The baryon has quark content

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model · Electroweak theory and the Standard Model

Particle Physics, Ch The Standard Model as a table you can predict from

Problem

The Ω−\Omega^- baryon has quark content ssssss, mass 1672.45 MeV/c21672.45\,\mathrm{MeV}/c^2, baryon number B=1B=1, strangeness S=−3S=-3 and spin J=3/2J=3/2. Two candidate final states are considered: ΛK−\Lambda K^-: Λ\Lambda mass 1115.68 MeV/c21115.68\,\mathrm{MeV}/c^2, S=−1S=-1; K−K^- mass 493.68 MeV/c2493.68\,\mathrm{MeV}/c^2, S=−1S=-1. Ξ0π−\Xi^0 \pi^-: Ξ0\Xi^0 mass 1314.86 MeV/c21314.86\,\mathrm{MeV}/c^2, S=−2S=-2; π−\pi^- mass 139.57 MeV/c2139.57\,\mathrm{MeV}/c^2, S=0S=0. ((a)) Check charge, baryon number, strangeness and mass for both channels, and state which interaction and quark-level vertex is needed for each. ((b)) Predict the order-of-magnitude lifetime band for the Ω−\Omega^-, and state which previously met particle lifetimes it should be comparable to. ((c)) CPT invariance predicts τ(Ωˉ+)=τ(Ω−)\tau(\bar\Omega^+) = \tau(\Omega^-). Given the measured values τ(Ω−)=8.21×10−11 s\tau(\Omega^-) = 8.21\times10^{-11}\,\mathrm{s} and τ(Ωˉ+)=8.20×10−11 s\tau(\bar\Omega^+) = 8.20\times10^{-11}\,\mathrm{s}, state whether this is consistent with CPT.

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