Search for the chiral magnetic effect through beam energy dependence of charge separation using event shape selection

Using a novel event shape selection method to suppress elliptic flow backgrounds in Au+Au collisions across the RHIC Beam Energy Scan, this study reports a statistically significant residual charge separation at intermediate energies (11.5–19.6 GeV) that may indicate the chiral magnetic effect, while finding consistent-with-zero results at lower and higher energies.

The Gist

Imagine two massive, super-charged trains (atomic nuclei) smashing into each other at nearly the speed of light. When they collide, they don't just make a mess; for a split second, they create a tiny, super-hot "soup" of particles called Quark-Gluon Plasma (QGP). This is the state of matter that existed just microseconds after the Big Bang.

Physicists have been hunting for a ghostly phenomenon in this soup called the Chiral Magnetic Effect (CME). Here is the simple breakdown of what they are looking for, the problem they faced, and how they finally got a clearer look.

1. The Ghost Hunt: What is the CME?

Think of the colliding trains as creating a massive, invisible magnetic field (like a giant magnet passing through the room). Inside the hot soup, the particles (quarks) have a property called "chirality," which is like a particle's "handedness" (left-handed or right-handed).

The CME theory says: If you have a mix of left and right-handed particles in a strong magnetic field, they should separate.

• Positive charges should flow one way.
• Negative charges should flow the other way.

It's like a magnetic field acting as a sorting machine, separating red marbles from blue marbles. If scientists can prove this happens, it would confirm some very deep, weird rules about how the universe works at its most fundamental level.

2. The Problem: The "Noise" in the Room

For twenty years, scientists have been trying to see this charge separation. But there's a huge problem: Background Noise.

Imagine you are trying to hear a whisper (the CME) in a crowded, noisy stadium (the heavy-ion collision).

• The "whisper" is the charge separation caused by the magnetic field.
• The "noise" is caused by the way the particles naturally flow out of the collision. Because the collision isn't perfectly head-on, the particles fly out in an oval shape (like a football). This natural flow creates a fake signal that looks exactly like the charge separation they are looking for.

Previous attempts to find the CME were like trying to hear that whisper while the stadium crowd was screaming. The "noise" was drowning out the "whisper."

3. The New Trick: "Event Shape Selection" (ESS)

In this new paper, the STAR Collaboration (a team of physicists at the RHIC collider) used a clever new method called Event Shape Selection (ESS).

Here is the analogy:
Imagine you are looking at a crowd of people running out of a stadium.

• The Old Way: You just looked at everyone running and tried to guess who was running because of the "whisper" and who was running because of the "oval track." It was messy.
• The New Way (ESS): The scientists decided to only look at the people running in a perfectly straight line (a circle), ignoring the ones running in an oval.

Why? Because the "oval" shape is caused by the background noise (the elliptic flow). If you select only the events where the particles fly out in a perfect circle, you have effectively turned off the noise machine.

By mathematically "subtracting" the oval-shaped events and looking only at the perfectly round ones, they could see what was left. If the "whisper" (CME) was real, it should still be there even when the "oval noise" is gone.

4. The Results: A Glimmer of Hope

After using this new "noise-canceling" technique on data from gold nuclei collisions at different energies, here is what they found:

• At very high energies (200 GeV): The signal disappeared. It was consistent with zero. This explains why previous experiments at the highest energies didn't find the CME; the magnetic field might fade away too quickly, or the effect is just too small to see.
• At medium energies (11.5 to 19.6 GeV): Bingo. They found a small but real signal!
  • In the "middle" collisions (not too head-on, not too glancing), they saw a charge separation that was 3 times more likely to be real than a fluke (3-sigma significance).
  • When they combined the data from this specific energy range, the confidence jumped to over 5 times (5-sigma), which is the gold standard in physics for a discovery.

5. Why Does This Matter?

The fact that they found this signal specifically at medium energies (between 10 and 20 GeV) is a huge clue.

• The Sweet Spot: It suggests that at these specific energies, the conditions are just right. The magnetic field lasts long enough, and the "soup" is hot enough for the particles to lose their mass and become "chiral" (handed), allowing the separation to happen.
• The Critical Point: This energy range is near where physicists think the "Critical Point" of the universe might be—a special state where matter changes phase dramatically. Finding the CME here is like finding a treasure map to a new state of matter.

The Bottom Line

The scientists didn't just find a signal; they found a signal that only appears when you turn off the noise. By using their new "Event Shape Selection" method, they filtered out the background chaos and revealed a faint but exciting whisper of the Chiral Magnetic Effect in the middle-energy collisions.

It's like finally hearing a ghost in a haunted house, not because the house is quiet, but because they built a special room where the wind (the background noise) can't blow, and the ghost (the CME) is still whispering.

Technical Summary

1. Problem Statement

The Chiral Magnetic Effect (CME) is a theoretical prediction in Quantum Chromodynamics (QCD) where an intense magnetic field ($\vec{B}$) generated in non-central heavy-ion collisions induces an electric current ($\vec{J} \propto \mu_5 \vec{B}$) due to local chirality imbalances in the Quark-Gluon Plasma (QGP). This effect should manifest as an electric charge separation along the magnetic field direction.

However, experimental verification has been hindered by significant background effects that mimic the CME signal. The primary background arises from elliptic flow ($v_2$) coupled with charge-dependent mechanisms such as local charge conservation (LCC), resonance decays, and transverse momentum conservation (TMC). These backgrounds produce a correlation between particle charges and the reaction plane that is indistinguishable from the CME signal in standard measurements. Previous attempts to isolate the signal, such as the isobar collision program ($^{96}\text{Ru}+^{96}\text{Ru}$ vs. $^{96}\text{Zr}+^{96}\text{Zr}$), yielded null results, suggesting that background subtraction methods were insufficient or that the CME signal was smaller than anticipated.

