Speaker
Description
In this talk, I will show a general expression for weighted cross sections in leptonic annihilation to hadrons based on time-ordered perturbation theory (TOPT). For any infrared-safe weight, the cancellation of infrared divergences is implemented locally at the integrand level, and in principle can be evaluated numerically in four dimensions. We go on to show that it is possible to eliminate unphysical singularities that appear in time-ordered perturbation theory for arbitrary amplitudes. This is done by reorganizing TOPT into an equivalent form that combines classes of time orderings into a “partially time-ordered perturbation theory”. This formalism is based on the poset structure inherently present in TOPT. I will apply this formalism to leptonic annihilation to show a formula for a generic weighted cross-section, only carrying singularities that correspond to unitarity cuts.
In the process of eliminating unphysical singularities, cuts that disconnect the graph into more than two pieces, we will find that long-time processes are encapsulated by real, non-local composite vertices. In the example of leptonic annihilation cross-sections, we will make this manifest through a local factorization between long-time and short-time processes. I will make some comments about potential connections between this formalism and the organization of power corrections in perturbation theory. I will also demonstrate how to carry out contour deformations in a generic Feynman parametrized amplitude, systematically, to all orders. We will see that our contour deformations automatically vanish on each pinch surface, admitting a physical singularity upon integrating around a pinch. We will find that, here, the difference of IR-safe weight functions vanishes in such a way that the integrand is locally finite.
