DOCSLIB.ORG

Exclusive Nucleons Reactions Involving Pions

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Exclusive Nucleons Reactions Involving Pions NASA/TP-2002-211957 Exclusive Reactions Involving Pions and Nucleons John W. Norbu O, and Steve R. Blattnig Universi O, o/ Wisconsin-Milwaukee, Milwaukee, Wisconsin R. K. Tripathi Langley Research Centel; Hampton, Virginia December 2002 J The NASA STI Program Office... in Profile Since its lbunding, NASA has been dedicated to the CONFERENCE PUBLICATION. advancement of aeronautics and space science. The Collected papers from scientific and NASA Scientific and Technical Information (STI) technical conferences, symposia, Program Office plays a key part in helping NASA seminars, or other meetings sponsored or maintain this important role. co-sponsored by NASA. The NASA STI Program Office is operated by SPECIAL PUBLICATION. Scientific, Langley Research Center, the lead center for NASA's technical, or historical information from scientific and technical information. The NASA STI NASA programs, projects, and missions, Program Office provides access to the NASA STI often concerned with subjects having Database, the largest collection of aeronautical and substantial public interest. space science STI in the world. The Program Office is also NASA's institutional mechanism for TECHNICAL TRANSLATION. English- disseminating the results of its research and language translations of foreign scientific development activities. These results are and technical material pertinent to published by NASA in the NASA ST[ Report NASA's mission. Series, which includes the following report types: Specialized services that complement the STI Program Office's diverse offerings include TECHNICAL PUBLICATION. Reports of creating custom thesauri, building customized completed research or a major significant databases, organizing and publishing phase of research that present the results research results.., even providing videos. of NASA programs and include extensive For more information about the NASA STI data or theoretical analysis. Includes compilations of significant scientific and technical data and Program Office, see the following: intbrmation deemed to be of continuing reference value. NASA counterpart of peer-reviewed formal • Access the NASA STI Program Home professional papers, but having less stringent Page at http://www.sti, nasa, gov limitations on manuscript length and extent of • Email your question via the Internet to graphic presentations. [email protected] TECHNICAL MEMORANDUM. • Fax your question to the NASA STI Scientific and technical findings that are Help Desk at (301) 621-0134 preliminary or of specialized interest, e.g., quick release reports, working • Telephone the NASA STI Help Desk at papers, and bibliographies that contain (301) 621-0390 minimal annotation. Does not contain extensive analysis. Write to: NASA STI Help Desk CONTRACTOR REPORT. Scientific and NASA Center for AeroSpace Information technical findings by NASA-sponsored 7121 Standard Drive contractors and grantees. Hanover, MD 21076-1320 NASA/TP-2002-211957 Exclusive Reactions Involving Pions and Nucleons John W. Norbu O' and Steve R. Blattnig Universi O, o[" Wisconsin-Milwaukee, Milwaukee, Wisconsin R. K. Tripathi Langley Research Center; Hampton, Virginia National Aeronautics and Space Administration Langley Research Center Hampton, Virginia 23681-2199 December 2002 Acknowledgments This work was supported by NASA grants NCC-1-354 and NGT-1-52217. John W. Norbury gratefillly acknowl- edges the hospitality of the Physics Department at La Trobe University, Bundoora, Australia, where part of the work was performed. Available from: NASA Center Jbr AeroSpace Information (CASI) National Technical Information Service (NTIS) 7121 Standard Drive 5285 Port