Light nuclei elliptic flow at mid-rapidity in s₍₍ = 3. 0-3. 9 GeV Au+Au collisions using coalescence model

Light nuclei collective flow is an important probe for understanding their production mechanisms in heavy-ion collisions. The STAR collaboration has reported that the atomic mass number (A) scaling of light nuclei elliptic flow v₂ is broken at s₍₍ = 3. 0-3. 9 GeV. The observations reveals that, while protons maintain negative v₂ values at mid-rapidity at both 3. 0 and 3. 2 GeV, light nuclei v₂ exhibit a sign change from negative at 3. 0 GeV to positive at 3. 2 GeV. In this study, we investigate v₂ of protons and deuterons in mid-central Au+Au Collisions at s₍₍ = 3. 0, 3. 2, 3. 5 and 3. 9 GeV using the JAM2 microscopic transport model. Deuterons are formed via nucleon coalescence, with the spatial distance ΔR and momentum difference ΔP between constituent protons and neutrons serving as the coalescence criteria. Our calculations successfully reproduce the sign change in deuteron v₂ at 3. 2 GeV. We observe a strong dependence of nucleon coalescence probability on the azimuthal angle relative to the reaction plane. This effect is primarily driven by the transverse momentum dependence of the mean spatial ΔR and momentum ΔP separations between nucleon pairs, which vary with the nucleon azimuthal angle. Moreover, our analysis demonstrates that the stiffness of the nuclear equation of state plays a crucial role in determining the energy dependence of this sign change in deuteron v₂ at s₍₍=3. 2 GeV.