DOCSLIB.ORG

A Young Physicist's Guide to the Higgs Boson

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

A Young Physicist’s Guide to the Higgs Boson Tel Aviv University Future Scientists – CERN Tour Presented by Stephen Sekula Associate Professor of Experimental Particle Physics SMU, Dallas, TX Programme ● You have a problem in your theory: (why do you need the Higgs Particle?) ● How to Make a Higgs Particle (One-at-a-Time) ● How to See a Higgs Particle (Without fooling yourself too much) ● A View from the Shadows: What are the New Questions? (An Epilogue) Stephen J. Sekula - SMU 2/44 You Have a Problem in Your Theory Credit for the ideas/example in this section goes to Prof. Daniel Stolarski (Carleton University) The Usual Explanation Usual Statement: “You need the Higgs Particle to explain mass.” 2 F=ma F=G m1 m2 /r Most of the mass of matter lies in the nucleus of the atom, and most of the mass of the nucleus arises from “binding energy” - the strength of the force that holds particles together to form nuclei imparts mass-energy to the nucleus (ala E = mc2). Corrected Statement: “You need the Higgs Particle to explain fundamental mass.” (e.g. the electron’s mass) E2=m2 c4+ p2 c2→( p=0)→ E=mc2 Stephen J. Sekula - SMU 4/44 Yes, the Higgs is important for mass, but let’s try this... ● No doubt, the Higgs particle plays a role in fundamental mass (I will come back to this point) ● But, as students who’ve been exposed to introductory physics (mechanics, electricity and magnetism) and some modern physics topics (quantum mechanics and special relativity) you are more familiar with... ● inverse-square laws for forces, e.g. Newton’s Law of Gravitation and Coulomb’s Law ● You have been working with models of nature that actually have fundamental problems in them, just like the Standard Model of Particle Physics would have if there was no Higgs Particle ● Let’s explore this idea: your theory has a flaw... what does it look like, and what does it imply? Stephen J. Sekula - SMU 5/44 Coulomb’s Force Law ⃗ F12 Model electric + - Two kinds of charges as points electric charge 1 2 Force that 2 exerts on 1 described by Coulomb’s Law: 1 q q F = 1 2 12 π ϵ 2 4 0 r12 Stephen J. Sekula - SMU 6/44 Electric Potential and Coulomb’s Law ⃗ F12 Model electric + - Two kinds of charges as points electric charge 1 2 Fundamental Concept: the Electric Potential of charge 2 1 q2 dV 2 V 2=− F12=q1 4 π ϵ0 r dr Stephen J. Sekula - SMU 7/44 Picturing Forces (“Interactions”) Electron (e) Electron - Deflected by Electric Field + anti-Muon - (μ+) μ “Classical Picture” “Quantum Picture” Feynman Diagram Stephen J. Sekula - SMU 10/44 From Early Physics to Advanced Physics: Coulomb’s Law as an Example of Theoretical Problems 1 q q 1 q Electric F = 1 2 V =− 2 Electric Force 12 π ϵ 2 2 π ϵ Potential 4 0 r12 4 0 r Discussion: how does the potential (energy per unit charge) of charge 2 change with your distance from it? Discussion: can we identified any problems in this classical description of electric potential/force? Stephen J. Sekula - SMU 11/44 From Early Physics to Advanced Physics: Coulomb’s Law as an Example of Theoretical Problems ● The Coulomb Potential “blows up” to infinity as the charge separation distance goes to zero ● Not very “physical” ● In other words, Coulomb’s Law doesn’t give us a clear picture of what happens right at the charge. ● An infinity in a physical theory is typically considered a sign of where the theory breaks down. Stephen J. Sekula - SMU 12/44 From Early Physics to Advanced Physics: Coulomb’s Law as an Example of Theoretical Problems 1 q1 q2 ● Perhaps classical U 1=q1 V = 4 π ϵ0 r electromagnetism is incomplete ● ... if some new rules take over at Maybe a broader theory of short distances, but in the limit of nature takes over at short large distances converges to the classical result... distances and modifies the law 1 q1 q2 U 1= ×( 1+f (r /rcutoff)) 4 π ϵ0 r Stephen J. Sekula - SMU 13/44 Uniting Quantum Mechanics and Relativity: the very small and the very fast When one successfully unites the theory of F⃗ =q⃗v×B⃗ the very fast (special relativity) with the theory of the very small (quantum mechanics), something new emerges... X Non-Relativistic Schroedinger Wave Magnetic Equation Field into ⃗v Page You have matter and forces, but you “twin” Fully Relativistic Dirac all matter: for every particle, you find there Equation must be an antiparticle with the same mass and opposite electric charge. Stephen J. Sekula - SMU 17/44 The Heisenberg Uncertainty Principle and Virtual Particles – A look back at an “electric field” As a consequence of the fundamental wave nature of matter and forces (quantum mechanics), one