Quark Fusion and Magic Numbers for Stability of Quark Compounds

We continue our work on the investigation of the properties of quarks, antiquarks and of quark-antiquark compounds with this theoretical paper on quark fusion, and on search for magic numbers for quark compounds, using some Python and Fortran codes that we developed. The fusion of b quarks from gluon splitting and sea-quark distributions at the LHC is vital for testing heavy Z0 models where the Z0 boson preferably couples to quarks in the third generations. We formulate a heavy-quark distribution function to combine the processes~\textit{QQ\textasciimacron }$\to H$~and~\textit{gQ}$\to $\textit{HQ}~with the process~\textit{gg}$\to $\textit{QQ\textasciimacron H,}~and obtain a cross section with potentially large logarithms, of order ln(mH/mQ) summed to all orders in the strong coupling scenario. For the multi-quark systems, the wave functions were first analyzed by group-theoretical techniques, with the antiquark having infinite mass and the quarks belonging to a multiplet. We also describe some possible laboratory experiments that may be used in testing our computational results.