This document presents a vector color-octet model to explain anomalies observed in top quark physics measurements at the Tevatron collider. The model introduces new vector color-octet resonances that can contribute to top quark pair production and give rise to asymmetries. Observables related to the top quark like the forward-backward asymmetry, charge asymmetry, and single top production are discussed. Constraints on the masses of the new vector resonances from LHC data are also presented. Simulation tools like MadGraph are used to study predictions of the model.
My introduction to electron correlation is based on multideterminant methods. I introduce the electron-electron cusp condition, configuration interaction, complete active space self consistent field (CASSCF), and just a little information about perturbation theories. These slides were part of a workshop I organized in 2014 at the University of Pittsburgh and for a guest lecture in a Chemical Engineering course at Pitt.
Response of dynamic systems to harmonic excitation is discussed. Single degree of freedom systems are considered. For general damped multi degree of freedom systems, see my book Structural Dynamic Analysis with Generalized Damping Models: Analysis (e.g., in Amazon http://buff.ly/NqwHEE)
Multiscale methods for next generation graphene based nanocomposites is proposed. This approach combines atomistic finite element method and classical continuum finite element method.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
My introduction to electron correlation is based on multideterminant methods. I introduce the electron-electron cusp condition, configuration interaction, complete active space self consistent field (CASSCF), and just a little information about perturbation theories. These slides were part of a workshop I organized in 2014 at the University of Pittsburgh and for a guest lecture in a Chemical Engineering course at Pitt.
Response of dynamic systems to harmonic excitation is discussed. Single degree of freedom systems are considered. For general damped multi degree of freedom systems, see my book Structural Dynamic Analysis with Generalized Damping Models: Analysis (e.g., in Amazon http://buff.ly/NqwHEE)
Multiscale methods for next generation graphene based nanocomposites is proposed. This approach combines atomistic finite element method and classical continuum finite element method.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
Slides of my talk at IISc Bangalore on nanomechanics and finite element analysis for statics and dynamics of nanoscale structures such as carbon nanotube, graphene, ZnO nanotube and BN nano sheet.
Localized Electrons with Wien2k
LDA+U, EECE, MLWF, DMFT
Elias Assmann
Vienna University of Technology, Institute for Solid State Physics
WIEN2013@PSU, Aug 14
Exact Sum Rules for Vector Channel at Finite Temperature and its Applications...Daisuke Satow
Slides used in presentation at:
“International School of Nuclear Physics 38th Course Nuclear matter under extreme conditions -Relativistic heavy-ion collisions”, in September, 2016 @ Erice, Italy
The all-electron GW method based on WIEN2k: Implementation and applications.ABDERRAHMANE REGGAD
The all-electron GW method based on WIEN2k:
Implementation and applications.
Ricardo I. G´omez-Abal
Fritz-Haber-Institut of the Max-Planck-Society
Faradayweg 4-6, D-14195, Berlin, Germany
15th. WIEN2k-Workshop
March, 29th. 2008
Branislav K. Nikoli
ć
Department of Physics and Astronomy, University of Delaware, U.S.A.
PHYS 624: Introduction to Solid State Physics
http://www.physics.udel.edu/~bnikolic/teaching/phys624/phys624.html
Slides of my talk at IISc Bangalore on nanomechanics and finite element analysis for statics and dynamics of nanoscale structures such as carbon nanotube, graphene, ZnO nanotube and BN nano sheet.
Localized Electrons with Wien2k
LDA+U, EECE, MLWF, DMFT
Elias Assmann
Vienna University of Technology, Institute for Solid State Physics
WIEN2013@PSU, Aug 14
Exact Sum Rules for Vector Channel at Finite Temperature and its Applications...Daisuke Satow
Slides used in presentation at:
“International School of Nuclear Physics 38th Course Nuclear matter under extreme conditions -Relativistic heavy-ion collisions”, in September, 2016 @ Erice, Italy
The all-electron GW method based on WIEN2k: Implementation and applications.ABDERRAHMANE REGGAD
The all-electron GW method based on WIEN2k:
Implementation and applications.
Ricardo I. G´omez-Abal
Fritz-Haber-Institut of the Max-Planck-Society
Faradayweg 4-6, D-14195, Berlin, Germany
15th. WIEN2k-Workshop
March, 29th. 2008
Branislav K. Nikoli
ć
Department of Physics and Astronomy, University of Delaware, U.S.A.
