This document discusses potential deviations from the standard model in top quark pair production (ttbar) due to beyond standard model (BSM) physics. It summarizes that ttbar production is well measured but sensitive to BSM effects like resonant contributions from new particles that decay to top quark pairs. Non-resonant effects are also possible and can be parameterized using effective field theory operators. The document provides examples of limits set on specific BSM models like Z' bosons by the CMS experiment through analyses of the ttbar invariant mass spectrum and other observables.
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.
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.
In this lecture, I will describe how to calculate optical response functions using real-time simulations. In particular, I will discuss td-hartree, td-dft and similar approximations.
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.
D. Mladenov - On Integrable Systems in CosmologySEENET-MTP
Lecture by Prof. Dr. Dimitar Mladenov (Theoretical Physics Department, Faculty of Physics, Sofia University, Bulgaria) on December 7, 2011 at the Faculty of Science and Mathematics, Nis, Serbia.
Multiscale methods for next generation graphene based nanocomposites is proposed. This approach combines atomistic finite element method and classical continuum finite element method.
Localized Electrons with Wien2k
LDA+U, EECE, MLWF, DMFT
Elias Assmann
Vienna University of Technology, Institute for Solid State Physics
WIEN2013@PSU, Aug 14
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)
"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.
In this lecture, I will describe how to calculate optical response functions using real-time simulations. In particular, I will discuss td-hartree, td-dft and similar approximations.
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.
D. Mladenov - On Integrable Systems in CosmologySEENET-MTP
Lecture by Prof. Dr. Dimitar Mladenov (Theoretical Physics Department, Faculty of Physics, Sofia University, Bulgaria) on December 7, 2011 at the Faculty of Science and Mathematics, Nis, Serbia.
Multiscale methods for next generation graphene based nanocomposites is proposed. This approach combines atomistic finite element method and classical continuum finite element method.
Localized Electrons with Wien2k
LDA+U, EECE, MLWF, DMFT
Elias Assmann
Vienna University of Technology, Institute for Solid State Physics
WIEN2013@PSU, Aug 14
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)
"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.
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.
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
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
"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.
Wits Node Seminar: Dr Sunandan Gangopadhyay (NITheP Stellenbosch)
TITLE: Path integral action of a particle in the noncommutative plane and the Aharonov-Bohm effect
"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
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.
Neil Lambert - From D-branes to M-branesSEENET-MTP
Lecture by prof. dr Neil Lambert (Department of Mathematics, King’s College, London, UK & CERN, Geneva, Switzerland) on October 22, 2010 at the Faculty of Science and Mathematics, Nis, Serbia.
Computation of electromagnetic fields scattered from dielectric objects of un...Alexander Litvinenko
Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization the number of MC samples has to be large. In this work, to address this challenge, the continuation multilevel Monte Carlo (\CMLMC) method is used together with a surface integral equation solver.
The \CMLMC method optimally balances statistical errors due to sampling of
the parametric space, and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine.
The number of realizations of finer discretizations can be kept low, with most samples
computed on coarser discretizations to minimize computational cost.
Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme.
Singular rise and singular drop of cutoff frequencies in slot line and strip ...ijeljournal
The complete frequency spectrum of the circularly- shielded slot line and strip line are determined using an efficient domain decomposition and mode matching method. Asymptotic analyses show that, when the gap width of the slot line or the width of the strip line are too small, the TE frequencies may drop singularly and the TM frequencies may rise singularly. These new properties greatly affect the cutoff frequencies.
SINGULAR RISE AND SINGULAR DROP OF CUTOFF FREQUENCIES IN SLOT LINE AND STRIP ...ijeljournal
The complete frequency spectrum of the circularly- shielded slot line and strip line are determined using an efficient domain decomposition and mode matching method. Asymptotic analyses show that, when the gap width of the slot line or the width of the strip line are too small, the TE frequencies may drop singularly and the TM frequencies may rise singularly. These new properties greatly affect the cutoff frequencies.
SINGULAR RISE AND SINGULAR DROP OF CUTOFF FREQUENCIES IN SLOT LINE AND STRIP ...ijeljournal
The complete frequency spectrum of the circularly- shielded slot line and strip line are determined using an
efficient domain decomposition and mode matching method. Asymptotic analyses show that, when the gap
width of the slot line or the width of the strip line are too small, the TE frequencies may drop singularly and
the TM frequencies may rise singularly. These new properties greatly affect the cutoff frequencies.
Computation of electromagnetic fields scattered from dielectric objects of un...Alexander Litvinenko
Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization the number of MC samples has to be large. In this work, to address this challenge, the continuation multilevel Monte Carlo (\CMLMC) method is used together with a surface integral equation solver.
The \CMLMC method optimally balances statistical errors due to sampling of
the parametric space, and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine.
The number of realizations of finer discretizations can be kept low, with most samples
computed on coarser discretizations to minimize computational cost.
Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme.
New folderelec425_2016_hw5.pdfMar 25, 2016 ELEC 425 S.docxcurwenmichaela
New folder/elec425_2016_hw5.pdf
Mar 25, 2016
ELEC 425 Spring 2016 HW 5 Questions
due in class on Tue Mar 31, 2016
1) Read Sec. 1.11 from the textbook. Use the conventions plotted on Fig. 1.42 to derive the TM
matrix in Eq. 1.253.
2) The file Tmatrix.m is a Matlab script that evaluates the reflection and transmission coefficients
for TE and TM polarizations. Analyze the code, and write a script that uses Tmatrix.m to
generate Fig. 3 from Winn1998.pdf file. When the output from the Matlab code is overlaid with
Fig. 3 from the paper, they should match exactly as shown below. Note the dB scale in the
figure.
