Symmetries and conservation Laws: Part 2

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 L_e=1 is assigned to electrons and electron neutrino, L_e=-1 to their anti particles ; all other particles have L_e=0
• L_μ=1 for muon and μ-neutrino and L_τ=1 for tau lepton and its neutrino.
• Significance of these numbers is that , in every process of whwtever kind , the total valuse of B, L_e,L_μ,L_τ separately remains constant.
• Conservation of leptons has a signefence for strond interactions.
• Another property that is conserved only in strong interactions is isospin.

Strangeness

• A number of particles were discovered that behsve 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 indepensently introduced the strangeness number.
• For photon , π⁰ and η⁰, B, L_e,L_μ, L_τ 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+π^-→η⁰+π⁰

Isospin

• There are number of hadron families whose numbers have similar masses but different charges. Thes families are called multiplets. Member of multiplet represents different charged states of a single fundemental 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

  $Q=e(I_3+\frac{B}{2}+\frac{S}{2})$

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 cillects isospin multiplets into submultiplets whose members have the same spin but different in isospin and a quantity called hypercharge.