finds this principle applies: Δ E Δ t≥ℏ/2 Δ p Δ x≥ℏ/2 So long as it obeys these rules, a photon can emit and be reabsorbed... μ μ μ A charged particle isn’t just “sitting ... and this is allowed, too. there” with nothing happening Stephen J. Sekula - SMU 18/44 How the Cutoff Manifests μ μ Quantum Mechanics + Relativity: Scattering “shielded” by virtual particles The closer the photon gets to the charge, the more “virtual” particles it encounters Stephen J. Sekula - SMU 19/44 Some Practice with Feynman Diagrams and Physics EXERCISE: Draw a Feynman Diagram that represents one electron scattering off of another electron (e-e- → e-e-) using as few lines as possible (minimum possible drawing). HINT: conservation laws hold, so conserve electric charge, energy, and momentum. Stephen J. Sekula - SMU 20/44 The Standard Model Picture Matter Particles ● Quarks: down, up, strange, charm, bottom, top ● Leptons: (electron, muon, tau neutrinos), electron, muon, tau Force-Carrying Particles ● Electromagnetism: photon ● Weak Interaction: W±,Z0 ● Strong Interaction: gluons Stephen J. Sekula - SMU 21/44 Let’s Scatter Something Else: W Bosons! (in a universe without the Higgs Particle) W W W W Here are some Feynman Diagrams of γ,Z ways, in the Standard Model picture, to scatter W bosons off one another. W W W W As long as electric charge, momentum, W W and other fundamental quantities are γ,Z conserved at each vertex, these are allowed. W W Stephen J. Sekula - SMU 22/44 An Aside: A Theory that Predicts the Probability of an Event Let’s say I have a mathematical theory that predicts the probability of a rainy day in Geneva, Switzerland: N 2 P(rain|Geneva)= 7 where N is the number of the day of the week (Sunday = 1). Any problems? Stephen J. Sekula - SMU 23/44 Let’s Scatter Something Else: W Bosons! (in a universe without the Higgs Particle) The W boson has a mass of MW=86⨯ mp. If one tries to predict the probability at which it scatters off of another W boson (proportional to a ), as a function of its energy (E), one finds: 0 g is a number that 2 2 : g E characterizes the degree a0= 2 of the weak interaction, 16 π M W g ~ 0.654 Discussion: thinking back to the problem with the classical Coulomb Potential, what problems arise here? Stephen J. Sekula - SMU 24/44 The Higgs Particle to the Rescue W W W W W W Now: γ,Z H 2 2 g M H a0= 2 W W W W W W 16 π M W W W W W a0 remains within its physical boundaries (corresponding to a γ,Z H total probability of not more than W W W W 100%) so long as MH < 1300mp. Stephen J. Sekula - SMU 25/44 Left-to-right: Tom Kibble, Gerald Guralnik, Carl Hagen, Francois Englert, Philip Warren Anderson Robert Brout, and Peter Higgs. 1962: Anderson noted, based on an argument from Julian Schwinger, that a classical field theory does not necessarily require zero-mass bosons. He was considering charged plasmas at the time, and speculated that a quantum field theory extension might be possible. 1964: three separate groups - Brout and Englert; Higgs; Guralnik, Hagen, and Kibble - propose mechanisms for quantum field theories in which force-carrying particles (“gauge bosons”) can acquire mass and thus allow for short- ranged forces, as inside the nucleus of the atom. Stephen J. Sekula - SMU 26/44 The Standard Model Higgs Particle The Standard Model of MASS Particle Physics (unpredicted) incorporates a Higgs CHARGE Boson whose (predicted) interactions with other SPIN particles yields their (predicted) inertial mass. Its mass is unpredicted and must be measured. Stephen J. Sekula - SMU 27/44 (Make it, or break it) it, or break (Make Boson Interactingthe Higgs with very heavy objects! particles with plenty of chanceLuckily, of makingwe have the ability to collide those. can hope to make Higgs particleswe from want to first make heavy particlesmass of so particles we with which itThe interacts, Higgs interaction so is proportional to the for scale, m scale, for proton = 0.939 GeV GeV 1 GeV ~ 0.939 = Stephen SekulaJ. - SMU Strength of the Higgs Interaction with a Particle 28 / 44 How to Make a Higgs Particle (One-at-a-Time) WHAT IS A PROTON? This picture gives you the idea: ● Three primary quarks – two up- quarks and one down-quark ● They are bound together by the “strong force,” carried by “gluons” This picture is utterly wrong otherwise. Stephen J. Sekula - SMU 30/44 WHAT IS A PROTON? This is a more honest picture, though still fairly inaccurate. At least we see now that most of the structure of the proton arises from the activity of the gluons, and the fact that virtual quark- antiquark pairs are popping into and out of existence constantly in this strong energy field.
Recommended publications
  • The Five Common Particles

