DOCSLIB.ORG

Electric Charges of Positrons and Antiprotons

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

VOLUME 69, NUMBER 4 PHYSICAL REVIEW LETTERS 27 JULY 1992 Electric Charges of Positrons and Antiprotons R. J. Hughes University of California, Physics DitisionL, os Alamos IVational Laboratory, Los Alamos, IVew Mexico 87545 B. I. Deutch Institute of Physics and Astronomy, University of Aarhus, DK 8000-Aarhus C, Denmark (Received 4 May 1992) Tests of the electric charges carried by the positron and antiproton are derived from recent measure- ments of the cyclotron frequencies of these particles, and from the spectroscopy of exotic atoms in which they are constituents. PACS numbers: 14.60.Cd, 11.30.Er, 14.20.Dh, 36.10.—k There has recently been considerable interest in high- a diA'erence between the magnitudes of the charges car- precision tests of the equality of particle and antiparticle ried by protons and electrons as small as one part in 10 masses that is required by CPT symmetry [1,21. A could account for the expansion of the Universe [13]. method that has been applied to electrons and positrons This idea led to further experimental tests, and the equal- [3] and protons and antiprotons [1] utilizes the cyclotron ity of the unit of charge on the electron and the proton frequency, co q8/trt, of a particle of mass m and charge has now been tested to very high precision [14]. For in- q in a magnetic field 8. Indeed, comparisons of the cyclo- stance, Marinelli and Morpurgo quote the limit [15] tron frequencies of electrons and protons (or ions that ~ (0.8 + 0.8) x 10 'e . (2) contain these particles as constituents) in the same mag- Aq, ~ netic field are regarded as tests of the particles' mass ra- The neutron had not been discovered at the time of tios, because there is independent inforination that the Einstein's original suggestion, and Piccard and Kessler's magnitudes of the electron and proton charges are equal. result did not constrain the neutron's charge. Therefore, However, there are no analogous tests for the charges there remained a possibility that because a rotating of electrons and positrons or protons and antiprotons. charged body has a magnetic dipole moment [16], the Therefore, cyclotron frequency comparisons for these magnetic fields of the Sun and planets could be explained particle-antiparticle pairs should strictly be regarded as with a nonzero neutron charge [17]. Likewise, the expan- comparisons of the particles' charge-to-mass ratios [4,5], sion of the Universe could be accounted for by a neutron unless the additional assumptions of either charge quanti- charge instead of an electron-proton charge difference zation or CPT symmetry for particle-antiparticle charges [18]. However, there is now a high-precision test of the are made. These assumptions involve concepts that are as neutrality of the neutron [19], fundamental as the equality of particle and antiparticle — masses and hence deserve their own independent tests. In q„=( 1.5 ~ 2.2) x10 e, this Letter we shall derive tests of the positron and an- which rules out these explanations. tiproton charges combining precision measurements of by There are also tests of the neutrality of the electron an- their frequencies with spectroscopic measure- cyclotron tineutrino [19] ments on positronium and antiprotonic atoms. Then we shall discuss how these tests could be improved with ex- q„- = (1.4+ 1.4) x 10 e, (4) periments on antihydrogen. We start by reviewing the 2-eV existing experimental tests of charge quantization. and for photons [20] The notion that electric charge is quantized (in units of (5) e), which dates back to the last century [6-8] can be ac- commodated in Kaluza-Klein theories [9], theories with that were derived under the assumption of charge conser- magnetic monopoles [10], and grand unified theories vation, which has itself been the subject of experimental [11]. But in 1924 Einstein suggested that a small dif- and theoretical attention [21]. [Experimental tests of ference in the charges carried by the proton and electron charge conservation, which are limited to strong con- could account for the magnetic fields of the Sun and straints on a few forbidden reactions [21], can be viewed Earth [12]. This suggestion led to the first experimental as tests of gauge invariance [22-24], because current test of the neutrality of matter by Piccard and Kessler nonconservation is inconsistent with the (gauge-invari- [12]. Then in 1959 it was suggested that, because the ant) Maxwell's equations, 8„F"'=j', but on the other electromagnetic interaction between an electron and a hand, can be consistent with the Proca equation, B„F"' proton is so much stronger than the gravitational one, +m~2'= j', in which the potentials attain physical significance. 