AcademyParticles and Cosmology
Academy
Particle Families
Level 1 - Physics topic page in Particles and Cosmology.
Principle
Matter particles are organized into leptons and quarks. Quarks form hadrons, while each particle has an antiparticle with opposite additive quantum numbers.
Notation
\(Q\)
electric charge in units of e
1
\(B\)
baryon number
1
\(L\)
lepton number
1
\(q\)
quark
\(\bar q\)
antiquark
\(e\)
elementary charge magnitude
\(\mathrm{C}\)
Method
Derivation 1: Classify by constituents
Leptons are fundamental in the Standard Model. Hadrons are composite states made from quarks.
Baryon content
\[qqq\]
Meson content
\[q\bar q\]
Derivation 2: Add charges
Hadron charge is the sum of constituent quark charges.
Proton
\[uud:\quad Q=\frac23+\frac23-\frac13=+1\]
Neutron
\[udd:\quad Q=\frac23-\frac13-\frac13=0\]
Derivation 3: Antiparticles reverse additive quantum numbers
Antiparticles have the same rest mass but opposite charge, baryon number, lepton number, and other additive quantum numbers.
Particle
\[Q,B,L\]
Antiparticle
\[-Q,-B,-L\]
Rules
Baryon structure
\[\mathrm{baryon}=qqq\]
Meson structure
\[\mathrm{meson}=q\bar q\]
Charge conservation
\[\sum Q_i=\sum Q_f\]
Examples
Question
Find the charge of a
\[u\bar d\]
meson.Answer
\[Q=+2/3+1/3=+1\]
so the meson is positively charged.Checks
- Leptons are not made of quarks.
- Baryons contain three quarks or three antiquarks.
- Mesons contain a quark and an antiquark.
- Charge, baryon number, and lepton number must balance in allowed reactions.