DOCSLIB.ORG

Lorentz Invariant Relative Velocity and Relativistic Binary Collisions

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Lorentz Invariant Relative Velocity and Relativistic Binary Collisions Lorentz invariant relative velocity and relativistic binary collisions Mirco Cannoni∗ Departamento de F´ısica Aplicada, Facultad de Ciencias Experimentales, Universidad de Huelva, 21071 Huelva, Spain (Dated: May 2, 2016) This article reviews the concept of Lorentz invariant relative velocity that is often misunderstood or unknown in high energy physics literature. The properties of the relative velocity allow to formulate the invariant flux and cross section without recurring to non–physical velocities or any assumption about the reference frame. Applications such as the luminosity of a collider, the use as kinematic variable, and the statistical theory of collisions in a relativistic classical gas are reviewed. It is emphasized how the hyperbolic properties of the velocity space explain the peculiarities of relativistic scattering. CONTENTS section. To fix the ideas we consider the total cross sec- tion for binary collisions 1 + 2 f where f is a final → I. Introduction 1 state with 2 or more particles. The basic quantity that is measured in experiments is II. The definition of invariant cross section: three the reaction rate, that is the number of events with the problems and a solution 2 final state f per unit volume per unit of time, A. Why collinear velocities? 2 dN dN The Møller’s flux 3 f f f = = 4 . (1) B. ‘Who’ is the relative velocity? 3 R dV dt d x C. Transformation of densities 4 The value of the reaction rate is proportional to the num- D. The Landau-Lifschitz solution 4 ber density of particles n1 and n2 that approach each other with a certain relative velocity, for example an in- III. Properties of the invariant relative velocity 5 cident beam on a fixed target or two colliding beams. A. Metric and hyperbolic properties 5 This is the so–called initial (or incident) flux F . The B. Manifestly invariant representations 6 physical quantity that gives the intrinsic quantum prob- ability for a transition independent from the details of IV. Lorentz invariant definition of flux 7 the initial state is the cross section defined as the ratio σ = f /F . V. Flux and luminosity at colliders 7 InR nonrelativistic scattering the initial flux is given by VI. Relative velocity as kinematic variable 8 Fnr = n1n2vr, (2) VII. Relative velocity and relativistic collisions in where gases 9 A. The relativistic classical gas 10 vr = v1 v2 , (3) | − | B. Thermal averaged cross section 11 1 C. Boltzmann equation 11 is the nonrelativistic relative velocity. D. Rate equation 12 Since the number of events Nf does not depend on the reference frame and d4x is invariant, it is essential arXiv:1605.00569v2 [hep-ph] 5 May 2016 VIII. Final comments 13 that the initial flux F and the cross section σ are invari- ant under proper Lorentz transformations such that their Acknowledgments 13 product f is invariant. The expressions (2) and (3) are not invariantR under Lorentz transformations and are not References 13 valid in the relativistic framework. We start this review, Section II, with a critical discus- sion of how the relativistic flux is presented in textbooks. I. INTRODUCTION This will lead us to review in Section III the properties of the invariant relative velocity and to discuss a simple In every book on relativistic quantum field theory and Lorentz invariant definition of the flux in Section IV. We particle physics a section or an appendix is necessarily devoted to the formulation of the Lorentz invariant cross 1 When explicitly written, we assume that the velocities are given in the laboratory frame. Although sometimes used as synony- mous, we here distinguish the laboratory from the rest frame of ∗ [email protected] massive particles. 