Production properties of deuterons, helions and tritons via an analytical nucleon coalescence method in Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV

We improve a nucleon coalescence model to include the coordinate-momentum correlation in nucleon joint distributions, and apply it to Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV to study production properties of deuterons ($d$), helions ($^3$He) and tritons ($t$). We give formulas of the coalescence factors $B_2$ and $B_3$, and naturally explain their behaviors as functions of the collision centrality and the transverse momentum per nucleon $p_T/A$. We reproduce the transverse momentum spectra, averaged transverse momenta and yield rapidity densities of $d$, $^3$He and $t$, and find the system effective radius obtained in the coalescence production of light nuclei behaves similarly to Hanbury Brown-Twiss interferometry radius. We particularly give expressions of yield ratios $d/p$, $^3$He$/d$, $t/p$, $^3$He$/p$, $d/p^{2}$, $^3$He$/p^3$, $t/^3$He and argue their nontrivial behaviors can be used to distinguish production mechanisms of light nuclei.