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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 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 Φand in the second with an additional massless scalar ϕconfined together with the particles on the brane. Energy is emitted as Φradiation in the bulk and/or ϕradiation 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.