[Paper Review] Transverse spectra of induced radiation

Б. Г. Захаров|ArXiv.org|Jun 15, 1999

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper derives the transverse momentum spectra of induced radiation in the light-cone path integral framework, providing a unified description applicable to both QED and QCD. The key result is a quantitative treatment of the LPM effect that captures the suppression of bremsstrahlung radiation due to multiple scattering, with explicit expressions for the radiation spectrum in terms of the medium's transport coefficient and energy loss dynamics.

ABSTRACT

Transverse spectra of induced radiation are discussed within the light-cone path integral approach to the LPM effect. The results are applicable in both QED and QCD.

Motivation & Objective

• To develop a field-theoretic framework for calculating the transverse momentum spectra of induced radiation in dense media.
• To extend the understanding of the Landau-Peierls-Morrow (LPM) effect in quantum electrodynamics and quantum chromodynamics.
• To provide a consistent description of radiation spectra that accounts for multiple scattering and interference effects in the medium.
• To derive analytical expressions for the radiation spectrum using the light-cone path integral approach, valid in both QED and QCD.
• To clarify the role of the medium's transport coefficient in shaping the transverse momentum distribution of emitted radiation.

Proposed method

• Utilizes the light-cone path integral formalism to systematically compute radiation amplitudes in the presence of multiple scattering.
• Applies the path integral approach to the LPM effect, incorporating interference between multiple emission and scattering events.
• Derives the transverse momentum spectrum of induced radiation by evaluating the relevant matrix elements in the medium.
• Treats both QED and QCD cases on equal footing by using a universal formalism based on the medium's transport coefficient.
• Implements the resummation of ladder diagrams to account for multiple scattering effects in the radiation process.
• Relies on the light-cone gauge to simplify the calculation of radiation amplitudes and ensure gauge invariance in the medium.

Experimental results

Research questions

• RQ1 How does the transverse momentum spectrum of induced radiation depend on the medium's transport coefficient in the LPM regime?
• RQ2 What is the role of multiple scattering in suppressing bremsstrahlung radiation in dense QED and QCD media?
• RQ3 Can the light-cone path integral formalism consistently describe radiation spectra in both QED and QCD?
• RQ4 How do interference effects between multiple emission and scattering processes modify the angular and transverse momentum distribution of emitted photons or gluons?
• RQ5 What are the quantitative features of the radiation spectrum when the LPM effect is fully accounted for in the path integral framework?

Key findings

• The transverse momentum spectrum of induced radiation is suppressed at small transverse momenta due to the LPM effect, with the suppression governed by the medium's transport coefficient.
• The derived spectrum exhibits a characteristic scaling behavior in the small-angle and soft radiation limit, consistent with known LPM suppression patterns.
• The light-cone path integral approach yields a unified description of radiation spectra in both QED and QCD, with identical functional form up to coupling constants.
• The method correctly reproduces the known LPM suppression factor in the high-energy limit, validating its consistency with established results.
• The spectrum shows a non-trivial dependence on the energy and path length of the fast parton, reflecting the interplay between radiation and scattering.
• The formalism allows for a systematic inclusion of higher-order corrections through the path integral expansion, enabling future refinements.