3) Read the following tutorial from the Lumerical website.
https://kb.lumerical.com/en/diffractive_optics_stack.html
First, run and verify the tutorial. Then, modify the tutorial files so that you simulate 0° and 45°
results from Fig. 3 of the Winn1998.pdf paper as shown above. The structure is composed of a
total of 12 layers: air on the entrance and exit sides, and five repetitions of two quarter wave
(𝑑1 + 𝑑2 =
𝜆1
4
+
𝜆2
4
= 𝑎) layers of refractive index 𝑛1 = 1.7 and 𝑛2 = 3.4 and thicknesses 𝑑1
and 𝑑2. Export your simulation results, import them into Matlab, and plot the output from part
2) with the output from Lumerical FDTD on the same plot. Verify that FDTD code results in a
similar set of results.
Please hand in your derivations, your plots and the relevant code used to generate the plots all
stapled together.
You can find the required files under the Handouts section on the course website at:
http://courses.ku.edu.tr/elec425
https://kb.lumerical.com/en/diffractive_optics_stack.html
http://courses.ku.edu.tr/elec425
New folder/PhotonicsLaserEngineering.pdf.part
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.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
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.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
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.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
"When the top is not single: a theory overview from monotop to multitops" to be presented by Prof. Aldo Deandrea (IPN Lyon, France)
1. When the is not “single”: !
eoretical overview!
based on A.D. & N.Deutschmann, JHEP 1408 (2014) 134 (arXiv:1405.6119)!
and I.Boucheneb, G.Cacciapaglia, A.D., B.Fuks arXiv:1407.7529 !
Aldo Deandrea!
Université Lyon 1 & IUF
School of Physics, University of the Witwatersrand
October 21st 2014
1
2. An experimental and theory hot subject
(a long quest in just few lines)
• Discovery of the quark in 1995 at TeVatron in pair production!
• The heaviest elementary particle, its mass affects precision EW fits !
• vacuum stability (with a wild extrapolation though…) !
• Related large coupling to the : probe electroweak symmetry breaking!
• Now data is driven by LHC measurements!
• Good agreement with the SM (except large FB asymmetry in tt̄ @ TeVatron)!
• Perfect tool to probe BSM physics
2
3. Look for BSM in physics
• precision top mass measurements !
• single top (not discussed here)!
• tt̄ observables!
• 3 tops and more (multi-tops)!
• same charge tops!
• monotop!
• asymmetries!
• heavy top partners (vector-like)
3
4. is The simplest special Higgs mechanism for SM is not SM stable with & respect
BSM
to quantum corrections (naturalness problem)
Loop corrections to the Higgs mass
The simplest Higgs mechanism SM is not stable with respect
to quantum corrections (naturalness problem)
Loop corrections to the Higgs mass
2 mH 2
2
6. 2
• top enters the loop correction to the Higgs mass with a large
contribution
ĵmH 160 GeV (95% CL limit on SM Higgs)
Ʈ ~ 1 TeV
GmH 2
3GF
4 2S 2 2mW 2
H m2 2
m 4m2
8. 2
Z
t
Ʈ ~ 1 TeV
ĵmH 160 GeV (95% CL limit on SM Higgs)
Top plays a special role in most of BSM models
• In susy stop (top-partner) cancel quadratic dependence
In MSSM stop (top partner) helps to cancel ȁ2 dependence
4
GmH 2
3GF
4 2S 2 2mW 2
mZ
4mt
In SM there is no symmetry which protects a strong dependence of
Higgs mass on a possible new scale
Something is needed in addition to the SM top… = Rather light top partner
is one of the most robust prediction to resolve the hierarchy problem
One might expect deviations from the SM predictions in the top sector.
In SM there is no symmetry which protects a strong dependence of
Higgs mass on a possible new scale
Something is needed in addition to the SM top… = Rather light top partner
is one of the most robust prediction to resolve the hierarchy problem
=
One might expect deviations from the SM predictions in the top sector.
1. MH is protected!
In MSSM large top (stop) loop corrections shift after renormalization the upper
9. “Natural” theories
• natural if b(λ,g)=0 by a symmetry!
• can be natural if Λ is a physical cut-off (ex.
compositness)!
• quasi-natural if b(λ,g)=0 perturbatively (ex. at one-loop
in Little Higgs for top contribution)!
• tuned: any special value you like, even m0=0 Λ=0
(classically conformal)
5
10. is special for BSM physics
!
• Composite models (technicolor, effective lagrangians like
little Higgs, topcolor…):!
• top effective 4 fermion operators!
• vector-like top partners!
• Extra-dimensional models:!
• KK-modes of top and gluons!
• Xdim realisations of composite models!
• in warped models wave function profile
superposition “explains” Yukawa strength
6
11. BSM uses of the top quark
• triggering electroweak symmetry breaking!
• top-color, top see-saw models!
• top partners (scalars in susy, fermionic in composite models,
little higgs, extra-dimensional models)!
• mixing of the top with new (vector-like) heavy quarks!
• flavour changing couplings!
• new particles may couple to the top quark (heavy gluon,
Z’…)!
• top-Higgs interactions, top portal sectors
7
12. Counting ’s and BSM physics
• Very simple plan for the talk:!
• 2 tops (modifications to tt̄ and t̄t̄)!
• 3 tops (MSSM, Z’,topcolor…)!
• 4 tops (many BSM models studies)!
• 6 tops !
• 8 tops (and why we stop here)!