Royal Road Hanover, MD 21076-1320 Springfield, VA 22161-2171 (301) 621-0390 (703) 605-6000 Nomenclature Note: the units used in this work are such that h = c = 1. EM electromagnetic 1 symbol for t)rojectile t)article ill tile reaction 1 + 2 -+ anything 2 symbol for target particle in the reaction 1 + 2 -+ arryth.in.q CIH symbol for (xmter of moinentmn frame, where Pl + P2 = 0 lab symbol for la|) (target) frame, where p_ = 0 _l; * denotes a variable :r ill the cm frame 2:lab denotes a varia.t)le x in the lab fnmle 2; denotes a variat)le :r ill the la.b flame or (teilotes ml invariant variable :r 1?'l, rr pion mass, GeV proton mass, GeV 'TII i mass of part.ich_ i, GeV T particle kinetic energs', GeV E t)article total energy, GeV P magnitude of 3-monmntunl, p = ]p], GeV Note: not t.o I)e confused with sylnbol for t)r()ton. Context will clarify. speed of crr_ fiame (Ulfitless) l (uifitless) rela.tivistic factor, ")- d3cr Lorentz inva.riant differential cross section, InI)/GeV 2 Ttp:_/ E d cr spectral distribution cross section, mb/GeV dE (Y total cross section, m|) d-' N single partMe dist.ributioIl in the t)ro.jectile-ml(;leon cm ti'ame dpltdP± total energy ill cm fra.ine, V/-d = Et c,,, + E'2 c,, =- Ec,,, GeV p;2 pion inomentunl in c7_ fralne, GeV *2 cm fl'alne, GeV P7r ?Tin:l: inaxinmm pion inonlentum in (_Tr 7?_(LX Inaxinmnl pion angle in lab frame ])1 lab magnitude of 3-inolnentunl of partMe 1 ill the lab frame for the reaction 1 + 2 --+ 3 + 4 Pl tat, = [Ptl lab, GeV L_'l lab total energy of t)artMe 1 in the lab frame for the reacti()u 1 + 2 -+ 3 + 4 E_ t._, = N,/tP[_ ,.,, + m_, GeV pP 4-momentum w_ctor,//' = (E, p), GeV (p" )2 square of 4-momentunl vector, (pt') 2 = E 2 -- p2 = m2 Gek,2 4-momentmn vector of partich' i, GeV ... 111 N syInbol for nucle(,n (either proton or neutron) TT, i_ TO neutron antineutron p, N + proton Note: not to b(, confilsed with Im_gnitu(h' of momentum. Context will clarify. ai_tiproton 71 symbol for pion (either n °, 7r+, or _--) C- electron C + I)ositron /) neutrin() antineutrino electron neutrino anti-electron neutrin() S intrinsic spin angular momentum Y (2 charge, Q = I: + ,-y A Ba_ryon mmll)er I is()sl)i,l I= z compo,mnt of isospin S strange quantuln nuinber (strangeness) C (:harm (luantum immber (charmness) B t )()tr (r()I_l (luant um number (bottomness) T top quantum mmfl)er (topness) hypercharge, Y-A+S+C+B+T=2<Q> S intrinsic spin angular momentum P parity Cp ('harg(' (,onjuga,tion parity G G-parity iv Abstract The HZETRN code requires inclusive c'_vss sections as i_tput. One of the meth.- ods used to calculate these cross sections requires knowledge of all e:cclusi've processes contributing to the inclusive reaction. Conservation laws are used to determine all possible ezclusivc reaction._ involving strong interactions betwcen pions and nuclcon.s. Inclusive particle masses arc subsequently determined and arc needed in cross-section calculations for inclusive pio_, production. 1. Introduction For long duration space flight, it is important to be able to predict the radiation cnviromnent inside spacecraft. References 1 through 37 form a representative list of the literature of direct relevance to the discussion of exclusive cross sections for pions and mleleons pertinent to space radiation at)plications to space missions. One princiI)al tool that has been used is the computer code HZETRN (refs. 1, 3, 4, and 5). In high energy interactions of cosmic rays, particles called mesons are copiously produced, but these t)articles have not yet been included in the HZETRN code. Work is currently underway to repair this deficiency, a n(t the t)resent work is part of this effort. The lightest meson is the pion, the most imp()rtant ()f the mesons to be included, an(l is the sut)ject of the t)resent paper. The next heaviest meson is the kaon, and