DOCSLIB.ORG

Neutrino Masses-How to Add Them to the Standard Model

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

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. The left-handedness of the neutrino mimics the they have identical strong, weak, and electromagnetic interactions. left-handedness of the charged-current weak interactions. In other words, the W In the Standard Model, quarks and leptons are assumed to obtain their masses gauge boson, which mediates all weak charge- in the same way that the W and Z0 bosons obtain theirs: through interactions with changing processes, acts only on the fields e Table I. Lepton Charges the mysterious Higgs boson (named the “God Particle” by Leon Lederman). But and n . The interaction with the W transforms Yw before we write down some simple formulas that describe the interactions of quarks e w 1 the left-handed neutrino into the left-handed Q 5 I3 }} and leptons with the Higgs boson, let us define some notation. 2 electron and vice versa (e ↔ n ) or the right- L eL NNParticle States I w Yw Q Defining the Lepton Fields. For every elementary particle, we associate a field handed antineutrino into the right-handed x 3 residing in space and time. Ripples in these fields describe the motions of these positron and vice versa (n ↔ e ). Thus, weR wR 11LeL21/2 21 21 particles. A quantum mechanical description of the fields, which allows one to we say that the fields e and ne, or the particles 11L1nL211/2 210 describe multiparticle systems, makes each field a quantum mechanical operator eL and neL, are a weak isospin doublet under that can create particles out of the ground state—called the vacuum. The act of the weak interactions. 21R e11/2 11 11 creating one or more particles in the vacuum is equivalent to describing a system These lepton fields carry two types of weak wR 21Rn21/2 110 w 1wR2 in which one or more ripples in the fabric of the field move through space-time. charge: The weak isotopic charge I3 couples Let us now discuss the simple system of one family of leptons. To be specific, them to the W and the Z0, and the weak 11R e 022 21 we will call the particles in this family the electron and the electron neutrino. hypercharge Yw couples them to the Z0. (The Z0 R 21Le 012 11 The electron field describes four types of ripples (or particles). We label these four is the neutral gauge boson that mediates neutral- wL 11R n 00 0 types by two quantum charges called fermion number N and handedness, or current weak interactions.) Electric charge Q is R 21LnL 00 0 chirality, Nx. For the electron field, the particle state with fermion number N = +1 related to the two weak charges through the w w w is the electron, and the particle state with N = 21 is the antielectron (or positron). equation Q 5 I3 1 Y /2. Table I lists the weak Each of these states comes as right-handed, Nx = R, and left-handed, Nx =L. charges for the particle states defined by the Handedness is a Lorentz invariant quantity that is related in a nontrivial way to three fields e, n , and ec. Note that the particle states e and e defined by e R wL helicity, the projection of the spin s in the direction of the momentum p. (For a the field ec do not couple to the W and have no weak isotopic charge. The field discussion of handedness versus helicity, see “The Oscillating Neutrino” on page 28.) and the particle states are thus called weak isotopic singlets. However, e and e R wL In relativistic quantum field theory, the right-handed and left-handed electron do carry weak hypercharge and electric charge and therefore couple to the Z0 and the right-handed and left-handed antielectron can be defined in terms of two and the photon. fields denoted by e and ec, where each field is a Weyl two-component left-handed Likewise, the field n c and its neutrino states n and n would be isotopic e R wL spinor. The compositions of the fields are such that singlets with no coupling to the W. But unlike their electron counterparts, they w w must be electrically neutral (Q 5 I3 1 Y /2 5 0), which implies they cannot 0 e annihilates a left-handed electron eL or creates a right-handed have weak hypercharge. Thus, they would not couple to the W, the Z , or the positron e , and photon. Having no interactions and, therefore, not being measurable, they wR are called sterile neutrinos and are not included in the Standard Model. However, ec annihilates a left-handed positron e or creates a right-handed if the left-handed neutrino has mass, it may oscillate into a sterile right-handed wL electron eR. neutrino, a possibility that could be invoked in trying to give consistency to all the data on neutrino oscillations. These fields are complex, and for the action of the Hermitian conjugate fields e† and ec†, just interchange the words annihilate and create above. For example, The Origin of Electron Mass in the Standard Model. What is mass? Mass is e† creates a left-handed electron or annihilates a right-handed positron. Hence, the the inertial energy of a particle. It is the energy a particle has when at rest and the fields e and ec and their complex conjugates can create or annihilate all the possi- measure of the resistance to an applied force according to Newton’s law F = ma. ble excitations of the physical electron. Note that parity (defined as the inversion A massless particle cannot exist at rest; it must always move at the speed of light. 4 Los Alamos Science Number 25 1997 Number 25 1997 Los Alamos Science he Oscillating Neutrino The Oscillating Neutrino A fermion (spin-1/2 particle) with mass has an additional constraint. It must exist for the neutrino that would mirror the mass term for the electron. It would in both right-handed and left-handed states because the only field operators that have the form yield a nonzero mass for fermions are bilinear products of fields that flip the parti- c cle’s handedness. For example, in the two-component notation introduced above, mnne ne . (5) the standard, or Dirac, mass term in the Lagrangian for free electrons is given by* c But, as we said above, the field ne is not included in the Standard Model c mee e . (1) because, so far, weak-interaction experiments have not required it. The neutrino, though, has no electric charge, which makes it possible to write down a mass term This fermion mass operator annihilates a left-handed electron and creates a right- from the existing neutrino field ne with the form handed electron in its place. The mass term does not change the charge of 1 the particle, so we say that it conserves electric charge. Also, because this mass } m n n . (6) 2 n e e term does not change a particle into an antiparticle, we say that it conserves fermion number N. However, the weak isospin symmetry forbids such a mass (Note that mn and mn refer just to the electron neutrinos, but similar masses can operator because it is not an invariant under that symmetry. (The field e is a be defined for the m and t neutrinos.) The mass operator in (6) annihilates a left- member of a weak isotopic doublet, whereas the field ec is a weak isotopic singlet, handed neutrino and creates a right-handed antineutrino, which means that it is a so that the product of the two is not a singlet as it should be to preserve the weak Majorana mass term. Any mass term that changes a particle to an antiparticle is isospin symmetry.) But the electron does have mass. We seem to be in a bind. called a Majorana mass term. In changing a neutrino to an antineutrino, this term The Standard Model solves this problem: the electron and electron neutrino violates fermion number N, changing it by two units.
Recommended publications
  • The Five Common Particles

