Question

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

(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 Σ0-hyperon via Σ0 → Λ + γ is electromagnetic. The explanation is the same as in (a)