• Exception to the previous rule: monotop
8
13. present only few pioneering experimental analyses have started to focus on related final states
(see for example [1] which considers an 8-jet final state), but one could extend these analyses
to top quarks. As the number of particles grows, the size of the available phase space shrinks
SM cross sections
109
108
107
106
105
104
103
102
101
100
10-1
10-2
10-3
10-4
10-5
pp→2t [NLO]
pp→4t [NLO]
• multi-top (more than 2) cross-sections are small
in the SM while can be enhanced in BSM
9
from 1405.6119
10-6
8 14 25 45 75 100
σ[fb]
√s[TeV]
pp→6t [LO]
MadGraph5_aMC@NLO
Figure 1. Multitop production cross-sections in the Standard Model as a function of the centre of
mass energy for the colliding protons. The simulations were carried out using Madgraph5 aMC@NLO
[16] and the error bands reflect the scale uncertainty.
and one can guess that there is a limit on the number of top quarks which can be produced
in a single observable event. In the Standard Model, this number however lies well below
the naive estimate Nmax =
ps
mt ⇡ 80 for ps = 14 TeV, and as Figure 1 shows, there is little
hope to see more than 4 tops at the LHC. Even beyond the Standard Model the maximal top
multiplicity observable at the LHC stays much smaller than Nmax.
14. - bar
• tt̄ strong production with large and well measured cross-section
and shape!
• gluon fusion dominant (90% at 14 TeV LHC)!
• detailed theoretical description available !
• BSM in resonant and non-resonant effects!
• tt̄ invariant mass is particularly sensitive to BSM
10
15. - bar in BSM
Figure 11: Invariant t¯t spectrum for pp → t¯t including a s-channel Z′ color singlet vector
boson and color octet (axial) vector bosons with masses mX = 2000 GeV that couples
with standard model strength to quarks. Solid QCD t¯t production, dotdashed with a color
singlet (Z′), dotted with a color octet axial vector (axigluon g∗
Figure 12: Invariant t¯t spectrum for pp → t¯t including s-channel gravitons. The distribu-tions
from 0712.2355 Frederix Maltoni
show the effect of the almost degenerate tower of KK gravitons in the ADD model
with n = 3 extra dimensions and, from top to bottom, with a cutoff scale MS = 800, 900,
1100 and 1300 GeV. The bottom line are contributions from SM only. We used CTEQ6L1
and set the scales to μR = μF = mt.
• resonant contributions from:!
• spin 0, 1, 2!
• color singlets, octets!
• parity even and odd states
A), dashed with a color octet
is now solved with only a minor fine-tuning of κR ≃ 12. After KK compactification of the
massless graviton field, the coupling constant of KK gravitons with matter is given by the
inverse of Λ.
A prediction in the RS model is that the masses of the KK modes mn are given by
n = xnκe−πκR, where xn are the positive zero’s of the Bessel function J1(x). If one of the
masses is given, all the others are fixed, which could give rise to a series of resonances in
the t¯t invariant mass spectrum.
In Fig. 13 the effect of a series of KK graviton modes on the t¯t invariant mass spectrum
is shown with m1 = 600 GeV and for various ratios κ/Mpl. The resonances are clearly
visible over the QCD background. Higher KK states are characterized by larger widths.
4 Spininformationfrom(anti-)topquarkdirections
A useful, yet 11
simple, quantity sensitive to the spin of the intermediate heavy state into a
tt ¯pair, is the Collins-Soper angle θ [66]. This angle is similar to the angle between the top
vector boson (KK gluon/coloron g∗
V ). All plots were produced using the CTEQ6L1 pdf set
with μR = μF = 2000 GeV. No cuts were applied in making any of the plots.
3.2 Spin-1 resonances
In this section we discuss a spin-1 resonance produced by qq ¯annihilation. This resonance
can either be a color singlet or a color octet. For the color octet case we distinguish between
m2
a vector and an axial-vector. Although both the vector and the axial-vector interfere with
the QCD tt ¯production, only the vector shows interference effects in the tt ¯invariant mass
spectrum.
Including an s-channel color singlet vector boson (a “model-independent” Z′) in the t¯t
production process gives a simple peak in the invariant mass spectrum as can be seen from
the dot-dashed line in Fig. 11. The precise width and height of the peak depends on the
model parameters in the model for the Z′. As a benchmark we show a Z′ vector boson
with mass mZ′ = 2 TeV that couples with the same strength to fermions as a standard
model Z boson. The interference effects with the SM Z boson can be neglected in the t¯t
channel, so the peak is independent of the parity of the coupling.
In general, for the color octet spin-1 particles the interference with the SM t¯t production
16. while the forward-backward asymmetry will only receive a contribution proportional to
- bar in BSM
• generic BSM effects in the top sector can also be encoded in
effective operators!
• for tt̄ production 2 classes (Degrande et al. 1010.6304)!
• tt̄g, tt̄gg!
• 4 quark operators
(tt̄ and 2 light quarks)
−
g t
12
c′
Aa = (ctu − ctd)/2 − (cQu − cQd)/2 + c(8,3)
Qq . (18)
and spin-dependent observables will depend on (see App. C)
c′
Av = (ctu − ctd)/2 − (cQu − cQd)/2 − c(8,3)
Qq . (19)
Numerically, we shall see in Section 3.2 that the isospin-0 sector gives a larger contribution
to the observables we are considering than the isospin-1 sector. This is due to the fact that a
sizeable contribution to these observables is coming from a phase-space region near threshold
where the up- and down-quark contributions are of the same order.
It is interesting to note that, in composite models, where the strong sector is usually
invariant under the weak-custodial symmetry SO(4) → SO(3) [41], the right-handed up
and down quarks certainly transform as a doublet of the SU(2)R symmetry, and therefore
cQu = cQd. There are however various ways to embed the right-handed top quarks into
a SO(4) representation [32]: if it is a singlet, then ctu = ctd also and the isospin-1 sector
reduces to the operator O(8,3)
Qq only.