PHYS 624: Introduction to Solid State Physics
http://www.physics.udel.edu/~bnikolic/teaching/phys624/phys624.html
"Curved extra-dimensions" by Nicolas Deutschmann (Institut de Physique Nuclea...Rene Kotze
Abstract: Universal Extra-Dimension models provide a promising framework for model building as they naturally have rich phenomenological implications, not the least of which is a potential natural dark matter candidate. This candidate takes the form of a Kaluza-Klein excitation of some neutral Standard Model field whose stability is ensured by some isometry of the extra-space. In five dimensions, such a symmetry has to be enforced in an ad-hoc fashion, which is why six-dimensional models have started prompting the interest of model builders. If flat 6D models have been thoroughly surveyed and studied, the realm of curved extra-dimensional models remains mostly uncharted. This talk aims at showing the features of extra dimensional models on a curved background, focusing mostly on positively curved spaces. I will show that the main difficulty for constructing a convincing model revolves around the issue of chiral fermions in the 4D effective theory and how it can be overcome by the addition of a new gauge field which has to be hidden from experimental reach by a symmetry breaking. After going over the phenomenological consequences of a model built using these ingredients, I will briefly review hyperbolic extra-dimensions, for which several problems appearing on positively curved spaces are solved or alleviated.
NITheP UKZN Seminar: Prof. Alexander Gorokhov (Samara State University, Russi...Rene Kotze
NITheP UKZN Seminar: Prof. Alexander Gorokhov (Samara State University, Russia)
TITLE: Dynamical Groups, Coherent States and Some of their Applications in Quantum Optics and Molecular Spectroscopy
Wits Node Seminar: Dr Sunandan Gangopadhyay (NITheP Stellenbosch)
TITLE: Path integral action of a particle in the noncommutative plane and the Aharonov-Bohm effect
Stochastic Gravity in Conformally-flat SpacetimesRene Kotze
The National Institute for Theoretical Physics, and the Mandelstam Institute for Theoretical Physics, School of Physics, would like to invite to its coming talk in the theoretical physics seminar series, entitled:
"Stochastic Gravity in Conformally-flat Spacetimes"
to be presented by Prof. Hing-Tong Cho (Tamkang University, Taiwan)
Abstract: The theory of stochastic gravity takes into account the effects of quantum field fluctuations onto the classical spacetime. The essential physics can be understood from the analogous Brownian motion model. We shall next concentrate on the case with conformally-flat spacetimes. Our main concern is to derive the so-called noise kernels. We shall also describe our on-going program to investigate the Einstein-Langevin equation in these spacetimes.
Dates: Tuesday, 17th February 2015
Venue: The Frank Nabarro lecture theatre, P216
Time: 13.20 - 14.10 - TODAY
"Quantum nanophotonics"
Abstract: Quantum nanophotonics is a rapidly growing field of research that involves the study of the quantum properties of light and its interaction with matter at the nanoscale. Here, surface plasmons – electromagnetic excitations coupled to electron charge density waves on metal-dielectric interfaces or localized on metallic nanostructures – enable the confinement of light to scales far below that of conventional optics. I will review recent progress in the theoretical investigation of the quantum properties of surface plasmons, their role in controlling light-matter interactions at the quantum level and potential applications in quantum information science.
"Planet Formation in Dense Star Clusters" presented by Dr. Henry Throop (Uni...Rene Kotze
NITheP WITS node seminar
"Planet Formation in Dense Star Clusters"
to be presented by Dr. Henry Throop (University of Pretoria)
http://www.nithep.ac.za/4hu.htm
Prof Tom Trainor (University of Washington, Seattle, USA)Rene Kotze
TITLE: Two cultures in high energy nuclear physics
Since the mid eighties a community originating within the Bevalac program at the LBNL has sought to achieve formation of a color-deconfined quark-gluon plasma in heavy ion (A-A) collisions using successively higher collision energies at the AGS, SPS, RHIC and now the LHC, emphasizing a flowing dense "partonic" medium as the principal phenomenon. During much of the same period the high energy physics (HEP) community studying elementary collisions (e-e, e-p, p-p) developed the modern theory of QCD, emphasizing dijet production (fragmentation of scattered partons to observable hadrons) as the principal (calculable) phenomenon. Initially it was assumed that the QGP phenomenon in most-central A-A collisions might be distinguished from the HEP dijet phenomenon in elementary collisions. However, strong overlaps in phenomenology have revealed significant conflicts between QGP and HEP "cultures," especially at RHIC and LHC energies. In this talk I review some of the history and contrast an assortment of experimental evidence and interpretations from the two cultures with suggested conflict resolution.
NITheP WITS node Seminar by Dr Dr. Roland Cristopher F. Caballar (NITheP/UKZN)
TITLE: "One-Dimensional Homogeneous Open Quantum Walks"
ABSTRACT: In this talk, we consider a system undergoing an open quantum walk on a one-dimensional lattice. Each jump of the system between adjacent lattice points in a given direction corresponds to a jump operator, with these jump operators either commuting or not commuting. We examine the dynamics of the system undergoing this open quantum walk, in particular deriving analytically the probability distribution of the system, as well as examining numerically the behavior of the probability distribution over long time steps. The resulting distribution is shown to have multiple components, which fall under two general categories, namely normal and solitonic components. The analytic computation of the probability distribution for the system undergoing this open quantum walk allows us to determine at any instant of time the dynamical properties of the system.