    The Five Common Particles

    The Five Common Particles The world around you consists of only three particles: protons, neutrons, and electrons. Protons and neutrons form the nuclei of atoms, and electrons glue everything together and create chemicals and materials. Along with the photon and the neutrino, these particles are essentially the only ones that exist in our solar system, because all the other subatomic particles have half-lives of typically 10-9 second or less, and vanish almost the instant they are created by nuclear reactions in the Sun, etc. Particles interact via the four fundamental forces of nature. Some basic properties of these forces are summarized below. (Other aspects of the fundamental forces are also discussed in the Summary of Particle Physics document on this web site.) Force Range Common Particles It Affects Conserved Quantity gravity infinite neutron, proton, electron, neutrino, photon mass-energy electromagnetic infinite proton, electron, photon charge -14 strong nuclear force ≈ 10 m neutron, proton baryon number -15 weak nuclear force ≈ 10 m neutron, proton, electron, neutrino lepton number Every particle in nature has specific values of all four of the conserved quantities associated with each force. The values for the five common particles are: Particle Rest Mass1 Charge2 Baryon # Lepton # proton 938.3 MeV/c2 +1 e +1 0 neutron 939.6 MeV/c2 0 +1 0 electron 0.511 MeV/c2 -1 e 0 +1 neutrino ≈ 1 eV/c2 0 0 +1 photon 0 eV/c2 0 0 0 1) MeV = mega-electron-volt = 106 eV. It is customary in particle physics to measure the mass of a particle in terms of how much energy it would represent if it were converted via E = mc2.
  • Higgs Bosons and Supersymmetry

    Higgs Bosons and Supersymmetry

    Higgs bosons and Supersymmetry 1. The Higgs mechanism in the Standard Model | The story so far | The SM Higgs boson at the LHC | Problems with the SM Higgs boson 2. Supersymmetry | Surpassing Poincar´e | Supersymmetry motivations | The MSSM 3. Conclusions & Summary D.J. Miller, Edinburgh, July 2, 2004 page 1 of 25 1. Electroweak Symmetry Breaking in the Standard Model 1. Electroweak Symmetry Breaking in the Standard Model Observation: Weak nuclear force mediated by W and Z bosons • M = 80:423 0:039GeV M = 91:1876 0:0021GeV W Z W couples only to left{handed fermions • Fermions have non-zero masses • Theory: We would like to describe electroweak physics by an SU(2) U(1) gauge theory. L ⊗ Y Left{handed fermions are SU(2) doublets Chiral theory ) right{handed fermions are SU(2) singlets f There are two problems with this, both concerning mass: gauge symmetry massless gauge bosons • SU(2) forbids m)( ¯ + ¯ ) terms massless fermions • L L R R L ) D.J. Miller, Edinburgh, July 2, 2004 page 2 of 25 1. Electroweak Symmetry Breaking in the Standard Model Higgs Mechanism Introduce new SU(2) doublet scalar field (φ) with potential V (φ) = λ φ 4 µ2 φ 2 j j − j j Minimum of the potential is not at zero 1 0 µ2 φ = with v = h i p2 v r λ Electroweak symmetry is broken Interactions with scalar field provide: Gauge boson masses • 1 1 2 2 MW = gv MZ = g + g0 v 2 2q Fermion masses • Y ¯ φ m = Y v=p2 f R L −! f f 4 degrees of freedom., 3 become longitudinal components of W and Z, one left over the Higgs boson D.J.
  • Fundamentals of Particle Physics