2 ] electric e 2 ~Planck a —10+ 39 Another challenge to the notion of charge quantization gravitational 6m~m, m~m, has come from recent discussion of the possibility of "mil- 578 1992 The American Physical Society VOLUME 69, NUMBER 4 PHYSICAL REVIEW LETTERS 27 JULY 1992 licharged particles" (q —10 e) [25], which could pro- 3 e Ree ee vide an expl'anation of the orthopositronium lifetime puz- R;, =0, (io) 2 zle [26]. The existence of such particles is poorly con- strained experimentally. for the charge ratio, where e; is the positron charge. For From this brief survey it is clear that there are fun- clarity, we assume to a first approximation that the damentally important cosmological, metrological, and charge ratio is approximately equal to 1, e;/e =1+e;, and field-theoretical reasons to test the charges of elementary so obtain an equation for the charge equality: particles. Therefore, it is quite unsatisfactory that there = —, are no tests of the charges on the positron or antiproton, e; (Aro;, +25R;,), particularly because without such tests the CPT symme- where we have used R;, =I+hR;, and co,—,=l+hco;„ of particle and antiparticle charges remains untested. try with AR;, and Aro;, small. Separate tests of the charges and masses of positrons Now we may use the experimental results for the ratio can be obtained combining measure- and antiprotons by of electron and positron cyclotron frequencies [3]: ments of their cyclotron frequencies with additional ex- perimental data that have a different functional depen- N;, = 1 ~ 1.3 && 10 (12) dence on their charges and masses, such as the Rydberg and the ratio of the Rydbergs in positronium and hydro- for exotic atoms that have the antiparticle as a constitu- gen [28]: ent. To see this, suppose that we are concerned with a m and e and a second particle ' particle of mass ~ charge ~, I&R;,1&4&&10 (90%CI. ). (i3) of m2 and (opposite) charge e2. The cyclotron frequen- We conclude that cies (in SI units) of the particles in a magnetic field of strength B are given by e;/e = I +4&10 (i4) in the fre- ro; e;8/m;, i =1,2, (6) Improvements the precision of cyclotron quency comparison to the level of one part in 10" have whereas the Rydberg of the hydrogenic atom formed been suggested [29], and the ultimate precision on mea- from the bound state of the pair would be surements of the IS-2S interval in positronium (from which the Rydberg for positronium can be deduced) is R2~ =pe~e~/8eoch (7) also 1 part in 10" [30]. Therefore we can anticipate an where p =m~m2/(m~+m2) is the reduced mass of the improvement of this test of the electron-positron charge pair. (We have assumed that the charges are unaltered equality by roughly 3 orders of magnitude, and hence the by being bound into an atomic state. ) For instance, par- equality of their masses could be tested with comparable ticles I and 2 might be an electron and a positron, in precision by comparison of their cyclotron frequencies. which case the exotic atom would be positronium, or a For the case in which particle 1 is a proton and particle proton and an antiproton where the atom would be the 2 an antiproton we have [1] proton-antiproton bound state, unaffected strong in- by =1 ~4x 1Q (is) teraction effects, or a positron and an antiproton, in which case the atom would be antihydrogen, etc. The cy- and we shall assume that the uncertainty of 5&&10 clotron frequencies can now be used to eliminate the par- quoted on the antiproton mass measured from the spec- ticles' masses from the Rydberg. troscopy of antiprotonic atoms [31]" reflects the uncertain- We next introduce the cyclotron frequency ratio ty in the "antiprotonic Rydberg, R~ . We can derive an equation for the ratio of the charge of the antiproton, e-, N2 m] e2 N2~ = to the electron's charge, e, N~ e~ m2 3 e& — e& and the ratio of Rydberg values 1 me R- N- + =Q, (i6) e 2 m ~p ~~ e 2 2 R2i 2p e&e2 R2)—: (9) and hence, putting ez/e = I+ ez, we find the equation R /2 m, e4 ' e~= —, (hro- +2AR- ), (17) where e is the electron or proton charge, m, is the elec- for the uncertainty in the antiproton's relative tron mass, and R =m, e /8eoch is the Rydberg of the = charge = hydrogen atom for infinite proton mass, which has recent- to the electron's, where co~~ 1+hco~~ and R~~ (1 ly been measured to a precision of 1.7 parts in 10' [27] +AR~~)mz/m, . The error here is clearly dominated by (limited by the existing optical frequency standard). the antiprotonic Rydberg, and we find For the case where particle 1 is an electron and particle e~/e = 1 ~ 2 x 10 2 is a positron we can eliminate their mass ratio between Eqs.
Recommended publications
  • (Anti)Proton Mass and Magnetic Moment

