2.1.7 Applications of Conservation Laws

Key Conservation Laws in Particle Physics

In all particle interactions, certain conservation laws must be upheld to ensure that the reaction is physically possible. The quantities that must always be conserved include:

• Energy and Momentum
• Charge
• Baryon Number
• Electron Lepton Number
• Muon Lepton Number Strangeness must also be conserved, but only in strong interactions. It does not need to be conserved in weak interactions (like beta decay).

Applying Conservation Laws in Interactions

To verify whether a given particle interaction obeys the conservation laws, we can evaluate each property before and after the interaction and ensure they match.

Property	Before Interaction	After Interaction	Change
Charge	$0$	$+1 + (-1) + 0 = 0$	$0$
Baryon Number	$1$	$1 + 0 + 0 = 1$	$0$
Electron Lepton Number	$0$	$0 + 1 + (-1) = 0$	$0$
Muon Lepton Number	$0$	$0 + 0 + 0 = 0$	$0$
Strangeness	$0$	$0$	$0$

Since all values are conserved, this interaction is allowed.

Beta Decay and Quark Changes

Beta-minus and beta-plus decay are both caused by the weak interaction, which allows for a change in quark type. This process can be visualised with Feynman diagrams:

1. Beta-minus $(β^-)$ Decay:

• Process: A down quark ($d$) in a neutron changes into an up quark ($u$), converting the neutron into a proton.
• Diagram: A $W^-$ boson is emitted, which then decays into an electron $( e^- )$ and an electron antineutrino $( \bar{\nu}_e )$.

2. Beta-plus $(β^+)$ Decay:

• Process: An up quark ($u$) in a proton changes into a down quark ($d$), converting the proton into a neutron.
• Diagram: A $W^+$ boson is emitted, which then decays into a positron $( e^+ )$ and an electron neutrino $( \nu_e )$.

These diagrams help illustrate how a change in quark type leads to the transformation of particles in weak interactions.