Octupole deformation of $^{208}$Pb does not resolve the ultracentral $v_2$ to $v_3$ puzzle

Recent measurements establish the sensitivity of ultracentral heavy-ion collisions to deformation parameters of non-spherical nuclei. In ${}^{ 129}$Xe collisions, a quadrupole deformation of nuclear profile led to an enhancement of elliptic flow in the most central collisions. In ${}^{ 208}$Pb collisions a discrepancy exists in similar centralities, where either elliptic flow is over-predicted or triangular flow is under-predicted by hydrodynamic models; this is known as the $v_2$-to-$v_3$ puzzle in ultracentral collisions. Motivated by low-energy nuclear structure calculations, we consider the possibility that $^{208}$Pb nuclei could have an octupole deformation, which has the effect of increasing triangular flow in central PbPb collisions. Using data from ALICE and ATLAS, we revisit the $v_2$-to-$v_3$ puzzle in ultracentral collisions, including new constraints from recent measurements of triangular cumulant ratio $v_3\{4\}/v_3\{2\}$ and comparing two different hydrodynamic models. We find that data is consistent with an octupole deformation $\beta_3$ of ${}^{ 208}$Pb less than $0.0375$ and that addition of an octupole deformation does not significantly improve the agreement with data.