TF Model for Mesonic Matters

Abstract

Lattice QCD is a very important tool used by particle physicists to investigate the properties of baryons and mesons. Lattice techniques are presently being employed to understand and elucidate the pentaquark and tetraquark observations made by Belle, BESIII, and LHCb. However, as the quark content increases, it becomes computationally expensive and time-intensive to do the lattice calculations. Every state must be investigated separately, which means a great deal of analysis on Wick contractions and specialized computer coding. In addition, as one adds more quarks, the states will become larger and the lattice used must also increase in volume. There is therefore a need for reliable quark models that can give an overview of many states to help guide these expensive lattice calculations. The MIT bag model and Nambu-Jona-Lasinio model are two of these quark models. Another approach, the Thomas-Fermi (TF) statistical model has been amazingly successful in the explanation of atomic spectra and structure, as well as nuclear applications. Our group has adopted the TF model and applied it to collections of many quarks. One advantage our model has over bag models is the inclusion of nonperturbative Coulombic interactions. One would expect that the TF quark model would become increasingly accurate as the number of constituents is increased, as a statistical treatment is more justified. The main usefulness will be to see systematic trends as the parameters of the model are varied. It could also be key to identifying families of bound states, rather than individual cases.