Renormalization Group Invariants in the Minimal Supersymmetric Standard Model
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Searches for Electroweak Production of Supersymmetric Gauginos and Sleptons and R-Parity Violating and Long-Lived Signatures with the ATLAS Detector
Searches for electroweak production of supersymmetric gauginos and sleptons and R-parity violating and long-lived signatures with the ATLAS detector Ruo yu Shang University of Illinois at Urbana-Champaign (for the ATLAS collaboration) Supersymmetry (SUSY) • Standard model does not answer: What is dark matter? Why is the mass of Higgs not at Planck scale? • SUSY states the existence of the super partners whose spin differing by 1/2. • A solution to cancel the quantum corrections and restore the Higgs mass. • Also provides a potential candidate to dark matter with a stable WIMP! 2 Search for SUSY at LHC squark gluino 1. Gluino, stop, higgsino are the most important ones to the problem of Higgs mass. 2. Standard search for gluino/squark (top- right plots) usually includes • large jet multiplicity • missing energy ɆT carried away by lightest SUSY particle (LSP) • See next talk by Dr. Vakhtang TSISKARIDZE. 3. Dozens of analyses have extensively excluded gluino mass up to ~2 TeV. Still no sign of SUSY. 4. What are we missing? 3 This talk • Alternative searches to probe supersymmetry. 1. Search for electroweak SUSY 2. Search for R-parity violating SUSY. 3. Search for long-lived particles. 4 Search for electroweak SUSY Look for strong interaction 1. Perhaps gluino mass is beyond LHC energy scale. gluino ↓ 2. Let’s try to find gauginos! multi-jets 3. For electroweak productions we look for Look for electroweak interaction • leptons (e/μ/τ) from chargino/neutralino decay. EW gaugino • ɆT carried away by LSP. ↓ multi-leptons 5 https://cds.cern.ch/record/2267406 Neutralino/chargino via WZ decay 2� 3� 2� SR ɆT [GeV] • Models assume gauginos decay to W/Z + LSP. -
Radiative Corrections in Curved Spacetime and Physical Implications to the Power Spectrum and Trispectrum for Different Inflationary Models
Radiative Corrections in Curved Spacetime and Physical Implications to the Power Spectrum and Trispectrum for different Inflationary Models Dissertation zur Erlangung des mathematisch-naturwissenschaftlichen Doktorgrades Doctor rerum naturalium der Georg-August-Universit¨atG¨ottingen Im Promotionsprogramm PROPHYS der Georg-August University School of Science (GAUSS) vorgelegt von Simone Dresti aus Locarno G¨ottingen,2018 Betreuungsausschuss: Prof. Dr. Laura Covi, Institut f¨urTheoretische Physik, Universit¨atG¨ottingen Prof. Dr. Karl-Henning Rehren, Institut f¨urTheoretische Physik, Universit¨atG¨ottingen Prof. Dr. Dorothea Bahns, Mathematisches Institut, Universit¨atG¨ottingen Miglieder der Prufungskommission:¨ Referentin: Prof. Dr. Laura Covi, Institut f¨urTheoretische Physik, Universit¨atG¨ottingen Korreferentin: Prof. Dr. Dorothea Bahns, Mathematisches Institut, Universit¨atG¨ottingen Weitere Mitglieder der Prufungskommission:¨ Prof. Dr. Karl-Henning Rehren, Institut f¨urTheoretische Physik, Universit¨atG¨ottingen Prof. Dr. Stefan Kehrein, Institut f¨urTheoretische Physik, Universit¨atG¨ottingen Prof. Dr. Jens Niemeyer, Institut f¨urAstrophysik, Universit¨atG¨ottingen Prof. Dr. Ariane Frey, II. Physikalisches Institut, Universit¨atG¨ottingen Tag der mundlichen¨ Prufung:¨ Mittwoch, 23. Mai 2018 Ai miei nonni Marina, Palmira e Pierino iv ABSTRACT In a quantum field theory with a time-dependent background, as in an expanding uni- verse, the time-translational symmetry is broken. We therefore expect loop corrections to cosmological observables to be time-dependent after renormalization for interacting fields. In this thesis we compute and discuss such radiative corrections to the primordial spectrum and higher order spectra in simple inflationary models. We investigate both massless and massive virtual fields, and we disentangle the time dependence caused by the background and by the initial state that is set to the Bunch-Davies vacuum at the beginning of inflation. -
The Nobel Prize in Physics 1999