    (Anti)Proton Mass and Magnetic Moment

    FFK Conference 2019, Tihany, Hungary Precision measurements of the (anti)proton mass and magnetic moment Wolfgang Quint GSI Darmstadt and University of Heidelberg on behalf of the BASE collaboration spokesperson: Stefan Ulmer 2019 / 06 / 12 BASE – Collaboration • Mainz: Measurement of the magnetic moment of the proton, implementation of new technologies. • CERN Antiproton Decelerator: Measurement of the magnetic moment of the antiproton and proton/antiproton q/m ratio • Hannover/PTB: Laser cooling project, new technologies Institutes: RIKEN, MPI-K, CERN, University of Mainz, Tokyo University, GSI Darmstadt, University of Hannover, PTB Braunschweig C. Smorra et al., EPJ-Special Topics, The BASE Experiment, (2015) WE HAVE A PROBLEM mechanism which created the obvious baryon/antibaryon asymmetry in the Universe is not understood One strategy: Compare the fundamental properties of matter / antimatter conjugates with ultra-high precision CPT tests based on particle/antiparticle comparisons R.S. Van Dyck et al., Phys. Rev. Lett. 59 , 26 (1987). Recent B. Schwingenheuer, et al., Phys. Rev. Lett. 74, 4376 (1995). Past CERN H. Dehmelt et al., Phys. Rev. Lett. 83 , 4694 (1999). G. W. Bennett et al., Phys. Rev. D 73 , 072003 (2006). Planned M. Hori et al., Nature 475 , 485 (2011). ALICE G. Gabriesle et al., PRL 82 , 3199(1999). J. DiSciacca et al., PRL 110 , 130801 (2013). S. Ulmer et al., Nature 524 , 196-200 (2015). ALICE Collaboration, Nature Physics 11 , 811–814 (2015). M. Hori et al., Science 354 , 610 (2016). H. Nagahama et al., Nat. Comm. 8, 14084 (2017). M. Ahmadi et al., Nature 541 , 506 (2017). M. Ahmadi et al., Nature 586 , doi:10.1038/s41586-018-0017 (2018).
  • Interactions of Antiprotons with Atoms and Molecules

    Interactions of Antiprotons with Atoms and Molecules

    University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln US Department of Energy Publications U.S. Department of Energy 1988 INTERACTIONS OF ANTIPROTONS WITH ATOMS AND MOLECULES Mitio Inokuti Argonne National Laboratory Follow this and additional works at: https://digitalcommons.unl.edu/usdoepub Part of the Bioresource and Agricultural Engineering Commons Inokuti, Mitio, "INTERACTIONS OF ANTIPROTONS WITH ATOMS AND MOLECULES" (1988). US Department of Energy Publications. 89. https://digitalcommons.unl.edu/usdoepub/89 This Article is brought to you for free and open access by the U.S. Department of Energy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in US Department of Energy Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. /'Iud Tracks Radial. Meas., Vol. 16, No. 2/3, pp. 115-123, 1989 0735-245X/89 $3.00 + 0.00 Inl. J. Radial. Appl .. Ins/rum., Part D Pergamon Press pic printed in Great Bntam INTERACTIONS OF ANTIPROTONS WITH ATOMS AND MOLECULES* Mmo INOKUTI Argonne National Laboratory, Argonne, Illinois 60439, U.S.A. (Received 14 November 1988) Abstract-Antiproton beams of relatively low energies (below hundreds of MeV) have recently become available. The present article discusses the significance of those beams in the contexts of radiation physics and of atomic and molecular physics. Studies on individual collisions of antiprotons with atoms and molecules are valuable for a better understanding of collisions of protons or electrons, a subject with many applications. An antiproton is unique as' a stable, negative heavy particle without electronic structure, and it provides an excellent opportunity to study atomic collision theory.
  • BOTTOM, STRANGE MESONS (B = ±1, S = ∓1) 0 0 ∗ Bs = Sb, Bs = S B, Similarly for Bs ’S

