Scattering amplitudes with open loops.

We introduce a new technique to generate scattering amplitudes at one loop. Traditional tree algorithms, which handle diagrams with fixed momenta, are promoted to generators of loop-momentum polynomials that we call open loops. Combining open loops with tensor-integral and Ossola-Papadopoulos-Pittau reduction results in a fully flexible, very fast, and numerically stable one-loop generator. As demonstrated with nontrivial applications, the open-loop approach will permit us to obtain precise predictions for a very wide range of collider processes.