Universal Energy Dependence of Measured Temperatures for Baryons Produced in Heavy-ion Collisions

From the data on baryon production in heavy-ion collisions it is shown that a set of measurable functions exist, one for each baryon type, that depend exponentially on transverse momenta up to the maximum values detected for all collision energies ranging from the low end of RHIC BES to the high end of CERN LHC. The implied temperatures satisfy a scaling law in collision energy with a universal exponent for all baryon types which is the novel discovery. A self-similar thermal source is implied. Furthermore, it is shown how the scaling behavior depends on centralities. Those features in the data are related to simple properties of light and strange quarks by use of the recombination model. Prediction of $\phi$ meson production is made and then verified by existing data.