The Nobel Prize in Physics 1999 The last Nobel Prize of the Millenium in Physics has been awarded jointly to Professor Gerardus ’t Hooft of the University of Utrecht in Holland and his thesis advisor Professor Emeritus Martinus J.G. Veltman of Holland. According to the Academy’s citation, the Nobel Prize has been awarded for ’elucidating the quantum structure of electroweak interaction in Physics’. It further goes on to say that they have placed particle physics theory on a firmer mathematical foundation. In this short note, we will try to understand both these aspects of the award. The work for which they have been awarded the Nobel Prize was done in 1971. However, the precise predictions of properties of particles that were made possible as a result of their work, were tested to a very high degree of accuracy only in this last decade. To understand the full significance of this Nobel Prize, we will have to summarise briefly the developement of our current theoretical framework about the basic constituents of matter and the forces which hold them together. In fact the path can be partially traced in a chain of Nobel prizes starting from one in 1965 to S. Tomonaga, J. Schwinger and R. Feynman, to the one to S.L. Glashow, A. Salam and S. Weinberg in 1979, and then to C. Rubia and Simon van der Meer in 1984 ending with the current one. In the article on ‘Search for a final theory of matter’ in this issue, Prof. Ashoke Sen has described the ‘Standard Model (SM)’ of particle physics, wherein he has listed all the elementary particles according to the SM. -
Scalar Quantum Electrodynamics
A complex system that works is invariably found to have evolved from a simple system that works. John Gall 17 Scalar Quantum Electrodynamics In nature, there exist scalar particles which are charged and are therefore coupled to the electromagnetic field. In three spatial dimensions, an important nonrelativistic example is provided by superconductors. The phenomenon of zero resistance at low temperature can be explained by the formation of so-called Cooper pairs of electrons of opposite momentum and spin. These behave like bosons of spin zero and charge q =2e, which are held together in some metals by the electron-phonon interaction. Many important predictions of experimental data can be derived from the Ginzburg- Landau theory of superconductivity [1]. The relativistic generalization of this theory to four spacetime dimensions is of great importance in elementary particle physics. In that form it is known as scalar quantum electrodynamics (scalar QED). 17.1 Action and Generating Functional The Ginzburg-Landau theory is a three-dimensional euclidean quantum field theory containing a complex scalar field ϕ(x)= ϕ1(x)+ iϕ2(x) (17.1) coupled to a magnetic vector potential A. The scalar field describes bound states of pairs of electrons, which arise in a superconductor at low temperatures due to an attraction coming from elastic forces. The detailed mechanism will not be of interest here; we only note that the pairs are bound in an s-wave and a spin singlet state of charge q =2e. Ignoring for a moment the magnetic interactions, the ensemble of these bound states may be described, in the neighborhood of the superconductive 4 transition temperature Tc, by a complex scalar field theory of the ϕ -type, by a euclidean action 2 3 1 m g 2 E = d x ∇ϕ∗∇ϕ + ϕ∗ϕ + (ϕ∗ϕ) . -
Asymptotically Flat, Spherical, Self-Interacting Scalar, Dirac and Proca Stars
S S symmetry Article Asymptotically Flat, Spherical, Self-Interacting Scalar, Dirac and Proca Stars Carlos A. R. Herdeiro and Eugen Radu * Departamento de Matemática da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications (CIDMA), Campus de Santiago, 3810-183 Aveiro, Portugal; [email protected] * Correspondence: [email protected] Received: 14 November 2020; Accepted: 1 December 2020; Published: 8 December 2020 Abstract: We present a comparative analysis of the self-gravitating solitons that arise in the Einstein–Klein–Gordon, Einstein–Dirac, and Einstein–Proca models, for the particular case of static, spherically symmetric spacetimes. Differently from the previous study by Herdeiro, Pombo and Radu in 2017, the matter fields possess suitable self-interacting terms in the Lagrangians, which