- 3 - 2 -1 0 1 2 3
y
d�d
y
AC = N(∆|y|>0)−N(∆|y|<0)N(∆|y|>0)+N(∆|y|<0)
,
∆|y | = |yt | − |yt |CMS: −1.3± 2.8(stat.)+2.9
−3.1(syst.)%
SM: 1.15± 0.06%
Consistent
Comparing predictions for AttFB and AC within a given model brings important
consequences for the model
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 6 / 34
Model
LqqV = gs
[
V0,A,µ8 uTAγµ(g
UL PL + gU
R PR)u +V0,A,µ8 dTAγµ(g
DL PL + gD
R PR)d
+(
V+,A,µ8 uTAγµ(CLPL + CRPR)d + h.c.
)]
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 7 / 34
Model
LqqV = gs
[
V0,A,µ8 uTAγµ(g
UL PL + gU
R PR)u +V0,A,µ8 dTAγµ(g
DL PL + gD
R PR)d
+(
V+,A,µ8 uTAγµ(CLPL + CRPR)d + h.c.
)]
Model parameters:Couplings: Flavor Conserving (FC) λij = g
qig tj , Flavor Violating (FV) κij = gut
i gutj ,
(i,j)=(L,R) in units of gs strong couplingMasses of resonances: MV 0
8, M
V±8
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 7 / 34
Model
LqqV = gs
[
V0,A,µ8 uTAγµ(g
UL PL + gU
R PR)u +V0,A,µ8 dTAγµ(g
DL PL + gD
R PR)d
+(
V+,A,µ8 uTAγµ(CLPL + CRPR)d + h.c.
)]
Model parameters:Couplings: Flavor Conserving (FC) λij = g
qig tj , Flavor Violating (FV) κij = gut
i gutj ,
(i,j)=(L,R) in units of gs strong couplingMasses of resonances: MV 0
8, M
V±8
Decay Width of Color-Octets:
ΓV8 =16αs [(g
2L + g 2
R){
M2V82
− m2q+m2
q′
4−
(
m2q−m2
q′
2MV8
)2}
+ 3mqmq′ gL gR ]λ12 (M2
V8,m2
q ,m2q′
)
M3V8
,
where λ(x , y , z) = x2 + y 2 + z2 − 2x · y − 2y · z − 2z · x
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 7 / 34
Model
LqqV = gs
[
V0,A,µ8 uTAγµ(g
UL PL + gU
R PR)u +V0,A,µ8 dTAγµ(g
DL PL + gD
R PR)d
+(
V+,A,µ8 uTAγµ(CLPL + CRPR)d + h.c.
)]
Model parameters:Couplings: Flavor Conserving (FC) λij = g
qig tj , Flavor Violating (FV) κij = gut
i gutj ,
(i,j)=(L,R) in units of gs strong couplingMasses of resonances: MV 0
8, M
V±8
Decay Width of Color-Octets:
ΓV8 =16αs [(g
2L + g 2
R){
M2V82
− m2q+m2
q′
4−
(
m2q−m2
q′
2MV8
)2}
+ 3mqmq′ gL gR ]λ12 (M2
V8,m2
q ,m2q′
)
M3V8
,
where λ(x , y , z) = x2 + y 2 + z2 − 2x · y − 2y · z − 2z · xResonant effect through:
Top-Pair ProductionSingle-TopSame-sign TopDijet
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 7 / 34
Rate and Constraints on Vector Color-Octet resonants
√s @ LHC = 7 TeV, L = 5fb−1
MV
±,08
GeV N(ud → V+8 ) N(du → V−
8 ) N(uu → V 08 ) N(dd → V 0
8 )
200 2.2×108 1.2×108 2.1×108 1.3×108
500 8.1×106 3.5×106 7.0×106 4.2×106
900 6.9×105 2.3×105 5.3×105 3.0×105
Assuming a coupling constant and branching ratio of unity,the current mass lower bounds on the vector colored octetresonance states from CMS ≈ 1.6 TeV. [arxiv:1010.4309]
ATLAS exclusion limits are between 0.60 TeV - 2.10 TeV(considering the coupling of the order of strong coupling αs)[PRL 105,161801]
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 8 / 34
Framework
MadGraph/MadEvent version 4.5.2
Collider: Tevatron√s = 1.96 TeV
PDF Set: CTEQ6L1
αs = 0.13
Top quark mass mt = 172.5 GeV/c2
µF = µR = µ = mt
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 9 / 34
