Griffiths Introduction to Elementary Particles · Problem 4.26
Bound States — David J. Griffiths
Physics — QFT · gell-mann-nishijima-generalized
Problem
(a) The Gell-Mann–Nishijima formula, equation (4.37), was proposed in the early fifties, which is to say long before the discovery of charm, beauty, or truth. Using the table of quark properties (on page 47), and the quark isospin assignments, equation (4.38), deduce the general formula expressing Q in terms of A, I3, S, C, B, and T.
(b) Because u and d are the only quarks with nonzero isospin, it should be possible to express I3 in terms of U (``upness'') and D (``downness''). What's the formula? Likewise, express A in terms of the flavor numbers U, D, S, C, B, and T.
(c) Putting it all together, obtain the formula for Q in terms of the flavor numbers (that is, eliminate A and I3 from your formula in part (a)). This final version represents the cleanest statement of the Gell-Mann–Nishijima formula, in the three-generation quark model.