Question

In which of the following reactions or decays is strangeness conserved? In each case, explain your reasoning.(a) K++μ++νμ$$K^{+}$$+\$$mu^{+}$$+
u_{\mu} (b) n+K+→p+π$$0n+K^{+}$$	o p+\$$pi^0 (c) K++K$$−→π0+π$$0K^{+}$+K^{-}$$	o\$$pi^0$$+\$$pi^0 (d) p+K$$−→Λ0+π$$0p+K^{-}$$	o\$$Lambda^0$$+\$$pi^0$$

Accepted Answer

Step 1: Understand the concept of strangeness conservation. Strangeness is a quantum number associated with the presence of strange quarks in particles. In strong and electromagnetic interactions, strangeness is conserved. However, in weak interactions, strangeness can change by ±1. Step 2: Analyze reaction (a): K⁺ + μ⁺ + ν_μ. The K⁺ meson contains a strange quark (s) and an up antiquark (u̅). The muon (μ⁺) and neutrino (ν_μ) are leptons and do not carry strangeness. This reaction involves the weak interaction (due to the presence of neutrinos), so strangeness may not be conserved. Check the initial and final states to confirm. Step 3: Analyze reaction (b): n + K⁺ → p + π⁰. The neutron (n) and proton (p) are baryons, while K⁺ and π⁰ are mesons. The K⁺ meson has a strangeness of +1, while the neutron, proton, and π⁰ have a strangeness of 0. Since the initial state has a total strangeness of +1 and the final state has a total strangeness of 0, strangeness is not conserved. This reaction likely involves the weak interaction. Step 4: Analyze reaction (c): K⁺ + K⁻ → π⁰ + π⁰. The K⁺ meson has a strangeness of +1, and the K⁻ meson has a strangeness of -1. The π⁰ mesons have a strangeness of 0. The total strangeness in the initial state is 0 (+1 + -1), and the total strangeness in the final state is also 0. Strangeness is conserved, so this reaction likely occurs via the strong interaction. Step 5: Analyze reaction (d): p + K⁻ → Λ⁰ + π⁰. The proton (p) has a strangeness of 0, the K⁻ meson has a strangeness of -1, the Λ⁰ baryon has a strangeness of -1, and the π⁰ meson has a strangeness of 0. The total strangeness in the initial state is -1 (0 + -1), and the total strangeness in the final state is also -1 (-1 + 0). Strangeness is conserved, so this reaction likely occurs via the strong interaction.

In which of the following reactions or decays is strangeness conserved? In each case, explain your reasoning.
(a) $K^{+} + μ^{+} + ν_{μ}$
(b) $n + K^{+} \to p + π^{0}$
(c) $K^{+} + K^{-} \to π^{0} + π^{0}$
(d) $p + K^{-} \to Λ^{0} + π^{0}$

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Key Concepts

Strangeness

Conservation Laws in Particle Physics

Types of Interactions