[Paper Review] Gluon polarization tensor in a thermo-magnetic medium

Alejandro Ayala, C. A. Domínguez+5 more|arXiv (Cornell University)|May 18, 2018

High-Energy Particle Collisions Research3 citations

TL;DR

This paper computes the gluon polarization tensor in a thermo-magnetic medium using Schwinger's proper time method for magnetic fields and the Hard Thermal Loop approximation for thermal effects. It reveals that at zero temperature with finite quark mass, the tensor coefficients acquire an imaginary part signaling quark-antiquark pair production thresholds, while at high temperature, massless approximations hold, and the separation of vacuum and matter contributions enables analysis of strong coupling evolution across four distinct regimes.

ABSTRACT

We compute the gluon polarization tensor in a thermo-magnetic environment in the weak and strong magnetic field cases, both at zero and at high temperature. The magnetic field effects are introduced using Schwinger's proper time method. Thermal effects are computed in the Hard Thermal Loop approximation. We find that for the zero temperature case and a non-vanishing quark mass, the coefficients of the tensor structures describing the polarization tensor develop an imaginary part corresponding to the threshold for quark-antiquark pair production. These coefficients are infrared finite and simplify considerably when the quark mass vanishes. In the high temperature case, the quark mass can be safely ignored. Nevertheless, we explicitly maintain this mass finite to separate the unrenormalized vacuum and matter contributions. We discuss how knowledge of this coefficients is useful in particular to study the thermo-magnetic evolution of the strong coupling in the four regimes hereby treated.

Motivation & Objective

• To investigate the behavior of the gluon polarization tensor in a medium subjected to both thermal and magnetic fields.
• To analyze the interplay between finite quark mass, magnetic field strength, and temperature on the tensor's structure and analytic properties.
• To disentangle unrenormalized vacuum and matter contributions by keeping the quark mass finite even at high temperature.
• To enable a systematic study of the thermo-magnetic evolution of the strong coupling constant across four distinct physical regimes.

Proposed method

• Employing Schwinger's proper time method to incorporate magnetic field effects into the gluon polarization tensor.
• Applying the Hard Thermal Loop (HTL) approximation to systematically include finite-temperature corrections.
• Maintaining a finite quark mass throughout calculations to cleanly separate vacuum and thermal contributions.
• Analyzing the tensor structure in terms of coefficient functions that encode the medium's response to gluonic modes.
• Using the resulting coefficients to study the running of the strong coupling constant under varying thermo-magnetic conditions.

Experimental results

Research questions

• RQ1 How does the gluon polarization tensor respond to the presence of a magnetic field at zero temperature with a finite quark mass?
• RQ2 What role does the quark mass play in generating imaginary parts in the tensor coefficients at zero temperature?
• RQ3 How do thermal corrections modify the tensor structure at high temperature, especially when the quark mass is negligible?
• RQ4 In what way do vacuum and matter contributions to the polarization tensor differ when the quark mass is kept finite?
• RQ5 How does the strong coupling constant evolve across the four distinct thermo-magnetic regimes defined by temperature and magnetic field strength?

Key findings

• At zero temperature and with a finite quark mass, the coefficients of the gluon polarization tensor acquire an imaginary part corresponding to the threshold for quark-antiquark pair production.
• The tensor coefficients remain infrared finite even in the presence of a magnetic field and finite quark mass.
• When the quark mass vanishes, the tensor coefficients simplify significantly, indicating a reduced dynamical complexity.
• At high temperature, the quark mass can be safely neglected, allowing for a simplified treatment of the thermal medium.
• The separation of unrenormalized vacuum and matter contributions is preserved by maintaining a finite quark mass, enabling clearer analysis of strong coupling evolution.
• Knowledge of the tensor coefficients allows for a detailed study of the thermo-magnetic evolution of the strong coupling constant across the four defined regimes.