Irreps of qqq and \(q q \bar{q}\) States by Recursive Pairing

Finding the irreps of a three-parton system abc can be done by first decomposing the parton pair ab into a sum of irreps \((ab)_\alpha \) , combining the third parton c with each of these irreps, and decomposing each product \((ab)_\alpha c\) using the tensor method studied in previous chapters. In principle, this simple “recursive pairing” method can be used to construct the irreps and associated projectors of systems with any number of partons. It is illustrated here in the simple cases of qqq and \(qq\bar{q}\) systems.