Viktor Urumov - Time-delay feedback control of nonlinear oscillatorsSEENET-MTP
Lecture by prof. dr Viktor Urumov (Faculty of Science and Mathematics, Saint Cyril and Methodius University, Skopje, Macedonia) on June 30, 2010 at the Faculty of Science and Mathematics, Nis, Serbia.
Talk presented at the Electromagnetic Interactions of Nucleons and Nuclei 2015 (EINN 2015) conference, Paphos, Cyprus. In this talk we present results on the axial charges of all forty light, strange and charm baryons from Lattice QCD calculations.
Los días 22 y 23 de junio de 2016 organizamos en la Fundación Ramón Areces un simposio internacional sobre 'Materiales bidimensionales: explorando los límites de la física y la ingeniería'. En colaboración con el Massachusetts Institute of Technology (MIT), científicos de este prestigioso centro de investigación mostraron las propiedades únicas de materiales como el grafeno, de solo un átomo de espesor, y al mismo tiempo más resistente que el acero y mucho más ligero.
Hands on instructions for NITheCS August mini - school Rene Kotze
For all students participating in the NITheCS Mini-School (continuing tomorrow 17 August 2021) - please follow these simple instructions to setup the software environment for the hands-on session for tomorrow.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Dr. Mukesh Kumar (NITheP/Wits) TITLE: "Top quark physics in the Vector Color-Octet Model"
1. 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
2. Outline
1 Introduction
Top Quark
AFB
AFB vs AC
2 Vector Color-Octet Model
Model
Observables and Processes at Tevatron
Consistency at LHC
Conclusion
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 2 / 34
3. Top mass and issues/anomaly in SM
its heavy mass
strong coupling to EWSB mechanism (t =
√2 mt
v
1)
good for pQCD, no hadronization (mt mW + mb, had 10−24s)
spin information preserved due to rapid decay (top 10−25s)
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 3 / 34
4. Top mass and issues/anomaly in SM
its heavy mass
strong coupling to EWSB mechanism (t =
√2 mt
v
1)
good for pQCD, no hadronization (mt mW + mb, had 10−24s)
spin information preserved due to rapid decay (top 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
5. Top mass and issues/anomaly in SM
its heavy mass
strong coupling to EWSB mechanism (t =
√2 mt
v
1)
good for pQCD, no hadronization (mt mW + mb, had 10−24s)
spin information preserved due to rapid decay (top 10−25s)
|Vtb| measurement (t → Wb)
Hierarchy problem in the Higgs mass stabilization (affected due to large top mass)
m2H
= m0H
2
+ 32
UV
4m2
82v2 −t + 2m2W
+ m2Z
+ m2H
→ 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
6. Top mass and issues/anomaly in SM
its heavy mass
strong coupling to EWSB mechanism (t =
√2 mt
v
1)
good for pQCD, no hadronization (mt mW + mb, had 10−24s)
spin information preserved due to rapid decay (top 10−25s)
|Vtb| measurement (t → Wb)
Hierarchy problem in the Higgs mass stabilization (affected due to large top mass)
m2H
= m0H
2
+ 32
UV
4m2
82v2 −t + 2m2W
+ m2Z
+ m2H
→ New Physics Models → Vector-Like Quarks (?? in experiments . . . )
Forward-backward asymmetry in t¯t
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
7. Top Pair-Production Mass at Tevatron
Tevatron Run II Preliminary *=preliminary
CDF dileptons * 7.47 ± 0.50 ± 0.70 pb 8.8 fb1
± 0.86 pb
CDF ANN l+jets 7.82 ± 0.38 ± 0.40 pb 4.6 fb1
± 0.55 pb
CDF SVX l+jets 7.32 ± 0.36 ± 0.61 pb 4.6 fb1
± 0.71 pb
CDF alljets
7.21 ± 0.50 ± 1.08 pb 2.9 fb1
