Worldline techniques for string theory solitons: recoil, annihilation and pair production

We analyze a model of interacting particles and strings described by a path integral with the Dirichlet boundary conditions. Such model is a natural framework to examine the processes involving the center-of-mass motion of string theory D0-branes: recoil, annihilation and pair production. We demonstrate that, within the proposed formalism, the exclusive annihilation/pair-production amplitudes admit a saddle point evaluation. Even though the saddle point equation cannot be solved analytically, it allows to extract valuable information on the coupling constant dependence of the amplitudes. In particular, D0-brane pair production turns out to be suppressed as exp[-O(1/g_{st}^2)], much stronger than the naive expectation exp[-O(1/g_{st})]. All our derivations generalize rather immediately to the case of unstable D0-brane decay. In conclusion, we briefly comment on the possible implications our results may have for the conventional soliton-anti-soliton annihilation.