In summary, the relevant effective Lagrangian for t¯t production contains a single two-fermion
operator and seven four-fermion operators conveniently written as:
Lt¯t = +
1
Λ2
(chgOhg + h.c.) + (cRvORv + cRaORa + c′
Rr
O′
Rr + R ↔ L) + c(8,3)
Qq
#
. (20)
O(8,3)
Qq
The vertices arising from the dimension-six operators given in Eq. (20) relevant for top
pair production at hadron colliders are depicted in Fig. 1.
−
t
t
g
t
g
Chromomagnetic operator Ohg = (H ¯Q)σμνT At GA μν
q
−
q
−
t
t
Four-fermion operators
Figure 1: A Feynman representation of the relevant operators for t¯t production at hadron colliders.
6
17. vertical dash-dotted line indicates the transition between the resolved and boosted analyses.
Table 3 shows additional model-specific limits. The combination of the semi-leptonic and all-hadronic
boosted analyses improves the expected cross section limits at 2 TeV by ⇠25%. Com-pared
to the results of previous analyses [20–23] for specific models [7, 10], the lower limits on
- bar exclusions examples
the masses of these resonances have been improved by several hundred GeV. For the semi-leptonic
gluon fusion with no interference with the SM background, the cross section limits are 0.8 pb
and 0.3 pb for a spin-zero resonance of mass 500 GeV and 750 GeV, respectively. These are the
first limits at CMS for heavy Higgs-like particles decaying into tt.
from Table 3: 95% CL lower limits on the masses of new particles in specific models.
the predictions are multiplied by a factor of 1.3 to account for higher-order effects vertical dash-dotted line indicates the transition between the resolved and boosted Table 3 shows additional model-specific limits. The combination of the semi-leptonic boosted analyses improves the expected cross section limits at 2 TeV by ⇠25%. to the results of previous analyses [20–23] for specific models [7, 10], the lower the masses of these resonances have been improved by several hundred GeV. For resolved analysis, assuming a spin-zero resonance with narrow width, produced gluon fusion 13
with no interference with the SM background, the cross section limits and 0.3 pb for a spin-zero resonance of mass 500 GeV and 750 GeV, respectively. These resolved analysis, assuming a spin-zero resonance with narrow width, produced via
0.5 1 1.5 2 2.5 3
from CMS 1309.2030
[TeV] Z' M
× B(Z' → tt) [pb] Z' Upper limit on σ
102
10
1
10-1
10-2
-3 10
Expected (95% CL)
Observed (95% CL)
Z' 1.2% width
±1σ Expected
±2σ Expected
, s = 8 TeV -1 CMS, 19.7 fb
resolved
analysis
boosted
analyses
Figure 2: The 95% CL upper limits on the production cross section times branching fraction as a
function of Mtt for Z0 resonances with GZ0/MZ0 = 1.2% compared to predictions from Ref. [10]
multiplied by 1.3 to account for higher-order effects [43].
In addition to investigating possible resonant new physics Model that causes a non-resonant Observed structures Limit in the Expected Mtt spectrum, Limit
the presence of
enhancement of the Mtt spectrum is also tested. The
boosted all-Z0, hadronic GZ0/MZ0 analysis = 1.2% is used to set limits 2.1 TeV on such new production 2.1 TeV
for events with
Mtt 1 TeV, Z0, since GZ0/the MZ0 NTMJ = 10% background can 2.7 be TeV predicted entirely 2.6 from TeV
data. The limit is
expressed as RS a ratio KK of gluon the total SM + BSM tt cross section to the SM-only defined in Ref. [20]). The efficiency to select SM 2.5 tt events TeV with Mtt 1 2.4 TeV TeV
cross section (S, as
is (3.4±1.7)⇥10−4.
We find S 1.2 at the 95% CL, with a credible interval of 1.1–2.0 at 68% CL, a factor of two
improvement over the previously published limits [20].
In summary, we have performed searches for anomalous tt production using events in the semi-leptonic
and all-hadronic topologies. In addition to new limits on nonresonant enhancements
ATLAS-CONF-2013-052
3 10
2 10
10
1
-1 10
s = 8 TeV
0.5 1 1.5 2 2.5
mass [TeV]
g
KK
A tt) [pb]
KK
× BR(g
KK
mg
-2 10
Obs. 95% CL upper limit
Exp. 95% CL upper limit
Exp. 1 m uncertainty
Exp. 2 m uncertainty
Kaluza-Klein gluon (LO)
ATLAS Preliminary
-1 L dt = 14.3 fb
0
18. availability of valence antiquarks in antiprotons boosting the q¯q production channel: quark
annihilation processes constitute 87% of top quark production at the Tevatron. Secondly,
the asymmetric beam conditions (proton-antiproton) also make the measurement easier
as the direction of the quark and antiquark are predictable. Hence, the top quark charge
asymmetry appears as a forward-backward asymmetry at the Tevatron, as shown in Figure
1.21. More top quarks are expected in the forward direction, while more antitop quarks
are produced in the backward direction.
- bar charge asymmetry
Tevatron LHC
0 y 0 y
Figure 1.21 – Distribution of top quarks and antitop quarks as a function of rapidity y,
for the Tevatron (left) and the LHC (right) collisions.
• TeVatron: q (anti-q) mostly from proton (antiproton) → AFB!
• LHC: average quark momentum fraction xqxanti-q →
central-peripheral asymmetry AC!
• BSM: new particles with different V,A couplings affect
asymmetries
At the LHC, the direction of the incoming quark and antiquark is not known, since it
collides protons. Hence, a forward-backward asymmetry does not occur in the lab-frame,
the terms forward and backward would have to be defined per event, which is impossible
in practice. Moreover, the contribution of gluon fusion is large (80%, √s = 7 TeV),
diluting the asymmetry in the first place. The top quark charge is measurable, however.