± 1.19 pb
CDF combined * 7.71 ± 0.31 ± 0.40 pb up to 8.8 fb1
± 0.51 pb
DØ dilepton 7.36 ± 0.85 pb 5.4 fb1
DØ l+jets 7.90 ± 0.74 pb 5.6 fb1
DØ combined 7.56 ± 0.20 ± 0.56 pb 5.6 fb1
± 0.59 pb
Tevatron combined *
September 2012
= 172.5 GeV t for m
7.65 ± 0.20 ± 0.36 pb up to 8.8 fb1
± 0.42 pb
6 7 8 9
pp ® tt cross section (pb) at s=1.96 TeV
7.3
Mass of the Top Quark in Different Decay Channels
March 2013 (* preliminary)
Lepton+jets 173.18 ±0.92 (±0.54 ± 0.75)
Dilepton 171.02 ±2.06 (±1.72 ± 1.14)
Alljets 172.70 ±1.94 (±1.46 ± 1.28)
MET+Jets * 173.76 ±1.79 (±1.30 ± 1.23)
Tevatron
combination *
173.20 ±0.87 (±0.51 ± 0.71)
(± stat ± syst)
168 169 170 171 172 173 174 175 176 177 178 179
(GeV/c2) t M
0
CDF March'07 12.40 ±2.66 (±1.50 ± 2.20)
10
9
8
7
6
5
Theory (scales + pdf)
Theory (scales)
CDF and D0, L=8.8fb-1
PPbar ® tt+X @ NNLO+NNLL
MSTW2008NNLO(68cl)
164 166 168 170 172 174 176 178 180 182
stot [pb]
mtop [GeV]
[arXiv:1303.6254]
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 4 / 34
8. Forward-Backward Asymmetry
q
✖q
❣
t
✖t
q
✖q
❣
❣
t
✖t
q
✖q
❣
t
✖t
q
✖q
❣
t
✖t
t t
Tevat ron
- 2 -1 0 1 2
y
dΣdy
At¯t
FB = Nt (cos 0)−Nt (cos 0)
AFB = N(y0)−N(y0)
E−pz
2 ln E+pz
Rapidity: y = 1
AFB References
Nt (cos 0)+Nt (cos 0)
N(y0)+N(y0) , y = yt − y¯t
0.162 ± 0.047 CDF 8.7 fb−1 [CDF Note 10807]
0.196 ± 0.065 D0 5.4 fb−1 [arxiv:1107.4995]
0.06 ± 0.01 NLO QCD t¯t
[PRD 78,73 (014008),77(014003)]
0.066 NLO (QCD+EW) t¯t
POWHEG [CDF Note 10807]
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 5 / 34
9. Forward-Backward Asymmetry vs Charge-Asymmetry
t t
Tevat ron
- 2 -1 0 1 2
y
dΣdy
AFB = N(y0)−N(y0)
N(y0)+N(y0) ,
y = yt − y¯t
CDF: 16.2 ± 4.7%
SM: 6 ± 1%
Inconsistent
t
LHC t
- 3 - 2 -1 0 1 2 3
y
dΣdy
AC = N(|y|0)−N(|y|0)
N(|y|0)+N(|y|0) ,
|y| = |yt | − |y¯t
|
CMS: −1.3 ± 2.8(stat.)+2.9
−3.1(syst.)%
SM: 1.15 ± 0.06%
Consistent
Comparing predictions for At¯t
FB 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
10. Model
Lq¯qV = gshV0,A,μ
8 ¯uTA
μ(gU
R PR)u +V0,A,μ
L PL + gU
8
¯dTA
μ(gD
L PL + gD
R PR)d
+V+,A,μ
8 ¯uTA
μ(CLPL + CRPR)d + h.c.i
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 7 / 34
11. Model
Lq¯qV = gshV0,A,μ
8 ¯uTA
μ(gU
R PR)u +V0,A,μ
L PL + gU
8
¯dTA
μ(gD
L PL + gD
R PR)d
+V+,A,μ
8 ¯uTA
μ(CLPL + CRPR)d + h.c.i
Model parameters:
Couplings: Flavor Conserving (FC) ij = gq
i gt
j , Flavor Violating (FV) ij = gut
i gut
j ,
(i,j)=(L,R) in units of gs strong coupling
Masses of resonances: MV0
8
, M
±
8
V
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 7 / 34
12. Model
Lq¯qV = gshV0,A,μ
8 ¯uTA
μ(gU
R PR)u +V0,A,μ
L PL + gU
8
¯dTA
μ(gD
L PL + gD
R PR)d
+V+,A,μ
8 ¯uTA
μ(CLPL + CRPR)d + h.c.i
Model parameters:
Couplings: Flavor Conserving (FC) ij = gq
i gt
j , Flavor Violating (FV) ij = gut
i gut
j ,
(i,j)=(L,R) in units of gs strong coupling
Masses of resonances: MV0
8
, M
±
8
V
Decay Width of Color-Octets:
6s [(g2
V8 = 1
R)nM2V
L + g2
8
2 −
m2
q+m2
4 − m2
q′
q−m2
2q′
o + 3mqmq′ gL gR]
2MV8
1
2 (M2V
8
q ,m2
,m2
q′ )
M3V
8
,
where (x, y, z) = x2 + y2 + 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
13. Model
Lq¯qV = gshV0,A,μ
8 ¯uTA
μ(gU
R PR)u +V0,A,μ
L PL + gU
8
¯dTA
μ(gD
L PL + gD
R PR)d
+V+,A,μ
8 ¯uTA
μ(CLPL + CRPR)d + h.c.i
Model parameters:
Couplings: Flavor Conserving (FC) ij = gq
i gt
j , Flavor Violating (FV) ij = gut
i gut
j ,
(i,j)=(L,R) in units of gs strong coupling
Masses of resonances: MV0
8
, M
±
8
V
Decay Width of Color-Octets:
6s [(g2
V8 = 1
R)nM2V
L + g2
8
2 −
m2
q+m2
4 − m2
q′
q−m2
2q′