    BOTTOM, STRANGE MESONS (B = ±1, S = ∓1) 0 0 ∗ Bs = Sb, Bs = S B, Similarly for Bs ’S

    Citation: P.A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2020, 083C01 (2020) BOTTOM, STRANGE MESONS (B = ±1, S = ∓1) 0 0 ∗ Bs = sb, Bs = s b, similarly for Bs ’s 0 P − Bs I (J ) = 0(0 ) I , J, P need confirmation. Quantum numbers shown are quark-model predictions. Mass m 0 = 5366.88 ± 0.14 MeV Bs m 0 − mB = 87.38 ± 0.16 MeV Bs Mean life τ = (1.515 ± 0.004) × 10−12 s cτ = 454.2 µm 12 −1 ∆Γ 0 = Γ 0 − Γ 0 = (0.085 ± 0.004) × 10 s Bs BsL Bs H 0 0 Bs -Bs mixing parameters 12 −1 ∆m 0 = m 0 – m 0 = (17.749 ± 0.020) × 10 ¯h s Bs Bs H BsL = (1.1683 ± 0.0013) × 10−8 MeV xs = ∆m 0 /Γ 0 = 26.89 ± 0.07 Bs Bs χs = 0.499312 ± 0.000004 0 CP violation parameters in Bs 2 −3 Re(ǫ 0 )/(1+ ǫ 0 )=(−0.15 ± 0.70) × 10 Bs Bs 0 + − CKK (Bs → K K )=0.14 ± 0.11 0 + − SKK (Bs → K K )=0.30 ± 0.13 0 ∓ ± +0.10 rB(Bs → Ds K )=0.37−0.09 0 ± ∓ ◦ δB(Bs → Ds K ) = (358 ± 14) −2 CP Violation phase βs = (2.55 ± 1.15) × 10 rad λ (B0 → J/ψ(1S)φ)=1.012 ± 0.017 s λ = 0.999 ± 0.017 A, CP violation parameter = −0.75 ± 0.12 C, CP violation parameter = 0.19 ± 0.06 S, CP violation parameter = 0.17 ± 0.06 L ∗ 0 ACP (Bs → J/ψ K (892) ) = −0.05 ± 0.06 k ∗ 0 ACP (Bs → J/ψ K (892) )=0.17 ± 0.15 ⊥ ∗ 0 ACP (Bs → J/ψ K (892) ) = −0.05 ± 0.10 + − ACP (Bs → π K ) = 0.221 ± 0.015 0 + − ∗ 0 ACP (Bs → [K K ]D K (892) ) = −0.04 ± 0.07 HTTP://PDG.LBL.GOV Page1 Created:6/1/202008:28 Citation: P.A.
  • 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.
  • Electron-Positron Pairs in Physics and Astrophysics