its interactions will be studied in fllture work. An czclusive reaction is one in which all final state particles are st)ecified, such as A + B -+ C + D (1) or A+B -+ C+D+E (2) or A+ B --+ C + D+ E + F (3) Let us suppose that only the above three exclusive reactions represent all of the pos- sible processes leading to produt:tion of the particle C. All of these eouht be ineasured experimentally and calculated theoretically (i.e., from Feynnmn rules). The exi)eriments would have to detect all the t)alticles C, D, E, F, and a calculation would involve calcu- lating each reaction separately for production of all t)articles C, D, E, F. Experimentally, it. may well be Inuch easier to detect only the particle C of interest. In that ease ()he measures the so-called inclusive reaction A + B --+ C + X (4) where X is a_!/tl/ing. From the abow_ analysis of the exclusive rea('tions, we know that X could be either D or D+E or D+E+F. Even though it is easier experimentally to mea,sme an inclusive er(_ss section rather than an exclusive one, it is actually more difficult to calculate witli a theory basedon Feynmanrulesbecausetile theoretical calculation of the inclusive cross section is simply the sum of each of the separate exclusive reactions. Thus, the inclusive calculation involves much more work than a single exclusive calculation. To summarize, inclusive cross sections are easier experimentally, whereas exclusive cross sections are easier theoretically. The HZETRN code requires only inclusive cross sections as input, and a major goal in space radiation research is to calculate such inclusiw_ (:ross sections. A method for developing tbrmulas for spectral and total inclusive cross sections has been developed previously (refs. 6 10). The method involves fitting curves to inclusive Lorentz invariant differential cross sections, which are then subsequently integrated to form inclusiw_ spec- tral distributions and total cross sections. This method involves integrations over angle (to fi:_rm spectral distributions) and over moinentum (to form total cross sections), where the angle and momentum are for the particle C of interest. One integrates from zero to the maxinmm possible values of angle and momentunl for particle C.
Load more

Recommended publications
  • Nutzung Der Gefundenen Werte Far F(1) | | Und P a Bestimmt Worden
    Reconstruction of B D*°e ve Decays and Determination of \Vcb\ DISSERTATION zur Erlangung des akademischen Grades Doctor rerum naturalium (Dr.rer.nat.) vorgelegt der Fakultat Mathematik und Naturwissenschaften der Technischen Universitat Dresden von Diplom-Physiker Jens Schubert geboren am 11.03.1977 in Pirna 1. Gutachter : Prof. Dr. Klaus R. Schubert 2. Gutachter : Prof. Dr. Michael Kobel 3. Gutachter : Dr. Jochen C. Dingfelder Eingereicht am: 01.12.2006 Abstract In this analysis the decay B- ^ D* 0e-Ve is measured. The underlying data sample consists of about 226 million BB-pairs accumulated on the Y(4S) resonance by the BABAR detector at the asymmetric e+e- collider PEP-II. The reconstruction of the decay uses the channels D*° ^ D0n0, D° ^ K-n+ and n0 ^ 77. The neutrino is not reconstructed. Since the rest frame of the B meson is unknown, the boost w of the D*° meson in the B meson rest frame is estimated by w. The W spectrum of the data is described in terms of the partial decay width dr/dw given by theory and the detector simulation translating each spectrum dr/dw into an expectation of the measured w spectrum. dr/dw depends on a form factor F(w) parameterizing the strong interaction in the decay process. To find the best descriptive dr/dw a fit to the data determines the following two parameters of dr/dw: (i) F(1)|VCb|, the product between F at zero D* 0-recoil and the CKM matrix element |Vcb|; (ii) p A , a parameter of the form factor F(w).
