The HTL Lagrangian at NLO: the photon case

Abstract

We calculate the two loop hard correction to the photon self-energy in an electron-positron plasma (EPP) for arbitrary soft momenta. This provides the only missing ingredient to obtain the Hard Thermal Loop (HTL) effective Lagrangian at next-to-leading order (NLO), and the full photon propagator at the same order. This result can be easily extended to obtain the soft photon propagator in a quark gluon plasma. We use the Keldysh representation of the real time formalism in the massless fermion limit, and dimensional regularization (DR) to regulate any ultraviolet (UV), infrared (IR) or collinear divergences that appear in the intermediate steps of the calculation. In the limit of soft photon momenta, our result is finite. It not only provides an $\mathcal{O}(\alpha )$ correction to the Debye mass, but also a new non-local structure. A consistent regularization of radial and angular integrals is crucial to get this new structure. As an application we calculate the plasmon dispersion relations at NLO.

14 pages, 2 figures. v2: typos fixed, added comments

References in corpus (3)

• Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory
• Power corrections to the HTL effective Lagrangian of QED
• Real time statistical field theory

Cited by in corpus (17)

• Perturbative Thermal QCD: Formalism and Applications
• Cold quark matter at N3LO: soft contributions
• Equation of State of Cold Quark Matter to $O({\alpha }_s^3\ln {\alpha }_s)$
• Two-loop thermal spectral functions with general kinematics
• Measuring chiral imbalance with collisional energy loss
• Hard Thermal Loop -- theory and applications
• Degenerate fermionic matter at N${}^3$LO: Quantum Electrodynamics
• Soft photon propagation in a hot and dense medium to next-to-leading order
• Soft gluon self-energy at finite temperature and density: hard NLO corrections in general covariant gauge
• Power corrections and gradient expansion in QED transport theory
• Two-loop hard thermal loops for any model
• Hamiltonian formalism for Fermi excitations in a plasma with a non-Abelian interaction
• NLO quark self-energy and dispersion relation using the hard thermal loop resummation
• Mass corrections to the hard thermal/dense loops
• Accounting for plasma constituent mass effects in heavy fermion energy loss calculations in hot QED and QCD
• Power corrections to the photon polarization tensor in a hot and dense medium of massive fermions
• Heavy Quarkonium at finite temperature and chemical potential