(g) charges of the up (u), down (d), strange (s), anti-up (ū), anti-down…

The idea

Quark charges are given as fractions of the elementary charge e. The up quark (u) has charge +2/3 e; the down quark (d) has charge −1/3 e; the strange quark (s) has charge −1/3 e. Anti-quarks carry opposite charge: anti-up (ū) has charge −2/3 e; anti-down (d̄) has charge +1/3 e; anti-strange (s̄) has charge +1/3 e. These fractional charges combine to give integer charges for hadrons. For example, a proton uud has charge (+2/3) + (+2/3) + (−1/3) = +1 e, and a π⁻ meson dū has charge (−1/3) + (−2/3) = −1 e. Knowing these values lets you deduce the charge of any hadron from its quark composition.

What earns the marks

• Up quark charge is +2/3 e.
• Down quark charge is −1/3 e.
• Strange quark charge is −1/3 e.
• Anti-up quark charge is −2/3 e.
• Anti-down quark charge is +1/3 e.
• Anti-strange quark charge is +1/3 e.
• Hadron charge is the sum of its quark charges.

Common mistakes and how to put them right

• Giving the strange quark charge as +2/3 e.

  Put it right by noting s has charge −1/3 e.

• Forgetting to reverse the sign for anti-quarks.

  Put it right by taking the opposite of the quark charge.

• Treating quark charges as whole numbers.

  Put it right by using fractions of e.

• Mixing up anti-down and anti-strange charges.

  Put it right by noting both are +1/3 e.

Exam tips

• Learn the six charges as a table: u +2/3, d −1/3, s −1/3, ū −2/3, d̄ +1/3, s̄ +1/3.
• When summing charges, convert to a common denominator to avoid arithmetic slips.
• Check that the total charge of a hadron is an integer multiple of e.
• Use the anti-quark rule: opposite sign to the corresponding quark.