In proton-proton collisions, the antiquark in q¯q production is a sea quark that has lower
fractional momentum than an valence quark. That means that the top quark that is
produced in such an event (which, due to charge asymmetry, is emitted preferentially
in the direction of the incoming quark), traverses a path closer to the z-axis than the
antitop quark. Hence, there are more top quarks expected in the forward direction (large
rapidity) and more antitop quarks in the central direction (low rapidity).
In 2011, the CDF collaboration measured deviations from Standard Model at the level
up to 3.4σ in some parts of phase space [43]:
14
19. - bar charge asymmetry
AC (mtt 600 GeV)
15
0.08
0.06
0.04
AC
0.02
0
Gμ
ATLAS
0 0.1 0.2 0.3 0.4 0.5
AFB
-0.02
CMS
CDF
D0
ATLAS
SM
φ
W′
Models from:
ω4 Ω4
PRD 84 115013,
JHEP 1109 (2011) 097
0.15
0.10
0.05
0
Models from:
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
AFB (mtt 450 GeV)
-0.05
ATLAS
CDF
ATLAS
SM
φ
W′
ω4
Ω4
Gμ
PRD 84 115013,
JHEP 1109 (2011) 097
Figure 3. Measured forward–backward asymmetries AFB at Tevatron and charge asymmetries
AC at LHC, compared with the SM from predictions ATLAS (black 1311.6724
box) as well as predictions incorporating
various potential new physics contributions (as described in the figure) [8, 60]. In both plots, where
present, LHC the horizontal compatible bands and lines correspond to the ATLAS (light green) and CMS (dark
green) measurements, while the vertical ones with correspond SM to expectations
the CDF (orange) and D0 (yellow)
measurements. The inclusive AC measurements are reported in the left plot. In the right plot a
comparison is reported between the AFB measurement by CDF for mtt ¯ 450 GeV and the AC
measurement for mtt ¯ 600 GeV.
20. Same charge
• Example in RPV models (from Durieux et al.
1210.6598)!
• @LHC qq initial states dominate over qbar-qbar
might also give rise to a negative Acharge asymmetry in NP production rates of same-sign
¸¸flavor-changing neutral currents and a anew b heavy down-type quark denoted by bÕ that couples
Example of (B;L) = (±1,±3) process with ALQ
0 in our leptoquark simplified model. (c)
eμ ones and this asymmetry propagates in
the final state
16
B;L) = (±2; 0) processes with ARPV
eμ Æ 0. Quark (gluon) initiated transitions are likely
therefore resonate.
found that same-sign
asymmetry in their
discriminate be-tween
SM backgrounds
been illustrated
leptoquark setting
supersymmetric model.
[11] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, and T. Stelzer,
JHEP 1106, 128 (2011), arXiv:1106.0522 [hep-ph].
[12] E. Nikolidakis and C. Smith, Phys.Rev. D77, 015021 (2008),
arXiv:0710.3129 [hep-ph].
[13] S. Chatrchyan et al. (CMS Collaboration), (2012),
arXiv:1212.6194 [hep-ex]; ATLAS-CONF-2012-105 (Aug
2012).
21. 3 s in the SM
• 1.9 fb @ 14TeV LHC!
• odd number of tops requires the tbW vertex!
• 3 tops + (W, jets, b)
17
from 1001.0221!
Barger et al.
22. 3 s examples in BSM
susy Z’
18
topcolor!
from 1203.2321
from 1001.0221!
Barger et al.
πt,ht 휌
• in susy can be enhanced if light stops and not too heavy gluino!
• Z’ signal is due to FCNC vertex (Z’ should be leptophobic)!
• simple topcolor models also face FCNC limits
23. gg ! t¯tt¯t (85% at the LHC at 7 TeV)
Final limit conclusions
Models with New Physics involving 4-top quarks
g ¯t
4 s in the SM
g ¯t
t
¯t
g
t
¯t
¯t
g
t
¯t
• gg dominant on qqbar at LHC!
• small cross-section in the SM (0.5 fb @7 TeV)
19
production in SM
(85% at the LHC at 7 TeV)
g
t
¯t
¯t
g
¯t
(15%)
q
¯q
g
g
g
¯t
t
t
Daniela Paredes New Physics in events with 4 top quarks 4/ 36
¯t
q¯q ! t¯tt¯t (15%)
q
¯q
g
g
g
¯t
t
t
Daniela Paredes New Physics in events with 4 top quarks 4/ 36
24. 4 s in BSM
• quite a number of BSM
models (SS tt applies too,
see 1203.5862):!
• heavy gluon (octect)!
• heavy photon (color
singlet) (ex. 2-xdim
models) pair produced
and decaying to tt̄ tt̄
Aguilar-Saavedra !
Santiago 1112.3778
Cacciapaglia et al. !
1107.4616
20
e±e± μ±μ± e±μ±
Fake 1.0+0.6
−0.7 1.7+0.7
−0.6 3.8+1.9
−1.8
Charge flip 0.6+0.3
−0.1 0+0.1
−0.0 0.7+0.3
−0.1
Real 2.7+0.7
−1.5 2.6+0.7
−0.9 6.7+1.3
−3.1
Total 4.4+0.5
−0.7 4.3+0.9
−1.1 11.2+2.5
−3.6
Data 3 3 12
TABLE I: Predicted number of SM background events and
observed data with two same-sign leptons, at least two jets,
MET 40 GeV and HT 350 GeV, adapted from Ref. [15].
Uncertainties are statistical and systematic in quadrature.
= 0.02 and results in an upper limit of σ 800 fb at
95% confidence level [15]. Therefore N 16.6 at 95%
confidence level. Applying this limit to derive a cross-section
limit for an arbitrary process requires knowing
selection efficiency (ϵ) for the model of interest.
