Elementary Particles Revision Notes (B.Sc. and GATE)

Elementary Particles revision notes

(1) Introduction

  • Elementary particles are those microscopic elementary constituents out of which all matter in this universe is made of.
  • Bound neutron is stable but unbound neutron is unstable and it decays according to equation
    $n \to p + e + \overline {{\nu _e}} $ (anti-nutrino)
    Half life of free neutron is 14 min 49 sec.

Fundamental interactions

  • There are four fundamental interactions between particles
    1. Strong
    2. Electromagnetic
    3. Week
    4. Gravitational

    InteractionParticles affectedrangerelative strengthparticles exchangedRole in universe
    StrongQuarks∼10-15m1gluonsHolds quarks together to form nucleus
    HadronsMesonsHolds nucleons together to form atomic nuclei
    Electro-magneticcharged particlesinfinite∼10-2photonsDetermine structure of atoms, molecules, solids etc., Important factor in astronomical universe.
    WeakQuarks and leptons∼10-17m∼10-5mIntermediate bosonsmediates transformations of quarks and leptons; helps determine composition of atomic nuclei
    Gravitationalallinfinite∼10-39mgravitonsAssemble matter into planet , galaxies and stars
  • Elementary particles can be divided into four groups
    1. Photons
    2. Leptons
    3. Mesons
    4. Baryons

Anti particles

  • A particle identical with proton except for negative charge, i.e., negative proton or antiproton was created by bombarding protons in a target with 6 GeV protons thereby inducing the reaction

    p +p + energy (6 GeV) → p + p+

    As soon as the antiproton slow down it is annihilated by a proton.

  • Particle and anti particle annihilate each other to give rise to a form of energy.
  • Positron is the anti particle of electron.
  • There must be an anti particle corresponding to each particle.
  • From the collection of anti particles a world of anti matter could be created.

Relationship between particle and anti particles is

propertyrelationship
Masssame
Spinsame
Magnetic momentof opposite sign but same magnitude
Chargeof opposite sign but same magnitude
Mean life in free decaysame
Annihilationin pair
Creationin pair
Total isotopic spinsame
Intrinsic paritysame for bosons but opposite for fermions
Strangeness numberof opposite sign but same magnitude

 

(2) Photons

  • It only participates in EM interactions.
  • Strong and weak interactions are not in photon domain of experience.
  • When particle annihilate with anti-particles the end product is often protons.
  • Photon is its own anti particle.
  • Under some circumstances it can disappear and can create particle -anti particle pair.
  • Rest mass of photon is zero.
  • Photon is a boson with angular momentum equal to 1.
  • Spin of photon is 1

(3) Leptons

  • A particle which are untouched by strong forces and which participates in weak interactions are called leptons.
  • All these particles (leptons) also have their corresponding anti particles.
  • Unlike baryons and mesons no heavier leptons have been detected.
  • Electrons with its anti-particle positron along with its associated neutrino and anti neutrino are leptons.
  • Muons with their respective neutrino and anti-particles of these are also leptons. Another pair of leptons known as tau,τ and its associated neutrino.
  • All tau’s are charged and decay into electrons, muons or pions along with appropriate neutrino.
  • The breakdown of parity conservation in weak interaction has important consequence for leptons.
  • The particles are left handed and anti-particles are right handed.
  • In normal weak interactions the particles (electrons, negative muons, neutrinos) behaves as if they were left handed screws; i.e., observer think they spin clockwise when they are travelling towards him.
  • Anti-particles are right handed screws; an observer thinks they are spinning counter clockwise as they approaches him.
  • Nature of weak interactions, with its violation of such established symmetries as parity, charge conjunction, isotopic spin and strangeness is physics greatest problems.
  • Muons were first discovered in decay of charged pionsCharged pion decay:π+→μ+μπ→μ+ ν μ ¯Neutral pion decay :

    π0→γ+γ

  • Muon decayμ+→e+e+ ν μ ¯

    μ→eμ+ ν e ¯

Leptons have (B=0) (fermions) and their properties are

ParticleSymbolSpinLeLμLτMass (in MeV)Mean Life
electrone1/2+1000.511stable
muonμ1/20+101062.2×10-6
tauτ1/200+117843.4×10-25
electron neutrinoνe1/2+1000stable
μ neutrinoνμ1/20+100stable
τ neutrinoντ1/200+10stable

 



(4) Mesons

  • Mesons are particles with zero or integral spin so they are Bosons.
  • The lightest meson is pion or π-meson, with other meson masses ranging beyond proton mass.
  • All mesons are unstable and decay in various ways.