    Electron-Positron Pairs in Physics and Astrophysics

    Electron-positron pairs in physics and astrophysics: from heavy nuclei to black holes Remo Ruffini1,2,3, Gregory Vereshchagin1 and She-Sheng Xue1 1 ICRANet and ICRA, p.le della Repubblica 10, 65100 Pescara, Italy, 2 Dip. di Fisica, Universit`adi Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy, 3 ICRANet, Universit´ede Nice Sophia Antipolis, Grand Chˆateau, BP 2135, 28, avenue de Valrose, 06103 NICE CEDEX 2, France. Abstract Due to the interaction of physics and astrophysics we are witnessing in these years a splendid synthesis of theoretical, experimental and observational results originating from three fundamental physical processes. They were originally proposed by Dirac, by Breit and Wheeler and by Sauter, Heisenberg, Euler and Schwinger. For almost seventy years they have all three been followed by a continued effort of experimental verification on Earth-based experiments. The Dirac process, e+e 2γ, has been by − → far the most successful. It has obtained extremely accurate experimental verification and has led as well to an enormous number of new physics in possibly one of the most fruitful experimental avenues by introduction of storage rings in Frascati and followed by the largest accelerators worldwide: DESY, SLAC etc. The Breit–Wheeler process, 2γ e+e , although conceptually simple, being the inverse process of the Dirac one, → − has been by far one of the most difficult to be verified experimentally. Only recently, through the technology based on free electron X-ray laser and its numerous applications in Earth-based experiments, some first indications of its possible verification have been reached. The vacuum polarization process in strong electromagnetic field, pioneered by Sauter, Heisenberg, Euler and Schwinger, introduced the concept of critical electric 2 3 field Ec = mec /(e ).
  • ANTIMATTER a Review of Its Role in the Universe and Its Applications

    ANTIMATTER a Review of Its Role in the Universe and Its Applications

    A review of its role in the ANTIMATTER universe and its applications THE DISCOVERY OF NATURE’S SYMMETRIES ntimatter plays an intrinsic role in our Aunderstanding of the subatomic world THE UNIVERSE THROUGH THE LOOKING-GLASS C.D. Anderson, Anderson, Emilio VisualSegrè Archives C.D. The beginning of the 20th century or vice versa, it absorbed or emitted saw a cascade of brilliant insights into quanta of electromagnetic radiation the nature of matter and energy. The of definite energy, giving rise to a first was Max Planck’s realisation that characteristic spectrum of bright or energy (in the form of electromagnetic dark lines at specific wavelengths. radiation i.e. light) had discrete values The Austrian physicist, Erwin – it was quantised. The second was Schrödinger laid down a more precise that energy and mass were equivalent, mathematical formulation of this as described by Einstein’s special behaviour based on wave theory and theory of relativity and his iconic probability – quantum mechanics. The first image of a positron track found in cosmic rays equation, E = mc2, where c is the The Schrödinger wave equation could speed of light in a vacuum; the theory predict the spectrum of the simplest or positron; when an electron also predicted that objects behave atom, hydrogen, which consists of met a positron, they would annihilate somewhat differently when moving a single electron orbiting a positive according to Einstein’s equation, proton. However, the spectrum generating two gamma rays in the featured additional lines that were not process. The concept of antimatter explained. In 1928, the British physicist was born.
  • 1 Drawing Feynman Diagrams

    1 Drawing Feynman Diagrams

    1 Drawing Feynman Diagrams 1. A fermion (quark, lepton, neutrino) is drawn by a straight line with an arrow pointing to the left: f f 2. An antifermion is drawn by a straight line with an arrow pointing to the right: f f 3. A photon or W ±, Z0 boson is drawn by a wavy line: γ W ±;Z0 4. A gluon is drawn by a curled line: g 5. The emission of a photon from a lepton or a quark doesn’t change the fermion: γ l; q l; q But a photon cannot be emitted from a neutrino: γ ν ν 6. The emission of a W ± from a fermion changes the flavour of the fermion in the following way: − − − 2 Q = −1 e µ τ u c t Q = + 3 1 Q = 0 νe νµ ντ d s b Q = − 3 But for quarks, we have an additional mixing between families: u c t d s b This means that when emitting a W ±, an u quark for example will mostly change into a d quark, but it has a small chance to change into a s quark instead, and an even smaller chance to change into a b quark. Similarly, a c will mostly change into a s quark, but has small chances of changing into an u or b. Note that there is no horizontal mixing, i.e. an u never changes into a c quark! In practice, we will limit ourselves to the light quarks (u; d; s): 1 DRAWING FEYNMAN DIAGRAMS 2 u d s Some examples for diagrams emitting a W ±: W − W + e− νe u d And using quark mixing: W + u s To know the sign of the W -boson, we use charge conservation: the sum of the charges at the left hand side must equal the sum of the charges at the right hand side.
  • Symmetric Tensor Gauge Theories on Curved Spaces