o + 3mqmq′ gL gR]
2MV8
1
2 (M2V
8
q ,m2
,m2
q′ )
M3V
8
,
where (x, y, z) = x2 + y2 + z2 − 2x · y − 2y · z − 2z · x
Resonant effect through:
Top-Pair Production
Single-Top
Same-sign Top
Dijet
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 7 / 34
14. Rate and Constraints on Vector Color-Octet resonants
√s @ LHC = 7 TeV, L = 5fb−1
MV
±,0
8
GeV N(u¯d → V+
8 ) N(d ¯d → V0
8 ) N(d¯u → V− 8 ) N(u¯u → V0
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 octet
resonance 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 s )
[PRL 105,161801]
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 8 / 34
15. Framework
MadGraph/MadEvent version 4.5.2
Collider: Tevatron √s = 1.96 TeV
PDF Set: CTEQ6L1
s = 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
16. Framework
MadGraph/MadEvent version 4.5.2
Collider: Tevatron √s = 1.96 TeV
PDF Set: CTEQ6L1
s = 0.13
Top quark mass mt = 172.5 GeV/c2
μF = μR = μ = mt
Collider: LHC √s = 7 TeV
mjj = 200 GeV, || ≤ 1.3, Both jet || ≤ 2.5
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 9 / 34
17. Top-Pair production at Tevatron (Flavor Conserving)
t¯t
References
7.50 ± 0.48 CDF 4.6 fb−1 [CDF Note 9913]
7.2 ± 0.37 SM NNLO [hep-ph/1205.3453]
8.2
8
7.8
7.6
7.4
7.2
7
6.8
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
s in pb
ÖlAA
200 GeV
350 GeV
500 GeV
700 GeV
900 GeV
CDF
SM NNLO
8.2
8
7.8
7.6
7.4
7.2
7
6.8
350 GeV
500 GeV
700 GeV
CDF
SM NNLO
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
s in pb
ÖlRR
200 GeV
900 GeV
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 10 / 34
18. Top-Pair production at Tevatron (Flavor Violating)
t¯t
References
7.50 ± 0.48 CDF 4.6 fb−1 [CDF Note 9913]
7.2 ± 0.37 SM NNLO [hep-ph/1205.3453]
8.2
8
7.8
7.6
7.4
7.2
7
6.8
0.2 0.4 0.6 0.8 1
s in pb
gut
AA
200 GeV
350 GeV
500 GeV
700 GeV
900 GeV
CDF
SM NNLO
8.2
8
7.8
7.6
7.4
7.2
7
6.8
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
s in pb
gut
RR
200 GeV
350 GeV
500 GeV
700 GeV
900 GeV
CDF
SM NNLO
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 11 / 34
19. mt¯t
y fit : Flavor-Conserving
Kinematic dependence of the asymmetry: [arXiv:1211.1003]
AFB(|y|) = N(y0)−N(y0)
, t
¯t
¯t
¯y = yt yN(y0)+N(y0) − AFB(Mt) = NF (Mt)−NB (Mtt )
¯NF (Mt¯t
)+NB (Mt¯t
) , Mt¯t
= invariant mass of top-antitop pair
2-Analysis: 2 = Pi
i −Oexp
(Oth
i )2
(Oi )2
Fitting points: (200 GeV, AA = 0.30), (500 GeV, RR = 0.11), (900 GeV,
NA = 0.35)
0.6
0.5
0.4
0.3
0.2
0.1
0
350 400 450 500 550 600 650 700 750 800
AFB
Mt-t
GeV
NLO
Data
200(0.30)
500(0.11)
900(0.35)
0.5
0.4
0.3
0.2
0.1
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
AFB
D y
NLO
Data
200(0.30)
500(0.11)
900(0.35)
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 12 / 34
20. mt¯t
y fit : Flavor-Violating
Kinematic dependence of the asymmetry:
AFB(|y|) = N(y0)−N(y0)
, t
¯t
¯t
¯y = yt yN(y0)+N(y0) − AFB(Mt) = NF (Mt)−NB (Mtt )
¯NF (Mt¯t
)+NB (Mt¯t
) , Mt¯t
= invariant mass of top-antitop pair
2-Analysis: 2 = Pi
i −Oexp
(Oth
i )2
(Oi )2
Fitting points: (200 GeV, gut
L = 0.26), (500 GeV, gut
R = −gut
R = −gut
L = 0.53), (900
R = 1.266= gut
GeV, gut
L = 0)
0.6
0.5
0.4
0.3
0.2
0.1
0
350 400 450 500 550 600 650 700 750 800
AFB
Mt-t
GeV
NLO
Data
200(0.26)
500(0.53)
900(1.26)
0.5
0.4
0.3
0.2
0.1
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
AFB
D y
NLO
Data
200(0.26)
500(0.53)
900(1.26)
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 13 / 34
21. Spin-Correlation
1
d2
d cos +d cos −
4 (1+Ct¯t
= 1
cos + cos −),
Ct¯t
= ↑↑+↓↓−↑↓−↓↑
↑↑+↓↓+↑↓+↓↑
.