allow for the existence of Q-ball-type solutions for these models in the flat spacetime limit. In spite of this important difference, our analysis shows that the high degree of universality that was observed by Herdeiro, Pombo and Radu remains, and various spin-independent common patterns are observed. Keywords: solitons; boson stars; Dirac stars 1. Introduction and Motivation 1.1. General Remarks The (modern) idea of solitons, as extended particle-like configurations, can be traced back (at least) to Lord Kelvin, around one and half centuries ago, who proposed that atoms are made of vortex knots [1]. However, the first explicit example of solitons in a relativistic field theory was found by Skyrme [2,3], (almost) one hundred years later. The latter, dubbed Skyrmions, exist in a model with four (real) scalars that are subject to a constraint. -
Quantum Mechanics Quantum Chromodynamics (QCD)
Quantum Mechanics_quantum chromodynamics (QCD) In theoretical physics, quantum chromodynamics (QCD) is a theory ofstrong interactions, a fundamental forcedescribing the interactions between quarksand gluons which make up hadrons such as the proton, neutron and pion. QCD is a type of Quantum field theory called a non- abelian gauge theory with symmetry group SU(3). The QCD analog of electric charge is a property called 'color'. Gluons are the force carrier of the theory, like photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of Particle physics. A huge body of experimental evidence for QCD has been gathered over the years. QCD enjoys two peculiar properties: Confinement, which means that the force between quarks does not diminish as they are separated. Because of this, when you do split the quark the energy is enough to create another quark thus creating another quark pair; they are forever bound into hadrons such as theproton and the neutron or the pion and kaon. Although analytically unproven, confinement is widely believed to be true because it explains the consistent failure of free quark searches, and it is easy to demonstrate in lattice QCD. Asymptotic freedom, which means that in very high-energy reactions, quarks and gluons interact very weakly creating a quark–gluon plasma. This prediction of QCD was first discovered in the early 1970s by David Politzer and by Frank Wilczek and David Gross. For this work they were awarded the 2004 Nobel Prize in Physics. There is no known phase-transition line separating these two properties; confinement is dominant in low-energy scales but, as energy increases, asymptotic freedom becomes dominant. -
Structure of Matter
STRUCTURE OF MATTER Discoveries and Mysteries Part 2 Rolf Landua CERN Particles Fields Electromagnetic Weak Strong 1895 - e Brownian Radio- 190 Photon motion activity 1 1905 0 Atom 191 Special relativity 0 Nucleus Quantum mechanics 192 p+ Wave / particle 0 Fermions / Bosons 193 Spin + n Fermi Beta- e Yukawa Antimatter Decay 0 π 194 μ - exchange 0 π 195 P, C, CP τ- QED violation p- 0 Particle zoo 196 νe W bosons Higgs 2 0 u d s EW unification νμ 197 GUT QCD c Colour 1975 0 τ- STANDARD MODEL SUSY 198 b ντ Superstrings g 0 W Z 199 3 generations 0 t 2000 ν mass 201 0 WEAK INTERACTION p n Electron (“Beta”) Z Z+1 Henri Becquerel (1900): Beta-radiation = electrons Two-body reaction? But electron energy/momentum is continuous: two-body two-body momentum energy W. Pauli (1930) postulate: - there is a third particle involved + + - neutral - very small or zero mass p n e 휈 - “Neutrino” (Fermi) FERMI THEORY (1934) p n Point-like interaction e 휈 Enrico Fermi W = Overlap of the four wave functions x Universal constant G -5 2 G ~ 10 / M p = “Fermi constant” FERMI: PREDICTION ABOUT NEUTRINO INTERACTIONS p n E = 1 MeV: σ = 10-43 cm2 휈 e (Range: 1020 cm ~ 100 l.yr) time Reines, Cowan (1956): Neutrino ‘beam’ from reactor Reactions prove existence of neutrinos and then ….. THE PREDICTION FAILED !! σ ‘Unitarity limit’ > 100 % probability E2 ~ 300 GeV GLASGOW REFORMULATES FERMI THEORY (1958) p n S. Glashow W(eak) boson Very short range interaction e 휈 If mass of W boson ~ 100 GeV : theory o.k. -
A Solvable Tensor Field Theory Arxiv:1903.02907V2 [Math-Ph]
