Testing hydrodynamic response to initial-state geometry in Pb+$d^\uparrow$ collisions

Deuterons with different polarization states have distinct shapes for their wavefunctions. This offers a unique opportunity to experimentally control the initial-state collision geometry with the polarization of the light-ion targets in relativistic heavy-ion experiments. We study the charged hadron elliptic flow coefficients with respect to the polarization angle of deuterons in Pb + polarized deuteron collisions using a hydrodynamics + hadronic transport model. Hydrodynamic response to initial-state geometry predicts a distinct sign of $v_2$ correlated with the deuteron's polarization states, providing a clean test case for elucidating the collective origin in small collision systems.