Ct¯t
= [(¯t
R tL)+(¯t
LtR )]−[(¯t
R tR )+(¯t
LtL)]
[(¯t
R tL)+(¯t
LtR )]+[(¯t
R tR )+(¯tLtL)]
≡ NO−NS
NO+NS
Ct¯t
beam Ct¯t
helicity References
0.72 ± 0.69 0.48 ± 0.53 CDF 5.3 fb−1 [CDF Note 10211]
0.777 0.352 SM NLO [hep-ph/0403035]
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 14 / 34
22. Spin-Correlation
1
d2
d cos +d cos −
4 (1+Ct¯t
= 1
cos + cos −),
Ct¯t
= ↑↑+↓↓−↑↓−↓↑
↑↑+↓↓+↑↓+↓↑
.
Ct¯t
= [(¯t
R tL)+(¯t
LtR )]−[(¯t
R tR )+(¯t
LtL)]
[(¯t
R tL)+(¯t
LtR )]+[(¯t
R tR )+(¯tLtL)]
≡ NO−NS
NO+NS
We found consistent region for model
parameters
Ct¯t
beam Ct¯t
helicity References
0.72 ± 0.69 0.48 ± 0.53 CDF 5.3 fb−1 [CDF Note 10211]
0.777 0.352 SM NLO [hep-ph/0403035]
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 14 / 34
23. Single-top Production at Tevatron
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 15 / 34
24. Single-top Production at Tevatron
In FC s- and t- channel in 5 flavor scheme.
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 16 / 34
25. Single-top Production at Tevatron
In FC s- and t- channel in 5 flavor scheme.
In FV combined s + t- channel
s-channel q¯q ! t¯u, where q = d, s, c, b
t-channel u¯q ! t¯q,
s + t-channel u¯u ! t¯u and t + u-channel uu ! tu
all via neutral color-octet V0
8 exchange.
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 16 / 34
26. Single-top Production at Tevatron
In FC s- and t- channel in 5 flavor scheme.
In FV combined s + t- channel
s-channel q¯q ! t¯u, where q = d, s, c, b
t-channel u¯q ! t¯q,
s + t-channel u¯u ! t¯u and t + u-channel uu ! tu
all via neutral color-octet V0
8 exchange.
For a given FC coupling single top production can constrain the FV coupling more
severely than the top-pair production.
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 16 / 34
27. Same-sign Top: Exclusion Plots at Tevatron
[CDF Note 10466] LL LR RR
¯t × BR(W → l)2 [fb] 54 51 44
tt+¯t
2
1.8
1.5
1.2
1
0.8
0.5
0.2
0.2 0.5 0.8 1 1.2 1.5 1.8 2
ut|
|gR
ut|
|gL
900 GeV
700 GeV
500 GeV
350 GeV
200 GeV
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 17 / 34
28. Top Pair-Production at LHC
NLO QCD (pp)
Approx. NNLO (pp)
NLO QCD (pp)
Approx. NNLO (pp)
CDF
D0
Single Lepton (8 TeV) 241 ± 32 pb
Single Lepton (7 TeV) 179 ± 12 pb
Dilepton 173
+17 pb
14
Allhadronic
167 ± 81 pb
Combined 177 +11
pb 10
250
200
1 2 3 4 5 6 7 8
s [TeV]
[pb] tt s
102
10
1
ATLAS Preliminary
7 8
150
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 18 / 34
29. Top Pair-Production at LHC
ATLAS Preliminary
+ 8 177 ± 3
168 ± 12 + 60
50 100 150 200 250 300 350
tt [pb] s
Data 2011, s = 7 TeV
Channel Lumi.
