Quark Coalescence: Formation of Mesons Including Excited States

We discuss the quantum mechanics of coalescence of quark-antiquark pairs into mesons using a non-relativistic quark model. We derive the coalescence probabilities assuming a harmonic oscillator potential and generic Gaussian wave packet shapes for the initial quarks and antiquarks. Our particular emphasis is on modeling excited states of the meson spectrum consistently. We provide the formalism to systematically include excited states from the Particle Data Book, and many more predicted by the quark model, up to $L=4$ and masses of about 2.2 GeV for light flavors. We provide estimates of masses and decay branching ratios for unconfirmed states. We use a phase space picture which is appropriate for the quasi-classical nature of the information typically available for the quarks and antiquarks in applications like Monte Carlo simulations. We demonstrate that for typical parton configurations expected in jets, excited meson states are populated abundantly.