A Solvable Tensor Field Theory R. Pascalie∗ Universit´ede Bordeaux, LaBRI, CNRS UMR 5800, Talence, France, EU Mathematisches Institut der Westf¨alischen Wilhelms-Universit¨at,M¨unster,Germany, EU August 3, 2020 Abstract We solve the closed Schwinger-Dyson equation for the 2-point function of a tensor field theory with a quartic melonic interaction, in terms of Lambert's W-function, using a perturbative expansion and Lagrange-B¨urmannresummation. Higher-point functions are then obtained recursively. 1 Introduction Tensor models have regained a considerable interest since the discovery of their large N limit (see [1], [2], [3] or the book [4]). Recently, tensor models have been related in [5] and [6], to the Sachdev-Ye-Kitaev model [7], [8], [9], [10], which is a promising toy-model for understanding black holes through holography (see also [11], [12], the lectures [13] and the review [14]). In this paper we study a specific type of tensor field theory (TFT) 1. More precisely, we consider a U(N)-invariant tensor models whose kinetic part is modified to include a Laplacian- like operator (this operator is a discrete Laplacian in the Fourier transformed space of the tensor index space). This type of tensor model has originally been used to implement renormalization techniques for tensor models (see [16], the review [17] or the thesis [18] and references within) and has also been studied as an SYK-like TFT [19]. Recently, the functional Renormalization Group (FRG) as been used in [20] to investigate the existence of a universal continuum limit in tensor models, see also the review [21]. -
PDF) of Partons I and J
TASI 2004 Lecture Notes on Higgs Boson Physics∗ Laura Reina1 1Physics Department, Florida State University, 315 Keen Building, Tallahassee, FL 32306-4350, USA E-mail: [email protected] Abstract In these lectures I briefly review the Higgs mechanism of spontaneous symmetry breaking and focus on the most relevant aspects of the phenomenology of the Standard Model and of the Minimal Supersymmetric Standard Model Higgs bosons at both hadron (Tevatron, Large Hadron Collider) and lepton (International Linear Collider) colliders. Some emphasis is put on the perturbative calculation of both Higgs boson branching ratios and production cross sections, including the most important radiative corrections. arXiv:hep-ph/0512377v1 30 Dec 2005 ∗ These lectures are dedicated to Filippo, who listened to them before he was born and behaved really well while I was writing these proceedings. 1 Contents I. Introduction 3 II. Theoretical framework: the Higgs mechanism and its consequences. 4 A. A brief introduction to the Higgs mechanism 5 B. The Higgs sector of the Standard Model 10 C. Theoretical constraints on the Standard Model Higgs bosonmass 13 1. Unitarity 14 2. Triviality and vacuum stability 16 3. Indirect bounds from electroweak precision measurements 17 4. Fine-tuning 22 D. The Higgs sector of the Minimal Supersymmetric Standard Model 24 1. About Two Higgs Doublet Models 25 2. The MSSM Higgs sector: introduction 27 3. MSSM Higgs boson couplings to electroweak gauge bosons 30 4. MSSM Higgs boson couplings to fermions 33 III. Phenomenology of the Higgs Boson 34 A. Standard Model Higgs boson decay branching ratios 34 1. General properties of radiative corrections to Higgs decays 37 + 2. -
Arxiv:2003.01034V1 [Hep-Th] 2 Mar 2020 Im Oe.Frta Esntelna Oe a Etogta Ge a Large As the Thought in Be Solved Be Can Can Model Models Linear These the One
Inhomogeneous states in two dimensional linear sigma model at large N A. Pikalov1,2∗ 1Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia 2Institute for Theoretical and Experimental Physics, Moscow, Russia (Dated: March 3, 2020) In this note we consider inhomogeneous solutions of two-dimensional linear sigma model in the large N limit. These solutions are similar to the ones found recently in two-dimensional CP N sigma model. The solution exists only for some range of coupling constant. We calculate energy of the solutions as function of parameters of the model and show that at some value of the coupling constant it changes sign signaling a possible phase transition. The case of the nonlinear model at finite temperature is also discussed. The free