describe the changes to quark composition that take place during β– and β+ decay

Fundamental Particles – Quark Changes in β‑Decay

In the Standard Model, nucleons are made of up‑type ($u$) and down‑type ($d$) quarks:

• Proton: $uud$
• Neutron: $udd$

β‑decay processes involve the weak interaction, which changes the flavour of a quark by the exchange of a $W^{\pm}$ boson. The change in quark composition is the key to understanding the transformation of one nucleon into another.

β⁻ (Beta‑minus) Decay

In β⁻ decay a neutron inside a nucleus is transformed into a proton, emitting an electron ($e^-$) and an electron antineutrino ($\bar{u}_e$).

At the quark level the reaction is:

$$d \;\rightarrow\; u + W^-$$ $$W^- \;\rightarrow\; e^- + \bar{u}_e$$

Thus the down‑quark ($d$) inside the neutron changes to an up‑quark ($u$), converting the neutron ($udd$) into a proton ($uud$).

β⁺ (Beta‑plus) Decay

In β⁺ decay a proton is transformed into a neutron, emitting a positron ($e^+$) and an electron neutrino ($u_e$). This occurs when a nucleus has too many protons.

At the quark level the reaction is:

$$u \;\rightarrow\; d + W^+$$ $$W^+ \;\rightarrow\; e^+ + u_e$$

Here an up‑quark ($u$) inside the proton changes to a down‑quark ($d$), turning the proton ($uud$) into a neutron ($udd$).

Summary of Quark Changes

Decay Type	Initial Nucleon (Quarks)	Quark Transition	Final Nucleon (Quarks)	Emitted Leptons
β⁻	Neutron $udd$	$d \rightarrow u + W^-$	Proton $uud$	$e^- + \bar{u}_e$
β⁺	Proton $uud$	$u \rightarrow d + W^+$	Neutron $udd$	$e^+ + u_e$

Key Points to Remember

1. The weak interaction changes quark flavour via $W^{\pm}$ boson exchange.
2. β⁻ decay: $d \rightarrow u$ (neutron → proton) + $e^- + \bar{u}_e$.
3. β⁺ decay: $u \rightarrow d$ (proton → neutron) + $e^+ + u_e$.
4. Overall charge is conserved because the $W^{\pm}$ boson carries the necessary charge.
5. Lepton number is conserved: each lepton emitted is accompanied by its corresponding antineutrino or neutrino.