Boson and Baryon Resonances
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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. -
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
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. -
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.. -
Glueball Searches Using Electron-Positron Annihilations with BESIII
FAIRNESS2019 IOP Publishing Journal of Physics: Conference Series 1667 (2020) 012019 doi:10.1088/1742-6596/1667/1/012019 Glueball searches using electron-positron annihilations with BESIII R Kappert and J G Messchendorp, for the BESIII collaboration KVI-CART, University of Groningen, Groningen, The Netherlands E-mail: [email protected] Abstract. Using a BESIII-data sample of 1:31 × 109 J= events collected in 2009 and 2012, the glueball-sensitive decay J= ! γpp¯ is analyzed. In the past, an exciting near-threshold enhancement X(pp¯) showed up. Furthermore, the poorly-understood properties of the ηc resonance, its radiative production, and many other interesting dynamics can be studied via this decay. The high statistics provided by BESIII enables to perform a partial-wave analysis (PWA) of the reaction channel. With a PWA, the spin-parity of the possible intermediate glueball state can be determined unambiguously and more information can be gained about the dynamics of other resonances, such as the ηc. The main background contributions are from final-state radiation and from the J= ! π0(γγ)pp¯ channel. In a follow-up study, we will investigate the possibilities to further suppress the background and to use data-driven methods to control them. 1. Introduction The discovery of the Higgs boson has been a breakthrough in the understanding of the origin of mass. However, this boson only explains 1% of the total mass of baryons. The remaining 99% originates, according to quantum chromodynamics (QCD), from the self-interaction of the gluons. The nature of gluons gives rise to the formation of exotic hadronic matter. -
Beyond the Standard Model Physics at CLIC
RM3-TH/19-2 Beyond the Standard Model physics at CLIC Roberto Franceschini Università degli Studi Roma Tre and INFN Roma Tre, Via della Vasca Navale 84, I-00146 Roma, ITALY Abstract A summary of the recent results from CERN Yellow Report on the CLIC potential for new physics is presented, with emphasis on the di- rect search for new physics scenarios motivated by the open issues of the Standard Model. arXiv:1902.10125v1 [hep-ph] 25 Feb 2019 Talk presented at the International Workshop on Future Linear Colliders (LCWS2018), Arlington, Texas, 22-26 October 2018. C18-10-22. 1 Introduction The Compact Linear Collider (CLIC) [1,2,3,4] is a proposed future linear e+e− collider based on a novel two-beam accelerator scheme [5], which in recent years has reached several milestones and established the feasibility of accelerating structures necessary for a new large scale accelerator facility (see e.g. [6]). The project is foreseen to be carried out in stages which aim at precision studies of Standard Model particles such as the Higgs boson and the top quark and allow the exploration of new physics at the high energy frontier. The detailed staging of the project is presented in Ref. [7,8], where plans for the target luminosities at each energy are outlined. These targets can be adjusted easily in case of discoveries at the Large Hadron Collider or at earlier CLIC stages. In fact the collision energy, up to 3 TeV, can be set by a suitable choice of the length of the accelerator and the duration of the data taking can also be adjusted to follow hints that the LHC may provide in the years to come. -
Baryon and Lepton Number Anomalies in the Standard Model
Appendix A Baryon and Lepton Number Anomalies in the Standard Model A.1 Baryon Number Anomalies The introduction of a gauged baryon number leads to the inclusion of quantum anomalies in the theory, refer to Fig. 1.2. The anomalies, for the baryonic current, are given by the following, 2 For SU(3) U(1)B , ⎛ ⎞ 3 A (SU(3)2U(1) ) = Tr[λaλb B]=3 × ⎝ B − B ⎠ = 0. (A.1) 1 B 2 i i lef t right 2 For SU(2) U(1)B , 3 × 3 3 A (SU(2)2U(1) ) = Tr[τ aτ b B]= B = . (A.2) 2 B 2 Q 2 ( )2 ( ) For U 1 Y U 1 B , 3 A (U(1)2 U(1) ) = Tr[YYB]=3 × 3(2Y 2 B − Y 2 B − Y 2 B ) =− . (A.3) 3 Y B Q Q u u d d 2 ( )2 ( ) For U 1 BU 1 Y , A ( ( )2 ( ) ) = [ ]= × ( 2 − 2 − 2 ) = . 4 U 1 BU 1 Y Tr BBY 3 3 2BQYQ Bu Yu Bd Yd 0 (A.4) ( )3 For U 1 B , A ( ( )3 ) = [ ]= × ( 3 − 3 − 3) = . 5 U 1 B Tr BBB 3 3 2BQ Bu Bd 0 (A.5) © Springer International Publishing AG, part of Springer Nature 2018 133 N. D. Barrie, Cosmological Implications of Quantum Anomalies, Springer Theses, https://doi.org/10.1007/978-3-319-94715-0 134 Appendix A: Baryon and Lepton Number Anomalies in the Standard Model 2 Fig. A.1 1-Loop corrections to a SU(2) U(1)B , where the loop contains only left-handed quarks, ( )2 ( ) and b U 1 Y U 1 B where the loop contains only quarks For U(1)B , A6(U(1)B ) = Tr[B]=3 × 3(2BQ − Bu − Bd ) = 0, (A.6) where the factor of 3 × 3 is a result of there being three generations of quarks and three colours for each quark. -
