Light-cone path integral approach to the Landau-Pomeranchuk-Migdal effect

TL;DR

This paper introduces a rigorous light-cone path integral method to analyze the Landau-Pomeranchuk-Migdal effect in QED and QCD, providing new theoretical formulas and predictions that align with experimental data and reveal energy-dependent radiation behaviors.

Contribution

It presents a novel light-cone path integral approach for the LPM effect, deriving new formulas for nuclear shadowing and predicting energy loss dependence on medium length and quark energy.

Findings

Predicted photon spectrum matches SLAC measurements.

Radiative energy loss scales as L^{2} at high energies.

Energy loss dependence weakens to L^{1} at lower energies.

Abstract

A new rigorous light-cone path integral approach to the Landau-Pomeranchuk-Migdal effect in QED and QCD is discussed. The rate of photon (gluon) radiation by an electron (quark) in a medium is expressed through the Green's function of a two-dimensional Schrodinger equation with an imaginary potential. In QED this potential is proportional to the dipole cross section for scattering of e+e- pair off an atom, in QCD it is proportional to the cross section of interaction of the color singlet quark-antiquark-gluon system with a medium constituent. In QED our predictions agree well with the photon spectrum measured recently at SLAC for 25 GeV electrons. In QCD for a sufficiently energetic quark produced inside a medium we predict the radiative energy loss proportional L^{2}, where L is the distance passed by the quark in the medium. It has a weak dependence on the initial quark energy. The L^{2} dependence transforms into L^{1} as the quark energy decreases. We also give new formulas for nuclear shadowing in hard reactions.