Optimal modeling of 1D azimuth correlations in the context of Bayesian inference

Abstract

Analysis and interpretation of spectrum and correlation data from high-energy nuclear collisions is currently controversial because two opposing physics narratives derive contradictory implications from the same data, one narrative claiming collision dynamics is dominated by dijet production and projectile-nucleon fragmentation, the other claiming collision dynamics is dominated by a dense, flowing QCD medium. Opposing interpretations seem to be supported by alternative data models, and current model-comparison schemes are unable to distinguish between them. There is clearly need for a convincing new methodology to break the deadlock. In this study we introduce Bayesian inference (BI) methods applied to angular correlation data as a basis to evaluate competing data models. For simplicity the data considered are projections of two-dimensional (2D) angular correlations onto a 1D azimuth from three centrality classes of 200-GeV Au-Au collisions. We consider several data models typical of current model choices, including Fourier series (FS) and a Gaussian plus various combinations of individual cosine components. We evaluate model performance with BI methods and with power-spectrum analysis. We find that FS-only models are rejected in all cases by Bayesian analysis, which always prefers a Gaussian. A cylindrical quadrupole $cos(2\ensuremath{\phi})$ is required in some cases but rejected for 0%--5%-central Au-Au collisions. Given a Gaussian centered at the azimuth origin, ``higher harmonics'' $cos(m\ensuremath{\phi})$ for $m>2$ are rejected. A model consisting of $\mathrm{Gaussian}+\mathrm{dipole}cos(\ensuremath{\phi})+\mathrm{quadrupole}cos(2\ensuremath{\phi})$ provides good 1D data descriptions in all cases.