Unified Equations of Boson and Fermion at High Energy and Some
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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. -
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
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. -
Supersymmetric Dark Matter
Supersymmetric dark matter G. Bélanger LAPTH- Annecy Plan | Dark matter : motivation | Introduction to supersymmetry | MSSM | Properties of neutralino | Status of LSP in various SUSY models | Other DM candidates z SUSY z Non-SUSY | DM : signals, direct detection, LHC Dark matter: a WIMP? | Strong evidence that DM dominates over visible matter. Data from rotation curves, clusters, supernovae, CMB all point to large DM component | DM a new particle? | SM is incomplete : arbitrary parameters, hierarchy problem z DM likely to be related to physics at weak scale, new physics at the weak scale can also solve EWSB z Stable particle protect by symmetry z Many solutions – supersymmetry is one best motivated alternative to SM | NP at electroweak scale could also explain baryonic asymetry in the universe Relic density of wimps | In early universe WIMPs are present in large number and they are in thermal equilibrium | As the universe expanded and cooled their density is reduced Freeze-out through pair annihilation | Eventually density is too low for annihilation process to keep up with expansion rate z Freeze-out temperature | LSP decouples from standard model particles, density depends only on expansion rate of the universe | Relic density | A relic density in agreement with present measurements (Ωh2 ~0.1) requires typical weak interactions cross-section Coannihilation | If M(NLSP)~M(LSP) then maintains thermal equilibrium between NLSP-LSP even after SUSY particles decouple from standard ones | Relic density then depends on rate for all processes -
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. -
Quantum Statistics: Is There an Effective Fermion Repulsion Or Boson Attraction? W
Quantum statistics: Is there an effective fermion repulsion or boson attraction? W. J. Mullin and G. Blaylock Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003 ͑Received 13 February 2003; accepted 16 May 2003͒ Physicists often claim that there is an effective repulsion between fermions, implied by the Pauli principle, and a corresponding effective attraction between bosons. We examine the origins and validity of such exchange force ideas and the areas where they are highly misleading. We propose that explanations of quantum statistics should avoid the idea of an effective force completely, and replace it with more appropriate physical insights, some of which are suggested here. © 2003 American Association of Physics Teachers. ͓DOI: 10.1119/1.1590658͔ ͒ϭ ͒ Ϫ␣ Ϫ ϩ ͒2 I. INTRODUCTION ͑x1 ,x2 ,t C͕f ͑x1 ,x2 exp͓ ͑x1 vt a Ϫ͑x ϩvtϪa͒2͔Ϫ f ͑x ,x ͒ The Pauli principle states that no two fermions can have 2 2 1 ϫ Ϫ␣ Ϫ ϩ ͒2Ϫ ϩ Ϫ ͒2 the same quantum numbers. The origin of this law is the exp͓ ͑x2 vt a ͑x1 vt a ͔͖, required antisymmetry of the multi-fermion wavefunction. ͑1͒ Most physicists have heard or read a shorthand way of ex- pressing the Pauli principle, which says something analogous where x1 and x2 are the particle coordinates, f (x1 ,x2) ϭ ͓ Ϫ ប͔ to fermions being ‘‘antisocial’’ and bosons ‘‘gregarious.’’ Of- exp imv(x1 x2)/ , C is a time-dependent factor, and the ten this intuitive approach involves the statement that there is packet width parameters ␣ and  are unequal. -
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. -
What Is the Dirac Equation?
What is the Dirac equation? M. Burak Erdo˘gan ∗ William R. Green y Ebru Toprak z July 15, 2021 at all times, and hence the model needs to be first or- der in time, [Tha92]. In addition, it should conserve In the early part of the 20th century huge advances the L2 norm of solutions. Dirac combined the quan- were made in theoretical physics that have led to tum mechanical notions of energy and momentum vast mathematical developments and exciting open operators E = i~@t, p = −i~rx with the relativis- 2 2 2 problems. Einstein's development of relativistic the- tic Pythagorean energy relation E = (cp) + (E0) 2 ory in the first decade was followed by Schr¨odinger's where E0 = mc is the rest energy. quantum mechanical theory in 1925. Einstein's the- Inserting the energy and momentum operators into ory could be used to describe bodies moving at great the energy relation leads to a Klein{Gordon equation speeds, while Schr¨odinger'stheory described the evo- 2 2 2 4 lution of very small particles. Both models break −~ tt = (−~ ∆x + m c ) : down when attempting to describe the evolution of The Klein{Gordon equation is second order, and does small particles moving at great speeds. In 1927, Paul not have an L2-conservation law. To remedy these Dirac sought to reconcile these theories and intro- shortcomings, Dirac sought to develop an operator1 duced the Dirac equation to describe relativitistic quantum mechanics. 2 Dm = −ic~α1@x1 − ic~α2@x2 − ic~α3@x3 + mc β Dirac's formulation of a hyperbolic system of par- tial differential equations has provided fundamental which could formally act as a square root of the Klein- 2 2 2 models and insights in a variety of fields from parti- Gordon operator, that is, satisfy Dm = −c ~ ∆ + 2 4 cle physics and quantum field theory to more recent m c . -
