Residual background in ESS intercept

Determine the magnitude and sign of the residual non–Chiral Magnetic Effect background in the Event-Shape Selection (ESS) intercept, defined as the v2=0 intercept of a linear fit to the charge-dependent three-point correlator Δγ versus single-particle v2 in event classes selected by pair q2 computed from the same particles of interest. Specifically, quantify whether the remaining background contribution in the ESS intercept is positive, negative, or zero under typical ESS configurations that use the same particles of interest to calculate q2, v2, and Δγ.

Background

The ESS method bins events by statistical fluctuations of the elliptic anisotropy using q2 computed from the same particles of interest (POIs) that enter the physics measurement of Δγ and v2. Because selection, measurement, and background sources all involve the same POIs, self-correlations and intertwined dependencies can bias the intercept at v2=0, which is intended to isolate CME contributions.

The paper focuses on the commonly used ESS configuration combining pair-based q2 for event selection with single-particle v2 for the Δγ vs. v2 regression, noting that self-correlation effects are hard to discern. The authors emphasize that the extent and even the sign of any residual non-CME background in the ESS intercept are not established and require clarification.

References

We therefore state the weaker claim that the data support: the phantom component's shape is generated by the acceptance rule rather than by event content, while its level is not fully accounted for by our null. We regard the residual as an open question rather than evidence of event content in the phantoms.

— Prevalence Determines Precision:Silent Contamination in Detector-Defined Datasets  (2609.11449 - Huang et al., 10 Sep 2026) in Section 5.3, paragraph “What the phantom component is” (Section 5, subsection “Mixture decomposition: the contaminated curve, exactly”)

However, since the same POIs are used for $q2$, $\vsing$ and $\dg$, self-correlations are present in the measurement whose effects/biases are hard to discern. It is unclear how much background is remaining in the ESS intercept, and whether the remaining background is positive or negative.

— Investigating the Event-Shape Methods in Search for the Chiral Magnetic Effect in Relativistic Heavy Ion Collisions  (2407.14489 - Li et al., 2024) in Section "The Event-Shape Techniques"