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 2D angular correlations onto 1D azimuth from three centrality classes of 200 GeV AuAu 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 (PS) analysis. We find that the FS-only model is rejected in all cases by Bayesian analysis which always prefers a Gaussian. A cylindrical quadrupole cos(2ϕ) is required in some cases but rejected for 0-5%-central AuAu collisions. Given a Gaussian centered at the azimuth origin "higher harmonics" cos(mϕ) for m > 2 are rejected. A model consisting of Gaussian + dipole cos(ϕ) + quadrupole cos(2ϕ) provides good 1D data descriptions in all cases.