Moving Average Method Disentangles Flow from Jet Signals in Heavy-Ion Collision Data

Physicists studying the hot matter created in collisions of heavy atomic nuclei face a stubborn bookkeeping problem: the signal they most want to measure, the imprint of jets ploughing through a quark-gluon plasma, is buried under a large and structured background produced by collective flow. A new methodological study now presents a practical way to separate the two, using a moving-average smoothing procedure applied to two-particle azimuthal correlations between high-momentum neutral pion trigger particles and associated charged particles in proton-proton and lead-lead collisions at the Large Hadron Collider.

The work, published in Discover Physics, reanalyzes complete experimental data taken from a published ALICE measurement. The data were collected during the 2011 LHC running period at a center-of-mass energy per nucleon pair of 2.76 TeV. The analysis focuses on trigger particles with transverse momenta between 8 and 16 GeV/c and associated charged particles between 0.5 and 6 GeV/c, with correlation functions constructed within a pseudorapidity interval of 0.8 in absolute value. No new collision data were taken; instead, the study develops and validates a background extraction technique on the existing published distributions.

The physical motivation lies in jet quenching. When two partons scatter hard in the early stage of a collision, they fly apart approximately back-to-back and later fragment into sprays of hadrons. In proton-proton collisions these dijet events can be characterized cleanly. In lead-lead collisions, however, the partons traverse a hot and dense medium before fragmenting, losing energy through gluon bremsstrahlung and elastic scattering. This energy loss shows up experimentally as a suppression of high-transverse-momentum hadrons and as modifications of dihadron correlations relative to proton-proton collisions. Two-particle angular correlations offer an indirect, statistical route to these effects: a high-momentum trigger particle tags a jet, and the distribution of associated particles around it reveals both the near-side peak at small angular separation and the away-side peak near 180 degrees.

The complication is that in heavy-ion collisions the measured correlations contain not only jet contributions but also collective flow, an anisotropic emission pattern arising from the collision geometry and initial-state fluctuations. Rather than a flat pedestal, as is typically assumed for proton-proton collisions, the combinatorial background in lead-lead collisions carries a multi-harmonic modulation. At low and intermediate transverse momenta this flow background dominates and must be estimated and subtracted carefully before any jet-related quantity can be extracted. Getting this subtraction wrong biases the per-trigger yields, the jet widths, and ultimately the nuclear modification factor that quantifies medium-induced jet modification.

For the proton-proton reference, the study employs several variants of the Zero Yield At Minimum, or ZYAM, method, which assumes that the jet contribution vanishes at the minimum of the correlation distribution. The variants include standard ZYAM averaging, a smoothed ZYAM determination in which a moving average of neighboring bins stabilizes the minimum against statistical fluctuations, a constant background fit over the interval between 1.0 and 1.57 radians in azimuthal separation, and a two-Gaussian peak fit over the full range. The spread among these approaches is taken as the systematic uncertainty on the extracted per-trigger yields. The authors note that ZYAM can oversubtract if a non-negligible jet contribution remains at the assumed minimum, particularly in central heavy-ion collisions at low and intermediate momenta where jet peaks may broaden or become strongly modified.

The central innovation concerns the lead-lead case. Here the analysis applies a region-dependent moving-average smoothing separately in the near-side region within 0.7 radians and the away-side region within 1.1 radians of the away-side peak, suppressing local jet-driven distortions while preserving the long-range azimuthal modulation. The smoothed distribution is then fitted with a two-source model: a Fourier-modulated background containing anisotropic flow coefficients up to the fifth harmonic, plus two Gaussian functions describing the near-side and away-side jet peaks. The flow coefficients extracted this way are compared with previously published measurements from ALICE and ATLAS, and the authors report that the method reproduces the published values for most kinematic intervals.

