Measure charge transport in high-energy nuclear collisions with an energy scan of isobaric collisions

This paper proposes a beam-energy scan of isobaric collisions (Ru+Ru vs. Zr+Zr) to precisely measure electric-charge transport and distinguish between competing microscopic mechanisms of conserved-charge redistribution in QCD matter by comparing the rapidity dependence of charge and baryon transport.

The Gist

Imagine two massive, high-speed trains smashing into each other. These aren't ordinary trains; they are atomic nuclei traveling at nearly the speed of light. When they collide, they create a tiny, super-hot "soup" of energy and particles called the Quark-Gluon Plasma (QGP). Physicists want to understand how this soup behaves, specifically how it moves things like electric charge (the positive and negative "oomph" of particles) and baryon number (a property that keeps track of matter, like protons and neutrons).

Here is the problem: It's incredibly hard to see how the electric charge moves. Why? Because the collision creates a massive amount of "noise." For every positive particle created, a negative one is usually created right next to it. It's like trying to hear a single whisper in a stadium full of people screaming. The signal (the net charge) is tiny compared to the background noise.

The "Twin" Solution: Isobars

To solve this, the authors propose a clever trick using Isobars. Think of these as "twin" atomic nuclei.

• Twin A (Ruthenium): Has 44 protons (positive charges) and 52 neutrons.
• Twin B (Zirconium): Has 40 protons and 56 neutrons.

They are identical in weight (mass) but different in their "charge makeup." Because they weigh the same, they crash in almost exactly the same way, creating the same amount of background noise. But because they have different numbers of protons, the difference in their electric charge is a clear, measurable signal.

The Analogy: Imagine two identical factories producing the same number of red and blue balls. Factory A makes 44 red balls and 52 blue ones. Factory B makes 40 red balls and 56 blue ones. If you mix the output of both factories, it's a mess. But if you compare the difference between Factory A and Factory B, you instantly know exactly how many extra red balls Factory A produced, ignoring all the noise.

The "Speed Scan" Experiment

The paper suggests running this experiment at different speeds (beam energies).

• Fast Speed: The nuclei smash together and fly apart quickly. The charge doesn't have time to travel far from the starting point.
• Slow Speed: The nuclei crash and stick together longer, allowing the charge to travel further toward the center of the collision.

By scanning different speeds, the scientists can map out exactly how far the electric charge travels before stopping. This is like testing how far a drop of ink spreads in water by changing how fast you stir it.

The Mystery of the "Baryon Junction"

The biggest question in this field is: What carries the "matter" (baryon number) through the soup?
There are two main theories:

1. The "Valence Quark" Theory: The matter is carried by the original "core" particles (quarks) of the nucleus, just like electric charge.
2. The "Baryon Junction" Theory: The matter is carried by a special, Y-shaped knot of energy (gluons) that forms during the crash. This knot is heavy and slow, so it should stop quickly, while the lighter electric charge zooms past it.

What the Computer Simulations Found

The authors ran massive computer simulations (using "UrQMD" and "Pythia8") to see which theory holds up. Here is what they discovered:

• The Charge Stops Fast: In all the models, the electric charge tends to stop moving relatively quickly as it travels away from the crash site.
• The Matter (Baryon) Goes Further: Surprisingly, the simulations showed that the "matter" (baryon number) traveled further than the electric charge.
• The Conflict: This contradicts the "Baryon Junction" theory. If the junction theory were true, the heavy "knots" should stop sooner than the light electric charge. Instead, the simulations show the opposite: the matter travels further.

Why This Matters

This paper proposes a new, highly precise way to measure these invisible forces. By comparing these "twin" nuclei at different speeds, scientists can finally get a clear picture of:

1. How electric charge moves in the early universe's "soup."
2. Whether the "Baryon Junction" theory is real or if matter is carried by something else entirely.

In a nutshell: The authors have designed a "microscope" using twin atomic nuclei to filter out the noise of high-energy crashes. They hope this will reveal the secret mechanics of how matter and charge move in the most extreme conditions in the universe, potentially rewriting our understanding of how the building blocks of the universe stick together.

Technical Summary

1. Problem Statement

The primary goal of ultra-relativistic heavy-ion collision experiments is to map the Quantum Chromodynamics (QCD) phase diagram and understand the properties of the Quark-Gluon Plasma (QGP). A critical aspect of this is understanding how conserved quantities—specifically baryon number ($B$) and electric charge ($Q$)—are transported from the beam rapidity to midrapidity.

• The Challenge: While baryon number transport has been extensively measured, direct measurement of electric-charge transport is nearly absent. This is because the produced medium is nearly charge-symmetric around midrapidity ($N_{\pi^+} \approx N_{\pi^-}$), making the net charge signal ($Q = N_+ - N_-$) extremely small compared to the large background of particle-antiparticle pair production.
• The Scientific Question: The microscopic carrier of baryon number remains debated. Is it transported solely by valence quarks, or does it involve baryon junctions (Y-shaped gluonic structures)? Current models yield conflicting predictions regarding the relative efficiency of baryon vs. charge transport.

2. Methodology

The authors propose a novel method combining isobaric collisions with a Beam Energy Scan (BES) to isolate and measure electric-charge transport.

