Spurious Singularities in Dipole Subtraction Cross Sections and their Damping with Convergence Factors
In the dipole subtraction algorithm, the real-virtual cancellation in NLO calculations of arbitrary observables is implemented by defining a subtraction cross section that matches all of the singularities of the real emission cross section. The converse, however, is not true: the subtraction cross section contains additional singularities, coming from the underlying Born matrix element, that the real cross section does not. We call these spurious singularities. If used as originally proposed, this is not a problem, because the value of the observable damps these singularities, but in applications such as dipole showers and matching algorithms, it can lead to poor statistical convergence, or dependence on unphysical regulators such as technical or generation cuts. In this paper, we show that additional factors, which we call convergence factors, can be applied to the subtraction cross section to damp these spurious singularities and improve the convergence. We perform the required phase-space integrals to yield modified dipole insertion operators, and verify numerically that they indeed remove the logarithmic dependence on generation cuts that arises in their absence. This paper is dedicated to the memory of Stefano Catani, with whom the work was originally started.