One interval proves harder. For associated particles between 4 and 6 GeV/c, the region-dependent smoothing fails to reproduce flow coefficients measured by independent methods, a discrepancy the authors attribute to the increasing importance of factorization breaking and residual jet contamination at high transverse momentum. For that interval the study adopts a global smoothing procedure over the entire 2-pi range, imposing periodic boundary conditions to preserve continuity across the histogram edges. The authors also explain why they extract the flow harmonics from the same correlation distributions used for the jet analysis rather than importing published flow coefficients: existing measurements are generally obtained with dedicated flow analyses and are not available for the specific trigger and associated transverse-momentum intervals and centralities required, so applying them would demand interpolation between different kinematic conditions. Extracting the harmonics simultaneously with the jet peaks keeps the background determination self-consistent.

With the flat and flow-modulated backgrounds subtracted, the near-side and away-side jet yields are obtained by integrating the correlation functions over the same angular windows, and the jet widths come from Gaussian fits centered at zero and at pi radians. The nuclear modification factor, defined as the ratio of lead-lead to proton-proton per-trigger yields, is then constructed. The results show that the near-side ratio lies above unity except in the highest associated-momentum bin, where it falls to about 0.85, while the away side shows the same general behavior except that its highest-momentum bin is much more strongly suppressed, at about 0.34. These values are consistent with the published ALICE results within systematic uncertainties. The away-side suppression at high associated momentum is consistent with parton energy loss in the hot and dense medium, while the enhancement observed at lower associated momentum may be related to medium-induced gluon radiation and other medium response effects. A moderate near-side enhancement is also observed, potentially reflecting modifications of the jet fragmentation process in the medium, such as changes to the fragmentation function or to the quark-to-gluon jet ratio.

The study also documents its uncertainty treatment in detail. Systematic uncertainties on the flow harmonics are estimated by varying the smoothing window sizes, shifting the jet integration boundaries by 0.127 radians, and repeating the fits with different maximum harmonic orders between two and five. The flat-background uncertainty is evaluated by comparing four independent background extraction methods, with the resulting background uncertainties ranging from 0.32 down to 0.02 across the four associated-momentum intervals. For the nuclear modification factor, the relative systematic uncertainty ranges from approximately 4 to 35 percent for near-side yields and from 7 to 37 percent for away-side yields, depending on associated transverse momentum. At low associated momentum the dominant contribution comes from the flat-background determination, whereas the flow-subtraction uncertainty grows in importance at intermediate momenta, and an additional uncertainty assigned to the highest momentum interval contributes significantly only there.

As a methods paper, the work does not claim new physics observations but offers a validated and self-consistent procedure for a long-standing experimental challenge. Its value lies in demonstrating that a simple smoothing technique, combined with a simultaneous two-source fit, can extract flow-modulated backgrounds and jet observables from the same correlation distributions, maintaining sensitivity to jet-related structures while reducing sensitivity to single-bin statistical fluctuations. The authors also flag a caveat: introducing the first harmonic coefficient in the background reconstruction introduces severe away-side discrepancies between methods, an issue they document explicitly. With heavy-ion programs at the LHC continuing to probe the quark-gluon plasma, techniques that cleanly separate flow from jet signals remain essential tools for interpreting the measured correlations and the medium effects they encode.

Subject of Research: Background extraction methods for two-particle azimuthal correlations in heavy-ion collisions

Article Title: Extraction of flow-modulated background in π0–hadron triggered correlations using a moving average method

Article References: Dordic, O. (2026). Extraction of flow-modulated background in π0–hadron triggered correlations using a moving average method. Discover Physics, 2(1), Article 11. https://doi.org/10.1007/s44418-026-00015-x

Image Credits: AI Generated

DOI: 10.1007/s44418-026-00015-x

Keywords: quark-gluon plasma, jet quenching, two-particle correlations, collective flow, ZYAM method, moving average, ALICE, LHC, lead-lead collisions, nuclear modification factor, flow harmonics, per-trigger yields