Multiplicity and transverse density as ordering variables of the $Λ/K^0_S$ ratio in oxygen-oxygen collisions at the LHC

Baryon-to-meson enhancements are commonly compared across collision systems at equal multiplicity. Using published data only, we test whether the $p_T$ dependence of the CMS $Λ/K^0_S$ ratio in minimum-bias O-O collisions at $\sqrt{s_{NN}}=5.36$ TeV can be obtained from CMS multiplicity-differential p-Pb and Pb-Pb measurements weighted with the O-O multiplicity distribution. The prediction from p-Pb collisions of equal multiplicity is harder than the data, with a tilt of $+0.35\pm0.04$ in $\ln(\mathrm{prediction}/\mathrm{data})$ versus $\ln p_T$, whereas that from peripheral Pb-Pb collisions is consistent with the data. In a Glauber model calibrated on O-O data, O-O and peripheral Pb-Pb collisions of equal multiplicity have similar transverse densities $ρ=\langle(dN_{ch}/dη)/S_\perp\rangle$, about half of that in p-Pb. Matching the p-Pb reference in $ρ$ instead of multiplicity reduces the tilt by about 60%, to $+0.14\pm0.04$, with nucleons as sources; the tension is fully removed ($-0.02\pm0.04$) only when sub-nucleonic structure is included (three constituents per nucleon), so the conclusion depends on the modeled size of high-multiplicity p-Pb collisions. The published blast-wave velocities of p-Pb and Pb-Pb collisions, which differ at equal multiplicity, are close at equal $ρ$. Multiplicity alone thus does not determine the $Λ/K^0_S$ shape across systems; the data are consistent with a radial boost governed by the transverse density, as expected from hydrodynamics. The same pattern is found in EPOS4, which has a hydrodynamic core, but not in PYTHIA Angantyr. For Ne-Ne collisions, which have the transverse density of O-O at equal multiplicity, the minimum-bias ratio is predicted to agree with O-O within 3-5%, as EPOS4 also predicts.