The Ds^+ meson (rest energy =1969 MeV, S=+1, C=+1 see Figure...

The $D_{s}^{+}$ meson (rest energy $=1969$ MeV, $S=+1, C=+1$ see Figure 14.15 ) has a lifetime of $0.5 \times 10^{-12} \mathrm{s}$. $(a)$ Which interaction is responsible for the decay? (b) Among the possible decay modes are $\phi+\pi^{+}, \mu^{+}+v_{\mu},$ and $\mathrm{K}^{+}+\mathrm{K}^{0}$ How do the $S$ and $C$ quantum numbers change in these three decays? The $\phi$ meson has a spin of $1,$ a rest energy of $1020 \mathrm{MeV},$ and a quark content of ss.) $(c)$ Analyze the three decay modes according to the quark content of the initial and final particles. (d) Why is the decay into $\mathrm{K}^{+}+$ $\pi^{+}+\pi^{-}$ allowed, while the decay into $\mathrm{K}^{-}+\pi^{+}+\pi^{+}$ is forbidden?

The $D_{s}^{+}$ meson (rest energy $=1969$ MeV, $S=+1, C=+1$ see Figure 14.15 ) has a lifetime of $0.5 \times 10^{-12} \mathrm{s}$. $(a)$ Which interaction is responsible for the decay? (b) Among the possible decay modes are $\phi+\pi^{+}, \mu^{+}+v_{\mu},$ and $\mathrm{K}^{+}+\mathrm{K}^{0}$
How do the $S$ and $C$ quantum numbers change in these three decays? The $\phi$ meson has a spin of $1,$ a rest energy of $1020 \mathrm{MeV},$ and a quark content of ss.) $(c)$ Analyze the three decay modes according to the quark content of the initial and final particles. (d) Why is the decay into $\mathrm{K}^{+}+$ $\pi^{+}+\pi^{-}$ allowed, while the decay into $\mathrm{K}^{-}+\pi^{+}+\pi^{+}$ is forbidden?

Key Concepts

Decay Mode Selection Rules

Selection rules dictate which decays are allowed based on conservation laws, symmetry principles, and the underlying dynamics of the interactions. Analyzing decays through these rules helps explain why certain decay channels, such as those respecting quark content, charge, and other quantum numbers, are permitted, while others that violate these conditions are forbidden.

Quark Content Analysis

This key idea involves examining the internal quark composition of both the initial and final state particles. By comparing the quark constituents, one can determine if a particular decay mode is allowed or forbidden according to the conservation of quantum numbers and the transformation properties of the weak interaction. It also provides insight into whether processes involve quark flavor changes.

Weak Interaction

This concept pertains to the fundamental force responsible for processes in which flavor quantum numbers such as charm or strangeness are not conserved. In particle physics, a decay with a lifetime on the order of 10?¹² seconds often implicates the weak interaction, which allows transitions between different quark types through the exchange of W bosons.

Quantum Number Conservation and Violation

In strong and electromagnetic interactions, certain quantum numbers—such as strangeness (S) and charm (C)—are strictly conserved. However, in weak decays, these numbers can change. Understanding which quantum numbers are conserved or altered in a decay, and how they vary across different decay channels, is essential for identifying the governing interaction.

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