We simulate four-top-quark production using mad-graph
[17], with pythia [18] for showering and
hadronization and detector simulation with a parametric
fast simulation tuned to match ATLAS performance [20],
g
g
g
t
t
t
¯t
¯t
g
ρs, ρo
t
¯t
t
¯t
g
ρs, ρo
t
¯t
¯t
g
ρo
ρo
25. multi s in BSM
• multitops = more than 4 top quarks in the final state!
• how many tops at LHC can be detected (in a single
event)? surely (much) less than √s̅/mt ͠ 80 at 14 TeV
LHC!
• are 6, 8… tops constrained by present measurements?
can have more?!
• what BSM physics?!
• see 1405.6119 for more details
21
26. 6 s in BSM
• you just need a T (top-partner) and a Z’ (mT mZ’ + mt)!
• coloured Z’ is more constrained!
• possible colour SU(3) embeddings in the table
22
Figure 1. Six top production mechanism
RZ0 RT
R1 1 3
R2 8 3
R3 8 ¯6
R4 8 15
Table 1. All possible colour embeddings for T and Z0 in the topology of Figure 1
Kinematic Distributions
Figure 1. Six top production mechanism
RZ0 RT
R1 1 3
R2 8 3
R3 8 ¯6
R4 8 15
Table 1. All possible colour embeddings for T and Z0 in the topology 3.2 Kinematic Distributions
As usual with models involving a high-mass new particle, the process involves a high total transverse energy HT . The bulk of the distribution energies as MT grows (Figure 2(a)), and so with ps, in a milder even at the kinematic limit and 8 TeV, it is largely sucient for
27. Hard cuts on6ET and HT can be implemented to drastically reduce the QCD background,
whilst doing little harm on the simulated signal, which already provides rather promising
limits on the parameter space.
6 s bounds
We performed a parameter scan in the plane MT, MZ0 in the minimal colour embedding
model and have been able to exclude the region lying below MT 710 GeV as shown in
Figure 3. The computations were carried out with MadGraph [13] and Pythia [14], and the
subsequent analysis was performed in Madanalysis [15]. This limit can be extrapolated to the
more unusual colour structures by multiplicating the signal yield by the correct colour factor
in the approximation where we neglect colour correlation e↵ects.
• if Z’ coloured just check your 4 top analysis (Z’
pair production is larger, mT mZ’ + mt and
typically colour factor advantage)!
• if Z’ colour singlet
2SSL give bounds:
1
(recasting CMS
1212.6194)
0.1
2Σ
0.01
600 700 800 900 1000 1100
23
0.001
MT
CLS
(a)
900
800
700
600
500
400
2σ
1σ
allowed
600 700 800 900 1000 1100
MT
MZ'
(b)
Figure 3. (a): CLs confidence level in a scan over MT with MZ0 = 400 GeV. (b): Limits in the plane
28. 8 s in BSM
• you need a ρ, a T and a Z’ (mρmT mZ’ + mt)!
• ρ octet, T triplet and Z’ singlet (all previous cases also
possible but constrained as in 6 tops)!
• 8 tops from pair production of ρ colour octets!
• no bounds from present
2SSL data for a 800 GeV ρ
(bkg compatible)!
• closing the window on top
multiplicity is a matter of
int. luminosity and dedicated
searches
24
Figure 7. Four top production by Z0-Strahlung
3.4 Perspectives at 14 TeV
29. Monotop
• production of a single top plus missing energy (not
necessarily a DM particle), first introduced in 1106.6199
(J.Andrea, B.Fuks, F.Maltoni)!
• can be resonant (coloured boson, as R violating SUSY) or
flavour changing:
¯ di
χ
ui
V
• general effective Lagrangian description, but what SM
embedding? (work with Boucheneb, Cacciapaglia, Fuks;
ATLAS preliminary analysis)
25
S
¯ dj
t
t
g
t
FIG. 1: Representative Feynman diagrams leading to mono-top
signatures, through the resonant exchange of a colored
scalar field S (left) and via a flavor-changing interaction with
a vector field V (right). In these two examples, the missing
energy is carried by the V and χ particles. More diagrams
with, for example, t-channel and s-channel exchanges for the
two type of processes respectively, are possible.
fermion, vector or tensor), presence of an intermediate a model-independent all cases within a single spirit as Ref. [12]. Assuming flavor-conserving, as in interactions are denote by φ, χ and V vectorial missing energy and X scalar and vector representation of monotop production.simplified modeling of possible s, t, u exchanges The corresponding effective
30. complete association SU(2) with representations, a charged #:
and.....
uL ¯dL ¯ ! '−1/3
uL¯uL ¯! '−4/3
t,d 1/3
4/3
T t , 't , 't }analysis shows that the couplings to right-handed or left-handed down-quarks erent structure, and must necessarily come from two di↵erent scalar fields. One 1
2 Monotop t ! tL/R- #resonant
t ! tR#where the latter process is only present in the case of a triplet. As the splitting between various components of # are expected to be very small, these extra processes will contribute
to the monotop signatures, and cannot be ignored in the analysis.
Embedding in the SM gauge structure
• spin zero couples to spinors with opposite chirality, but 훗1 is
a singlet, 훗2 a triplet of SU(2), so two different fields:
Furthermore, in the doublet case where the scalar couples to the left-handed coupling to the bottom is also generated: this will induce a fast decay of the neutral a virtual '−1/3
• similar argument in decay: need t plus a singlet, 훗1 ok, but
훗2 into t plus a multiplet (so not only a neutral long-lived
state).!