    The Five Common Particles

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

    The Seesaw Mechanism

    C. Amsler, Nuclear and Particle Physics The seesaw mechanism This section deals with a model to explain the triflingly small neutrino mass (< 2 eV), which is much smaller than that of other fermions such as the next lightest one, the elec- tron (0.5 MeV). In the standard model neutrinos and antineutrinos are different (Dirac) particles. The chirality of the neutrino is negative, that of the antineutrino positive (see *15.79*). The neutrinos and antineutrinos involved in the weak interaction with other particles are represented by the spinors 1 − γ5 1 + γ5 = and ( c) = c; (1) L 2 R 2 respectively, where and c are solution of the Dirac equation (chapter *15*). The spinors 1 + γ5 1 − γ5 = and ( c) = c (2) R 2 L 2 correspond to sterile neutrinos and antineutrinos. The following discussion deals with only one flavour of neutrinos, say νe, but is ap- plicable to νµ and ντ as well. We shall denote the neutrino spinor by and that of the charge conjugated antineutrino by c. We have shown in section *15.5* that T T c = C = iγ2γ0 : (3) Table1 lists a few useful relations satisfied by the charge conjugation C, which are easily verified by using the properties of γ matrices derived in chapter *15*. Table 1: Some properties of the charge conjugation. Cy = CT = −C C2 = −1 CCy = 1 CCT = 1 Cγ0C = γ0 γ0Cγ0 = −C We have seen e.g. in section *14.4* that the neutrino is observed to be left-handed and the corresponding antineutrino right-handed. As discussed in section *15.3* the spinors (1) and (2) are eigenstates of the chirality operator γ5, but chirality is equivalent to han- dedness in the limit of vanishing masses, hence the subscripts L and R in (1) and (2).
  • 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.
  • The Particle World