2 then review some important applications to the theory Now we note that2 of relativistic scattering: the luminosity of a collider in 2 2 2 Section V, the use of the invariant relative velocity as (p1 p2) m m = F ≡ · − 1 2 kinematic variable in Section VI, and the theory of colli- [m2pq2 + m2p2 2E E p p + p2p2 + (p p )2]1/2, sions in a relativistic gas in Section VII. Overall, we shall 2 1 2 2 1 2 1 2 1 2 1 2 − · · (7) emphasize how the hyperbolic nature of the relativistic velocity space manifests itself in concrete physical appli- where we used again the relativistic energy formula. If cations. the velocities are collinear, the last two terms in (7) are equal and sum to give the last term in (6). In this case the expressions (6) and (7) coincide and the flux (5) becomes II. THE DEFINITION OF INVARIANT CROSS n n F = 1 2 . (8) SECTION: THREE PROBLEMS AND A E1E2 F SOLUTION The product of the number densities is n1n2 = 4E1E2, hence In quantum field theory the invariant rate corresponds to the probability per unit time per unit volume of a F =4 . (9) single transition i f, th = dPfi and is given by F → Rfi dV dt This is the most popular form of the flux in particle n 3 physics also reported in the review of the Particle Data d p + th = 2(2π)4δ4(P P ) j . (4) Group [O 14]. Rfi |Mfi| i − f (2π)32E j=3 j Z Y A. Why collinear velocities? Equation (4) refers to the scattering of unpolarized par- ticles, hence the square of the amplitude is summed over the final spins and averaged over the initial spins. With If we start from Eq. (5), the assumption of collinear- ity is necessary because, taking the velocities along the Pi and Pf we indicate the total 4-momentum of the initial and final states, respectively. z axis for example, the expression E1E2 v1z v2z = E p E p is at least invariant under| boosts− along| In (4) we use the normalization of one–particle states | 2 1z − 1 2z | 3 3 the z axis, even if not under a general Lorentz transfor- p p′ = (2π) 2Eδ (p p′) both for bosons and fermions, whichh | i corresponds to− ‘2E particles per unit volume’ in- mation. This corresponds to the simplification of the last stead of ‘one particle per unit volume’. The densities ap- terms in Eq. (7). The final expression (9) is anyway a Lorentz scalar, pearing in the flux according to this convention are thus 3 n = 2E. We shall see that for an experimentalist or in hence also valid for noncollinear velocities as can be eas- the case of a gas of particles, the densities are something ily seen in the following way. Dividing Eq. (7) by E1E2, more concrete. the right hand side can be written as Although in the Introduction we argued that Eq. (2) is 1/2 p p 2 p p 2 p 2 p 2 not valid in the relativistic framework, the starting point 1 2 + 1 2 1 2 E − E E · E − E E of quantum field theory and particle physics textbooks is " 1 2 1 2 1 2 # nonetheless the nonrelativistic expression = [(v v )2 + (v v )2 v2v2]1/2. (10) 1 − 2 1 · 2 − 1 2 F = n n v v , (5) Using the vector identity 1 2| 1 − 2| (a b)2 = a2b2 (a b)2 (11) where velocities v1 and v2 are required to be collinear. × − · This includes as particular cases the expression of the flux in the rest frame of massive particles and in the center of momentum frame. We shall discuss in a moment this 2 Four-vectors are indicated as a = (a0, a) and the Minkowski 0 0 assumption. Let us proceed and use v = p/E to rewrite scalar product as a b = a b a b. Natural units ~ = c = kB = 1 · − · Eq. (5) as are used. 3 In many textbooks, for example [BD64], [HM84], [Bro94], [Kak93], [GR08], [Tul11] it is incorrectly stated E2p1 E1p2 that Eq. (9) is valid only for collinear velocities. The motivation n1n2 − . E1E2 is that the cross section must be invariant under boosts along the perpendicular direction in order to transform as an area 2 2 p2 transverse to the beams direction, see also [PS95], [Zee10]. Employing E = m + we find This argument is irrelevant for the definition of the theoretical quantum cross section, and we shall see in Section V, when discussing luminosity of a collider, that collisions with real E2p1 E1p2 | − | beams are almost never collinear, thus full Lorentz invariance is 2 2 2 2 2 2 1/2 = [m p + m p 2E E p p +2p p ] . (6) necessary. 2 1 2 2 − 1 2 1 · 2 1 2 3 in (10), it follows B. ‘Who’ is the relative velocity? 2 2 F = (v1 v2) (v1 v2) v.¯ (12) It is important to remark that Møller puts the product E1E2 − − × ≡ p E1E2 in ratio with the product of densities n1n2, not with Therefore for every v1 and v2 we can write the scalar B. He does not introduce any ‘Møller velocity’ 2 2 F = n1n2 (v1 v2) (v1 v2) . (13) or call relative velocity the quantityv ¯ defined in (12). − − × The misleading identification ofv ¯ = /E1E2 with a The collinear flux (5p) is just a particular case of the in- relative velocity or a ‘Møller velocity’ isF posterior, prob- variant expression (13) when v v = 0. 1 × 2 ably suggested by the deceptive similarity of F = n1n2v¯ with the nonrelativistic expression Fnr = n1n2vr. As a matter of fact, in particle physics literature, some The Møller’s flux authors consider the quantityv ¯ as the relative velocity that generalizes the nonrelativistic expression vr, for oth- Formula (13) was proposed a long time ago in [Mø45].