Framework
MadGraph/MadEvent version 4.5.2
Collider: Tevatron√s = 1.96 TeV
PDF Set: CTEQ6L1
αs = 0.13
Top quark mass mt = 172.5 GeV/c2
µF = µR = µ = mt
Collider: LHC√s = 7 TeV
mjj = 200 GeV, |∆η| ≤ 1.3, Both jet |η| ≤ 2.5
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 9 / 34
Top-Pair production at Tevatron (Flavor Conserving)
σtt References
7.50± 0.48 CDF 4.6 fb−1 [CDF Note 9913]
7.2± 0.37 SM NNLO [hep-ph/1205.3453]
6.8
7
7.2
7.4
7.6
7.8
8
8.2
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
σ i
n p
b
√λAA
200
GeV
350
GeV
500
GeV
700
GeV
900 G
eV
CDFSM NNLO
6.8
7
7.2
7.4
7.6
7.8
8
8.2
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
σ i
n p
b
√λRR20
0 G
eV
350 G
eV50
0 G
eV
700
GeV
900
GeV
CDFSM NNLO
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 10 / 34
Top-Pair production at Tevatron (Flavor Violating)
σtt References
7.50± 0.48 CDF 4.6 fb−1 [CDF Note 9913]
7.2± 0.37 SM NNLO [hep-ph/1205.3453]
6.8
7
7.2
7.4
7.6
7.8
8
8.2
0.2 0.4 0.6 0.8 1
σ i
n p
b
gutAA
200
GeV
350
GeV
500
GeV
700
GeV
900 GeV
CDF
SM NNLO
6.8
7
7.2
7.4
7.6
7.8
8
8.2
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
σ i
n p
b
gutRR
200
GeV
350
GeV
500
GeV
700
GeV
900 G
eV
CDF
SM NNLO
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 11 / 34
mtt & ∆y fit : Flavor-Conserving
Kinematic dependence of the asymmetry: [arXiv:1211.1003]
AFB(|∆y |) = N(∆y>0)−N(∆y<0)N(∆y>0)+N(∆y<0)
, ∆y = yt − yt
AFB(Mtt) =NF (Mtt )−NB (Mtt )
NF (Mtt )+NB (Mtt ), Mtt = invariant mass of top-antitop pair
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 28 / 34
THANK YOU ALL !!
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 29 / 34
BACKUP SLIDES
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 30 / 34
Issues!!
Anomaly cancellation in Axi-gluon case and |gqA | < |g t
A|Solution: Non-universal models
introducing exotic quarks (vector-like quarks) [arxiv: 1101.5203, Bai et.al.; arxiv:9903387, 0911.2955, Frampton et.al.]extending the gauge sector so that new color-octet spin-1 fields does not change thestructure of the couplings (only the value of coupling constant changes) [arxiv:0908.3116, 1103.0956, Zerwekh]
Two gluons and one massive spin-1 color octet: In axigluon model this kind ofcoupling is forbidden if we assume that strong interactions (QCD) is parityconserving while in case of coloron, gauge invariance protect this kind of interactionterms with dimension 4 or less [Zerwekh, Rosenfeld arXiv: 0103159] (howeverpossible to construct such non-renormalizable dimension-6 interaction [Chivukula etal arXiv: 0109029])
Coloron production via gluon-fusion (one-loop) is typically 4 orders of magnitudesmaller than quark annihilation contribution at LHC [Chivukula et al arXiv:1303.1120]
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 31 / 34
Constraints from Flavor Physics on vector color octets
nonuniversal FCNC couplings between the up quarks of the first and third gen.