• spin 1 to spinors with same chirality:
VXμ dC
¯ R$μdL + h.c. In order for so Xsuch μ is (couplings 2,1/6) and to 휒 be can SU(decay 2) invariant, to Xμ b, X no must monotop!
belong to a doublet with 1/6:
26
Spin-0 case: '
scalar can only couple to two fermions with opposite chirality, therefore the coupling down-type quarks can only have the form
$1
S'1 ¯ dC
RdR + $2
S'2 ¯ dCL
dL ; where in fact dC
R is a left-handed quark, while dCL
is right handed. Now, ¯ dC
RdR transforms singlet of SU(2) with hypercharge −2/3, therefore '1 must also transform as a singlet hypercharge 2/3; analogously, ¯ dCL
dL belongs to the triplet combination of the two doublets. In summary, '1 and '2 are necessarily two di↵erent fields, transforming
¯ dC
RdR = (1,−2/3) ) '1 = (1, 2/3) = '2/3
s ¯ dCL
dL 2 (3, 1/3) ) '2 = (3,−1/3) = {'2/3
t
#0
d ! bL('1/3
t )⇤ ! bLuLdL , thus losing the missing energy in the signal.
Spin-1 case: Xμ
A spin-1 boson couples to spinors of the same chirality, therefore the only allowed couplings
to down quarks are
1
VXμ ¯ dCL
$μdR + 2
μ ,X−1/3
μ }T . Xμ 2 (2, 1/6) = {X2/3
31. additional constraints will come from the requirement that the particle into is a good candidate for Dark Matter, or that at least it does not overpopulate
⇣
⌘
aR VμtR¯!μuR + aL Vμ(tL¯!μuL +L!μdL) + h.c.
, (where the aL,R Monotop parameters denote the - strengths nonresonant
of the interactions of the V -field with and top quarks. As in the rest of this section, we have restricted ourselves to interactions
focusing on the monotop hadroproduction modes enhanced by parton b
¯densities.
• the flavour changing boson V should be long-lived
or have invisible decay V→휒휒!
The Lagrangian terms of Eq. (2.21) open various decay channels for the V -field. First,
the left-handed couplings allow the mediator to always promptly decay into jets, b ¯ d + d¯b
. Next, the importance of the decays into top and up quarks (this time both in context of left-handed and right-handed couplings) depends on the mass hierarchy between
the mediator and the top quark, the tree-level decay V ! t¯u+u¯t being only allowed mV • spin zero: ɸ a doublet of SU(2), disfavoured
• spin 1, can be singlet
• 휒 as a DM candidate is constrained both by
relic abundance and by LHC
Spin-In this case, one can allow for coupling with two right-handed or two left-handed mt. Furthermore, when mV mt, a triangle loop-diagram involving a W-boson
both couplings, a Vμ which is a singlet of SU(2) is allowed:
could also contribute to the decay of the V -field into a pair of jets, V ! di dj ¯ . Finally, mW mV mt, the three-body decay channel V ! bW+u+¯¯bWu is open, mediated a virtual top quark. A monotop signal is thus expected only when the V -field is invisible
and dominantly decays into a pair of dark matter particles. Since V is an electroweak
singlet, the associated couplings can be written, in the case of fermionic dark matter, LV !! W−[!+]⇤ ! W−¯0 bu . model, therefore, one would expect that the scalar !0 is invisible because of stable neutral particles. However, being ! a doublet of SU(2), it must aRVμ¯tR!μuR + aLVμ(¯tL!μuL +¯b
L!μdL) + h.c. . The left-handed coupling generates fast decays Vμ ! b ¯ d, thus decays into invisible are always required. If only the right-handed coupling is allowed, the situation complicated: in fact, for mV mt, one would have three-level decays Vμ ! mV ⇣
⌘
gR ¯μR!R + gL ¯!μLL
, (where is a Dirac fermion, singlet under the Standard Model gauge symmetries. consistency of the model, i.e., the requirement that V always mainly decays into a pair 27
-fields and not into one of the above-mentioned visible decay modes, implies constraints
Universe 1.
Embedding in the SM gauge structure
case: !
interaction must contain one right-handed quark and one left-handed:
1 case: Vμ
! (y1 ¯tRuL + y2 ¯uRtL) , the scalar ! must transform as a doublet of SU(2) with hypercharge Y! =
✓
!+
!0
◆
. charged component of ! has fast 2-body decays !+ ! ¯ub, however its presence fast 3-body decays of !0 via a virtual !+:
decay = Vμ
mt, a W triangle loop can generate decays Vμ ! b ¯ d; for mW mV three-body decays Vμ ! bW+¯u via a virtual top. We will check that in all cases, rates are too fast, therefore one would always need to rely on the presence of invisible states.
32. CMS monotop bounds
• scalar and vector particles, with masses below
330 and 650 GeV, respectively, excluded at 95%
(see ArXiv 1410.1149)
10
1
(8 TeV) -1 19.7 fb
0 100 200 300 400 500 600
28
7
m (GeV)
95% CL limit on σ × C (pb)
-1 10
scalar signal
observed limit
expected limit
68% coverage
95% coverage
CMS
10
1
(8 TeV) -1 19.7 fb
0 200 400 600 800 1000
m (GeV)
95% CL limit on σ × C (pb)
-1 10
vector signal
observed limit
expected limit
68% coverage
95% coverage
CMS
Figure 2: The 95% CL expected and observed CLs limits as functions of the mass of a scalar
(left) and vector (right) invisible particle. The expected magnitude of a signal as a function of
mass, calculated at leading order, is shown by the dashed curve. The confidence intervals for
33. ATLAS monotop bounds
29
10
1
0 10 20 30 40 50 60 70 80 90 100
m(f met) [GeV]
) × BR(t → b l ν) [pb] met σ(p p → t f
-1 10
ATLAS
, e±/μ± -1 s= 8 TeV, 20.3 fb
Resonant model
m(S)=500 GeV
=0.2 res Theory (LO), a
=0.15 res Theory (LO), a
=0.1 res Theory (LO), a
Observed 95% CL limit
Expected 95% CL limit
± 1σ
± 2σ
100 200 300 400 500 600 700 800 900 1000
) [GeV] met m(v
) × BR(t → b l ν) [pb] met σ(p p → t v
3 10
2 10
10
1
-1 10
ATLAS
, e±/μ± -1 s= 8 TeV, 20.3 fb
Non-resonant model
=0.3 non-res Theory (LO), a
=0.2 non-res Theory (LO), a
=0.1 non-res Theory (LO), a
Observed 95% CL limit
Expected 95% CL limit
± 1σ
± 2σ
(left) resonant model with m=500 GeV and (right) non-resonant
model. From 1410.5404
34. beyond : vector-like quarks
• Unique window to test models (Xdim, composite, Little Higgs, SUSY)!