π-mesons

  • This particle is to transmit nuclear forces, it must interact strongly with nuclei, and therefore it should be scattered and absorbed quickly by matter through which it passes.
  • π mesons are thus hypothetical particles responsible for the nuclear forces and had properties predicted by Yukawa.
  • Protons and neutrons can be transferred into one another by emitting or absorbing one of these particles.
  • There are three kinds of pions π+, π and π0. π is the anti particle of π+.
  • These new particles can be thought of making bonds between (n,n) , (p,p) and (n,p) or (p,n)

K mesons

  • These are heavier unstable particles and have a great variety of different decay modes.
  • There are six different ways that K+ mesons commonly decay, in each case giving two or three less massive particles
    K+→π+0K+→μ+μ

    K+→π++0

    K+→π+00

    K+→e++ν+π0

  • Mass of K+ is 966me.
  • K are anti particles of K+ mesons and have the same decay modes with appropriate exchange of decay products for their anti particles.
  • K0 and K 0 ¯ are anti particles.

Mesons (B=0) Bosons

ParticleSymbolMass MeV/c2Mean life (s)spinSYII3
Pionπ+1402.6×10-80001+1
π01358.7×10-170
π1402.6×10-8-1
KonK+4941.2×10-80+1+11/2+1/2
K04989×10-11
K4945×10-8-1/2
Etaη05496×10-1900000

 

(5) Baryons

  • There is another whole class of unstable particles known as ‘hyperons’ , whose masses are each greater than that of protons.
  • The first hyperon was found in cosmic rays named as Λ0 hypron , a neutral decaying particle.
  • Charged particles seen in the decay were identified as proton and π meson, indicating a process
    Λ0 →p+π
  • Anti-Λ0 hypron decay to an anti proton and π+-meson.
  • The family of hyprons with greatest number of members is Σ-family.
  • First if it to be observed is Σ+ with mass about 2328me , and two prominent decay schemes are
    Σ+→p+π0 ; Σ+→n+π+
  • Σ has just one set of decay products
    Σ→n+π
    its mass being slightly greater than Σ+ and is 2341 me.
  • Neutral Σ hyperons decays as
    Σ0→Λ0
    its mass is 2328me
  • The Σ hyperon form a triplet Σ+ and Σ0. A corresponding triplet of anti Σ hyperon also exists.
  • The anti-particle of Σ+ cannot be Σ because the two have slightly different masses, whereas particle anti particle must have exactly same masses.
  • Another group of members belonging to hyperon family is Ξ hyperon originally called cascade particles.
  • Their negative and neutral forms have been observed with decay processes
    Ξ→Λ0

    Ξ0→Λ00

    Their masses are about 2582 me

  • Anti Ξ hyperons have been detected.
  • Together with nucleons (p and n) , the hyperons form the family of baryons.

Baryons (B=+1, Le=Lμ=Lτ=0)

ParticleSymbolmean life (s)spinSYII3Mass MeV/c2
Nucleon nstable1/20+11/2-1/2938.3
 p886+1/2936.6
Lambda Λ02.6×10-101/2-10001116
Sigma Σ+8.0×10-111/2-101+11189
 Σ06×10-2001193
 Σ1.5×10-10-11197
Xi Ξ02.9×10-101/2-2-11/2+1/21315
 Ξ1.6×10-10-1/21321
Omega Ω8.2×10-113/2-3-201672
  • There is a sequence of decay for Ω baryonΩ→Ξ0→Λ0 +π0 ….

    Final result of decay is proton , two electrons and two photons.