A Young Physicist's Guide to the Higgs Boson
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.. -
Dirac Equation - Wikipedia
Dirac equation - Wikipedia https://en.wikipedia.org/wiki/Dirac_equation Dirac equation From Wikipedia, the free encyclopedia In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it 1 describes all spin-2 massive particles such as electrons and quarks for which parity is a symmetry. It is consistent with both the principles of quantum mechanics and the theory of special relativity,[1] and was the first theory to account fully for special relativity in the context of quantum mechanics. It was validated by accounting for the fine details of the hydrogen spectrum in a completely rigorous way. The equation also implied the existence of a new form of matter, antimatter, previously unsuspected and unobserved and which was experimentally confirmed several years later. It also provided a theoretical justification for the introduction of several component wave functions in Pauli's phenomenological theory of spin; the wave functions in the Dirac theory are vectors of four complex numbers (known as bispinors), two of which resemble the Pauli wavefunction in the non-relativistic limit, in contrast to the Schrödinger equation which described wave functions of only one complex value. Moreover, in the limit of zero mass, the Dirac equation reduces to the Weyl equation. Although Dirac did not at first fully appreciate the importance of his results, the entailed explanation of spin as a consequence of the union of quantum mechanics and relativity—and the eventual discovery of the positron—represents one of the great triumphs of theoretical physics. -
Higgsino DM Is Dead
Cornering Higgsino at the LHC Satoshi Shirai (Kavli IPMU) Based on H. Fukuda, N. Nagata, H. Oide, H. Otono, and SS, “Higgsino Dark Matter in High-Scale Supersymmetry,” JHEP 1501 (2015) 029, “Higgsino Dark Matter or Not,” Phys.Lett. B781 (2018) 306 “Cornering Higgsino: Use of Soft Displaced Track ”, arXiv:1910.08065 1. Higgsino Dark Matter 2. Current Status of Higgsino @LHC mono-jet, dilepton, disappearing track 3. Prospect of Higgsino Use of soft track 4. Summary 2 DM Candidates • Axion • (Primordial) Black hole • WIMP • Others… 3 WIMP Dark Matter Weakly Interacting Massive Particle DM abundance DM Standard Model (SM) particle 500 GeV DM DM SM Time 4 WIMP Miracle 5 What is Higgsino? Higgsino is (pseudo)Dirac fermion Hypercharge |Y|=1/2 SU(2)doublet <1 TeV 6 Pure Higgsino Spectrum two Dirac Fermions ~ 300 MeV Radiative correction 7 Pure Higgsino DM is Dead DM is neutral Dirac Fermion HUGE spin-independent cross section 8 Pure Higgsino DM is Dead DM is neutral Dirac Fermion Purepure Higgsino Higgsino HUGE spin-independent cross section 9 Higgsino Spectrum (with gaugino) With Gauginos, fermion number is violated Dirac fermion into two Majorana fermions 10 Higgsino Spectrum (with gaugino) 11 Higgsino Spectrum (with gaugino) No SI elastic cross section via Z-boson 12 [N. Nagata & SS 2015] Gaugino induced Observables Mass splitting DM direct detection SM fermion EDM 13 Correlation These observables are controlled by gaugino mass Strong correlation among these observables for large tanb 14 Correlation These observables are controlled by gaugino mass Strong correlation among these observables for large tanb XENON1T constraint 15 Viable Higgsino Spectrum 16 Current Status of Higgsino @LHC 17 Collider Signals of DM p, e- DM DM is invisible p, e+ DM 18 Collider Signals of DM p, e- DM DM is invisible p, e+ DM Additional objects are needed to see DM. -
Abdus Salam United Nations Educational, Scientific and Cultural International XA0101583 Organization Centre
the 1(72001/34 abdus salam united nations educational, scientific and cultural international XA0101583 organization centre international atomic energy agency for theoretical physics NEW DIMENSIONS NEW HOPES Utpal Sarkar Available at: http://www.ictp.trieste.it/-pub-off IC/2001/34 United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS NEW DIMENSIONS NEW HOPES Utpal Sarkar1 Physics Department, Visva Bharati University, Santiniketan 731235, India and The Abdus Salam Insternational Centre for Theoretical Physics, Trieste, Italy. Abstract We live in a four dimensional world. But the idea of unification of fundamental interactions lead us to higher dimensional theories. Recently a new theory with extra dimensions has emerged, where only gravity propagates in the extra dimension and all other interactions are confined in only four dimensions. This theory gives us many new hopes. In earlier theories unification of strong, weak and the electromagnetic forces was possible at around 1016 GeV in a grand unified theory (GUT) and it could get unified with gravity at around the Planck scale of 1019 GeV. With this new idea it is possible to bring down all unification scales within the reach of the next generation accelerators, i.e., around 104 GeV. MIRAMARE - TRIESTE May 2001 1 Regular Associate of the Abdus Salam ICTP. E-mail: [email protected] 1 Introduction In particle physics we try to find out what are the fundamental particles and how they interact. This is motivated from the belief that there must be some fundamental law that governs ev- erything.