Acceptance effect on the $N_{\mathrm{t}}{N}_{\mathrm{p}}\mathrm{/}{N}_{\mathrm{d}}^2$ ratio of light nuclei coalescence yields as a probe of nucleon density fluctuations

We employ a coalescence model to form deuterons ($\mathrm{d}$), tritons ($\mathrm{t}$) and helium-3 (${}^3\mathrm{H}\mathrm{e}$) nuclei from a uniformly distributed volume of protons ({\rm p}) and neutrons ({\rm n}). We study the ratio $N_{\mathrm{t}}{N}_{\mathrm{p}}\mathrm{/}{N}_{\mathrm{d}}^2$ of light nuclei yields as a function of the neutron density fluctuations. We investigate the effect of finite transverse momentum ($p_{\mathrm{T}}$) acceptance on the ratio, in particular, the “extrapolation factor” ($f$) for the ratio as functions of the $p_{\mathrm{T}}$ spectral shape and the magnitude of neutron density fluctuations. It is found that $f$ is monotonic in $p_{\mathrm{T}}$ spectra “temperature” parameter and neutron density fluctuation magnitude; variations in the latter are relatively small. We also examine $f$ in realistic simulations using kinematic distributions of protons measured in heavy ion collision data. It is found that $f$ is smooth and monotonic as a function of beam energy. We conclude that extrapolation from limited $p_{\mathrm{T}}$ ranges would not create, enhance, or reduce a local peak of the $N_{\mathrm{t}}{N}_{\mathrm{p}}\mathrm{/}{N}_{\mathrm{d}}^2$ ratio in beam energy. Our study provides a necessary benchmark for light nuclei ratios as a probe of nucleon density fluctuations, an important observable in the search for the critical point of nuclear matter.