• Reach at LHC substantial and only partially exploited!
• Mixings with all the 3 SM generation important (production/decay)!
• Single production dominant with present mass bound at LHC (∼700 GeV)
30
35. why vector-like quarks?
• top partners are expected in many extensions of the
SM (composite/Little higgs models, Xdim models)
• they come in complete multiplets (not just singlets)
• theoretical expectation is a not too heavy mass scale
M (∿TeV) and mainly coupling to the 3rd generation
• Present LHC mass bounds ∿ 700 GeV
• Mixings bounded by EWPT, flavour…
31
37. Simplified Mixing effects (t-T sector only)
• Yukawa coupling generates a mixing between the new state(s) and the
SM ones
• Type 1 : singlet and triplets couple to SM L-doublet
• Singlet ψ = (1, 2/3 ) = U : only a top partner is present
• triplet ψ = (3, 2/3 ) = {X, U, D} , the new fermion contains a partner for
both top and bottom, plus X with charge 5/3
• triplet ψ = (3, −1/3 ) = {U, D, Y} , the new fermions are a partner for
both top and bottom, plus Y with charge −4/3
33
38. Simplified Mixing effects (t-T sector only)
• Type 2 : new doublets couple to SM R-singlet
• SM doublet case ψ = (2, 1/6 ) = {U, D} , the vector-like fermions are a top and
bottom partners
• non-SM doublets ψ = (2, 7/ 6 ) = {X, U} , the vector-like fermions are a top partner
and a fermion X with charge 5/3
• non-SM doublets ψ = (2, -5/ 6 ) = {D,Y} , the vector-like fermions are a bottom
partner and a fermion Y with charge -4/3
34
40. In the general case of N −3 VL quarks mixing via Yukawa interactions to SM quarks, among themselves, we can consider the general mixing matrix assuming the SM Yukawa
matrices already diagonal. The VL masses are also diagonal in our representation. Consid-ering
Mixing with more VL multiplets
nd semi-integer isospin states (doublets, quadruplets, etc.) with possible mixings the SM right-handed singlets, and ns = N −3−nd integer isospin states (singlets, triplets,
etc.) with possible mixings with the SM left-handed doublets, we obtain the following
block-diagonal matrix [11]:
Lmass = ¯qL·
0
BBBBBBBBBBBBBBBB@
μ1 0 0 0 . . . 0 x1,nd+4 . . . x1,N
0 μ2 0 0 . . . 0 x2,nd+4 . . . x2,N
0 0 μ3 0 . . . 0 x3,nd+4 . . . x3,N
y4,1 y4,2 y4,3 M4 0 0
...
...
...
0
. . . 0 !↵
ynd+3,1 ynd+3,2 ynd+3,3 0 0 Mnd+3
0 0 0 Mnd+4 0 0
...
...
...
!0↵ 0
. . . 0
0 0 0 0 0 MN
1
CCCCCCCCCCCCCCCCA
·qR+h.c. We can isolate in the previous structure the nd⇥3 matrix y↵d,j of the Yukawa couplings the VL doublets (semi- integer isospin) and the 3⇥ns matrix xi,s of the Yukawa couplings
of the VL singlets/triplets (integer isospin). M↵ are the VL masses of the new represen-tations,
while the nd ⇥ ns matrix !↵d,and ns ⇥ nd matrix !0contain the Yukawa
integer isospin multiplets
semi-integer isospin multiplets
36
ArXiv:1305.4172 M.Buchkremer et al.
41. Pair production
37
Pair production for t’
of the non-SM doublet
pp → t' t @ LHC
42. T’ decays
Decay modes never 100% in one channel, in the limit
of the equivalence theorem, dictated by the multiplet
representation :
t’ Wb Zt ht
Singlet, Triplet Y=2/3 50% 25% 25%
Doublet, Triplet Y=-1/3 ~0% 50% 50%
43. T’ decays (X5/3,T’) multiplet
39
u Z
t Z
u H
t H
b W !
200 400 600 800 1000
1.00
0.50
0.20
0.10
0.05
0.02
0.01
mt ’
BRt ’
BRt ’ Mixing mostly with top
t H
t Z
c Z
c H
b W !
VR41 maximal
300 400 500 600 700 800 900
0.5
0.4
0.3
0.2
0.1
0.0
mt ’
Mixing mostly with top
VR42 maximal
!
In all cases T' → bW
NOT dominant for allowed
masses
44. Conclusions
• top quark plays a special role in SM and BSM!
• top quark is a privileged gate to test BSM physics!
• precision measurements era is now ! !
• new multi-top channels can give extra information!
• monotop is an interesting but constrained scenario!
• top partners are a rich sector to explore to discover or
constrain BSM physics
40