    Fundamentals of Particle Physics

    Fundamentals of Par0cle Physics Particle Physics Masterclass Emmanuel Olaiya 1 The Universe u The universe is 15 billion years old u Around 150 billion galaxies (150,000,000,000) u Each galaxy has around 300 billion stars (300,000,000,000) u 150 billion x 300 billion stars (that is a lot of stars!) u That is a huge amount of material u That is an unimaginable amount of particles u How do we even begin to understand all of matter? 2 How many elementary particles does it take to describe the matter around us? 3 We can describe the material around us using just 3 particles . 3 Matter Particles +2/3 U Point like elementary particles that protons and neutrons are made from. Quarks Hence we can construct all nuclei using these two particles -1/3 d -1 Electrons orbit the nuclei and are help to e form molecules. These are also point like elementary particles Leptons We can build the world around us with these 3 particles. But how do they interact. To understand their interactions we have to introduce forces! Force carriers g1 g2 g3 g4 g5 g6 g7 g8 The gluon, of which there are 8 is the force carrier for nuclear forces Consider 2 forces: nuclear forces, and electromagnetism The photon, ie light is the force carrier when experiencing forces such and electricity and magnetism γ SOME FAMILAR THE ATOM PARTICLES ≈10-10m electron (-) 0.511 MeV A Fundamental (“pointlike”) Particle THE NUCLEUS proton (+) 938.3 MeV neutron (0) 939.6 MeV E=mc2. Einstein’s equation tells us mass and energy are equivalent Wave/Particle Duality (Quantum Mechanics) Einstein E
  • Introduction to Particle Physics

    Introduction to Particle Physics

    SFB 676 – Projekt B2 Introduction to Particle Physics Christian Sander (Universität Hamburg) DESY Summer Student Lectures – Hamburg – 20th July '11 Outline ● Introduction ● History: From Democrit to Thomson ● The Standard Model ● Gauge Invariance ● The Higgs Mechanism ● Symmetries … Break ● Shortcomings of the Standard Model ● Physics Beyond the Standard Model ● Recent Results from the LHC ● Outlook Disclaimer: Very personal selection of topics and for sure many important things are left out! 20th July '11 Introduction to Particle Physics 2 20th July '11 Introduction to Particle PhysicsX Files: Season 2, Episode 233 … für Chester war das nur ein Weg das Geld für das eigentlich theoretische Zeugs aufzubringen, was ihn interessierte … die Erforschung Dunkler Materie, …ähm… Quantenpartikel, Neutrinos, Gluonen, Mesonen und Quarks. Subatomare Teilchen Die Geheimnisse des Universums! Theoretisch gesehen sind sie sogar die Bausteine der Wirklichkeit ! Aber niemand weiß, ob sie wirklich existieren !? 20th July '11 Introduction to Particle PhysicsX Files: Season 2, Episode 234 The First Particle Physicist? By convention ['nomos'] sweet is sweet, bitter is bitter, hot is hot, cold is cold, color is color; but in truth there are only atoms and the void. Democrit, * ~460 BC, †~360 BC in Abdera Hypothesis: ● Atoms have same constituents ● Atoms different in shape (assumption: geometrical shapes) ● Iron atoms are solid and strong with hooks that lock them into a solid ● Water atoms are smooth and slippery ● Salt atoms, because of their taste, are sharp and pointed ● Air atoms are light and whirling, pervading all other materials 20th July '11 Introduction to Particle Physics 5 Corpuscular Theory of Light Light consist out of particles (Newton et al.) ↕ Light is a wave (Huygens et al.) ● Mainly because of Newtons prestige, the corpuscle theory was widely accepted (more than 100 years) Sir Isaac Newton ● Failing to describe interference, diffraction, and *1643, †1727 polarization (e.g.
  • Read About the Particle Nature of Matter