(6) Symmetries and conservation Laws

  • In addition to transnational symmetry, space also has a rotational symmetry.
  • This symmetry of space gives rise to another conserved quantity, angular momentum.
  • This law is also of general validity for all types of interactions.
  • It is related to the invariance of the physical laws under rotation (isotropy of space).
  • The orbital and spin angular momentum may be separately conserved.

Parity Conservation

  • Holds for strong, nuclear and electromagnetic interactions but is violated in case of week interactions.
  • Related to the invariance of the physical laws under inversion of space co-ordinates. x,y,z are replaced by -x.-y,-z.
  • Is equivalent to combined reflection and rotation.
  • Physical laws do not depend on the right handedness of co-ordinate system.
  • Parity operation symmetry represents discrete symmetry (reflection and rotation through 180 degree)
  • Every particle with non-zero mass has an intrinsic parity  π which can either be +1(even) or -1 (odd). Thus total parity of a system of n particles is the product of their intrinsic parities and the orbital parity (-1)l.
  • Thus, πtot1π2π3…….πn(-1)l
  • Intrinsic parity of peons is odd.

Conservation of charge

  • Conservation of electric charge is related to gauge transformations which are shifts in the zeros of the scalar and vector electromagnetic potentials V and A
  • Gauge transformations leave E and B unaffected since the latter are obtained by differentiating potentials, and this invariance leads to charge conservation.
  • Charge and baryon number are conserved in all interactions.

Baryon and Lepton numbers

  • The Baryon number B=1 is assigned to all baryons and B=-1 is assigned to all anti baryons: all other particles have B=0.
  • The lepton number Le=1 is assigned to electrons and electron neutrino, Le=-1 to their anti-particles ; all other particles have Le=0
  • Lμ=1 for muon and μ-neutrino and Lτ=1 for tau lepton and its neutrino.
  • Significance of these numbers is that, in every process of whatever kind, the total values of B, Le,Lμ,Lτ separately remains constant.
  • Conservation of leptons has significance for strong interactions.
  • Another property that is conserved only in strong interactions is isospin.

Strangeness

  • A number of particles were discovered that behaves so unexpectedly that they were called strange particles.
  • They were created in pairs, and decay only in certain ways but not in others that were allowed by existing conservation laws.
  • To clarify the observation Gell-Mann and Nishijina independently introduced the strangeness number.
  • For photon , π0 and η0, B, Le,Lμ, Lτ and S are zero . There is no way to distinguish between them and their antiparticles, and they are regarded as their own anti particles.
  • Strangeness number is conserved in all processes mediated by strong and electromagnetic interactions.
  • The multiple creation of particles with S≠0 is the result of this conservation principle
  • S can change in an event mediated by the week interaction. Decays that proceed via a week interaction are relatively slow, a billion tomes slower than the interactions proceeded via strong interactions.
  • Week interactions does not allow S to change by more than ±1 in a decay. For example, Ξ decays in two steps  Ξ →Λ0→η00

Isospin

  • There are number of hadrons families whose numbers have similar masses but different charges. These families are called multiplets. Member of multiplet represents different charged states of a single fundamental entity.
  • Each multiplet according to number of charge states exhibits a number I such that the multiplicity of state is given by 2I+1.
  • Isospin can be represented by vector I in an abstract iso space whose component in any specific direction is governed by the quantum number denoted by I3.
  • Possible values of I3 varies from I, I-1 to -I. The charge of a baryon is related to its baryon numberB, its strangeness number S and the component I3 of its isotopic spin by the formula Q = e ( I 3 + B 2 + S 2 )

Conservation of statistics

  • The interchange of identicle particles in a system is a type of symmetry operation which leads to the preservation of the wave
  • Conservation of statistics signifies that no process occuring within an isolated system can change the statistical behaviour of the system.

Hypercharge

  • Hypercharge is defined as Y=S+B
  • Classification system for hadrons encompasses many short lived particles as well as relatively stable hadrons
  • This scheme collects isospin multiplets into submultiplets whose members have the same spin but different in isospin and a quantity called hypercharge.