Classical ultrarelativistic bremsstrahlung in extra dimensions

TL;DR

This paper calculates the classical scalar bremsstrahlung energy and cross-section in high-energy particle collisions within higher-dimensional Minkowski space and brane-world models, highlighting differences from quantum results.

Contribution

It provides the first leading-order classical calculations of scalar bremsstrahlung in extra-dimensional settings, including bulk and brane emissions, with explicit formulas and validity conditions.

Findings

Energy emitted as scalar radiation in bulk and brane

Results agree with classical electrodynamics in four dimensions

Classical approach yields unambiguous results unlike quantum approximation

Abstract

The emitted energy and the cross-section of classical scalar bremsstrahlung in massive particle collisions in D=4+d dimensional Minkowski space M_D as well as in the brane world M_4 \times T^d is computed to leading ultra-relativistic order. The particles are taken to interact in the first case via the exchange of a bulk massless scalar field \Phi and in the second with an additional massless scalar \phi confined together with the particles on the brane. Energy is emitted as \Phi radiation in the bulk and/or \phi radiation on the brane. In contrast to the quantum Born approximation, the classical result is unambiguous and valid in a kinematical region which is also specified. For D=4 the results are in agreement with corresponding expressions in classical electrodynamics.