    Read About the Particle Nature of Matter

    READING MATERIAL Read About the Particle Nature of Matter PARTICLES OF MATTER DEFINITION Matter is anything that has weight and takes up space. A particle is the smallest possible unit of matter. Understanding that matter is made of tiny particles too small to be seen can help us understand the behavior and properties of matter. To better understand how the 3 states of matter work…. LET’S BREAK IT DOWN! All matter is made of particles that are too small to be seen. Everything you can see and touch is made of matter. It is all the “stuff” in the universe. Things that are not made of matter include energy, and ideas like peace and love. Matter is made up of small particles that are too small to be seen, even with a powerful microscope. They are so small that you would have to put about 100,000 particles in a line to equal the width of a human hair! Page 1 The arrangement of particles determines the state of matter. Particles are arranged and move differently in each state of matter. Solids contain particles that are tightly packed, with very little space between particles. If an object can hold its own shape and is difficult to compress, it is a solid. Liquids contain particles that are more loosely packed than solids, but still closely packed compared to gases. Particles in liquids are able to slide past each other, or flow, to take the shape of their container. Particles are even more spread apart in gases. Gases will fill any container, but if they are not in a container, they will escape into the air.
  • Quantum Field Theory*

    Quantum Field Theory*

    Quantum Field Theory y Frank Wilczek Institute for Advanced Study, School of Natural Science, Olden Lane, Princeton, NJ 08540 I discuss the general principles underlying quantum eld theory, and attempt to identify its most profound consequences. The deep est of these consequences result from the in nite number of degrees of freedom invoked to implement lo cality.Imention a few of its most striking successes, b oth achieved and prosp ective. Possible limitation s of quantum eld theory are viewed in the light of its history. I. SURVEY Quantum eld theory is the framework in which the regnant theories of the electroweak and strong interactions, which together form the Standard Mo del, are formulated. Quantum electro dynamics (QED), b esides providing a com- plete foundation for atomic physics and chemistry, has supp orted calculations of physical quantities with unparalleled precision. The exp erimentally measured value of the magnetic dip ole moment of the muon, 11 (g 2) = 233 184 600 (1680) 10 ; (1) exp: for example, should b e compared with the theoretical prediction 11 (g 2) = 233 183 478 (308) 10 : (2) theor: In quantum chromo dynamics (QCD) we cannot, for the forseeable future, aspire to to comparable accuracy.Yet QCD provides di erent, and at least equally impressive, evidence for the validity of the basic principles of quantum eld theory. Indeed, b ecause in QCD the interactions are stronger, QCD manifests a wider variety of phenomena characteristic of quantum eld theory. These include esp ecially running of the e ective coupling with distance or energy scale and the phenomenon of con nement.
  • THE STRONG INTERACTION by J

    THE STRONG INTERACTION by J

    MISN-0-280 THE STRONG INTERACTION by J. R. Christman 1. Abstract . 1 2. Readings . 1 THE STRONG INTERACTION 3. Description a. General E®ects, Range, Lifetimes, Conserved Quantities . 1 b. Hadron Exchange: Exchanged Mass & Interaction Time . 1 s 0 c. Charge Exchange . 2 d L u 4. Hadron States a. Virtual Particles: Necessity, Examples . 3 - s u - S d e b. Open- and Closed-Channel States . 3 d n c. Comparison of Virtual and Real Decays . 4 d e 5. Resonance Particles L0 a. Particles as Resonances . .4 b. Overview of Resonance Particles . .5 - c. Resonance-Particle Symbols . 6 - _ e S p p- _ 6. Particle Names n T Y n e a. Baryon Names; , . 6 b. Meson Names; G-Parity, T , Y . 6 c. Evolution of Names . .7 d. The Berkeley Particle Data Group Hadron Tables . 7 7. Hadron Structure a. All Hadrons: Possible Exchange Particles . 8 b. The Excited State Hypothesis . 8 c. Quarks as Hadron Constituents . 8 Acknowledgments. .8 Project PHYSNET·Physics Bldg.·Michigan State University·East Lansing, MI 1 2 ID Sheet: MISN-0-280 THIS IS A DEVELOPMENTAL-STAGE PUBLICATION Title: The Strong Interaction OF PROJECT PHYSNET Author: J. R. Christman, Dept. of Physical Science, U. S. Coast Guard The goal of our project is to assist a network of educators and scientists in Academy, New London, CT transferring physics from one person to another. We support manuscript Version: 11/8/2001 Evaluation: Stage B1 processing and distribution, along with communication and information systems. We also work with employers to identify basic scienti¯c skills Length: 2 hr; 12 pages as well as physics topics that are needed in science and technology.
  • A Discussion on Characteristics of the Quantum Vacuum