    [Show full text]
  • 10 Progressing Beyond the Standard Models
    i i “proc16” — 2016/12/12 — 10:17 — page 177 — #193 i i BLED WORKSHOPS Proceedings to the 19th Workshop IN PHYSICS What Comes Beyond ::: (p. 177) VOL. 17, NO. 2 Bled, Slovenia, July 11–19, 2016 10 Progressing Beyond the Standard Models B.A. Robson ? The Australian National University, Canberra, ACT 2601, Australia Abstract. The Standard Model of particle physics (SMPP) has enjoyed considerable success in describing a whole range of phenomena in particle physics. However, the model is con- sidered incomplete because it provides little understanding of other empirical observations such as the existence of three generations of leptons and quarks, which apart from mass have similar properties. This paper examines the basic assumptions upon which the SMPP is built and compares these with the assumptions of an alternative model, the Generation Model (GM). The GM provides agreement with the SMPP for those phenomena which the SMPP is able to describe, but it is shown that the assumptions inherent in the GM allow progress beyond the SMPP. In particular the GM leads to new paradigms for both mass and gravity. The new theory for gravity provides an understanding of both dark matter and dark energy, representing progress beyond the Standard Model of Cosmology (SMC). Povzetek. Standardni Model elektrosibkeˇ in barvne interakcije zelo uspesnoˇ opiseˇ veliko pojavov v fiziki osnovnih delcev. Model imajo kljub temu za nepopoln, ker ne pojasni vrste empiricnihˇ dejstev, kot je obstoj treh generacij leptonov in kvarkov, ki imajo, razen razlicnihˇ mas, zelo podobne lastnosti. V prispevku obravnavamo osnovne predpostavke, na katerih so zgradili ta model in jih primerjamo s predpostavkami alternativnega modela, generacijskega modela.
    [Show full text]
  • The Flavour Puzzle, Discreet Family Symmetries
    The flavour puzzle, discreet family symmetries 27. 10. 2017 Marek Zrałek Particle Physics and Field Theory Department University of Silesia Outline 1. Some remarks about the history of the flavour problem. 2. Flavour in the Standard Model. 3. Current meaning of the flavour problem? 4. Discrete family symmetries for lepton. 4.1. Abelian symmetries, texture zeros. 4.2. Non-abelian symmetries in the Standard Model and beyond 5. Summary. 1. Some remarks about the history of the flavour problem The flavour problem (History began with the leptons) I.I. Rabi Who ordered that? Discovered by Anderson and Neddermayer, 1936 - Why there is such a duplication in nature? - Is the muon an excited state of the electron? - Great saga of the µ → e γ decay, (Hincks and Pontecorvo, 1948) − − - Muon decay µ → e ν ν , (Tiomno ,Wheeler (1949) and others) - Looking for muon – electron conversion process (Paris, Lagarrigue, Payrou, 1952) Neutrinos and charged leptons Electron neutrino e− 1956r ν e 1897r n p Muon neutrinos 1962r Tau neutrinos − 1936r ν µ µ 2000r n − ντ τ 1977r p n p (Later the same things happen for quark sector) Eightfold Way Murray Gell-Mann and Yuval Ne’eman (1964) Quark Model Murray Gell-Mann and George Zweig (1964) „Young man, if I could remember the names of these particles, I „Had I foreseen that, I would would have been a botanist”, have gone into botany”, Enrico Fermi to advise his student Leon Wofgang Pauli Lederman Flavour - property (quantum numbers) that distinguishes Six flavours of different members in the two groups, quarks and
    [Show full text]
  • Lecture 5: Quarks & Leptons, Mesons & Baryons