• Isobaric Systems: The study compares collisions of two isobar nuclei: $^{96}_{44}\text{Ru} + ^{96}_{44}\text{Ru}$ and $^{96}_{40}\text{Zr} + ^{96}_{40}\text{Zr}$. These nuclei have identical mass numbers ($A=96$) but different atomic numbers ($Z=44$ vs. $Z=40$).
• Double-Ratio Technique: To extract the charge difference ($\Delta Q = Q_{\text{Ru}} - Q_{\text{Zr}}$) with high precision, the authors use a double-ratio method. This technique exploits the near-equality of particle multiplicities in the two systems to cancel out experimental systematic uncertainties (such as detector acceptance and efficiency).
  • The charge difference is approximated as: $\Delta Q \approx N_{\pi}(R^2_{\pi} - 1) + N_{K}(R^2_{K} - 1) + N_{p}(R^2_{p} - 1)$, where $R^2$ represents the double ratio of particle yields.
• Beam Energy Scan (BES): By varying the collision energy ($\sqrt{s_{NN}}$), the beam rapidity ($y_{\text{beam}}$) changes while the measurement point (midrapidity, $y_Q \approx 0$) remains fixed. This allows the system to systematically scan the rapidity gap ($\Delta y = y_{\text{beam}} - y_Q$) over which charge is transported.
• Simulation Models: The study utilizes two event generators to simulate Ru+Ru and Zr+Zr collisions at $\sqrt{s_{NN}} = 19.6, 27, 39, 62.4,$ and $200$ GeV:
  1. UrQMD: A microscopic transport model where baryon number and charge are carried solely by valence quarks.
  2. Pythia8 (Angantyr): A generator simulating heavy-ion collisions as a superposition of nucleon-nucleon sub-collisions. Two configurations are tested:
     • Without B-Junctions: Baryons form via diquark pairs; transport is limited.
     • With B-Junctions: Includes dynamical formation of gluonic junctions, enhancing baryon transport.

3. Key Contributions

• Proposal of a Precision Measurement: Demonstrates that an isobaric BES can precisely measure electric-charge transport, a quantity previously inaccessible due to background noise.
• Model Discrimination: Establishes a clear signature to distinguish between valence-quark transport and baryon-junction mechanisms by comparing the rapidity slopes of charge vs. baryon transport.
• Systematic Scanning: Shows how varying beam energy allows for the mapping of charge transport efficiency as a function of rapidity loss ($\Delta y$).

4. Key Results

• Exponential Decay of $\Delta Q$: The midrapidity charge difference ($\Delta Q$) decreases exponentially with increasing rapidity gap ($\Delta y$). This indicates that charge transport becomes less efficient over larger rapidity intervals.
  • The decay is characterized by a slope parameter $\alpha_Q$.
• Centrality Dependence:
  • In UrQMD, $\alpha_Q$ increases slightly from central to peripheral collisions. This suggests stronger valence-quark stopping (more scatterings) in central events.
  • In Pythia8, $\alpha_Q$ values are roughly twice as large as in UrQMD, indicating less efficient transport in the Pythia baseline.
  • The inclusion of baryon junctions in Pythia8 reduces $\alpha_Q$ slightly, implying that junctions enhance long-range charge transport.
• Comparison of Charge vs. Baryon Transport ($R(\text{Isobar})$):
  • The ratio $R(\text{Isobar}) = \frac{\langle B \rangle}{\Delta Q} \times \frac{\Delta Z}{A}$ is used to compare transport efficiencies.
  • UrQMD & Pythia8 (No Junctions): Both show a negative slope for $R(\text{Isobar})$ vs. $\Delta y$. This means baryon number is transported more efficiently than electric charge at large rapidity gaps (i.e., the rapidity slope for baryons is steeper).
  • Pythia8 (With Junctions): While still showing a negative slope, the values are higher, and $R(\text{Isobar})$ remains $>1$ across the energy range.
• Theoretical Tension: The results from all models (negative slope) contradict the theoretical expectation of baryon junctions, which predicts that junctions (composed of low-momentum gluons) should be stopped more easily than valence quarks, leading to an increasing $R(\text{Isobar})$ with $\Delta y$. This also conflicts with existing STAR measurements at 200 GeV where $R(\text{Isobar}) > 1$.

5. Significance

• New Probe for QCD Matter: This work provides a realistic, experimentally feasible pathway to measure electric-charge transport, offering new constraints on the microscopic mechanisms governing conserved-charge redistribution.
• Insight into Baryon Carriers: The discrepancy between the model predictions (negative slope) and the theoretical expectation for baryon junctions (positive slope) highlights a gap in current understanding. Future measurements of this specific observable in an isobaric BES are crucial for determining whether baryon number is carried by valence quarks or gluonic junctions.
• Future Applications: The methodology is applicable to future facilities, including the Electron-Ion Collider (EIC) and the LHC fixed-target program, to further refine QCD phase diagram mapping and transport models.

In summary, the paper proposes a robust experimental strategy using isobaric collisions to solve the "charge transport" problem in heavy-ion physics, revealing distinct transport patterns for charge and baryon number that challenge current theoretical models regarding baryon junctions.