1 Introduction

For more than a decade, the STAR Collaboration has been searching for evidence of chiral magnetic effects (CME) [1-3]. CME [4, 5] refers to the induction of an electric current (${\overrightarrow{J}}_{\text{e}}$) by the magnetic field ($\overrightarrow{B}$) in a chiral system: ${\overrightarrow{J}}_{\text{e}}\propto {\mu }_5\overrightarrow{B}$. A chiral system bears a nonzero μ₅, which characterizes the imbalance of right-handed and left-handed fermions in the system. The discovery of CME in high-energy heavy-ion collisions would confirm the simultaneous existence of ultra-strong magnetic fields, chiral symmetry restoration, and topological charge changing transitions in these collisions. On average, $\overrightarrow{B}$ is perpendicular to the reaction plane (Ψ_RP) that contains the impact parameter and the beam momenta. CME, therefore, will manifest a charge transport across the reaction plane.

A set of observables common to CME searches are the charge-separation fluctuations perpendicular to Ψ_RP, e.g. with a three-point correlator [6], γ (ϕα + ϕβ -2Ψ_RP), where averaging is done over all particles in an event and over all events. To draw firm conclusions on the presence of CME, an effective way is needed to disentangle the signal and background contributions, the latter of which are intertwined with collective flow. Collisions of isobaric nuclei, e.g. ${}_{44}^{96}Ru{+}_{44}^{96}Ru$ and ${}_{40}^{96}Zr{+}_{40}^{96}Zr$, present an opportunity to vary the initial magnetic field while keeping background conditions approximately the same [7]. Ruthenium-96 and Zirconium-96 each have 96 nucleons but with different numbers of protons, 44 and 40 for Ru and Zr, respectively. Monte Carlo Glauber simulations indicate ${}_{44}^{96}Ru{+}_{44}^{96}Ru$ and ${}_{40}^{96}Zr{+}_{40}^{96}Zr$ collisions at the same beam energy are almost identical in terms of particle production [8]. The ratio of the multiplicity distributions from the two collision systems is consistent with unity almost everywhere, except in 0-5% most central collisions, where the slightly larger charge radius of Ru (R₀ = 5.085 fm) plays a role against that of Zr (R₀ = 5.02 fm). CME analyses can focus on the centrality range of 20-60%, where the background difference due to the multiplicity are negligible. A theoretical calculation using the HIJING model \cite{Deng:2016knn} indicates the relative difference in the square of the initial magnetic field between $$${}_{44}^{96}\text{Ru}{+}_{44}^{96}\text{Ru}$ and ${}_{40}^{96}\text{Zr}{+}_{40}^{96}\text{Zr}$ collisions approaches 15-18% for peripheral events and ≈13% for central events. These estimates translate into a relative difference in the CME signal observable between the two isobars of 3%, assuming an 80% background from elliptic flow, requiring a minimum of 1.2 × 10⁹ events to pass the various analysis selection criteria to achieve a result of 5σ significance. Due to the small difference in the CME signal observables, of critical importance to the analysis is control of systematic uncertainties, in particular those related to detector acceptance and efficiency, which may vary in a time-dependent way.

In 2018, STAR collected data from isobar collisions, ${}_{44}^{96}\text{Ru}{+}_{44}^{96}\text{Ru}$ and ${}_{40}^{96}\text{Zr}{+}_{40}^{96}\text{Zr}$, at $\sqrt{s_{\text{NN}}}=200$ GeV. For the first time, the STAR Collaboration has implemented blind analyses of these data in studies related to CME. While blind analyses are not uncommon in particle physics, e.g. Ref. [9], the typical methods were not found to be suitable for the specific needs of STAR CME analyses. What follows is the description of the blind analysis procedure for the 2018 isobar collision data. The procedure was accepted by the STAR Collaboration prior to CME data-taking. While primarily relevant for CME-related studies, the opportunity for a blind analysis was open to all STAR analyses of 2018 isobar data. In identifying as a “STAR blind analysis” for the 2018 isobar running, analysts adhere to the following procedure. Subsequent STAR publications clearly identify as a blind analysis or an “un-blind” analysis according to the accepted procedure. The following procedure takes advantage of frequent switching of the isobar collision species during 2018 RHIC running to interleave isobar data samples from each species in a way that respects the time-variation of data running conditions. STAR collected 6.3 billion isobar events, evenly split between the two species, during the two months of isobar running. The RHIC isobar stores or “fills” typically lasted 20 hours, with STAR collecting data during 30-minute “runs” of the data acquisition system. Accelerator operators adjusted the beam optics throughout the 20 hour fills to maintain nearly constant collision rates, with the same target rate for the two isobar species.

