Challenging the utility of third-order azimuth harmonics in the description of ultra-relativistic heavy-ion collisions

In recent years it has become conventional practice to include higher-order cylindrical harmonics in the phenomenological description of two-particle angular correlations from ultra-relativistic heavy-ion collisions. These model elements, whose dependence on relative azimuth angle has the form $\cos[m(\phi_1-\phi_2)]$ where $m > 2$, were introduced to support a hydrodynamic flow interpretation of the same-side ($|\phi_1-\phi_2| < \pi/2$) 2D peak in the correlations. Previous studies have shown that the $m > 2$ harmonics are not required by the data, that they destabilize the fitting models, and that their net effect is to decompose the same-side peak into two components, one being dependent on and the other being independent of relative pseudorapidity. Thus we are lead to question whether descriptions of angular correlation data including higher-order harmonics inform our understanding of the same-side peak or heavy-ion collisions in general. Results from analysis of two-dimensional angular correlation data from the Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider (LHC) show that the RHIC data do not exclude a single-Gaussian hypothesis for the same-side peak. We find that the net effect of including the $m = 3$ harmonic or azimuth sextupole in the fitting model is the inclusion of small non-Gaussian dependence in the mathematical description of the same-side peak. Those non-Gaussian effects are systematically insignificant and can be accommodated by minor perturbations to the same-side 2D Gaussian peak model, which act locally at small relative azimuth. We also demonstrate that the 0-1% 2D angular correlation data for 2.76 TeV Pb+Pb collisions from ATLAS, which display an away-side double peak on azimuth, do not require a sextupole and exclude a positive same-side sextupole.