Load more

Recommended publications
  • Simulating Gamma-Ray Binaries with a Relativistic Extension of RAMSES? A
    A&A 560, A79 (2013) Astronomy DOI: 10.1051/0004-6361/201322266 & c ESO 2013 Astrophysics Simulating gamma-ray binaries with a relativistic extension of RAMSES? A. Lamberts1;2, S. Fromang3, G. Dubus1, and R. Teyssier3;4 1 UJF-Grenoble 1 / CNRS-INSU, Institut de Planétologie et d’Astrophysique de Grenoble (IPAG) UMR 5274, 38041 Grenoble, France e-mail: [email protected] 2 Physics Department, University of Wisconsin-Milwaukee, Milwaukee WI 53211, USA 3 Laboratoire AIM, CEA/DSM - CNRS - Université Paris 7, Irfu/Service d’Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette, France 4 Institute for Theoretical Physics, University of Zürich, Winterthurestrasse 190, 8057 Zürich, Switzerland Received 11 July 2013 / Accepted 29 September 2013 ABSTRACT Context. Gamma-ray binaries are composed of a massive star and a rotation-powered pulsar with a highly relativistic wind. The collision between the winds from both objects creates a shock structure where particles are accelerated, which results in the observed high-energy emission. Aims. We want to understand the impact of the relativistic nature of the pulsar wind on the structure and stability of the colliding wind region and highlight the differences with colliding winds from massive stars. We focus on how the structure evolves with increasing values of the Lorentz factor of the pulsar wind, keeping in mind that current simulations are unable to reach the expected values of pulsar wind Lorentz factors by orders of magnitude. Methods. We use high-resolution numerical simulations with a relativistic extension to the hydrodynamics code RAMSES we have developed. We perform two-dimensional simulations, and focus on the region close to the binary, where orbital motion can be ne- glected.
    [Show full text]
  • Important Remarks on the Problem of Neutrino Passing Through the Matter Бештоев X
    E2-2011-20 Kh.M. Beshtoev IMPORTANT REMARKS ON THE PROBLEM OF NEUTRINO PASSING THROUGH THE MATTER Бештоев X. М. E2-2011-20 Важные замечания к проблеме прохождения нейтрино через вещество Считается, что при прохождении нейтрино через вещество возникает ре- зонансное усиление осцилляций нейтрино. Показано, что уравнение Вольфен- штейна, описывающее прохождение нейтрино через вещество, имеет недоста- ток (не учитывает закон сохранения импульса, т. е. предполагается, что энер- гия нейтрино в веществе изменяется, а импульс остается неизменным). Это приводит, например, к изменению эффективной массы нейтрино на величину 0,87 • 10-2 эВ, которая возникает от мизерной энергии поляризации вещества, равной 5 • 10-12 эВ. После устранения этого недостатка, т.е. после учета из- менения импульса нейтрино в веществе, получены решения данного уравнения. В этих решениях возникают очень маленькие усиления осцилляции нейтрино в солнечном веществе из-за маленького значения энергии поляризации вещества при прохождении нейтрино. Также получены решения этого уравнения для двух предельных случаев. Работа выполнена в Лаборатории физики высоких энергий им. В. И. Векслера и А. М. Балдина ОИЯИ. Сообщение Объединенного института ядерных исследований. Дубна, 2011 Beshtoev Kh. M. E2-2011-20 Important Remarks on the Problem of Neutrino Passing through the Matter It is supposed that resonance enhancement of neutrino oscillations in the matter appears while a neutrino is passing through the matter. It is shown that Wolfenstein's equation, for a neutrino passing through the matter, has a disadvantage (it does not take into account the law of momentum conservation; i.e., it is supposed that in the matter the neutrino energy changes, but its momentum does not). It leads, for example, to changing the effective mass of the neutrino by the value 0.87 • 10-2 eV from a very small value of energy polarization of the matter caused by the neutrino, which is equal to 5 • 10-12 eV.
