Studying Bremsstrahlung in Polarized Background Field at EIC and EicC

TL;DR

We address bremsstrahlung of an electron in a linearly polarized background field by expressing the background through photon TMDs $f_1^\gamma$ and $h_1^{\bot\gamma}$ and applying Sudakov resummation for soft radiation. Coulomb corrections are incorporated with a gauge-link formalism, yielding a background-modified photon propagator with distinct unpolarized and linearly polarized contributions. In Bethe–Heitler kinematics at the EIC and EicC, the emitted photon beam inherits the background's linear polarization, producing a $\cos 2\phi$ azimuthal modulation of a few percent, with Sudakov suppression at low $q_\perp$ and mild Coulomb enhancement at higher $q_\perp$. The framework provides a principled way to access polarization information of nuclear photon backgrounds and can be extended to other QED processes in polarized media.

Abstract

We present a quantum-field-theoretical study of bremsstrahlung from an electron propagating in a linearly polarized background photon field. Starting from the photon two-point correlator, the background-modified photon propagator is parameterized via transverse-momentum-dependent photon distributions. Coulomb correction is incorporated through a gauge-link formalism and soft-photon radiation is resummed with a Sudakov factor, yielding an analytic form of the polarized Bethe-Heitler spectrum. Numerical illustrations show a characteristic $\cos 2φ$ azimuthal modulation of a few percent in the differential distribution, with Sudakov suppression at low transverse momentum and mild Coulomb-induced enhancement at larger $q_\perp$.

Figures (2)

• Figure 1: The azimuthal asymmetry as a function of $q_{\perp}$ (left panel) and $y_\gamma$ (right panel) with and without taking into account the Coulomb corrections (cc) or Sudakov for a Pb target at EicC. The asymmetry is averaged over the $P_{\perp}$ region $[0.3~\mathrm{GeV}, 0.4 ~\mathrm{GeV}]$. In the left plot, the emitted photon rapidity $y_\gamma$ is integrated over the region $[0.5,1]$. In the right plot, the total transverse momentum $q_{\perp}$ is fixed to be 50 MeV .
• Figure 2: The azimuthal asymmetry as a function of $q_{\perp}$ (left panel) and $y_\gamma$ (right panel) with and without taking into account the Coulomb corrections (cc) or Sudakov for a Pb target at EIC. The asymmetry is averaged over the $P_{\perp}$ region $[1.5 ~\mathrm{GeV}, 2 ~\mathrm{GeV}]$. In the left plot, the emitted photon rapidity $y_\gamma$ is integrated over the region $[2,2.8]$. In the right plot, the total transverse momentum $q_{\perp}$ is fixed to be 50 MeV .