    Physics 3: Particle Physics Lecture 5: Quarks & Leptons, Mesons & Baryons February 25th 2008 Leptons • Quantum Numbers Quarks • Quantum Numbers • Isospin • Quark Model and a little History • Baryons, Mesons and colour charge 1 Leptons − − − • Six leptons: e µ τ νe νµ ντ + + + • Six anti-leptons: e µ τ νe̅ νµ̅ ντ̅ • Four quantum numbers used to characterise leptons: • Electron number, Le, muon number, Lµ, tau number Lτ • Total Lepton number: L= Le + Lµ + Lτ • Le, Lµ, Lτ & L are conserved in all interactions Lepton Le Lµ Lτ Q(e) electron e− +1 0 0 1 Think of Le, Lµ and Lτ like − muon µ− 0 +1 0 1 electric charge: − tau τ − 0 0 +1 1 They have to be conserved − • electron neutrino νe +1 0 0 0 at every vertex. muon neutrino νµ 0 +1 0 0 • They are conserved in every tau neutrino ντ 0 0 +1 0 decay and scattering anti-electron e+ 1 0 0 +1 anti-muon µ+ −0 1 0 +1 anti-tau τ + 0 −0 1 +1 Parity: intrinsic quantum number. − electron anti-neutrino ν¯e 1 0 0 0 π=+1 for lepton − muon anti-neutrino ν¯µ 0 1 0 0 π=−1 for anti-leptons tau anti-neutrino ν¯ 0 −0 1 0 τ − 2 Introduction to Quarks • Six quarks: d u s c t b Parity: intrinsic quantum number • Six anti-quarks: d ̅ u ̅ s ̅ c ̅ t ̅ b̅ π=+1 for quarks π=−1 for anti-quarks • Lots of quantum numbers used to describe quarks: • Baryon Number, B - (total number of quarks)/3 • B=+1/3 for quarks, B=−1/3 for anti-quarks • Strangness: S, Charm: C, Bottomness: B, Topness: T - number of s, c, b, t • S=N(s)̅ −N(s) C=N(c)−N(c)̅ B=N(b)̅ −N(b) T=N( t )−N( t )̅ • Isospin: I, IZ - describe up and down quarks B conserved in all Quark I I S C B T Q(e) • Z interactions down d 1/2 1/2 0 0 0 0 1/3 up u 1/2 −1/2 0 0 0 0 +2− /3 • S, C, B, T conserved in strange s 0 0 1 0 0 0 1/3 strong and charm c 0 0 −0 +1 0 0 +2− /3 electromagnetic bottom b 0 0 0 0 1 0 1/3 • I, IZ conserved in strong top t 0 0 0 0 −0 +1 +2− /3 interactions only 3 Much Ado about Isospin • Isospin was introduced as a quantum number before it was known that hadrons are composed of quarks.
    [Show full text]
  • Pos(ICHEP2012)321
    Parity of Pions and CP Violation in Neutral Kaon System PoS(ICHEP2012)321 Brian Robson Department of Theoretical Physics, Research School of Physics and Engineering The Australian National University, Canberra, ACT 0200, Australia E-mail: [email protected] The parity of pions is discussed within the framework of the Generation Model of particle physics and it is shown that both the 1954 determination of the parity of the charged pions and the 2008 determination of the parity of the neutral pion are compatible with the mixed-parity nature of the pions predicted by a recent composite Generation Model. The development of the Generation Model as an alternative to the Standard Model of particle physics is discussed. It is demonstrated how the Generation Model leads to a unified classification of leptons and quarks and how this makes feasible a composite model of the fundamental particles of the Standard Model. In particular it is shown that the 1964 CP violating experiment of Christenson et al. may be understood without CP violation. 36th International Conference on High Energy Physics July 4-11, 2012 Melbourne, Australia Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it Parity of Pions and CP Violation in Neutral Kaon System Brian Robson 1. Introduction This paper summarizes the Generation Model (GM) of particle physics, which has been developed over the last decade [1-4]. Essentially, the GM is obtained from the Standard Model (SM) [5] by making two postulates, which together maintain the same transition probabilities for both hadronic and leptonic processes as the SM so that agreement with experiment is preserved.