    A Discussion on Characteristics of the Quantum Vacuum

    A Discussion on Characteristics of the Quantum Vacuum Harold \Sonny" White∗ NASA/Johnson Space Center, 2101 NASA Pkwy M/C EP411, Houston, TX (Dated: September 17, 2015) This paper will begin by considering the quantum vacuum at the cosmological scale to show that the gravitational coupling constant may be viewed as an emergent phenomenon, or rather a long wavelength consequence of the quantum vacuum. This cosmological viewpoint will be reconsidered on a microscopic scale in the presence of concentrations of \ordinary" matter to determine the impact on the energy state of the quantum vacuum. The derived relationship will be used to predict a radius of the hydrogen atom which will be compared to the Bohr radius for validation. The ramifications of this equation will be explored in the context of the predicted electron mass, the electrostatic force, and the energy density of the electric field around the hydrogen nucleus. It will finally be shown that this perturbed energy state of the quan- tum vacuum can be successfully modeled as a virtual electron-positron plasma, or the Dirac vacuum. PACS numbers: 95.30.Sf, 04.60.Bc, 95.30.Qd, 95.30.Cq, 95.36.+x I. BACKGROUND ON STANDARD MODEL OF COSMOLOGY Prior to developing the central theme of the paper, it will be useful to present the reader with an executive summary of the characteristics and mathematical relationships central to what is now commonly referred to as the standard model of Big Bang cosmology, the Friedmann-Lema^ıtre-Robertson-Walker metric. The Friedmann equations are analytic solutions of the Einstein field equations using the FLRW metric, and Equation(s) (1) show some commonly used forms that include the cosmological constant[1], Λ.
  • A Generalization of the One-Dimensional Boson-Fermion Duality Through the Path-Integral Formalsim

    A Generalization of the One-Dimensional Boson-Fermion Duality Through the Path-Integral Formalsim

    A Generalization of the One-Dimensional Boson-Fermion Duality Through the Path-Integral Formalism Satoshi Ohya Institute of Quantum Science, Nihon University, Kanda-Surugadai 1-8-14, Chiyoda, Tokyo 101-8308, Japan [email protected] (Dated: May 11, 2021) Abstract We study boson-fermion dualities in one-dimensional many-body problems of identical parti- cles interacting only through two-body contacts. By using the path-integral formalism as well as the configuration-space approach to indistinguishable particles, we find a generalization of the boson-fermion duality between the Lieb-Liniger model and the Cheon-Shigehara model. We present an explicit construction of n-boson and n-fermion models which are dual to each other and characterized by n−1 distinct (coordinate-dependent) coupling constants. These models enjoy the spectral equivalence, the boson-fermion mapping, and the strong-weak duality. We also discuss a scale-invariant generalization of the boson-fermion duality. arXiv:2105.04288v1 [quant-ph] 10 May 2021 1 1 Introduction Inhisseminalpaper[1] in 1960, Girardeau proved the one-to-one correspondence—the duality—between one-dimensional spinless bosons and fermions with hard-core interparticle interactions. By using this duality, he presented a celebrated example of the spectral equivalence between impenetrable bosons and free fermions. Since then, the one-dimensional boson-fermion duality has been a testing ground for studying strongly-interacting many-body problems, especially in the field of integrable models. So far there have been proposed several generalizations of the Girardeau’s finding, the most promi- nent of which was given by Cheon and Shigehara in 1998 [2]: they discovered the fermionic dual of the Lieb-Liniger model [3] by using the generalized pointlike interactions.
  • 1 Standard Model: Successes and Problems

