Investigating the coalescence-inspired sum rule for light nuclei and hypernuclei in heavy-ion collisions

Abstract

A data-driven idea is presented to test if light nuclei and hypernuclei obey the coalescence-inspired sum rule, i.e., to test if the flow of a light nucleus or hypernucleus is the summed flow of each of its constituents. Here, the mass difference and charge difference among the constituents of light nuclei and hypernuclei are treated appropriately. The idea is applied to the available data for $\sqrt{{s}_{NN}}=3$ GeV fixed-target $\mathrm{Au}+\mathrm{Au}$ collisions at the Relativistic Heavy Ion Collider (RHIC), published by the STAR Collaboration. It is found that the sum rule for light nuclei is approximately valid near midrapidity ($\ensuremath{-}0.3<y<0$), but there is a clear violation of the sum rule at large rapidity ($y<\ensuremath{-}0.3$). The Jet AA Microscopic Transport Model (JAM), with baryonic mean-field plus nucleon coalescence, generates a similar pattern as obtained from the experimental data. In the present approach, the rapidity dependence of directed flow of the hypernuclei ${}_{\mathrm{\ensuremath{\Lambda}}}^{3}\mathrm{H}$ and ${}_{\mathrm{\ensuremath{\Lambda}}}^{4}\mathrm{H}$ is predicted in a model-independent way for $\sqrt{{s}_{NN}}=3$ GeV $\mathrm{Au}+\mathrm{Au}$ collisions, which will be explored by ongoing and future measurements from STAR.