Spherical bootstrap calculation ofqqq-baryon and multiquark-hadron masses

Recently a way of implementing the dualtopological unitarization program has been found, in which baryons and other multiquark hadrons are put on the sphere and appear at the same topologicalcomplexity level as ordinary \(q\bar q\) mesons. This permits one to have a lowest-order “spherical bootstrap”, within which unitarity, duality and crossing can be consistently satisfied. In the present paper we use this framework to calculate hadron masses by imposing duality on an infinite sum of ladder graphs generated from spherical unitarity. By making a certain simple dynamical approximation, we derive an explicit generic Regge-trajectory formula for any given process. If we then make certain reasonable dynamical assumptions and require simultaneous consistency for entire sets of processes, we are able to calculate the masses of all the lowest \(q\bar q,qqq,qq\bar q\bar q,qq\bar qqq,qq\bar qq\bar q\bar q\) states withq=u, d, and the Regge trajectories associated with each of them. The only arbitrary parameter is the mass of the ?, which merely serves to set the mass scale.