    1 Standard Model: Successes and Problems

    Searching for new particles at the Large Hadron Collider James Hirschauer (Fermi National Accelerator Laboratory) Sambamurti Memorial Lecture : August 7, 2017 Our current theory of the most fundamental laws of physics, known as the standard model (SM), works very well to explain many aspects of nature. Most recently, the Higgs boson, predicted to exist in the late 1960s, was discovered by the CMS and ATLAS collaborations at the Large Hadron Collider at CERN in 2012 [1] marking the first observation of the full spectrum of predicted SM particles. Despite the great success of this theory, there are several aspects of nature for which the SM description is completely lacking or unsatisfactory, including the identity of the astronomically observed dark matter and the mass of newly discovered Higgs boson. These and other apparent limitations of the SM motivate the search for new phenomena beyond the SM either directly at the LHC or indirectly with lower energy, high precision experiments. In these proceedings, the successes and some of the shortcomings of the SM are described, followed by a description of the methods and status of the search for new phenomena at the LHC, with some focus on supersymmetry (SUSY) [2], a specific theory of physics beyond the standard model (BSM). 1 Standard model: successes and problems The standard model of particle physics describes the interactions of fundamental matter particles (quarks and leptons) via the fundamental forces (mediated by the force carrying particles: the photon, gluon, and weak bosons). The Higgs boson, also a fundamental SM particle, plays a central role in the mechanism that determines the masses of the photon and weak bosons, as well as the rest of the standard model particles.
  • Lesson 1: the Single Electron Atom: Hydrogen

    Lesson 1: the Single Electron Atom: Hydrogen

    Lesson 1: The Single Electron Atom: Hydrogen Irene K. Metz, Joseph W. Bennett, and Sara E. Mason (Dated: July 24, 2018) Learning Objectives: 1. Utilize quantum numbers and atomic radii information to create input files and run a single-electron calculation. 2. Learn how to read the log and report files to obtain atomic orbital information. 3. Plot the all-electron wavefunction to determine where the electron is likely to be posi- tioned relative to the nucleus. Before doing this exercise, be sure to read through the Ins and Outs of Operation document. So, what do we need to build an atom? Protons, neutrons, and electrons of course! But the mass of a proton is 1800 times greater than that of an electron. Therefore, based on de Broglie’s wave equation, the wavelength of an electron is larger when compared to that of a proton. In other words, the wave-like properties of an electron are important whereas we think of protons and neutrons as particle-like. The separation of the electron from the nucleus is called the Born-Oppenheimer approximation. So now we need the wave-like description of the Hydrogen electron. Hydrogen is the simplest atom on the periodic table and the most abundant element in the universe, and therefore the perfect starting point for atomic orbitals and energies. The compu- tational tool we are going to use is called OPIUM (silly name, right?). Before we get started, we should know what’s needed to create an input file, which OPIUM calls a parameter files. Each parameter file consist of a sequence of ”keyblocks”, containing sets of related parameters.
  • 1.1. Introduction the Phenomenon of Positron Annihilation Spectroscopy

    1.1. Introduction the Phenomenon of Positron Annihilation Spectroscopy

    PRINCIPLES OF POSITRON ANNIHILATION Chapter-1 __________________________________________________________________________________________ 1.1. Introduction The phenomenon of positron annihilation spectroscopy (PAS) has been utilized as nuclear method to probe a variety of material properties as well as to research problems in solid state physics. The field of solid state investigation with positrons started in the early fifties, when it was recognized that information could be obtained about the properties of solids by studying the annihilation of a positron and an electron as given by Dumond et al. [1] and Bendetti and Roichings [2]. In particular, the discovery of the interaction of positrons with defects in crystal solids by Mckenize et al. [3] has given a strong impetus to a further elaboration of the PAS. Currently, PAS is amongst the best nuclear methods, and its most recent developments are documented in the proceedings of the latest positron annihilation conferences [4-8]. PAS is successfully applied for the investigation of electron characteristics and defect structures present in materials, magnetic structures of solids, plastic deformation at low and high temperature, and phase transformations in alloys, semiconductors, polymers, porous material, etc. Its applications extend from advanced problems of solid state physics and materials science to industrial use. It is also widely used in chemistry, biology, and medicine (e.g. locating tumors). As the process of measurement does not mostly influence the properties of the investigated sample, PAS is a non-destructive testing approach that allows the subsequent study of a sample by other methods. As experimental equipment for many applications, PAS is commercially produced and is relatively cheap, thus, increasingly more research laboratories are using PAS for basic research, diagnostics of machine parts working in hard conditions, and for characterization of high-tech materials.