    The Particle World

    The Particle World ² What is our Universe made of? This talk: ² Where does it come from? ² particles as we understand them now ² Why does it behave the way it does? (the Standard Model) Particle physics tries to answer these ² prepare you for the exercise questions. Later: future of particle physics. JMF Southampton Masterclass 22–23 Mar 2004 1/26 Beginning of the 20th century: atoms have a nucleus and a surrounding cloud of electrons. The electrons are responsible for almost all behaviour of matter: ² emission of light ² electricity and magnetism ² electronics ² chemistry ² mechanical properties . technology. JMF Southampton Masterclass 22–23 Mar 2004 2/26 Nucleus at the centre of the atom: tiny Subsequently, particle physicists have yet contains almost all the mass of the discovered four more types of quark, two atom. Yet, it’s composite, made up of more pairs of heavier copies of the up protons and neutrons (or nucleons). and down: Open up a nucleon . it contains ² c or charm quark, charge +2=3 quarks. ² s or strange quark, charge ¡1=3 Normal matter can be understood with ² t or top quark, charge +2=3 just two types of quark. ² b or bottom quark, charge ¡1=3 ² + u or up quark, charge 2=3 Existed only in the early stages of the ² ¡ d or down quark, charge 1=3 universe and nowadays created in high energy physics experiments. JMF Southampton Masterclass 22–23 Mar 2004 3/26 But this is not all. The electron has a friend the electron-neutrino, ºe. Needed to ensure energy and momentum are conserved in ¯-decay: ¡ n ! p + e + º¯e Neutrino: no electric charge, (almost) no mass, hardly interacts at all.
  • Decays of the Tau Lepton*

    Decays of the Tau Lepton*

    SLAC - 292 UC - 34D (E) DECAYS OF THE TAU LEPTON* Patricia R. Burchat Stanford Linear Accelerator Center Stanford University Stanford, California 94305 February 1986 Prepared for the Department of Energy under contract number DE-AC03-76SF00515 Printed in the United States of America. Available from the National Techni- cal Information Service, U.S. Department of Commerce, 5285 Port Royal Road, Springfield, Virginia 22161. Price: Printed Copy A07, Microfiche AOl. JC Ph.D. Dissertation. Abstract Previous measurements of the branching fractions of the tau lepton result in a discrepancy between the inclusive branching fraction and the sum of the exclusive branching fractions to final states containing one charged particle. The sum of the exclusive branching fractions is significantly smaller than the inclusive branching fraction. In this analysis, the branching fractions for all the major decay modes are measured simultaneously with the sum of the branching fractions constrained to be one. The branching fractions are measured using an unbiased sample of tau decays, with little background, selected from 207 pb-l of data accumulated with the Mark II detector at the PEP e+e- storage ring. The sample is selected using the decay products of one member of the r+~- pair produced in e+e- annihilation to identify the event and then including the opposite member of the pair in the sample. The sample is divided into subgroups according to charged and neutral particle multiplicity, and charged particle identification. The branching fractions are simultaneously measured using an unfold technique and a maximum likelihood fit. The results of this analysis indicate that the discrepancy found in previous experiments is possibly due to two sources.
  • Lepton Flavor and Number Conservation, and Physics Beyond the Standard Model