20 Dec 2012
Theory (approx. NNLO)
= 172.5 GeV t for m
stat. uncertainty
total uncertainty
±(stat) ±(syst) ±(lumi) tt s
Single lepton 0.70 fb1
179 ± 4 ± 9 ± 7 pb
Dilepton 1
0.70 fb pb 7
+ 8 11
173 ± 6 + 14
All hadronic
1.02 fb1
167 ± 18 ± 78 ± 6 pb
Combination ± 7 pb 7
Single lepton, b ® Xμn
1
4.66 fb
165 ± 2 ± 17 ± 3 pb
+ jets had t 1.67 fb1
194 ± 18 ± 46 pb
+ lepton had t 2.05 fb1
186 ± 13 ± 20 ± 7 pb
All hadronic
4.7 fb1
± 6 pb 57
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 19 / 34
30. Top Mass at LHC
summary May
2013, L top ATLAS m
ATLAS 2010, l+jets* 169.30 ± 4.00 ± 4.90
CONF2011033,
L
= 35 pb1
int ATLAS 2011, l+jets 174.53 ± 0.61 ± 0.43 ± 2.27
= 1.04 fb1
int
Eur. Phys. J. C72 (2012) 2046, L
ATLAS 2011, all jets* 174.90 ± 2.10 ± 3.80
CONF2012030,
L
= 2.05 fb1
int ATLAS 2011, dilepton* 175.20 ± 1.60 ± 3.00
CONF2012082,
L
= 4.7 fb1
int ATLAS 2011, l+jets* 172.31 ± 0.23 ± 0.27 ± 0.67 ± 1.35
CONF2013046,
L
= 4.7 fb1
int CMS Average September 2012
JSFÅsyst. ± 0.91 stat. 173.36 ± 0.38
Tevatron Average May 2013
155 160 165 170 175 180 185 190 195
[GeV] top m
9
1
JSFÅsyst. ± 0.71 stat. 173.20 ± 0.51
= 35 pb1
4.7
fb1
(*Preliminary)
int
± stat. ± JSF ± bJSF ± syst.
stat. uncertainty
stat. Å JSF Å bJSF uncertainty
total uncertainty
ATLAS Preliminary
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 20 / 34
31. Top-Pair Production
182
180
178
176
174
172
170
168
166
164
200 GeV,l A A =0.30
500 GeV,l R R =0.11
900 GeV,l N A =0.35
NNLO
7.2 7.4 7.6 7.8 8 8.2
LHC (pb)
st-t
Tevatron (pb)
st-t
171
170
169
168
167
166
165
200 GeV,gut
R=-gut
L=0.26
500 GeV,gut
R=-gut
L=0.53
900 GeV,gut
R=1.26,gut
L=0
7.2 7.4 7.6 7.8 8 8.2
LHC (pb)
st-t
Tevatron (pb)
st-t
NNLO
t¯t
(pb) References
173.3 ± 10.1 [ATLAS-CONF-2012-134]
165.2 SM NNLO [hep-ph/1205.3453]
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 21 / 34
32. Forward-Backward Asymmetry vs Charge-Asymmetry
0.03
0.02
0.01
0
-0.01
-0.02
200 GeV,l A A =0.30
500 GeV,l R R =0.11
900 GeV,l N A =0.35
0.05 0.1 0.15 0.2 0.25 0.3
AC
AFB
Theory
0.03
0.025
0.02
0.015
0.01
0.005
0
-0.005
-0.01
200 GeV,gut
0.05 0.1 0.15 0.2 0.25
AC
AFB
R=-gut
L=0.26
500 GeV,gut
R=-gut
L=0.53
900 GeV,gut
R=1.26,gut
L=0
Theory
AC References
−0.013 ± 0.028(stat.)+0.029
−0.031(syst.) [CMS/1112.5100]
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 22 / 34
33. Spin-Correlation at Tevatron LHC
Spin-Correlation
0.26
0.25
0.24
0.23
0.22
0.21
0.2
0.19
0.18
0.17
0.16
0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6 0.62
LHC
Ct-t
Tevatron
Ct-t
200 GeV,l A A =0.30
500 GeV,l R R =0.11
900 GeV,l N A =0.35
0.26
0.25
0.24
0.23
0.22
0.21
0.2
0.19
0.18
0.17
0.16
-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6
LHC
Ct-t
Tevatron
Ct-t
200 GeV,gut
R=-gut
L=0.26
500 GeV,gut
R=-gut
L=0.53
900 GeV,gut
R=1.26,gut
L=0
Ct¯t
helicity References
0.24 ± 0.02(stat.) ± 0.08(syst.) [CMS/TOP-12-004-PAS]
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 23 / 34
34. Top-invariant mass and pT Distributions @ 7 TeV LHC
Top-Quark invariant mass
101
100
10-1
10-2
400 600 800 1000 1200 1400
(pb/20 GeV)
ds/dmt-t
mt-t
(GeV)
SM
200 GeV,l A A =0.30
500 GeV,l R R =0.11
900 Gev,l N A =0.35
Top-Quark pT
101
100
10-1
10-2
10-3
0 100 200 300 400 500 600 700
ds/dpT (pb/10 GeV)
pT (GeV)
SM
200 GeV,l A A =0.30
500 GeV,l R R =0.11
900 GeV,l N A =0.35
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 24 / 34