    [Show full text]
  • Isospin and Isospin/Strangeness Correlations in Relativistic Heavy Ion Collisions
    Isospin and Isospin/Strangeness Correlations in Relativistic Heavy Ion Collisions Aram Mekjian Rutgers University, Department of Physics and Astronomy, Piscataway, NJ. 08854 & California Institute of Technology, Kellogg Radiation Lab 106-38, Pasadena, Ca 91125 Abstract A fundamental symmetry of nuclear and particle physics is isospin whose third component is the Gell-Mann/Nishijima expression I Z =Q − (B + S) / 2 . The role of isospin symmetry in relativistic heavy ion collisions is studied. An isospin I Z , strangeness S correlation is shown to be a direct and simple measure of flavor correlations, vanishing in a Qg phase of uncorrelated flavors in both symmetric N = Z and asymmetric N ≠ Z systems. By contrast, in a hadron phase, a I Z / S correlation exists as long as the electrostatic charge chemical potential µQ ≠ 0 as in N ≠ Z asymmetric systems. A parallel is drawn with a Zeeman effect which breaks a spin degeneracy PACS numbers: 25.75.-q, 25.75.Gz, 25.75.Nq Introduction A goal of relativistic high energy collisions such as those done at CERN or BNL RHIC is the creation of a new state of matter known as the quark gluon plasma. This phase is produced in the initial stages of a collision where a high density ρ and temperatureT are produced. A heavy ion collision then proceeds through a subsequent expansion to lower ρ andT where the colored quarks and anti-quarks form isolated colorless objects which are the well known particles whose properties are tabulated in ref[1]. Isospin plays an important role in the classification of these particles [1,2].
    [Show full text]
  • Arxiv:1609.04034V1 [Physics.Gen-Ph] 8 Sep 2016 Asnme() 26.C 53.Q 98.80.Bp 95.30.Cq, 12.60.Rc, Number(S): PACS Atom
    The generation model of particle physics and the cosmological matter-antimatter asymmetry problem B.A. Robson∗ Department of Theoretical Physics, Research School of Physics and Engineering, The Australian National University, Acton ACT 2601, Australia ∗[email protected] The matter-antimatter asymmetry problem, corresponding to the virtual nonexis- tence of antimatter in the universe, is one of the greatest mysteries of cosmology. Within the framework of the Generation Model (GM) of particle physics, it is demon- strated that the matter-antimatter asymmetry problem may be understood in terms of the composite leptons and quarks of the GM. It is concluded that there is essen- tially no matter-antimatter asymmetry in the present universe and that the observed hydrogen-antihydrogen asymmetry may be understood in terms of statistical fluctu- ations associated with the complex many-body processes involved in the formation of either a hydrogen atom or an antihydrogen atom. Keywords: Generation model; antimatter; big bang. PACS Number(s): 12.60.Rc, 95.30.Cq, 98.80.Bp arXiv:1609.04034v1 [physics.gen-ph] 8 Sep 2016 1. Introduction The matter-antimatter asymmetry problem, corresponding to the virtual nonexis- tence of antimatter in the universe, is one of the greatest mysteries of cosmology, along with dark matter and dark energy.1 Recently, an understanding of both dark matter and dark energy has been provided by the development of a new quan- tum theory of gravity,2,3 which is based on the Generation Model (GM) of particle physics.4 In this paper it is demonstrated that the matter-antimatter asymmetry problem may also be understood in terms of the composite leptons and quarks of the GM, contrary to the elementary leptons and quarks of the Standard Model (SM) of particle physics.5 According to the SM of particle physics, the universe is made essentially of mat- ter comprising three kinds of elementary particles: electrons, up quarks and down quarks.