Properties of Baryons in the Chiral Quark Model
Properties of Baryons in the Chiral Quark Model Tommy Ohlsson Teknologie licentiatavhandling Kungliga Tekniska Hogskolan¨ Stockholm 1997 Properties of Baryons in the Chiral Quark Model Tommy Ohlsson Licentiate Dissertation Theoretical Physics Department of Physics Royal Institute of Technology Stockholm, Sweden 1997 Typeset in LATEX Akademisk avhandling f¨or teknologie licentiatexamen (TeknL) inom ¨amnesomr˚adet teoretisk fysik. Scientific thesis for the degree of Licentiate of Engineering (Lic Eng) in the subject area of Theoretical Physics. TRITA-FYS-8026 ISSN 0280-316X ISRN KTH/FYS/TEO/R--97/9--SE ISBN 91-7170-211-3 c Tommy Ohlsson 1997 Printed in Sweden by KTH H¨ogskoletryckeriet, Stockholm 1997 Properties of Baryons in the Chiral Quark Model Tommy Ohlsson Teoretisk fysik, Institutionen f¨or fysik, Kungliga Tekniska H¨ogskolan SE-100 44 Stockholm SWEDEN E-mail: [email protected] Abstract In this thesis, several properties of baryons are studied using the chiral quark model. The chiral quark model is a theory which can be used to describe low energy phenomena of baryons. In Paper 1, the chiral quark model is studied using wave functions with configuration mixing. This study is motivated by the fact that the chiral quark model cannot otherwise break the Coleman–Glashow sum-rule for the magnetic moments of the octet baryons, which is experimentally broken by about ten standard deviations. Configuration mixing with quark-diquark components is also able to reproduce the octet baryon magnetic moments very accurately. In Paper 2, the chiral quark model is used to calculate the decuplet baryon ++ magnetic moments. The values for the magnetic moments of the ∆ and Ω− are in good agreement with the experimental results. -
Lectures on BSM and Dark Matter Theory (2Nd Class)
Lectures on BSM and Dark Matter theory (2nd class) Stefania Gori UC Santa Cruz 15th annual Fermilab - CERN Hadron Collider Physics Summer School August 10-21, 2020 Twin Higgs models & the hierarchy problem SMA x SMB x Z2 Global symmetry of the scalar potential (e.g. SU(4)) The SM Higgs is a (massless) Nambu-Goldstone boson ~SM Higgs doublet Twin Higgs doublet S.Gori 23 Twin Higgs models & the hierarchy problem SMA x SMB x Z2 Global symmetry of the scalar potential (e.g. SU(4)) The SM Higgs is a (massless) Nambu-Goldstone boson ~SM Higgs doublet Twin Higgs doublet Loop corrections to the Higgs mass: HA HA HB HB yA yA yB yB top twin-top Loop corrections to mass are SU(4) symmetric no quadratically divergent corrections! S.Gori 23 Twin Higgs models & the hierarchy problem SMA x SMB x Z2 Global symmetry of the scalar potential (e.g. SU(4)) The SM Higgs is a (massless) Nambu-Goldstone boson ~SM Higgs doublet Twin Higgs doublet Loop corrections to the Higgs mass: HA HA HB HB SU(4) and Z2 are (softly) broken: yA yA yB yB top twin-top Loop corrections to mass are SU(4) symmetric no quadratically divergent corrections! S.Gori 23 Phenomenology of the twin Higgs A typical spectrum: Htwin Twin tops Twin W, Z SM Higgs Twin bottoms Twin taus Glueballs S.Gori 24 Phenomenology of the twin Higgs 1. Production of the twin Higgs The twin Higgs will mix with the 125 GeV Higgs with a mixing angle ~ v2 / f2 Because of this mixing, it can be produced as a SM Higgs boson (reduced rates!) A typical spectrum: Htwin Twin tops Twin W, Z SM Higgs Twin bottoms Twin taus Glueballs S.Gori 24 Phenomenology of the twin Higgs 1. -
Search for a Higgs Boson Decaying Into a Z and a Photon in Pp
EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN) CERN-PH-EP/2013-037 2015/09/07 CMS-HIG-13-006 Search for a Higgs boson decayingp into a Z and a photon in pp collisions at s = 7 and 8 TeV The CMS Collaboration∗ Abstract A search for a Higgs boson decaying into a Z boson and a photon is described. The analysis is performed using proton-proton collision datasets recorded by the CMS de- tector at the LHC. Events were collected at center-of-mass energies of 7 TeV and 8 TeV, corresponding to integrated luminosities of 5.0 fb−1 and 19.6 fb−1, respectively. The selected events are required to have opposite-sign electron or muon pairs. No excess above standard model predictions has been found in the 120–160 GeV mass range and the first limits on the Higgs boson production cross section times the H ! Zg branch- ing fraction at the LHC have been derived. The observed limits are between about 4 and 25 times the standard model cross section times the branching fraction. The ob- served and expected limits for m``g at 125 GeV are within one order of magnitude of the standard model prediction. Models predicting the Higgs boson production cross section times the H ! Zg branching fraction to be larger than one order of magni- tude of the standard model prediction are excluded for most of the 125–157 GeV mass range. arXiv:1307.5515v3 [hep-ex] 4 Sep 2015 Published in Physics Letters B as doi:10.1016/j.physletb.2013.09.057. -
Standard Model & Baryogenesis at 50 Years
Standard Model & Baryogenesis at 50 Years Rocky Kolb The University of Chicago The Standard Model and Baryogenesis at 50 Years 1967 For the universe to evolve from B = 0 to B ¹ 0, requires: 1. Baryon number violation 2. C and CP violation 3. Departure from thermal equilibrium The Standard Model and Baryogenesis at 50 Years 95% of the Mass/Energy of the Universe is Mysterious The Standard Model and Baryogenesis at 50 Years 95% of the Mass/Energy of the Universe is Mysterious Baryon Asymmetry Baryon Asymmetry Baryon Asymmetry The Standard Model and Baryogenesis at 50 Years 99.825% of the Mass/Energy of the Universe is Mysterious The Standard Model and Baryogenesis at 50 Years Ω 2 = 0.02230 ± 0.00014 CMB (Planck 2015): B h Increasing baryon component in baryon-photon fluid: • Reduces sound speed. −1 c 3 ρ c =+1 B S ρ 3 4 γ • Decreases size of sound horizon. η rdc()η = ηη′′ ( ) SS0 • Peaks moves to smaller angular scales (larger k, larger l). = π knrPEAKS S • Baryon loading increases compression peaks, lowers rarefaction peaks. Wayne Hu The Standard Model and Baryogenesis at 50 Years 0.021 ≤ Ω 2 ≤0.024 BBN (PDG 2016): B h Increasing baryon component in baryon-photon fluid: • Increases baryon-to-photon ratio η. • In NSE abundance of species proportional to η A−1. • D, 3He, 3H build up slightly earlier leading to more 4He. • Amount of D, 3He, 3H left unburnt decreases. Discrepancy is fake news The Standard Model and Baryogenesis at 50 Years = (0.861 ± 0.005) × 10 −10 Baryon Asymmetry: nB/s • Why is there an asymmetry between matter and antimatter? o Initial (anthropic?) conditions: . -
P-Shell Hyperon Binding Energies
fruin&£t& P-Shell Hyperon Binding Energies D. Koetsier and K. Amos School of Physics University of Melbourne Parkville, Victoria 3052 Australia A shell model for lambda hypernuclei has been used to determine the binding energy of the hyperon in nuclei throughout the p shell. Conventional (Cohen and Kurath) potential energies for nucleon-nucleon interactions were used with hyperon-nucieon interactions taken from Nijmegen one boson exchange poten tials. The hyperon binding energies calculated from these potentials compare well with measured values. Although many studies have been made of hypernuclear structure1, most have been concerned with only a small number of hypernuclei. We consider the mass variation of hyperon binding energies in single hyperon hypernuclei throughout the entire p shell. We do so with the assumption that the ground states of p shell hypernuclei art- described by Os shell hypeions coupled to complex nuclear cores; cores which have closed Os shells and partially filled Op shells. Hypernuclear wavefunctions can then be determined by the diagonalisation of an appropriate Hamiltonian using the basis formed by such coupled states. The Hamiltonian to be considered is described in terms of one and two body matrix elements. The one body matrix elements were those of Cohen and Kurath2 for nucle- ons but were taken from data for the hyperon. The Cohen and Kurath (8-16)2BME potential energies were used for the two nucleon matrix elements, while the two body hyperon-nucleon matrix elements were calculated from the Nijmegen one boson ex change potentials3. These hyperon-nucleon potentials include amplitudes associated with several different meson exchanges, but do not allow for medium effects due to the presence of the other particles, for the transfer of more than one boson, or for basis space truncation.