2 Blinding Techniques

3 Implementation and Timeline for Blinded Analyses

No STAR physics analyses had access to species information prior to un-blinding. The timelines for un-blinding are estimated by the blind analysts, who present regular updates to their respective physics working groups (PWG) to document progress and to inform adjustments to the timeline. Decisions to un-blind are based upon a review of thoroughly documented analysis procedures, codes, and analysis reports–including estimates of measurement uncertainty–by the relevant PWG. In addition, for blind analyses of the isobar data, so-called “godparent committees” or “GPCs,” are set early and follow analyses closely throughout their development. The GPCs serve an important role in verifying that analyses are ready to proceed to the next stages of the blinding procedure. After the step-1 data are available, blind-data analysts estimate a timeline for completing the necessary analyses for advancing to step-2. Based on this input from the analysts, management approves a date for the beginning of the second step. Analysts present regular updates to document progress. Regardless of progress, un-blinding occurs no earlier than the original estimate unless all blind analyses are deemed ready to proceed by STAR Management. Based upon the progress reports, un-blinding may be delayed to ensure the quality of the final results. An analogous timeline procedure is done for the full un-blinding. Prior to the first un-blinding step, analysts prepare detailed notes documenting the procedures, cuts, corrections, systematic uncertainties, and criteria for any future run-by-run cuts and corrections. Prior to the second un-blinding step, analysts ensure that the documentation is updated and complete, including the run-by-run portion of analyses. Prior to each un-blinding step, analysts provide analysis codes for vetting and Q/A by the GPC in addition to the standard vetting within the physics working groups.

When the GPC is satisfied that an analysis is ready for un-blinding, analysts present the status of their analyses to the physics working group conveners and the physics analysis coordinator. As the un-blinding date approaches, analysts discuss with STAR management any need for delays to un-blinding to ensure the quality of results. If an unresolved disagreement exists between analysts, the decision to un-blind or extend the date lies with STAR management. After physics results are produced with un-blinded data, a review is conducted to verify that the frozen analysis code was used to produce the results.

While un-blinded data are not accessible to physics analyses until the blinding timeline is completed, management uses discretion in applying blinding to any calibration analysis. To ensure the integrity of calibrations, e.g. those of the beamline and TPC [14], STAR calibration experts may require access to un-blind data. Without robust calibrations, the physics analyses may not be able to achieve the required precision for deciphering a CME signal. Therefore, the relevant experts are allowed access to the un-blind data for these tasks. Furthermore, access to un-blind data is restricted to these experts alone and the experts recuse themselves from participation in any blind physics analysis.

4 Mock data challenge

As the recommended analysis blinding procedure represents a substantial departure from that typical for STAR analyses, testing feasibility is critical. Toward this end, a “mock data challenge” was conducted utilizing data from Au+Au collisions at $\sqrt{s_{\text{NN}}}=27$ GeV, also collected in 2018. Additionally, this exercise served as an opportunity for the software and computing team to develop, tune, and test the machinery necessary for producing the blind data samples. “Blinded” samples of these data were provided to analysts, utilizing the same techniques intended for blinding the isobar data. One sample was provided with output data files containing events from a mixture of data-taking runs, simulating the first stage of blinding, where data files contain a mix of isobar species. Another sample was provided using output files containing events from single data-taking runs but still blinding certain variables that in the isobar data sample could be used to identify the isobar species. For completeness, a final un-mixed sample was provided with no information obscured, simulating the fully “un-blind” phase of the analysis. Analysts used the two mock blind-data samples to perform quality control studies and appropriately tune analysis codes, selection cuts, and corrections. Once completed, the analysts then ran the same codes over the un-blind data sample to verify that the analysis was feasible with the given data structures and that results were appropriately consistent within the statistical differences between the samples. Example quality assurance plots for the three different samples are shown in Fig. 1. Note that the different samples did not contain identical sets of events.

Fig. 1.Full-screen View

Mean transverse momentum of charged particle tracks associated with the primary collision vertex for three mock data samples: (top) “mixed-blind,” (middle) “unmixed-blind,” and (bottom) “un-blind.” The data were taken from Au+Au collisions at $\sqrt{s}=27$ GeV and provided to analysts using the computing machinery developed for the blind analysis of isobar data. Note that the three samples shown here do not contain identical sets of events. The “mixed-blind” data contain events from a mixture of data-taking runs, combined together in an output datafile for analysis. The “unmixed-blind” samples do not mix across data-taking runs but do blind other information that could be used to identify the isobar species, e.g. the proper data-taking run ID number. The “mixed-blind” and “unmixed-blind” datafiles are assigned psuedo-run-numbers (shown across the top of the upper two panels, where the actual run number is shown in the lower panel) that prevent the analysts from identifying the collision species from a run database. The “un-blind” samples are presented to analysts with no information obscured. The calculated observable is shown as a function of an arbitrary run index.

5 After Un-blinding

After un-blinding, only changes to correct “mistakes,” defined for this purpose as errors in arithmetic or unintended departures from the approved and documented analysis procedures, are allowed. If such a correction is made, the analysis results with the error will also be provided with a detailed explanation of the specific correction applied and why it was needed. On a case-by-case basis, the collaboration considers announcing the result from a blind analysis simultaneously with the submission of the corresponding paper to the journal and the preprint arXiv. Regardless, only one set of “final” results from the blind analysis will be released, e.g. there will be no set of “preliminary” results prior to the “final” results. All STAR publications of 2018 results state explicitly whether the analysis followed the approved STAR blinding procedure.

6 Conclusion

The STAR Collaboration has developed a procedure to carry out blind analyses of isobar collision data, collected in 2018. The procedure described in this manuscript was accepted by the STAR Council in January 2018, prior to the isobar collision runs. The initial step in the procedure is an analysis of blinded data samples that interleave events from the two collision species, while the second step involves analysis of blinded data samples that do not mix events from the two collision species, followed by complete un-blinding of the data. Prior to commencing with analysis of the isobar data, a mock data challenge was successfully conducted to demonstrate the feasibility of the procedure both from an analysis standpoint and a computational standpoint. Analyses of the blind data are underway, following the procedure outlined in this manuscript.