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{\nu}_e\$).

At the quark level the reaction is:

\$d \;\rightarrow\; u + W^-\$

\$W^- \;\rightarrow\; e^- + \bar{\nu}_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 (\$\nu_e\$). This occurs when a nucleus has too many protons.

At the quark level the reaction is:

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

\$W^+ \;\rightarrow\; e^+ + \nu_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

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{\nu}_e\$.
3. β⁺ decay: \$u \rightarrow d\$ (proton → neutron) + \$e^+ + \nu_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.