2. Methodology

The STAR Collaboration utilized data from the RHIC Beam Energy Scan (BES-II) phase, covering Au+Au collisions at center-of-mass energies ($\sqrt{s_{NN}}$) ranging from 7.7 GeV to 27 GeV, plus top energy data at 200 GeV.

Key Methodological Innovations:

• Event Shape Selection (ESS): Unlike previous "Event Shape Engineering" (ESE) methods that extrapolate to zero flow using variables defined by particles excluding the particles of interest (POI), this study employs a novel ESS method.
  • Variable Construction: The event shape variable is constructed using Particle Pairs of Interest (PPOI) rather than single particles. This captures both the initial collision geometry and final-state emission properties more accurately.
  • Background Suppression: Events are categorized based on the magnitude of the elliptic flow vector ($q_2$). The analysis projects the charge separation observable ($\Delta\gamma_{112}$) onto the zero-flow limit ($v_2 \to 0$) via linear extrapolation. This effectively removes flow-related backgrounds without relying on large, uncertain extrapolations.
• Reaction Plane Reconstruction: To minimize non-flow correlations, the reaction plane (and thus the magnetic field direction) is reconstructed using spectator nucleons detected by the Zero Degree Calorimeter (ZDC) at high energies and the Event Plane Detector (EPD) at lower energies.
• Background Indicator ($\Delta\gamma_{132}$): The study introduces a secondary correlator, $\Delta\gamma_{132}$, which is theoretically expected to contain negligible CME contribution but is sensitive to the same flow-related backgrounds as $\Delta\gamma_{112}$. If the ESS method works, $\Delta\gamma_{132}^{\text{ESS}}$ should vanish.
• Particle Selection: The analysis focuses on charged mesons ($\pi^\pm, K^\pm$) to avoid complications from baryon transport and varying elliptic flow behaviors between baryons and mesons. (Anti)protons are explicitly rejected.

3. Key Contributions

• Novel Background Subtraction: The paper validates the ESS method as a robust tool for isolating CME signals by demonstrating that the background indicator $\Delta\gamma_{132}$ reduces to zero after suppression, confirming the removal of flow-related backgrounds.
• Extraction of Background Coupling Constants: The authors derive universal background coupling constants ($\kappa_{112}^{\text{bg}} \approx 2.5$ and $\kappa_{132}^{\text{bg}} \approx 1$) that describe the relationship between elliptic flow and two-particle correlations. These constants are found to be independent of centrality and beam energy, providing a unique constraint for theoretical models.
• Systematic Beam Energy Scan: The study provides the most comprehensive scan of CME observables across the critical energy region (10–20 GeV) where the QCD critical point is hypothesized to exist.

4. Results

After applying the ESS method to suppress flow backgrounds, the results for the residual charge separation signal ($\Delta\gamma_{112}^{\text{ESS}}$) are as follows:

• High Energy (200 GeV): The signal is consistent with zero, confirming previous findings that the CME is either absent or heavily suppressed at top RHIC energies, likely due to the rapid decay of the magnetic field before QGP formation.
• Low Energy (7.7, 9.2 GeV): The signal is consistent with zero. This suggests that at these energies, chiral symmetry restoration may not be fully achieved, or partonic degrees of freedom are insufficient to sustain the CME.
• Intermediate Energy (10–20 GeV): A finite, positive charge separation is observed:
  • 11.5 GeV: $2.6\sigma$ significance.
  • 14.6 GeV: $3.1\sigma$ significance.
  • 19.6 GeV: $3.3\sigma$ significance.
  • Combined (10–20 GeV): The significance rises to over $5\sigma$.
  • 17.3 GeV and 27 GeV: Positive values are observed but with lower significance ($1.3\sigma$ and $1.1\sigma$, respectively).
• Background Validation: The background indicator $\Delta\gamma_{132}^{\text{ESS}}$ aligns with zero across all energies and centralities, validating the efficacy of the background subtraction.
• Model Comparison: The extracted background coupling constants ($\kappa_{112}^{\text{bg}} \approx 2.5$) are significantly higher than predictions from the AMPT model ($\approx 1.3$) but align well with the EBE-AVFD model, suggesting that local charge conservation plays a dominant role in the background.

5. Significance

• Evidence for CME in a Specific Window: The results suggest that the CME is most likely to be observed in mid-central Au+Au collisions at $\sqrt{s_{NN}}$ between 10 and 20 GeV. This energy range coincides with the presumed location of the QCD critical point, where topological vacuum transitions are expected to be frequent, and the magnetic field lifetime is long enough to influence the QGP.
• Resolution of the "Isobar Puzzle": The finding that the CME signal is small at 200 GeV (where isobar data was taken) explains why the isobar program failed to detect a significant difference between Ru and Zr collisions; the signal-to-background ratio was too low at that energy.
• Theoretical Constraints: The discovery of a "window" for CME detection provides a crucial benchmark for theoretical models. It implies that the interplay between the magnetic field lifetime, chiral symmetry restoration, and topological charge fluctuations is highly energy-dependent.
• Future Directions: The paper calls for higher-statistics experiments in the 10–20 GeV range (e.g., future BES phases or FAIR/NICA) to confirm the $5\sigma$ signal. It also suggests that applying the ESS technique to LHC data could further clarify the energy dependence of the CME.

In conclusion, this work represents a major step forward in the search for the Chiral Magnetic Effect by successfully isolating a statistically significant signal in a specific energy window using a novel, data-driven background suppression technique, while simultaneously ruling out the effect at higher and lower energies.