    [Show full text]
  • The Physics of Tachyons II. Tachyon Dynamics*
    Aust. J. Phys., 1992, 45, 725-38 The Physics of Tachyons II. Tachyon Dynamics* Ross L. Dawe A and Kenneth C. Hines School of Physics, University of Melbourne, Parkville, Vic. 3052, Australia. A Present address: Maritime Operations Division, Materials Research Laboratory, P.O. Box 1750, Salisbury, S.A. 5108, Australia. Abstract This paper extends the development of a new formulation of the theory of tachyons to encompass tachyon dynamics. Topics discussed include tachyonic energy and momentum, proper mass, force and acceleration. 1. Introduction The aim of this paper is to build upon the work of Dawe and Hines (1992) (hereafter referred to as Paper I) in developing a new formulation of the theory of tachyons which is logical and self-consistent. The material in this paper extends the theory of tachyons to cover the subject of dynamics and discusses topics such as energy, momentum, proper mass, force and acceleration. The overall result of Paper I was to show that the framework of special relativity (SR) can be extended to include particles having a relative speed greater than the speed of light in free space. The requirements necessary to allow this extension of special relativity into extended relativity (ER) are the switching principle (expressed mathematically as the '1'-rule'), a standard convention for decomposing imaginary square roots and the minor modification of some familiar definitions such as 'source' and 'detector'. The results and definitions of ER automatically reduce to those of SR as soon as the objects appear to the observer to be bradyons. Some terms will be in common usage throughout this work, so they will be defined here.
    [Show full text]
  • Neutrino Masses and Oscillations in Theories Beyond the Standard Model
    HELSINKI INSTITUTE OF PHYSICS INTERNAL REPORT SERIES HIP-2018-02 Neutrino masses and oscillations in theories beyond the Standard Model By TIMO J. KÄRKKÄINEN Helsinki Institute of Physics and Department of Physics Faculty of Science UNIVERSITY OF HELSINKI FINLAND An academic dissertation for the the degree of DOCTOR OF PHILOSOPHY to be presented with the permission of the Fac- ulty of Science of University of Helsinki, for public criticism in the lecture hall E204 of Physicum (Gustaf Hällströmin katu 2, Helsinki) on Friday, 19th of October, 2018 at 12 o’clock. HELSINKI 2018 This thesis is typeset in LATEX, using memoir class. HIP internal report series HIP-2018-02 ISBN (paper) 978-951-51-1275-0 ISBN (pdf) 978-951-51-1276-7 ISSN 1455-0563 © Timo Kärkkäinen, 2018 Printed in Finland by Unigrafia. TABLE OF CONTENTS Page 1 Introduction 1 1.1 History ................................... 1 1.1.1 History of non-oscillation neutrino physics . ...... 1 1.1.2 History of neutrino oscillations ................ 3 1.1.3 History of speculative neutrino physics ........... 5 1.2 Standard Model . ........................... 6 1.2.1 Gauge sector . .......................... 8 1.2.2 Kinetic sector . .......................... 9 1.2.3 Brout-Englert-Higgs mechanism ............... 10 1.2.4 Yukawa sector . .......................... 12 1.3 Some problems in the Standard Model ................ 13 1.3.1 Flavour problem ......................... 13 1.3.2 Neutrino masses ......................... 13 1.3.3 Hierarchy problem ........................ 14 1.3.4 Cosmological issues ....................... 14 1.3.5 Strong CP problem ........................ 15 2 Phenomenology of massive light neutrinos 16 2.1 Dirac mass term . ........................... 17 2.2 Weak lepton current ..........................
