On non-flow suppression in an MLE-based flow analysis

Abstract

We show that the maximum likelihood estimator (MLE) is an effective tool for mitigating non-flow effects in flow analysis. To this end, one constructs two toy models that simulate non-flow contributions corresponding to particle decay and momentum conservation, respectively. The performance of MLE is analyzed by comparing it against standard approaches such as particle correlation and event plane methods. For both cases, MLE is observed to provide a reasonable estimate of the underlying flow harmonics, and in particular, its performance can be further improved when the specific form of the likelihood in the presence of non-flow can be assessed. The dependencies of extracted flow harmonics on the multiplicity of individual events and the total number of events are analyzed. Additionally, it is shown that the proposed approach performs efficiently in addressing deficiencies in detector acceptance. These findings suggest MLE as a compelling alternative to standard methods for flow analysis.

Figures (5)

• Figure 1: The two toy models devised in the present study. Left: The first scenario mimics particle decays. Each particle might randomly split into two daughter particles separated by an angle drawn from a Gaussian distribution Eq. \ref{['GDisDecay']}. Right: The second scenario incorporates momentum conservation. The emission of additional particles guarantees the total momentum conservation. To enhance the non-flow effect, the conservation is enforced for all individual subsets consisting of only a few particles.
• Figure 2: Flow harmonics evaluated using particle correlators, the event-plane method, and MLE. The events are generated from the emission of particle pairs with a prescribed opening angle, superimposed on a background collective flow $v_2 = 0.1$. The input flow harmonics, where applicable, are indicated by a dashed black horizontal line, while the true values governed by Eqs. \ref{['vnUncorrTrue']} and \ref{['vnCorrTrue']} are shown by a thin red line. The analysis is performed for 10,000 events, each of which contains a total of 500 particles. Left column: The particle pairs are back-to-back, and the elliptic flow is evaluated as a function of the number of particle pairs. Right column: The number of particle pairs is fixed to 50, and the elliptic flow is evaluated as a function of the opening angle. Top row: The particle pairs are correlated with the symmetry plane, with one particle of each pair emitted according to the background one-particle distribution. Bottom row: The same as the top row, but the particle pairs are uncorrelated with the symmetry plane.
• Figure 3: Correlators and flow harmonics evaluated using events without any background harmonic flow but with independent particle emission under exact global momentum conservation. The events are generated via the RAMBO algorithm jet-ph-05. The analysis is performed for 10,000 events across various multiplicities. Top: The calculated $c_1\{2\}$ and $c_2\{2\}$ as functions of the multiplicity. Bottom: The corresponding event-average MLE estimators $\langle v_1(\mathrm{MLE})\rangle$ and $\sqrt{\langle v_1(\mathrm{MLE})^2\rangle}$ as functions of the multiplicity.
• Figure 4: (Color Online) The results for a simplified detector's acceptance given by a step function Eq. \ref{['eqeffpiecef']}. For the calculations, a total of 1,000 events are generated by toy model I. Left: The azimuthal particle distribution observed by the detector with a uniform (solid black squares) and non-uniform (solid red circles) acceptance. Right: The distribution of the estimated $v_2$ on an event-by-event basis using the MLE method, evaluated by considering the correction to the detector's acceptance (empty blue circles). The results are compared with those obtained without considering the correction (empty red triangles) and with a perfect detector (solid black squares).
• Figure 5: (Color Online) The same as Fig. \ref{['piecefcorr1']} but for the detector's acceptance given by Eq. \ref{['eqeff2']} and the correction scheme is applied to simulated data generated by toy model II.