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Based on the coalescence model, we analyse the light-nuclei production nearthe critical point by expanding the phase-space distribution function$f(\mathbf{r},\mathbf{p})$ in terms of the phase-space cumulants $\sim \langler^m p^m\rangle_c$. We show that the dominant contribution of the phase-spacedistribution to the yield of light nuclei is determined by the second-orderphase-space cumulants. Here, we identify the fireball size, the homogeneitylength, and the effective temperature, which are encoded in the second-orderphase-space cumulants, as the relevant scales in explaining the yield of lightnuclei. These scales are typically much larger than the correlation length ofthe critical fluctuations created in the rapid expansion of the heavy-ionsystems, so we need to eliminate this dominant contribution of the relevantscales in order to isolate the critical contribution from the yield of lightnuclei. We find that the second-order phase-space cumulants appeared in theyields of light-nuclei with different mass numbers share a similar structure.This property allows us to construct ratios of light-nuclei yields inappropriate combinations so that the effect of the relevant scales of thelight-nuclei yield cancels, which isolates the critical effects.

Scales in light-nuclei production near the QCD critical point