    [Show full text]
  • Neutrino Oscillations and Thus for Physics Beyond the Standard Model of Par- Ticle Physics
    The Pennsylvania State University The Graduate School NEUTRINO FLAVOR OSCILLATIONS IN THE ICECUBE DEEPCORE ARRAY A Dissertation in Physics by Gerardo Giordano ⃝c 2011 Gerardo Giordano Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2011 The dissertation of Gerardo Giordano was reviewed and approved∗ by the following: Irina Mocioiu Associate Professor of Physics Dissertation Advisor, Chair of Committee Tyce DeYoung Assistant Professor of Physics Jorge Sofo Professor of Physics P´eterM´esz´aros Professor of Astrophysics Nitin Samarth Professor of Physics Associate Head of the Department of Physics ∗Signatures are on file in the Graduate School. Abstract A large number of experiments of different types have provided strong evidence for neutrino oscillations and thus for physics beyond the Standard Model of Par- ticle Physics. New experiments are being built and designed to further investigate neutrino oscillations, to obtain precision measurements of dominant oscillation parameters and discover sub-dominant effects. On the other hand, neutrino tele- scopes, like IceCube and the IceCube DeepCore Array, are using neutrinos as a means of learning about astrophysical sources, discovering dark matter and other high energy phenomena. Atmospheric neutrinos constitute a background for these searches. This dissertation shows that the large number of atmospheric neutri- nos that the IceCube DeepCore detector will accumulate can be used in order to extract useful information about neutrino oscillations. Atmospheric neutrino interactions within the IceCube DeepCore array are ex- amined in the context of neutrino flavor oscillations. The detection of an ap- pearance of a tau-flavored neutrino flux, not present in the original atmospheric neutrino flux is calculated and quantified using the statistical interpretation of the neutrino-induced electromagnetic and hadronic cascades within the detector.
    [Show full text]
  • Cosmological and Astrophysical Limits on Brane Fluctuations
    PHYSICAL REVIEW D 68, 103505 ͑2003͒ Cosmological and astrophysical limits on brane fluctuations J. A. R. Cembranos, A. Dobado, and A. L. Maroto Departamento de Fı´sica Teo´rica, Universidad Complutense de Madrid, 28040 Madrid, Spain ͑Received 11 July 2003; published 17 November 2003͒ We consider a general brane-world model parametrized by the brane tension scale f and the branon mass M. For a low tension compared to the fundamental gravitational scale, we calculate the relic branon abundance and its contribution to the cosmological dark matter. We compare this result with the current observational limits on the total and hot dark matter energy densities and derive the corresponding bounds on f and M. Using the nucleosynthesis bounds on the number of relativistic species, we also set a limit on the number of light branons in terms of the brane tension. Finally, we estimate the bounds coming from the energy loss rate in supernovae explosions due to massive branon emission. DOI: 10.1103/PhysRevD.68.103505 PACS number͑s͒: 95.35.ϩd, 11.10.Kk, 11.25.Ϫw I. INTRODUCTION nario ͑BWS͒, which is becoming one of the most popular extensions of the SM. In these models, the standard model The increasing observational precision is making cosmol- particles are bound to live on a three-dimensional brane em- ogy a useful tool in probing certain properties of particle bedded in a higher dimensional (Dϭ4ϩN) space-time, physics theories beyond the standard model ͑SM͒. The limits whereas gravity is able to propagate in the whole bulk space. on the neutrino masses and the number of neutrino families The fundamental scale of gravity in D dimensions M D can are probably the most clear examples ͓1,2͔.
    [Show full text]
  • Mphys Advanced Cosmology 2007–2008
    N I V E R U S E I T H Y T O H F G E R D I N B U MPhys Advanced Cosmology 2007–2008 J.A. Peacock Room C20, Royal Observatory; [email protected] http://www.roe.ac.uk/japwww/teaching/cos5.html Synopsis This course is intended to act as an extension of the current 4th-year course on Astrophysical Cosmology, which develops the basic tools for dealing with observations in an expanding universe, and gives an overview of some of the central topics in contemporary research. The aim here is to revisit this material at a level of detail more suitable as a foundation for understanding current research. Cosmology has a standard model for understanding the universe, in which the dominant theme is the energy density of the vacuum. This is observed to be non-zero today, and is hypothesised to have been much larger in the past, causing the phenomenon of ‘inflation’. An inflationary phase can not only launch the expanding universe, but can also seed irregularities that subsequently grow under gravity to create galaxies, superclusters and anisotropies in the microwave background. The course will present the methods for analysing these phenomena, leading on to some of the frontier issues in cosmology, particularly the possible existence of extra dimensions and many universes. It is intended that the course should be self contained; previous attendance at courses on cosmology or general relativity will be useful, but not essential. Recommended books (in reserve section of ROE library) Peacock: Cosmological Physics (CUP) Gives an overview of cosmology at the level of this course, but contains much more than will be covered here.