    [Show full text]
  • Introduction to Elementary Particle Physics
    Introduction to Elementary Particle Physics Néda Sadooghi Department of Physics Sharif University of Technology Tehran - Iran Elementary Particle Physics Lecture 9 and 10: Esfand 18 and 20, 1397 1397-98-II Leptons and quarks Lectrue 9 Leptons Lectrue 9 Remarks: I Lepton flavor number conservation: - Lepton flavor number of leptons Le; Lµ; Lτ = +1 - Lepton flavor number of antileptons Le; Lµ; Lτ = −1 Assumption: No neutrino mixing + + − + + Ex.: π ! µ + νµ; n ! p + e +ν ¯e; µ ! e + νe +ν ¯µ But, µ+ ! e+ + γ is forbidden I Two other quantum numbers for leptons - Weak hypercharge YW : It is 1 for all left-handed leptons - Weak isospin T3: ( ) ( ) e− − 1 ! 2 For each lepton generation, for example T3 = 1 νe + 2 I Type of interaction: - Charged leptons undergo both EM and weak interactions - Neutrinos interact only weakly Lectrue 9 Quarks Lectrue 9 Remarks I Hadrons are bound states of constituent (valence) quarks I Bare (current) quarks are not dressed. We denote the current quark mass by m0 I Dressed quarks are surrounded by a cloud of virtual quarks and gluons (Sea quarks) I This cloud explains the large constituent-quark mass M I For hadrons the constituent quark mass M = the binding energy required to make the hadrons spontaneously emit a meson containing the valence quark For light quarks (u,d,s): m0 ≪ M For heavy quarks (c,b,t): m0 ' M Lectrue 9 Remarks: I Type of interaction: - All quarks undergo EM and strong interactions I Mean lifetime (typical time of interaction): In general, - Particles which mainly decay through strong interactions have a mean lifetime of about 10−23 sec - Particles which mainly decay through electromagnetic interactions, signaled by the production of photons, have a mean lifetime in the range of 10−20 − 10−16 sec - Particles that decay through weak forces have a mean lifetime in the range of 10−10 − 10−8 sec Lectrue 9 Other quantum numbers (see Perkins Chapter 4) Flavor Baryon Spin Isospin Charm Strangeness Topness Bottomness El.
    [Show full text]
  • Particle Properties
    Particle Properties You don’t have to remember this information! In an exam the masses of the particles are given on the constant sheet. Any other required information will be given to you. What you should know, or be able to work out, is: • the quantum numbers, and if they are conserved are or not • the force responsible for a decay, from the lifetime • the main decay modes, using a Feynman diagram • that the +, − and 0 superscripts correspond to the electric charge of the particles • the relationship between a particle and its antiparticle. Anti-particles are not named in the tables. Anti-particles have the same mass, same lifetime, opposite quantum numbers from the particle. Anti-particles decay into the anti-particles of the shown modes. For example, an anti-muon, µ+, has a mass of 2 −6 105.7 MeV/c and a lifetime of 2.197 × 10 s. Its quantum numbers are Le = 0,Lµ = + + −1,Lτ = 0 and Q = +1. Its main decay mode is µ → e νeν¯µ. Quantum Numbers The following quantum numbers are conserved in all reactions: • Total quark number, Nq = N(q) − N(¯q). – Nq = +1 for all quarks – Nq = −1 for all anti-quarks – Nq = 0 for all leptons and anti-leptons – Nq = 3 for baryons and Nq = 0 for mesons. • The three lepton flavour quantum numbers: − + – Electron Number: Le = N(e ) − N(e ) + N(νe) − N(¯νe) − + – Muon Number: Lµ = N(µ ) − N(µ ) + N(νµ) − N(¯νµ) − + – Tau Number: Lτ = N(τ ) − N(τ ) + N(ντ ) − N(¯ντ ) • Electric charge, Q.
    [Show full text]
  • 2S from Charmless Two-Body Decays of Beauty Mesons
    Alma Mater Studiorum · Università di Bologna Scuola di Scienze Dipartimento di Fisica e Astronomia Corso di Laurea in Fisica Determination of CKM phases γ and −2βs from charmless two-body decays of beauty mesons Relatore: Presentata da: Prof./Dott.Angelo Carbone Davide Fasolo Correlatore: (eventuale) Prof./Dott. Stefano Perazzini Year 2017/2018 Abstract An important task of the modern research in particle physics is to measure the properties of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. The CKM matrix governs the mixing between mass and flavour eigenstates of quarks and is responsible of the breaking of the CP symmetry in the Standard Model (SM), hence, in the very end, of the imbalance between matter and anti-matter in the Universe. Probing the consistency and the unitarity of the CKM matrix is fundamental to verify the validity of the SM and to look for physics beyond. Using the measurements of CP-violation parameters and branching ratios 0 + − 0 0 0 + + 0 0 + − of the B → π π , B → π π , B → π π and Bs → K K de- cays, a bayesian analysis is performed to determine two parameters of 0 the CKM matrix: the angle γ and the mixing phase, −2βs, of the Bs meson. Contents 1 Standard Model 5 1.1 Introduction to the Standard Model5 1.2 The Feynman diagrams7 1.3 The CKM matrix8 1.4 Wolfenstein parameterization of the CKM matrix and unitary triangles 12 2 Hadronic two-body B decays 15 2.1 Direct CP asymmetries 16 2.2 Mixing of neutral B mesons 17 3 Bayesian analysis 21 3.1 Bayes theorem 21 3.2 Parametric inference 22 + 0− 4 Measurement of the CKM parameters γ and −2βs using B → h h decays 25 4.1 Decay amplitudes 26 0 + − 0 + − 4.2 Determination of γ and −2βs from B → π π and Bs → K K decays 28 4.3 Inclusion of B0 → π0π0 and B+ → π+π0 35 5 Conclusions 39 Introduction The study of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is directly related to the flavour dynamics of quarks, and governs CP violation in the Standard Model (SM).