    Lepton Flavor and Number Conservation, and Physics Beyond the Standard Model

    Lepton Flavor and Number Conservation, and Physics Beyond the Standard Model Andr´ede Gouv^ea1 and Petr Vogel2 1 Department of Physics and Astronomy, Northwestern University, Evanston, Illinois, 60208, USA 2 Kellogg Radiation Laboratory, Caltech, Pasadena, California, 91125, USA April 1, 2013 Abstract The physics responsible for neutrino masses and lepton mixing remains unknown. More ex- perimental data are needed to constrain and guide possible generalizations of the standard model of particle physics, and reveal the mechanism behind nonzero neutrino masses. Here, the physics associated with searches for the violation of lepton-flavor conservation in charged-lepton processes and the violation of lepton-number conservation in nuclear physics processes is summarized. In the first part, several aspects of charged-lepton flavor violation are discussed, especially its sensitivity to new particles and interactions beyond the standard model of particle physics. The discussion concentrates mostly on rare processes involving muons and electrons. In the second part, the sta- tus of the conservation of total lepton number is discussed. The discussion here concentrates on current and future probes of this apparent law of Nature via searches for neutrinoless double beta decay, which is also the most sensitive probe of the potential Majorana nature of neutrinos. arXiv:1303.4097v2 [hep-ph] 29 Mar 2013 1 1 Introduction In the absence of interactions that lead to nonzero neutrino masses, the Standard Model Lagrangian is invariant under global U(1)e × U(1)µ × U(1)τ rotations of the lepton fields. In other words, if neutrinos are massless, individual lepton-flavor numbers { electron-number, muon-number, and tau-number { are expected to be conserved.
  • The Seesaw Mechanism and Renormalization Group Effects

    The Seesaw Mechanism and Renormalization Group Effects

    November 14, 2004 20:49 Proceedings Trim Size: 9in x 6in lindner THE SEESAW MECHANISM AND RENORMALIZATION GROUP EFFECTS M. LINDNER Physik Department, Technische Universit¨at M¨unchen James-Franck-Str., D-85748 Garching/M¨unchen, Germany E-mail: [email protected] Neutrino mass models predict masses and mixings typically at very high scales, while the measured values are determined at low energies. The renormalization group running which connects models with measurements is discussed in this paper. Analytic formulae for the running which include both Dirac- and Majorana CP phases are provided and they allow a systematic understanding of all effects. Some applications and numerical examples are shown. 1. Introduction The determination of neutrino masses and mixings has made enormous progress in recent years. Furthermore it is expected that precision neu- trino physics will become possible in the future such that the lepton sector may ultimately provide the most precise information on flavour structures. Already now exists enough information to try to understand the patterns of masses and mixings in different models of flavour, but this will become much more interesting in the future with growing precision. One class of models is, for example, given by discrete flavour symmetries which might emerge as unbroken subgroups of broken flavour gauge symmetries. There are different reasons why the scale where an understanding of flavour be- comes possible is very high. This has the consequence, that like in the quark sector 1,2 renormalization group (RGE) effects must potentially be taken into account when high energy predictions are compared with low energy measurements.
  • 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.
  • B2.IV Nuclear and Particle Physics

    B2.IV Nuclear and Particle Physics

    B2.IV Nuclear and Particle Physics A.J. Barr February 13, 2014 ii Contents 1 Introduction 1 2 Nuclear 3 2.1 Structure of matter and energy scales . 3 2.2 Binding Energy . 4 2.2.1 Semi-empirical mass formula . 4 2.3 Decays and reactions . 8 2.3.1 Alpha Decays . 10 2.3.2 Beta decays . 13 2.4 Nuclear Scattering . 18 2.4.1 Cross sections . 18 2.4.2 Resonances and the Breit-Wigner formula . 19 2.4.3 Nuclear scattering and form factors . 22 2.5 Key points . 24 Appendices 25 2.A Natural units . 25 2.B Tools . 26 2.B.1 Decays and the Fermi Golden Rule . 26 2.B.2 Density of states . 26 2.B.3 Fermi G.R. example . 27 2.B.4 Lifetimes and decays . 27 2.B.5 The flux factor . 28 2.B.6 Luminosity . 28 2.C Shell Model § ............................. 29 2.D Gamma decays § ............................ 29 3 Hadrons 33 3.1 Introduction . 33 3.1.1 Pions . 33 3.1.2 Baryon number conservation . 34 3.1.3 Delta baryons . 35 3.2 Linear Accelerators . 36 iii CONTENTS CONTENTS 3.3 Symmetries . 36 3.3.1 Baryons . 37 3.3.2 Mesons . 37 3.3.3 Quark flow diagrams . 38 3.3.4 Strangeness . 39 3.3.5 Pseudoscalar octet . 40 3.3.6 Baryon octet . 40 3.4 Colour . 41 3.5 Heavier quarks . 43 3.6 Charmonium . 45 3.7 Hadron decays . 47 Appendices 48 3.A Isospin § ................................ 49 3.B Discovery of the Omega § ......................
  • Accessible Lepton-Number-Violating Models and Negligible Neutrino Masses