    [Show full text]
  • Physica a Thermostat for a Relativistic
    Physica A 561 (2021) 125261 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Thermostat for a relativistic gas ∗ Noah Kubli a, Hans J. Herrmann b,c, a Institut für Theoretische Physik, ETH Zürich, Switzerland b PMMH, ESPCI, 7 quai St. Bernard, 75005 Paris, France c Dept. de Física, UFC, Fortaleza, Brazil article info a b s t r a c t Article history: Molecular dynamics simulations of a three dimensional relativistic gas with a soft Available online 15 September 2020 potential are conducted with different interactions and particle masses. For all cases the velocity distribution agrees numerically with the Jüttner distribution. We show how In memory of Dietrich Stauffer the relativistic gas can be coupled to a thermostat to simulate the canonical ensemble at a given temperature T . The behaviour of the thermostat is investigated as a function of the thermal inertia and its appropriate range is determined by evaluating the kinetic energy fluctuations. ' 2020 Elsevier B.V. All rights reserved. 1. Introduction The velocity distribution of a gas is classically described by the Maxwell–Boltzmann distribution. However, this distribution does not hold in special relativity as can be seen from the fact that there would be a finite probability for particles to exceed the speed of light. This problem becomes more severe for higher temperatures. Jüttner generalised the Maxwell–Boltzmann distribution in 1911 to relativistic gases [1]. Maximising the entropy, he derived the following velocity distribution: ( 2 ) 1 3 5 mc γ (v) f (vx; vy; vz ) D m γ (v) exp − (1) Z(m; kBT ; N) kBT where T is the temperature, k the Boltzmann constant, m the mass of the particles, N the number of particles, γ (v) D p B 1= 1 − v2=c2 the Lorentz factor and c the speed of light.
    [Show full text]
  • Transition Radiation of Ultrarelativistic Neutral Particles*
    AT9800503 UWThPh-1994-40 October 7, 1994 Transition Radiation of Ultrarelativistic Neutral Particles* W. Grimus and H. Neufeld Institut fiir Theoretische Physik Universitat Wien Boltzmanngasse 5, A-1090 Wien Abstract We perform a quantum theoretical calculation of transition radiation by neutral particles with spin 1/2 equipped with magnetic moments and/or electric dipole moments. The limit of vanishing masses is treated exactly for arbitrary refraction index. Finally we apply our result to the solar neutrino flux. Suppor ed in part by Jubilaumsfonds der Osterreichischen Nationalbank, Project No. 5051 30- 10 Neutrinos seem to be likely candidates for carrying features of physics beyond the Stan- dard Model. Apart from masses and mixings also magnetic moments (MM) and electric dipole moments (EDM) are signs of new physics and are of relevance in terrestrial experiments, the solar neutrino problem [1], astrophysics and cosmology. Elastic v-e~ scattering restricts MMs 18 to//*. +2.1//^ < 1.16-10~ fi% [2] and \fxVr\ < 5.4-10"VB [3] where fiB is the Bohr magneton. Limits on //„,. from e+e~ —> vi/j are an order of magnitude weaker [4]. Note that in the above inequalities /z2 can be replaced by fi2 + d2 since MMs // and EDMs d become indistinguishable when neutrino masses can be neglected. Astrophysical and cosmological bounds are considerably tighter but subject to additional assumptions (see e.g. [5]). In this paper we explore the possibility of using electromagnetic interactions of neutrinos with polarizable media to get information on neutrino MMs and EDMs. The case of an in- finitely extended homogeneous medium where Cherenkov radiation is emitted has already been discussed in a previous paper [6].
    [Show full text]
  • Dark Matter, Millicharges, Axion and Scalar Particles, Gauge Bosons, and Other New Physics with LDMX
    PHYSICAL REVIEW D 99, 075001 (2019) Dark matter, millicharges, axion and scalar particles, gauge bosons, and other new physics with LDMX Asher Berlin,1 Nikita Blinov,1 Gordan Krnjaic,2 Philip Schuster,1 and Natalia Toro1 1SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA 2Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA (Received 1 October 2018; published 1 April 2019) The proposed LDMX experiment would provide roughly a meter-long region of instrumented tracking and calorimetry that acts as a beam stop for multi-GeV electrons in which each electron is tagged and its evolution measured. This would offer an unprecedented opportunity to access both collider-invisible and ultrashort-lifetime decays of new particles produced in electron (or muon) nuclear fixed-target collisions. In this paper, we show that the missing momentum channel and displaced decay signals in such an experiment could provide world-leading sensitivity to sub-GeV dark matter, millicharged particles, and visibly or invisibly decaying axions, scalars, dark photons, and a range of other new physics scenarios. DOI: 10.1103/PhysRevD.99.075001 I. INTRODUCTION energy search by NA64 at CERN [2] and provides roughly a meter-long region of instrumented tracking and calorim- Particle dark matter (DM) science is undergoing a etry that acts as a beam stop. The detector concept revolution, driven simultaneously by recent advances in allows each individual electron to be tagged and its theory and experiment. New theory insight has motivated evolution measured as it passes through a thin target, broadening the mass range for DM searches to include the tracking planes, and a high-granularity silicon-tungsten entire MeV–TeV range and beyond, extending the traditional calorimeter.