keeping u-t coupling large and simultaneously making c-t and u-c couplings smallresults no strong bounds
CC sector can be controlled by align the mixing matrix with CKM
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 32 / 34
Constraints from Flavor Physics on vector color octets
nonuniversal FCNC couplings between the up quarks of the first and third gen.
keeping u-t coupling large and simultaneously making c-t and u-c couplings smallresults no strong bounds
CC sector can be controlled by align the mixing matrix with CKM
Ref. [arXiv: 1101.5203]
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 32 / 34
Constraints from Flavor Physics on vector color octets
nonuniversal FCNC couplings between the up quarks of the first and third gen.
keeping u-t coupling large and simultaneously making c-t and u-c couplings smallresults no strong bounds
CC sector can be controlled by align the mixing matrix with CKM
Ref. [arXiv: 1101.5203]
Bd (Bs): MG ′ & (100TeV)
[
(
CDL,31
)2+
(
CDR,31
)2− 27CD
L,31CDR,31
]1/2
D − D: MG ′ & (600TeV)
[
(
CUL,21
)2+
(
CUR,21
)2− 60CU
L,21CUR,21
]1/2
etc...
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 32 / 34
Top-Pair Production: FC, FV Channel
d σFC
d cos θ=
πβα2s
9s
{(
2− β2 sin2 θ)
+1
2
s(s −m2V 08)
(s −m2V 08)2 +m2
V 08Γ2V 08
×[
(gqL + g
qR)(g
tL + g
tR)(
2− β2 sin2 θ)
+ (gqL − g
qR)(g
tL − g
tR)(
2β cos θ)]
+1
4
s2
(s −m2V 08)2 +m2
V 08Γ2V 08
×[
(gqL
2+ g
qR
2)(g t
L2+ g
tR2)(
1 +2g t
LgtR
g tL2 + g t
R2(1− β2) + (β cos θ)2
)
+ (gqL
2 − gqR
2)(g t
L2 − g
tR2)(
2β cos θ)]}
,whereβ =√
1− 4m2t /s
the top quark velocity in c.m. frame of reference of qq.
d σFV
d cos θ=πβα2
s
9s
{(
2− β2 sin2 θ)
− 1
6
s
(t −m2V 08)(1 + β cos θ)2(gut
L2+ g
utR
2)
+1
4
s2
(t −m2V 08)2
[
(gutL
4+ g
utR
4)(
1 + β cos θ)2
+ 8gutL
2gutR
2(1 + β2)
]}
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 33 / 34
Constraints on FV couplings: Same-Sign Top quark
L4F = 12CLL
Λ2 (uLγµtL)(uLγµtL) +
12CRR
Λ2 (uRγµtR)(uRγµtR)− 1
2CLR
Λ2 (uLγµtL)(uRγµtR)−
12
C ′LR
Λ2 (uLaγµtLb )(uRb
γµtRa) + h.c.
σtt+t t = 2[
14.48Λ4 (|CLL|2 + |CRR |2)+ 1.811
Λ4 (|CLR |2 + |C ′LR |2)− 0.52
Λ4 Re(CLRC′∗LR)
]
fb ·TeV4.
[arxiv:1108.3562]
Set limit on vector or axial-vector Z ′ boson for CLL = CRR = ∓ 12CLR ≡ C
[CDF Note 10466] LL LR RR
σtt+t t× BR(W → lν)2 [fb] 54 51 44
|C |/Λ2 [TeV−2] 4.1 11.3 3.7
d σ
d cos θ=
πβα2s
(t −m2V 08)2
s
18
[
2(gutL
4+ g
utR
4) + g
utL
2gutR
2(1 + β cos θ)2
]
+2πβα2
s
(t −m2V 08)(u −m2
V 08)
s
9
[
(gutL
4+ g
utR
4)− 2gut
L2gutR
2m2t
s
]
+πβα2
s
(u −m2V 08)2
s
18
[
2(gutL
4+ g
utR
4) + g
utL
2gutR
2(1− β cos θ)2
]
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 34 / 34