Researchers have quantified the impact of dynamic light-cluster formation (deuterons, tritons, helium-3, and helium-4) on the collective flows of protons and these nuclei in Au+Au heavy-ion collisions. Using a Boltzmann-Uehling-Uhlenbeck transport model coupled to a kinetic approach for cluster formation, the study focused on beam energies from $120$ to $1500 A$ MeV. The results indicate that the explicit inclusion of light-cluster degrees of freedom significantly modifies the directed ($v_1$), elliptic ($v_2$), triangular ($v_3$), and quadrangular ($v_4$) flows of protons, especially at lower beam energies.

The effect of dynamic light-cluster formation is most pronounced in the $120$ to $150 A$ MeV range, remains visible between $250$ and $400 A$ MeV, and gradually weakens above $600 A$ MeV. For light nuclei, the kinetic approach reproduces the overall beam-energy dependence of FOPI experimental flow data, showing better agreement for energies at or above $400 A$ MeV. Furthermore, the model qualitatively reproduces the nucleon-number scaling of the elliptic flow per nucleon ($v_2/A$), a behavior observed experimentally.

These findings highlight the importance of a dynamic treatment of light-cluster formation for accurate interpretation of collective flows in heavy-ion collisions, particularly in the energy regime below about $600 A$ MeV. Although clustering effects on proton flows are minor at higher collision energies, their inclusion is crucial for understanding the dynamics of nuclear matter under extreme conditions and for refining theoretical models of quantum chromodynamics at lower energies.