Classical ultrarelativistic bremsstrahlung in extra dimensions

The emitted energy and the cross-section of classical scalar bremsstrahlung in massive particle collisions in D = 4 + d−dimensional Minkowski space \( {\mathcal{M}_D} \) as well as in the brane world \( {\mathcal{M}_4} \times {\mathcal{T}^d} \) 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 Φ and in the second with an additional massless scalar φ confined together with the particles on the brane. Energy is emitted as Φ radiation in the bulk and/or φ 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.