Possible octupole deformation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Pb</mml:mi><mml:mprescripts/><mml:none/><mml:mn>208</mml:mn></mml:mmultiscripts></mml:math> and the ultracentral <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>v</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>v</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> puzzle

Abstract

Recent measurements have established the sensitivity of ultracentral heavy-ion collisions to the deformation parameters of nonspherical nuclei. In the case of $^{129}\mathrm{Xe}$ collisions, a quadrupole deformation of the nuclear profile led to an enhancement of elliptic flow in the most central collisions. In $^{208}\mathrm{Pb}$ collisions a discrepancy exists in similar centralities, where either elliptic flow is overpredicted or triangular flow is underpredicted 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 $^{208}\mathrm{Pb}$ nuclei could have a pear-shape deformation (octupole), which has the effect of increasing triangular flow in central PbPb collisions. Using the recent data from ALICE and ATLAS, we reexamine the ${v}_{2}$-to-${v}_{3}$ puzzle in ultracentral collisions, including new constraints from recent measurements of the triangular cumulant ratio ${v}_{3}\left\{4\right\}/{v}_{3}\left\{2\right\}$ and comparing two different hydrodynamic models. We find that while an octupole deformation would slightly improve the ratio between ${v}_{2}$ and ${v}_{3}$, it is at the expense of a significantly worse triangular flow cumulant ratio. In fact, the latter observable prefers no octupole deformation, with ${\ensuremath{\beta}}_{3}\ensuremath{\lesssim}0.0375$ for $^{208}\mathrm{Pb}$, and is therefore consistent with the expectation for a doubly-magic nucleus even at top collider energies. The ${v}_{2}$-to-${v}_{3}$ puzzle remains a challenge for hydrodynamic models.

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