[Paper Review] Fast vacuum decay into particle pairs in strong electric and magnetic fields

Yoshimasa Hidaka, Takumi Iritani+1 more|arXiv (Cornell University)|Feb 1, 2011

Cold Atom Physics and Bose-Einstein Condensates3 citations

TL;DR

This paper demonstrates that in strong electric and magnetic fields, the vacuum decay rate into fermion pairs diverges for massless fermions due to dominance of the lowest Landau level (LLL), leading to immediate pair production. Using LLL-projected effective field theory, the authors derive a solvable 1+1 dimensional Schwinger model, showing finite pair production rates and dynamical photon mass generation via the axial anomaly, with no thermalization in the LLL-dominated regime.

ABSTRACT

We discuss fermion pair productions in strong electric and magnetic fields. We point out that, in the case of massless fermions, the vacuum persistency probability per unit time and volume is zero in the strong electric and magnetic fields, while it is finite when the magnetic field is absent. The contribution from the lowest Landau level (LLL) dominates this phenomenon. We also discuss dynamics of the vacuum decay, using an effective theory of the LLL projection, taking into account the back reaction.

Motivation & Objective

• To investigate vacuum decay into fermion pairs in coexisting strong electric and magnetic fields.
• To resolve the divergence of the vacuum decay rate in the presence of both fields, particularly for massless fermions.
• To develop an effective field theory based on LLL projection to describe dynamics and back-reaction in strong-field vacuum decay.
• To clarify the role of the lowest Landau level in driving the instability and infinite pair production rate.
• To explore implications for quark-gluon plasma formation in heavy-ion collisions, especially in the Glasma stage.

Proposed method

• The authors use covariantly constant electric and magnetic fields to model strong-field conditions in QED and QCD.
• They apply LLL projection to reduce the 3+1 dimensional dynamics to a 1+1 dimensional effective theory, focusing on the dominant contribution from the lowest Landau level.
• The effective action is derived as a quadratic form in the gauge field, leading to a dynamical photon mass via the axial anomaly.
• The Schwinger mechanism is generalized to non-Abelian fields, with the fermion determinant mapping to a Wess-Zumino-Witten action in strong magnetic fields.
• The equations of motion for the gauge field are solved analytically, yielding oscillating electric fields and time-dependent pair production rates.
• The back-reaction is incorporated via the effective action, and the axial current is computed to confirm anomaly matching.

Experimental results

Research questions

• RQ1 Why does the vacuum decay rate diverge in the presence of both strong electric and magnetic fields when fermions are massless?
• RQ2 What is the dominant contribution to vacuum decay in strong magnetic fields, and how does the lowest Landau level influence this?
• RQ3 How can an effective 1+1 dimensional theory describe the full 3+1 dimensional vacuum decay process in strong fields?
• RQ4 What are the implications of the dynamical photon mass and axial anomaly in the LLL-dominated regime?
• RQ5 Does the LLL-dominated vacuum decay process lead to thermalization or chaotic dynamics?

Key findings

• The vacuum persistency probability per unit time and volume vanishes for massless fermions in coexisting strong E and B fields, indicating immediate and complete decay.
• The divergence of the pair production rate w in the massless limit arises from the infinite contribution of the lowest Landau level (LLL) in the presence of a magnetic field.
• The effective theory derived via LLL projection reduces the system to a solvable 1+1 dimensional Schwinger model with a dynamical photon mass mγ² = e³B/(2π²).
• The axial anomaly is preserved in the effective theory, with ∂μj₅μ = (e²B/2π²)E, confirming anomaly matching in the reduced dimensionality.
• The number density of produced pairs is proportional to the axial current, and for spatially homogeneous fields, it grows linearly with time, consistent with numerical results.
• Thermalization does not occur in the LLL-dominated process, as the effective theory is exactly solvable and lacks chaotic behavior.