Griffiths Introduction to Elementary Particles · Problem 1.17

Elementary Particle Dynamics — David J. Griffiths

Physics — QFT · shupe-preon-model-quarks-leptons

Problem

M.\ Shupe [Phys.\ Lett.\ 86B, 87 (1979)] has proposed that all quarks and leptons are composed of two even more elementary constituents: cc (with charge −1/3-1/3) and nn (with charge zero)---and their respective antiparticles, cˉ\bar{c} and nˉ\bar{n}. You're allowed to combine them in groups of three particles or three antiparticles (ccnccn, for example, or nˉnˉnˉ\bar{n}\bar{n}\bar{n}). Construct all of the eight quarks and leptons in the first generation in this manner. (The other generations are supposed to be excited states.) Notice that each of the quark states admits three possible permutations (ccnccn, cnccnc, nccncc, for example)---these correspond to the three colors. Mediators can be constructed from three particles plus three antiparticles. W±W^\pm, Z0Z^0, and γ\gamma involve three like particles and three like antiparticles (W−=cccnˉnˉnˉW^- = ccc\bar{n}\bar{n}\bar{n}, for instance). Construct W+W^+, Z0Z^0, and γ\gamma in this way. Gluons involve mixed combinations (ccncˉnˉnˉccn\bar{c}\bar{n}\bar{n}, for instance). How many possibilities are there in all? Can you think of a way to reduce this down to eight?

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