    Symmetric Tensor Gauge Theories on Curved Spaces

    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Caltech Authors Symmetric Tensor Gauge Theories on Curved Spaces Kevin Slagle Department of Physics, University of Toronto Toronto, Ontario M5S 1A7, Canada Department of Physics and Institute for Quantum Information and Matter California Institute of Technology, Pasadena, California 91125, USA Abhinav Prem, Michael Pretko Department of Physics and Center for Theory of Quantum Matter University of Colorado, Boulder, CO 80309 Abstract Fractons and other subdimensional particles are an exotic class of emergent quasi-particle excitations with severely restricted mobility. A wide class of models featuring these quasi-particles have a natural description in the language of symmetric tensor gauge theories, which feature conservation laws restricting the motion of particles to lower-dimensional sub-spaces, such as lines or points. In this work, we investigate the fate of symmetric tensor gauge theories in the presence of spatial curvature. We find that weak curvature can induce small (exponentially suppressed) violations on the mobility restrictions of charges, leaving a sense of asymptotic fractonic/sub-dimensional behavior on generic manifolds. Nevertheless, we show that certain symmetric tensor gauge theories maintain sharp mobility restrictions and gauge invariance on certain special curved spaces, such as Einstein manifolds or spaces of constant curvature. Contents 1 Introduction 2 2 Review of Symmetric Tensor Gauge Theories3 2.1 Scalar Charge Theory . .3 2.2 Traceless Scalar Charge Theory . .4 2.3 Vector Charge Theory . .4 2.4 Traceless Vector Charge Theory . .5 3 Curvature-Induced Violation of Mobility Restrictions6 4 Robustness of Fractons on Einstein Manifolds8 4.1 Traceless Scalar Charge Theory .
  • Atsuko K. Ichikawa, Kyoto University

    Atsuko K. Ichikawa, Kyoto University

    EXPLORING PARTICLE-ANTIPARTICLE ASYMMETRY IN NEUTRINO OSCILLATION Atsuko K. Ichikawa, Kyoto University INTRODUCTION OF MYSELF • Got PhD by detecting doubly-strange nuclei using emulsion • After that, working on accelerator-based long- baseline neutrino oscillation experiments in Japan, especially on neutrino production, neutrino detector in accelerator-site and analysis. • Recently, started a high- pressure Xenon gas project for double-beta decay search 2 CONSTITUENTS OF THIS WORLD How can we distinguish btw. u, c and t Electric d, s and b charge e, and e, and Same spin, same charge… Only by mass! Except for ’s. + (Higgs, dark matter, dark energy…..?) Fig. from FNAL home page 3 HOW CAN WE DISTINGUISH NEUTRINOS? - IT IS TWO SIDES OF COINS- Neutrinos do interact with matter and 4 HOW CAN WE DISTINGUISH NEUTRINOS? - IT IS TWO SIDES OF COINS- Neutrinos do interact with matter and • An electron neutrino changes to an electron. We call this • A muon neutrino changes to a muon. categorization • A tau neutrino changes to atau. ‘flavor’. And it was believed that electron neutrino only changes to electron, never into muon nor tau before the neutrino oscillation was found. 5 NEUTRINOS DO INTERACT, BUT …. photon Concrete Wall X-ray ~1cm High Energy Mean Free path ~10cm of particles High Energy proton ~30cm ~1GeV muon ~200cm ~1GeV neutrino (atmospheric, accelerator) ~108 km≒distance btw. Solar and earth ~1MeV neutrino (solar, reactor) ~1014 km≒100 light-year 6 SUPER-KAMIOKANDE 7 SUPER-KAMIOKANDE • Since April 1996 • Water Cherenkov detector w/
  • Chapter 6. Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws

