Coalescence probabilities of polarized and unpolarized mesons

The recombination of two particles into angular momentum eigenstates in a 3D isotropic harmonic oscillator potential was explored. Recently, the probabilities for coalescence of two particles into a bound state with well-defined angular momentum quantum number l, and summed over the magnetic quantum number m, where the particles are represented by generic wave packets, was computed in “Angular momentum of the isotropic 3-D harmonic oscillator: Phase-Space-Distributions and coalescence probabilities” [Kordell II, Fries, and Ko, Ann. Phys. 443, 168960 (2022)]. We have added to this work by computing probabilities dependent on m, which allows us to consider the polarization of mesons coalescing from quarks. We have utilized Monte Carlo integration to compute the spectrum of mesons if the initial quarks are given by thermal distributions with various temperatures and collective motion. We have tested our Monte Carlo integration in limiting cases where analytic results are known. We have demonstrated that polarization of mesons can be produced directly from the orbital angular momentum of quarks.