Analytical coalescence formula for particle production in relativistic heavy-ion collisions

Based on a covariant coalescence model with a blast-wave-like parametrization for the phase-space configuration of constituent particles at freeze-out, we derive an approximate analytical formula for the yields of clusters produced in relativistic heavy-ion collisions. Compared to previous existing formulae, the present work additionally considers the contributions from the longitudinal dimension in momentum space, the relativistic corrections and the finite size effects of the produced clusters relative to the spatial distribution of constituent particles at freeze-out. The new analytical coalescence formula provides a useful tool to evaluate the yield of produced clusters, such as light nuclei from nucleon coalescence and hadrons from quark coalescence, in heavy-ion collisions. As a first application of the new analytical formula, we explore the strangeness population factor $S_3 = ^3_{\Lambda}$H/($^3$He$\times \Lambda/$p) based on nucleon/$\Lambda$ coalescence as well as the production of exotic hadrons based on quark coalescence, in central Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. The results are compared with the predictions from other models.