Zeno Capatti

A bstract: The Local Unitarity (LU) formalism provides a constructive, integrand-level realisation of the Kinoshita-Lee-Nauenberg (KLN) theorem, by combining loop and phase-space integrals appearing in scattering cross-sections in such a way that their final-state infrared singularities cancel before integration. Supplemented with localised ultraviolet renormalisation, it enables the direct Monte Carlo integration of cross sections at arbitrary perturbative order in four-dimensional spacetime. In this paper, we present its application to the next-to-next-to-leading order (NNLO) QCD total cross sections for heavy-quark pair production in direct photon fusion, involving the contribution from 138 distinct forward-scattering diagrams where external photons couple only to heavy quarks. By combining NNLO QCD with next-to-leading order (NLO) electroweak (EW) corrections and next-to-leading power (NLP) Coulomb resummation, we obtain state-of-the-art predictions for top-, bottom-, and charm-quark production in ultraperipheral hadron collisions and at e ⁺ e ⁻ colliders.

We present a systematic diagrammatic investigation of the classical limit of observables computed from scattering amplitudes in quantum field theory through the Kosower-Maybee-O’Connell formalism, motivated by the study of gravitational waves from black hole binaries. We achieve the manifest cancellation of divergences in the ℏ → 0 limit at the integrand level beyond one loop by employing the Schwinger parametrization to rewrite both cut and uncut propagators in a worldlinelike representation before they are combined. The resulting finite classical integrand takes the same form as the counterpart in the worldline formalisms such as post-Minkowskian effective field theory and worldline quantum field theory, and in fact exactly coincides with the latter in various examples, showing explicitly the equivalence between scattering amplitude and worldline formalisms. The classical causality flow, as expressed by the retarded propagator prescription, appears as an emergent feature. Examples are presented for impulse observables in electrodynamics and a scalar model at two loops, as well as certain subclasses of diagrams to higher orders and all orders.

I work out in full detail the derivation of the Cross-Free Family (CFF) representation for the box diagram, and highlight the differences with its Time Ordered Perturbation Theory (TOPT) representation. I briefly discuss implications for the threshold singularity structure of the diagram.

I work out in full detail the derivation of the Cross-Free Family (CFF) representation for the box diagram, and highlight the differences with its Time Ordered Perturbation Theory (TOPT) representation. I briefly discuss implications for the threshold singularity structure of the diagram.

The understanding of the physical laws determining the infrared behavior of amplitudes is a longstanding and topical problem. In this paper, we show that energy conservation alone implies strong constraints on the threshold singularity structure of Feynman diagrams. In particular, we show that it implies a representation of loop integrals in terms of Fourier transforms of nonsimplicial convex cones. We then engineer a triangulation that has a direct diagrammatic interpretation in terms of a straightforward edge-contraction operation. We use it to develop an algorithmic procedure that performs the Fourier integrations in closed form, yielding the novel cross-free family three-dimensional representation of loop integrals. Its singularity structure is entirely and elegantly expressed in terms of the graph-theoretic notions of connectedness and crossing. These results can be used to study the Kinoshita-Lee-Nauenberg cancellation mechanism, numerically evaluate loop integrals and to simplify threshold regularization procedures.

We introduce a new diagrammatic approach to perturbative quantum field theory, which we call flow-oriented perturbation theory (FOPT). Within it, Feynman graphs are replaced by strongly connected directed graphs (digraphs). FOPT is a coordinate space analogue of time-ordered perturbation theory and loop-tree duality, but it has the advantage of having combinatorial and canonical Feynman rules, combined with a simplified iε dependence of the resulting integrals. Moreover, we introduce a novel digraph-based representation for the S-matrix. The associated integrals involve the Fourier transform of the flow polytope. Due to this polytope’s properties, our S-matrix representation exhibits manifest infrared singularity factorization on a per-diagram level. Our findings reveal an interesting interplay between spurious singularities and Fourier transforms of polytopes.

The understanding of the physical laws determining the infrared behaviour of amplitudes is a longstanding and topical problem. In this paper, we show that energy conservation alone implies strong constraints on the threshold singularity structure of Feynman diagrams. In particular, we show that it implies a representation of loop integrals in terms of Fourier transforms of non-simplicial convex cones. We then engineer a triangulation that has a direct diagrammatic interpretation in terms of a straightforward edge-contraction operation. We use it to develop an algorithmic procedure that performs the Fourier integrations in closed form, yielding the novel Cross-Free Family three-dimensional representation of loop integrals. Contrary to the TOPT and LTD representations, its singularity structure is entirely and elegantly expressed in terms of the graph-theoretic notions of connectedness and crossing. These results can be used to classify infrared-finite scattering theories, numerically evaluate loop integrals and to simplify threshold regularisation procedures.