For each of the following reactions establish whether it is...

For each of the following reactions establish whether it is allowed or not; if it is not, give the reasons: (1) $\mu^{+} \rightarrow e^{+}+\gamma$, (2) $e^{-} \rightarrow v_e+\gamma$; (3) $p+p \rightarrow$ $\Sigma^{+}+K^{+}$; (4) $p+p \rightarrow p+\Sigma^{+}+K^{-}$; (5) $p \rightarrow e^{+}+v_e$; (6) $p+p \rightarrow A+\Sigma^{+}$; (7) $p+n \rightarrow A+\Sigma^{+}$; (8) $p+n \rightarrow \Xi^0+p$; (9) $p \rightarrow n+e^{+}+v_e$; (10) $n \rightarrow p$ $+e^{-}+v_e$.

Key Concepts

Conservation Laws

Conservation laws are the fundamental rules that require certain physical quantities to remain constant in particle interactions and decays. These include energy, momentum, angular momentum, electric charge, baryon number, and lepton number. Any reaction must obey these conservation rules in order to be physically allowed, and checking these laws helps determine whether a reaction can occur in nature.

Electric Charge Conservation

Electric charge conservation mandates that the total electric charge before and after a reaction must be equal. When analyzing particle reactions, it is essential to account for the charges of all incoming and outgoing particles to ensure that the net charge remains unchanged, which is a basic and non-negotiable requirement for any allowed process.

Baryon Number Conservation

Baryon number conservation is a principle which states that the total baryon number—assigned to particles like protons and neutrons—remains constant in isolated reactions. This rule prevents processes that would lead to the creation or destruction of baryons without an appropriate compensating change, thereby constraining possible nuclear and hadronic reactions.

Lepton Number and Lepton Flavor Conservation

Lepton number conservation requires that the total number of leptons (and their associated flavors, such as electron, muon, and tau) remains constant during particle interactions. In many reactions, especially those involving weak interactions, each type of lepton must be balanced separately. Failure to conserve lepton numbers or flavors leads to forbidden decay channels under the Standard Model.

Energy–Momentum Conservation

Energy and momentum conservation in relativistic particle reactions means that the sum total of energy and the vector sum of momentum must be the same before and after any reaction. This imposes severe kinematic constraints on possible reactions and decays, ruling out processes that are energetically forbidden or that cannot balance momentum among all products.

Interaction Types in Particle Physics

Different fundamental interactions—such as electromagnetic, weak, and strong forces—have their own selection rules and matrix elements, which dictate how particles can transform or decay. For instance, decays mediated by the weak interaction often involve neutrinos and changes in flavor, while electromagnetic processes must conserve charge and angular momentum in very specific ways. Recognizing the interaction type is crucial for understanding why certain reactions are allowed and others are forbidden.

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