Signatures of local acceleration of quark-gluon plasma in the dilepton production

Dilepton production is one of the key probes of the Quark-Gluon Plasma (QGP) that encodes the imaginary part of the electromagnetic current-current correlator. We investigate the effect of local acceleration on the dilepton production by treating acceleration as a small perturbation. Using the thermal Dirac propagator in an accelerated frame within the imaginary-time formalism, we compute the photon polarization tensor and extract its imaginary part. Comparison with the zero-acceleration case isolates the distinct contributions of acceleration to dilepton yields.

💡 Research Summary

The paper investigates how a locally accelerating quark‑gluon plasma (QGP) modifies the dilepton production rate, a key observable that directly probes the imaginary part of the electromagnetic current‑current correlator. The authors treat the acceleration as a small perturbation, introducing a dimensionless parameter α = a/T (acceleration a over temperature T) and assuming α ≪ 1. Within the imaginary‑time (Euclidean) formalism they construct the thermal Dirac propagator in a frame uniformly accelerated along the z‑axis. By expanding the coordinate transformation to first order in α, the propagator separates into the standard finite‑temperature piece S⁽⁰⁾ and a linear correction S⁽¹⁾ that carries explicit dependence on the average coordinate X, thereby breaking translational invariance.

Using these propagators the one‑loop photon polarization tensor Cμ μ(q) is built. The zeroth‑order term reproduces the familiar Born dilepton rate, while the first‑order term yields a rather involved expression containing logarithms of Fermi‑Dirac and Bose‑Einstein factors, the kinematic variables ω± (functions of the external four‑momentum and quark mass), and explicit factors of α. Because the acceleration is taken to point only in the z‑direction, the authors simplify the external three‑momentum by setting |q| = q_z, which eliminates transverse components from the final formulas.

The dilepton production rate (DR) is proportional to the imaginary part of Cμ μ. The authors define the ratio DR(α)/DR(0) = 1 + α