For each of the following reactions (a) establish whether it...

For each of the following reactions (a) establish whether it is allowed or not, (b) if it is not, give the reasons (there may be more than one), (c) establish the types of interaction that allow it: (1) $\pi^{-} p \rightarrow \pi^0+n$; (2) $\pi^{+} \rightarrow \mu^{+}+v_\mu$; (3) $\pi^{+} \rightarrow \mu^{+}+\bar{v}_\mu$; (4) $\pi^0 \rightarrow 2 \gamma$; (5) $\pi^0 \rightarrow 3 \gamma$; (6) $e^{+}+e^{-} \rightarrow \gamma$; (7) $p+\bar{p} \rightarrow$ $A+A$; (8) $p+p \rightarrow \Sigma^{+}+\pi^{+}$; (9) $n \rightarrow p+e^{-}$; (10) $n \rightarrow p+\pi^{-}$.

Key Concepts

Conservation Laws

In particle physics, all reactions and decays must satisfy several fundamental conservation laws. These include conservation of energy and momentum, electric charge, baryon number, and lepton number. Violation of any of these conservation laws renders a reaction forbidden. Such laws serve as essential constraints in determining whether a given reaction can physically occur.

Strong Interaction

The strong interaction is the force that binds quarks together within hadrons and is responsible for many hadronic reactions and scattering processes. It conserves most flavor quantum numbers, such as isospin and strangeness, and proceeds much faster than other interactions. Reactions dominated by the strong force typically involve the exchange of gluons and occur with high probability if energetically allowed.

Electromagnetic Interaction

The electromagnetic interaction governs processes that involve electrically charged particles interacting via photon exchange. It is characterized by the conservation of electric charge and additional symmetry constraints such as charge conjugation (C) symmetry. Electromagnetic decays often result in the production of photons and must comply with selection rules, for example, restrictions on the number of photons in the final state based on C-parity considerations.

Weak Interaction

The weak interaction is responsible for processes that cause flavor changes among elementary particles, such as quark transitions in hadronic decays or changes in lepton types, and is mediated by W and Z bosons. It allows decays that are forbidden under strong or electromagnetic interactions but typically occurs at a slower rate. Weak processes often involve neutrinos and are characterized by the violation of parity symmetry.

Symmetry and Selection Rules

Symmetry principles, including parity, charge conjugation (C-parity), and G-parity, play a crucial role in determining whether certain reactions can occur. These selection rules impose additional constraints beyond the basic conservation laws, particularly in electromagnetic interactions, where the symmetry properties of the photon, such as its C-parity, dictate the allowed number of photons produced in a decay or reaction.

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