    [Show full text]
  • Electromagnetic Catastrophe in Ultrarelativistic Shocks and the Prompt Emission of Gamma-Ray Bursts  Boris E
    Mon. Not. R. Astron. Soc. 345, 590–600 (2003) Electromagnetic catastrophe in ultrarelativistic shocks and the prompt emission of gamma-ray bursts Boris E. Stern1,2 1Institute for Nuclear Research, Russian Academy of Sciences, Moscow 117312, Russia 2Astro Space Centre of Lebedev Physical Institute, Moscow, Profsoyuznaya 84/32, 117997, Russia Accepted 2003 June 30. Received 2003 June 23; in original form 2003 January 20 Downloaded from https://academic.oup.com/mnras/article/345/2/590/1747042 by guest on 25 September 2021 ABSTRACT It is shown that an ultrarelativistic shock with the Lorentz factor of the order of tens or higher, propagating in a moderately dense interstellar medium (density above ∼1000 cm−3), undergoes a fast dramatic transformation into a highly radiative state. The process leading to this phenomenon resembles the first-order Fermi acceleration with the difference that the energy is transported across the shock front by photons rather than protons. The reflection of the energy flux crossing the shock front in both directions is due to photon–photon pair production and Compton scattering. Such a mechanism initiates a runaway non-linear pair cascade fed directly by the kinetic energy of the shock. Eventually, the cascade feeds back the fluid dynamics, converting the sharp shock front into a smooth velocity gradient and the runaway evolution changes to a quasi-steady-state regime. This effect has been studied numerically using the non- linear large particle Monte Carlo code for the electromagnetic component and a simplified hydrodynamic description of the fluid. The most interesting application of the effect is the phenomenon of gamma-ray bursts (GRBs) where it explains a high radiative efficiency and gives a perspective to explain spectra of GRBs and their time variability.
    [Show full text]
  • What Is Matter According to Particle Physics, and Why Try to Observe Its Creation in a Lab?
    universe Review What Is Matter According to Particle Physics, and Why Try to Observe Its Creation in a Lab? Francesco Vissani 1,2 1 INFN, Laboratori Nazionali del Gran Sasso, 67100 L’Aquila, Italy; [email protected]; Tel.: +39-346-73-28-009 2 Gran Sasso Science Institute, 67100 L’Aquila, Italy Abstract: The standard model of elementary interactions has long qualified as a theory of matter, in which the postulated conservation laws (one baryonic and three leptonic) acquire theoretical mean- ing. However, recent observations of lepton number violations—neutrino oscillations—demonstrate its incompleteness. We discuss why these considerations suggest the correctness of Ettore Majorana’s ideas on the nature of neutrino mass and add further interest to the search for an ultra-rare nuclear process in which two particles of matter (electrons) are created, commonly called neutrinoless double beta decay. The approach of the discussion is mainly historical, and its character is introductory. Some technical considerations, which highlight the usefulness of Majorana’s representation of gamma matrices, are presented in the appendix. Keywords: standard model extensions; neutrino masses; Majorana neutrinos; lepton number violation 1. Introduction The discussion of the nature of things is very old. We can experience the wonder of Citation: Vissani, F. What Is Matter nature, but it is almost inevitable to reason about how to reconcile the evident mutability According to Particle Physics, and of what is around us with an equally evident degree of permanence. The hypothesis ad- Why Try to Observe Its Creation in a vanced by Greek atomism is that of a simple and permanent substance, even if not directly Lab? Universe 2021, 7, 61.
    [Show full text]