Question

(a) Explain the following statements. The mean lifetime of the π⁺ meson is 2.6 × 10⁻⁸ s while that of π0 is 0.8 × 10⁻¹⁶ s. 

(b) The π⁺ and π⁻ mesons are of equal mass, but the Σ⁺ and Σ⁻ baryon masses differ by 8 MeV/c² 

(c) The mean life of the Σ⁰ baryon is many orders of magnitude smaller than those of the Λ and E⁰ baryons.

Answer 1

(a) The charged pions π^± decay by weak interactions π → μ + ν, and so their mean lifetime is relatively longer, while the neutral pion π⁰ decays via π⁰ → 2γ, electromagnetically and therefore their mean life time is shorter. 

(b) The π⁺ and π⁻ are particle and antiparticle pair and they are expected to have the same mass by the CPT theorem. On the other hand Σ⁺ and Σ⁻ hyperons are not particle-antiparticle. Actually bar Σ ⁻ is the antiparticle of Σ⁺. Σ⁺ and Σ⁻ are the members of the isospin triplet (Σ⁺, Σ⁰, Σ⁻) and because of difference in their charges can slightly differ in their mass similar to the masses of neutron and proton for the isospin doublet of nucleon. 

(c) Λ-hyperon decays via Λ → p + π⁻ or n + π⁰, the interaction is weak. Similarly the hyperon E₀ decays via E₀ → Λ + π₀, which is also a weak decay. In both the cases the lifetimes are relatively long on the nuclear scale. On the other hand the decay of Σ^0-hyperon via Σ⁰ → Λ + γ is electromagnetic. The explanation is the same as in (a)