    [Show full text]
  • Quantum Mechanics Electric Charge
    Quantum Mechanics_Electric charge Electric field of a positive and a negative point charge. Electric charge is the physical property of matterthat causes it to experience a force when placed in an electromagnetic field. There are two types of electric charges – positive and negative. Positively charged substances are repelled from other positively charged substances, but attracted to negatively charged substances; negatively charged substances are repelled from negative and attracted to positive. An object will be negatively charged if it has an excess of electrons, and will otherwise be positively charged or uncharged. The SI derived unit of electric charge is the coulomb (C), although in electrical engineering it is also common to use theampere-hour (Ah), and in chemistry it is common to use the elementary charge (e) as a unit. The symbol Qis often used to denote a charge. The study of how charged substances interact is classical electrodynamics, which is accurate insofar asquantum effects can be ignored. The electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields. The interaction between a moving charge and an electromagnetic field is the source of the electromagnetic force, which is one of the four fundamental forces (See also: Magnetic field). Twentieth-century experiments demonstrated that electric charge is quantized; that is, it comes in integer multiples of individual small units called theelementary charge, e, approximately equal to1.602×10−19 coulombs (except for particles calledquarks, which have charges that are integer multiples of e/3). The proton has a charge of e, and the electron has a charge of −e.
    [Show full text]
  • Isospin and Isospin/Strangeness Correlations in Relativistic Heavy-Ion Collisions
    October 2007 EPL, 80 (2007) 22002 www.epljournal.org doi: 10.1209/0295-5075/80/22002 Isospin and isospin/strangeness correlations in relativistic heavy-ion collisions A. Mekjian Rutgers University, Department of Physics and Astronomy - Piscataway, NJ 08854, USA and California Institute of Technology, Kellogg Radiation Lab 106-38 - Pasadena, CA 91125, USA received 3 July 2007; accepted in final form 3 September 2007 published online 28 September 2007 PACS 25.75.-q – Relativistic heavy-ion collisions PACS 25.75.Gz – Particle correlations PACS 25.75.Nq – Quark deconfinement, quark-gluon plasma production, and phase transitions Abstract – A fundamental symmetry of nuclear and particle physics is isospin whose third component is the Gell-Mann/Nishijima expression IZ = Q − (B + S)/2. The role of isospin symmetry in relativistic heavy-ion collisions is studied. An isospin IZ , strangeness S correlation is shown to be a direct and simple measure of flavor correlations, vanishing in a Qg phase of uncorrelated flavors in both symmetric N = Z and asymmetric N = Z systems. By contrast, in a hadron phase, a IZ /S correlation exists as long as the electrostatic charge chemical potential µQ =0 asin N = Z asymmetric systems. A parallel is drawn with a Zeeman effect which breaks a spin degeneracy. Copyright c EPLA, 2007 W Introduction. – A goal of relativistic high-energy consequences [2]. IZ is also given by a Gell-Mann/ collisions such as those done at CERN or BNL RHIC is Nishijima expression. the creation of a new state of matter known as the quark For nuclei and particles made of u, d quarks only, gluon plasma.
    [Show full text]