Factorization and Precision Calculations in Particle Physics

Abstract

We state and prove to all orders in perturbation theory a factorization theorem in Quantum Chromodynamics that concisely describes the separation of the physics associated with jet formation from that associated with the hard-scattering in high-energy particle collisions. We show how the factorization theorem, which provides an equality between amplitudes in gauge theories, can be readily applied to precision calculations of cross-sections. In the resulting factorized cross sections, the components relevant to jet production are universal and perturbatively calculable. Their renormalization group evolution can be used to sum large logarithms of scale ratios to all orders in perturbation theory, thus enabling quantitive predictions in the regime of disparate scales relevant to many important collider-physics observables. As an application, we calculate the observable 2-subjettiness at next-to-next-to-next-to-leading-logarithmic order for the decay of boosted heavy color-singlet particles such as Electroweak bosons. Our calculation is the first analytic calculation of a jet substructure observable.