QCE Physics - Unit 4 - The Standard Model
Particle Interactions | QCE Physics
Learn QCE Physics particle interactions with lepton number, baryon number, conservation checks, decay diagrams and symmetry principles.
Updated 2026-06-15 - 4 min read
QCAA official coverage - Physics 2025 v1.3
Exact syllabus points covered
- Describe the concepts of lepton number and baryon number.
- Solve problems relating to the conservation of lepton number and baryon number in particle interactions using $B = n_b - n_{\bar{b}}$, $B = \frac{1}{3}(n_q - n_{\bar{q}})$ and $L = n_l - n_{\bar{l}}$.
- Describe electron/electron, electron/positron and neutron decay interactions using particle interaction diagrams.
- Describe how symmetry in particle interactions occurs to maintain the principles of conservation.
Particle interactions are analysed by checking what is conserved before and after an interaction. QCE Physics focuses on baryon number, lepton number and interaction diagrams for electron/electron, electron/positron and neutron decay processes.
Original Sylligence diagram for physics particle conservation check.
Baryon number
Baryon number counts baryons minus antibaryons:
$ B = n_b - n_{\bar{b}} $
A baryon has $B=+1$, an antibaryon has $B=-1$, and particles that are not baryons have $B=0$.
Because baryons are made of three quarks, baryon number can also be counted from quarks:
$ B = \frac{1}{3}(n_q-n_{\bar{q}}) $
Each quark contributes $+\frac{1}{3}$ and each antiquark contributes $-\frac{1}{3}$. A proton with three quarks has $B=+1$. A meson with one quark and one antiquark has $B=0$.
Lepton number
Lepton number counts leptons minus antileptons:
$ L = n_l - n_{\bar{l}} $
A lepton has $L=+1$, an antilepton has $L=-1$, and non-leptons have $L=0$. In more advanced particle physics, lepton family numbers can be tracked separately, but the QCE syllabus wording focuses on lepton number as a conservation concept.
Conservation checks
To test a proposed interaction:
- List all particles before and after.
- Assign baryon number and lepton number to each.
- Add totals on each side.
- Compare before and after totals.
- Check charge if the reaction data includes it.
If a number is not conserved, the interaction is not allowed under that conservation rule.
Neutron beta decay
A common Standard Model interaction is neutron beta decay:
$ n \rightarrow p + e^- + \bar{\nu}_e $
Baryon number before: neutron has $B=+1$. Baryon number after: proton has $B=+1$, electron and antineutrino have $B=0$. Baryon number is conserved.
Lepton number before: neutron has $L=0$. After: electron has $L=+1$ and electron antineutrino has $L=-1$, so total lepton number is $0$. Lepton number is conserved.
Charge before: neutron has charge $0$. After: proton $+1$, electron $-1$, antineutrino $0$, total $0$. Charge is conserved.
This decay is associated with the weak interaction. At the quark level, one down quark changes into an up quark, producing a $W^-$ boson that decays into an electron and electron antineutrino.
Electron/electron and electron/positron interactions
Two electrons can interact electromagnetically by exchanging a photon. A simple interaction diagram would show two electron lines with a photon exchanged between them. The particles remain electrons, and charge and lepton number are conserved.
An electron and positron can annihilate:
$ e^- + e^+ \rightarrow \gamma + \gamma $
The electron has lepton number $+1$ and the positron has lepton number $-1$, so total lepton number before is zero. Photons have lepton number zero, so lepton number after is also zero. Charge is also conserved.
Symmetry and conservation
Symmetry in particle interactions means the rules do not change when a valid transformation is applied. Conservation laws are deeply connected to symmetry. In QCE terms, this means interaction diagrams and equations must preserve quantities such as charge, baryon number and lepton number across the interaction.
Do not overcomplicate the exam answer. If asked how symmetry maintains conservation, explain that the same conserved quantities appear before and after the interaction, and use the particle numbers in the given process to show it.