    Chapter 6. Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws

    Chapter 6. Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws 6.1 Displacement Current The magnetic field due to a current distribution satisfies Ampere’s law, (5.45) Using Stokes’s theorem we can transform this equation into an integral form: ∮ ∫ (5.47) We shall examine this law, show that it sometimes fails, and find a generalization that is always valid. Magnetic field near a charging capacitor loop C Fig 6.1 parallel plate capacitor Consider the circuit shown in Fig. 6.1, which consists of a parallel plate capacitor being charged by a constant current . Ampere’s law applied to the loop C and the surface leads to ∫ ∫ (6.1) If, on the other hand, Ampere’s law is applied to the loop C and the surface , we find (6.2) ∫ ∫ Equations 6.1 and 6.2 contradict each other and thus cannot both be correct. The origin of this contradiction is that Ampere’s law is a faulty equation, not consistent with charge conservation: (6.3) ∫ ∫ ∫ ∫ 1 Generalization of Ampere’s law by Maxwell Ampere’s law was derived for steady-state current phenomena with . Using the continuity equation for charge and current (6.4) and Coulombs law (6.5) we obtain ( ) (6.6) Ampere’s law is generalized by the replacement (6.7) i.e., (6.8) Maxwell equations Maxwell equations consist of Eq. 6.8 plus three equations with which we are already familiar: (6.9) 6.2 Vector and Scalar Potentials Definition of and Since , we can still define in terms of a vector potential: (6.10) Then Faradays law can be written ( ) The vanishing curl means that we can define a scalar potential satisfying (6.11) or (6.12) 2 Maxwell equations in terms of vector and scalar potentials and defined as Eqs.
  • Neutrino Masses-How to Add Them to the Standard Model

    Neutrino Masses-How to Add Them to the Standard Model

    he Oscillating Neutrino The Oscillating Neutrino of spatial coordinates) has the property of interchanging the two states eR and eL. Neutrino Masses What about the neutrino? The right-handed neutrino has never been observed, How to add them to the Standard Model and it is not known whether that particle state and the left-handed antineutrino c exist. In the Standard Model, the field ne , which would create those states, is not Stuart Raby and Richard Slansky included. Instead, the neutrino is associated with only two types of ripples (particle states) and is defined by a single field ne: n annihilates a left-handed electron neutrino n or creates a right-handed he Standard Model includes a set of particles—the quarks and leptons e eL electron antineutrino n . —and their interactions. The quarks and leptons are spin-1/2 particles, or weR fermions. They fall into three families that differ only in the masses of the T The left-handed electron neutrino has fermion number N = +1, and the right- member particles. The origin of those masses is one of the greatest unsolved handed electron antineutrino has fermion number N = 21. This description of the mysteries of particle physics. The greatest success of the Standard Model is the neutrino is not invariant under the parity operation. Parity interchanges left-handed description of the forces of nature in terms of local symmetries. The three families and right-handed particles, but we just said that, in the Standard Model, the right- of quarks and leptons transform identically under these local symmetries, and thus handed neutrino does not exist.
  • Introduction to Gauge Theories and the Standard Model*

    Introduction to Gauge Theories and the Standard Model*

    INTRODUCTION TO GAUGE THEORIES AND THE STANDARD MODEL* B. de Wit Institute for Theoretical Physics P.O.B. 80.006, 3508 TA Utrecht The Netherlands Contents The action Feynman rules Photons Annihilation of spinless particles by electromagnetic interaction Gauge theory of U(1) Current conservation Conserved charges Nonabelian gauge fields Gauge invariant Lagrangians for spin-0 and spin-g Helds 10. The gauge field Lagrangian 11. Spontaneously broken symmetry 12. The Brout—Englert-Higgs mechanism 13. Massive SU (2) gauge Helds 14. The prototype model for SU (2) ® U(1) electroweak interactions The purpose of these lectures is to give an introduction to gauge theories and the standard model. Much of this material has also been covered in previous Cem Academic Training courses. This time I intend to start from section 5 and develop the conceptual basis of gauge theories in order to enable the construction of generic models. Subsequently spontaneous symmetry breaking is discussed and its relevance is explained for the renormalizability of theories with massive vector fields. Then we discuss the derivation of the standard model and its most conspicuous features. When time permits we will address some of the more practical questions that arise in the evaluation of quantum corrections to particle scattering and decay reactions. That material is not covered by these notes. CERN Academic Training Programme — 23-27 October 1995 OCR Output 1. The action Field theories are usually defined in terms of a Lagrangian, or an action. The action, which has the dimension of Planck’s constant 7i, and the Lagrangian are well-known concepts in classical mechanics.