Event-by-event fluctuations of magnetic and electric fields in heavy ion collisions

Abstract: We show that fluctuating proton positions in the colliding nuclei generate, on the event-by-event basis, very strong magnetic and electric fields in the direction both parallel and perpendicular to the reaction plane. The magnitude of E and B fields in each event is of the order of m_pi^2 \approx 10^18 Gauss. Implications on the observation of electric dipole in heavy ion collisions is discussed, and the possibility of measuring the electric conductivity of the hot medium is pointed out.

• The paper demonstrates that proton position fluctuations produce comparable magnetic and electric fields in heavy ion collision events.
• The study reveals non-negligible Bx components, challenging past assumptions that averaged fields are uniformly directed.
• Provided histograms and numerical results enable refined assessments of the chiral magnetic effect and electric conductivity in the collision medium.

Event-by-event Fluctuations of Magnetic and Electric Fields in Heavy Ion Collisions

The paper by Adam Bzdak and Vladimir Skokov presents an examination of the electric and magnetic fields generated on an event-by-event basis in high-energy heavy ion collisions. The focus here is on the fluctuations in the positions of protons within the nuclei involved in these collisions. This research provides insights into the fundamental electromagnetic properties that arise during such events, with particular emphasis on their implications for the chiral magnetic effect (CME) and possible measurements of the electric conductivity of the created medium.

Summary of Key Findings

The authors demonstrate that proton position fluctuations lead to substantial magnetic and electric fields, both parallel and perpendicular to the reaction plane. These fields reach magnitudes on the order of $m_{\pi}^{2} \approx 10^{18}$ Gauss in individual events. Notably, the analysis shows that on an event-by-event basis, the $(x)$ component of the magnetic field $B_x$ and the corresponding electric field components $E_x$ and $E_y$, although averaged over many events, exhibit significant deviations indicating that these components are not negligible when considering single collision events.

Several strong numerical results are highlighted in this work:

1. Field Comparison: The field magnitudes in each event become comparable across different components, $B_x \approx B_y$ and $E_x \approx E_y$. This contrasts with prior studies that predominantly considered average fields over many events.
2. Field Fluctuations: The study finds that these fluctuations lead to $B_x$, which is traditionally neglected in averaged over events, being non-zero and comparable in magnitude to $B_y$. This implies that the effects of the magnetic field may manifest not only perpendicularly to the reaction plane but also in-plane.
3. Histograms of Field Distributions: The researchers provide histograms for $B_x$, $B_y$, $E_x$, and $E_y$ that show the variability of these components across events, further confirming the comparable magnitudes due to proton fluctuations.

Implications of the Findings

Practical Implications: The accurate characterization of electromagnetic field fluctuations is crucial for probing the chiral magnetic effect in heavy ion collisions. The presence of a strong electric field can potentially overshadow the CME signals if not properly accounted for. Importantly, this study suggests that the electric current induced by these fields must be incorporated into any analysis considering the chiral magnetic properties of the collision outcome. By analyzing charge separation patterns, one could infer information about the medium's electric conductivity, thus providing insights into its thermal and structural properties.

Theoretical Implications: On a theoretical level, the study necessitates a reevaluation of the assumptions used in prior work regarding the uniformity and dominance of magnetic fields in the event plane. The authors highlight the need for models assessing the CME to incorporate consideration of fluctuating fields, particularly when dealing with observables that respond to both magnetic and electric components concomitantly.

Speculations on Future Developments: The insights provided here pave the road for more sophisticated models that could better predict and explain outcomes in relativistic heavy ion collisions. Future theoretical and experimental research is likely to explore the spatial and temporal evolution of these fields with more precision, perhaps with an eye towards identifying novel electromagnetic phenomena in extreme conditions akin to those present in the early universe.

In conclusion, the paper by Bzdak and Skokov advances the understanding of electromagnetic fields in heavy ion collisions by highlighting the significance of event-by-event fluctuations. Their findings emphasize the necessity of incorporating such considerations into theoretical models and experimental analyses, ensuring a comprehensive approach to studying the fundamental interactions at play in these high-energy environments.