35. Color-Octet and Dijet @ 7 TeV LHC
Dijet invariant mass
104
103
102
101
100
10-1
10-2
10-3
200 400 600 800 1000 1200 1400 1600 1800
ds/dmjj (pb/50 GeV)
mjj (GeV)
SM
200 GeV,l A A =0.30
500 GeV,l R R =0.11
900 GeV,l N A =0.35
Dijet pT
103
102
101
100
10-1
10-2
0 50 100 150 200 250 300 350 400 450 500
(pb/10 GeV)
ds/dpTj
(GeV)
pTj
SM
200 GeV,l A A =0.30
500 GeV,l R R =0.11
900 Gev,l N A =0.35
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 25 / 34
37. Conclusion
Appreciable Contribution to At¯t
FB and Ct¯t
without transgressing 1- experimental
production cross-section at Tevatron
2 analysis: favorable focus points ⇒ Possible solution for AFB anomaly
Large parameter-region is allowed by 1- and 2- experimental observation for both s
and t- channel single top production
FCNC parameters are more sensitive for single top w.r .t pair-production
Consistent with the non-observability of large Same-sign top events
pT and invaraint-mass distribution of top and dijet production with experimental
data give some favorable parameters
Parameter space are consistent with t¯t
cross-section, measured charge asymmetry
and spin-correlation at LHC
The benchmark points are consistent with all the observables w.r.t low energy
stringent bounds from B and D physics
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 27 / 34
38. Update: p¯p ! YY ! jjjj
[arXiv: 1303.2699]
3-jets with ET 20 GeV and
Pjets ET 130 GeV
Within radius of R = 0.4
After trigger selection, at least 4 jets
with ET 15 GeV and || 2.4
✶✡✓
✶✡
▲ ❞t ❂ ❅❃❅ ❢❜ ➢❇ ♣♣ ❆❂❁❃❄❅ ❚❡❱ ✵✻✼ ✽✾✿❀❀
✺✡ ✶✡✡ ✶✺✡ ☛✡✡ ☛✺✡ ✸✡✡ ✸✺✡ ✹✡✡ ✹✺✡ ✺✡✡
❘✁✆✝✞✟✞☎✁ ✠✟✆✆ ✠❨ ✥✁✂✄☎✷❪
☞☞☞☞✌ ✍ ✎ ✏ ✑
➤
✒ ✒
➤✎✭ ✎
s
✶
❊✔✕✖✗✘✖✙ ✚✛✜✛✘ ✢✘ ✣✤✦ ✧★
❖✩✪✖✫✬✖✙ ✚✛✜✛✘
❊✔✕✖✗✘✖✙ ✚✛✜✛✘ ➧ ✯✮
❊✔✕✖✗✘✖✙ ✚✛✜✛✘ ➧ ✓ ✮
✧❈✚❈✫❈✰ ★❖
✪✘❈✕ ✱✲✢✫✳ ✴★❖
♣♣ ❋ ●● ❋ ❉❉❉❉
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 28 / 34
39. THANK YOU ALL !!
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 29 / 34
40. BACKUP SLIDES
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 30 / 34
41. Issues!!
Anomaly cancellation in Axi-gluon case and |gq
A| |gt
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 the
structure 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 of
coupling is forbidden if we assume that strong interactions (QCD) is parity
conserving while in case of coloron, gauge invariance protect this kind of interaction
terms with dimension 4 or less [Zerwekh, Rosenfeld arXiv: 0103159] (however
possible to construct such non-renormalizable dimension-6 interaction [Chivukula et
al arXiv: 0109029])
Coloron production via gluon-fusion (one-loop) is typically 4 orders of magnitude
smaller 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
42. 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 small
results 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
43. 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 small
results 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
44. 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 small
results no strong bounds
CC sector can be controlled by align the mixing matrix with CKM
Ref. [arXiv: 1101.5203]
Bd (Bs ): MG′ (100TeV) CD
L,312
R,312
+ CD
L,31CD
− 27CD
R,311/2
D − ¯D
: MG′ (600TeV) CU
L,212
R,212
+ CU
L,21CU
R,211/2
− 60CU
etc...
Mukesh Kumar (University of the Witwatersrand) Top Quark Physics in the Vector Color-Octet Model September 2, 2014 32 / 34