    Accessible Lepton-Number-Violating Models and Negligible Neutrino Masses

    PHYSICAL REVIEW D 100, 075033 (2019) Accessible lepton-number-violating models and negligible neutrino masses † ‡ Andr´e de Gouvêa ,1,* Wei-Chih Huang,2, Johannes König,2, and Manibrata Sen 1,3,§ 1Northwestern University, Department of Physics and Astronomy, 2145 Sheridan Road, Evanston, Illinois 60208, USA 2CP3-Origins, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark 3Department of Physics, University of California Berkeley, Berkeley, California 94720, USA (Received 18 July 2019; published 25 October 2019) Lepton-number violation (LNV), in general, implies nonzero Majorana masses for the Standard Model neutrinos. Since neutrino masses are very small, for generic candidate models of the physics responsible for LNV, the rates for almost all experimentally accessible LNV observables—except for neutrinoless double- beta decay—are expected to be exceedingly small. Guided by effective-operator considerations of LNV phenomena, we identify a complete family of models where lepton number is violated but the generated Majorana neutrino masses are tiny, even if the new-physics scale is below 1 TeV. We explore the phenomenology of these models, including charged-lepton flavor-violating phenomena and baryon- number-violating phenomena, identifying scenarios where the allowed rates for μ− → eþ-conversion in nuclei are potentially accessible to next-generation experiments. DOI: 10.1103/PhysRevD.100.075033 I. INTRODUCTION Experimentally, in spite of ambitious ongoing experi- Lepton number and baryon number are, at the classical mental efforts, there is no evidence for the violation of level, accidental global symmetries of the renormalizable lepton-number or baryon-number conservation [5]. There Standard Model (SM) Lagrangian.1 If one allows for are a few different potential explanations for these (neg- generic nonrenormalizable operators consistent with the ative) experimental results, assuming degrees-of-freedom SM gauge symmetries and particle content, lepton number beyond those of the SM exist.
  • Chirality-Assisted Lateral Momentum Transfer for Bidirectional

    Chirality-Assisted Lateral Momentum Transfer for Bidirectional

    Shi et al. Light: Science & Applications (2020) 9:62 Official journal of the CIOMP 2047-7538 https://doi.org/10.1038/s41377-020-0293-0 www.nature.com/lsa ARTICLE Open Access Chirality-assisted lateral momentum transfer for bidirectional enantioselective separation Yuzhi Shi 1,2, Tongtong Zhu3,4,5, Tianhang Zhang3, Alfredo Mazzulla 6, Din Ping Tsai 7,WeiqiangDing 5, Ai Qun Liu 2, Gabriella Cipparrone6,8, Juan José Sáenz9 and Cheng-Wei Qiu 3 Abstract Lateral optical forces induced by linearly polarized laser beams have been predicted to deflect dipolar particles with opposite chiralities toward opposite transversal directions. These “chirality-dependent” forces can offer new possibilities for passive all-optical enantioselective sorting of chiral particles, which is essential to the nanoscience and drug industries. However, previous chiral sorting experiments focused on large particles with diameters in the geometrical-optics regime. Here, we demonstrate, for the first time, the robust sorting of Mie (size ~ wavelength) chiral particles with different handedness at an air–water interface using optical lateral forces induced by a single linearly polarized laser beam. The nontrivial physical interactions underlying these chirality-dependent forces distinctly differ from those predicted for dipolar or geometrical-optics particles. The lateral forces emerge from a complex interplay between the light polarization, lateral momentum enhancement, and out-of-plane light refraction at the particle-water interface. The sign of the lateral force could be reversed by changing the particle size, incident angle, and polarization of the obliquely incident light. 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; Introduction interface15,16. The displacements of particles controlled by Enantiomer sorting has attracted tremendous attention thespinofthelightcanbeperpendiculartothedirectionof – owing to its significant applications in both material science the light beam17 19.