energy of the inhomogeneous solution is shown to change sign at some critical temperature. I. INTRODUCTION Two-dimensional linear sigma model is a theory of N real scalar fields and quartic O(N) symmetric interaction. The model has two dimensionful parameters: mass of the particles and coupling constant. In the limit of infinite coupling one can obtain the nonlinear O(N) arXiv:2003.01034v1 [hep-th] 2 Mar 2020 sigma model. For that reason the linear model can be thought as a generalization of the nonlinear one. These models can be solved in the large N limit, see [1] for a review. In turn O(N) sigma model is quite similar to the CP N sigma model. Recently the large N CP N sigma model was considered on a finite interval with various boundary conditions [2–8] and on circle [9–12]. -
Physics 215C: Particles and Fields Spring 2019
Physics 215C: Particles and Fields Spring 2019 Lecturer: McGreevy These lecture notes live here. Please email corrections to mcgreevy at physics dot ucsd dot edu. Last updated: 2021/04/20, 14:28:40 1 Contents 0.1 Introductory remarks for the third quarter................4 0.2 Sources and acknowledgement.......................7 0.3 Conventions.................................8 1 Anomalies9 2 Effective field theory 20 2.1 A parable on integrating out degrees of freedom............. 20 2.2 Introduction to effective field theory.................... 25 2.3 The color of the sky............................. 30 2.4 Fermi theory of Weak Interactions..................... 32 2.5 Loops in EFT................................ 33 2.6 The Standard Model as an EFT...................... 39 2.7 Superconductors.............................. 42 2.8 Effective field theory of Fermi surfaces.................. 47 3 Geometric and topological terms in field theory actions 58 3.1 Coherent state path integrals for bosons................. 58 3.2 Coherent state path integral for fermions................. 66 3.3 Path integrals for spin systems....................... 73 3.4 Topological terms from integrating out fermions............. 86 3.5 Pions..................................... 89 4 Field theory of spin systems 99 4.1 Transverse-Field Ising Model........................ 99 4.2 Ferromagnets and antiferromagnets..................... 131 4.3 The beta function for 2d non-linear sigma models............ 136 4.4 CP1 representation and large-N ...................... 138 5 Duality 148 5.1 XY transition from superfluid to Mott insulator, and T-duality..... 148 6 Conformal field theory 158 6.1 The stress tensor and conformal invariance (abstract CFT)....... 160 6.2 Radial quantization............................. 166 6.3 Back to general dimensions......................... 172 7 Duality, part 2 179 7.1 (2+1)-d XY is dual to (2+1)d electrodynamics............. -
Electro-Weak Interactions
Electro-weak interactions Marcello Fanti Physics Dept. | University of Milan M. Fanti (Physics Dep., UniMi) Fundamental Interactions 1 / 36 The ElectroWeak model M. Fanti (Physics Dep., UniMi) Fundamental Interactions 2 / 36 Electromagnetic vs weak interaction Electromagnetic interactions mediated by a photon, treat left/right fermions in the same way g M = [¯u (eγµ)u ] − µν [¯u (eγν)u ] 3 1 q2 4 2 1 − γ5 Weak charged interactions only apply to left-handed component: = L 2 Fermi theory (effective low-energy theory): GF µ 5 ν 5 M = p u¯3γ (1 − γ )u1 gµν u¯4γ (1 − γ )u2 2 Complete theory with a vector boson W mediator: g 1 − γ5 g g 1 − γ5 p µ µν p ν M = u¯3 γ u1 − 2 2 u¯4 γ u2 2 2 q − MW 2 2 2 g µ 5 ν 5 −−−! u¯3γ (1 − γ )u1 gµν u¯4γ (1 − γ )u2 2 2 low q 8 MW p 2 2 g −5 −2 ) GF = | and from weak decays GF = (1:1663787 ± 0:0000006) · 10 GeV 8 MW M. Fanti (Physics Dep., UniMi) Fundamental Interactions 3 / 36 Experimental facts e e Electromagnetic interactions γ Conserves charge along fermion lines ¡ Perfectly left/right symmetric e e Long-range interaction electromagnetic µ ) neutral mass-less mediator field A (the photon, γ) currents eL νL Weak charged current interactions Produces charge variation in the fermions, ∆Q = ±1 W ± Acts only on left-handed component, !! ¡ L u Short-range interaction L dL ) charged massive mediator field (W ±)µ weak charged − − − currents E.g.