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

A coalescence model was employed to form deuterons ({\rm d}), tritons ({\rm t}), and helium-3 (\ensuremath{^3{\rm He}}) nuclei from a uniformly-distributed volume of protons ({\rm p}) and neutrons ({\rm n}).We studied the ratio $N_{\rm t} N_{\rm p}/N_{\rm d}^2$ of light nuclei yields as a function of the neutron density fluctuations.We investigated the effect of finite transverse momentum ($\ensuremath{p_{\rm{T}}}$) acceptance on the ratio, in particular, the ''extrapolation factor'' ($f$) for the ratio as a function of the $\ensuremath{p_{\rm{T}}}$ spectral shape and the magnitude of neutron density fluctuations.The nature of $f$ was found to be monotonic in $\ensuremath{p_{\rm{T}}}$ spectra ''temperature'' parameter and neutron density fluctuation magnitude; variations in the latter are relatively small.We also examined $f$ in realistic simulations using the kinematic distributions of protons measured from the heavy-ion collision data. The nature of $f$ was found to be smooth and monotonic as a function of the beam energy. Therefore, we conclude that extrapolation from limited $\ensuremath{p_{\rm{T}}}$ ranges does not create, enhance, or reduce the local peak of the $N_{\rm t} N_{\rm p}/N_{\rm d}^2$ ratio in the beam energy.Our study provides a necessary benchmark for light nuclei ratios as a probe for nucleon density fluctuations, an important observation in the search for the critical point of nuclear matter.