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Recent measurements have established the sensitivity of ultracentralheavy-ion collisions to the deformation parameters of non-spherical nuclei. Inthe case of ${}^{ 129}$Xe collisions, a quadrupole deformation of the nuclearprofile led to an enhancement of elliptic flow in the most central collisions.In ${}^{ 208}$Pb collisions a discrepancy exists in similar centralities, whereeither elliptic flow is over-predicted or triangular flow is under-predicted byhydrodynamic models; this is known as the $v_2$-to-$v_3$ puzzle in ultracentralcollisions. Motivated by low-energy nuclear structure calculations, we considerthe possibility that $^{208}$Pb nuclei could have a pear shape deformation(octupole), which has the effect of increasing triangular flow in central PbPbcollisions. Using the recent data from ALICE and ATLAS, we revisit the$v_2$-to-$v_3$ puzzle in ultracentral collisions, including new constraintsfrom recent measurements of the triangular cumulant ratio$v_3\left\{4\right\}/v_3\left\{2\right\}$ and comparing two differenthydrodynamic models. We find that, while an octupole deformation would slightlyimprove the ratio between $v_2$ and $v_3$, it is at the expense of asignificantly worse triangular flow cumulant ratio. In fact, the latterobservable prefers no octupole deformation, with $\beta_3\lesssim 0.0375$ for${}^{ 208}$Pb, and is therefore consistent with the expectation for adoubly-magic nucleus even at top collider energies. The $v_2$-to-$v_3$ puzzleremains a challenge for hydrodynamic models.

Possible octupole deformation of $^{208}$Pb and the ultracentral $v_2$ to $v_3$ puzzle