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 $p_T\mathrm{/}A$. 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 $d\mathrm{/}p$, ${}^3$He$\mathrm{/}d$, $t\mathrm{/}p$, ${}^3$He$\mathrm{/}p$, $d\mathrm{/}{p}^2$, ${}^3$He$\mathrm{/}{p}^3$, $t{\mathrm{/}}^3$He and argue their nontrivial behaviors can be used to distinguish production mechanisms of light nuclei.