A beam of negative pions of momentum strikes protons at rest

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment · Particles, interactions and experiment

Particle Physics, Ch Quantum numbers, conservation laws and allowed reactions

Problem

A beam of negative pions of momentum 0.90 GeV/c0.90\,\mathrm{GeV}/c strikes protons at rest. Two reactions are proposed: π−+p→K++?\pi^-+p\to K^++{?}, where the missing particle is a single baryon, and π−+p→K++n\pi^-+p\to K^++n. Use mπ−c2=139.6 MeVm_{\pi^-}c^2=139.6\,\mathrm{MeV}, mpc2=938.3 MeVm_pc^2=938.3\,\mathrm{MeV}, mK+c2=493.7 MeVm_{K^+}c^2=493.7\,\mathrm{MeV} (K+=usˉK^+=u\bar s) and the baryons given in the data below. Data (particle: content, QQ, SS, mass in MeV/c2\mathrm{MeV}/c^2): nn: uddudd, 00, 00, 939.6939.6; Λ\Lambda: udsuds, 00, −1-1, 1115.71115.7; Σ+\Sigma^+: uusuus, +1+1, −1-1, 1189.41189.4; Σ−\Sigma^-: ddsdds, −1-1, −1-1, 1197.41197.4; Ξ−\Xi^-: dssdss, −1-1, −2-2, 1321.71321.7. ((a)) Test π−+p→K++n\pi^-+p\to K^++n against charge, baryon number and strangeness, and give its verdict. ((b)) Find the charge, baryon number and strangeness the missing baryon in π−+p→K++?\pi^-+p\to K^++{?} must carry, and name it from the table. ((c)) Say which interaction can produce the completed reaction of part (b), with a reason. ((d)) Using the fixed-target relation of Chapter 2, find s\sqrt{s} at this beam momentum and the minimum beam momentum for the completed reaction. Say whether, at 0.90 GeV/c0.90\,\mathrm{GeV}/c, it is forbidden, below threshold or able to run, and what would change the verdict for each of the two reactions.

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