Leonardo Vernazza

A bstract: Scattering amplitudes are expected to admit a factorised structure in special kinematic limits, such as the Regge, soft and collinear limits. However, less is known about the precise mechanisms through which factorisation of n -particle scattering amplitudes is realised at high perturbative orders, where more complex structures arise. Starting with the soft anomalous dimension, in this work we investigate the multi-particle collinear limits of massless amplitudes at three- and four-loop orders. Using colour conservation and rescaling symmetry, we show how strict collinear factorisation of multiple massless final-state coloured particles is realised, and provide results for the corresponding splitting amplitude soft anomalous dimensions. In particular, we demonstrate through four loops that the conditions on the structure of the massless soft anomalous dimension that are required by strict collinear factorisation in all two-particle collinear limits, are sufficient to guarantee such factorisation also in any multiple collinear limit. Then, assuming that strict collinear factorisation of massless partons holds also for amplitudes containing massive coloured particles, we derive new constraints on the soft anomalous dimension from multi-collinear limits.

A bstract: We investigate the factorization properties of the massive fermion form factor in QED, to next-to-leading power in the fermion mass, and up to two-loop order. For this purpose we define new jet functions that have multiple connections to the hard part as operator matrix elements, and compute them to second order in the coupling. We test our factorization formula using these new jet functions in a region-based analysis and find that factorization indeed holds. We address a number of subtle aspects such as rapidity regulators and external line corrections, and we find an interesting sequence of relations among the jet functions.

High-energy factorization of 2 -> 2 amplitudes in QCD has been recently pushed to the next-to-next-to-leading logarithmic order by determining the three-loop gluon Regge trajectory. This was based on computing multi-Reggeon exchanges using rapidity evolution in the shock-wave formalism, and disentangling between the Regge pole and Regge cut contributions. In the present paper we extend the relevant theoretical framework to 2 -> 3 processes, and compute all multi-Reggeon exchanges necessary for extracting the two-loop Reggeon-gluon-Reggeon Lipatov vertex from 2 -> 3 amplitudes. Then, specializing general amplitude methods to multi-Regge kinematics, we derive analytic expressions for non-planar two-loop gg -> ggg, gq -> ggq and qq -> qgq QCD amplitudes in that limit. Matching these to the multi-Reggeon computation, we determine the QCD Lipatov vertex in dimensional regularization at two loops through finite terms. We also determine the one-loop vertex through O(epsilon^4). All results are expressed in a compact form in terms of a basis of single-valued generalised polylogarithms, manifesting target-projectile symmetry and reality properties. Furthermore, our basis of functions is explicitly finite in the soft limit, featuring delicate cancellation of spurious rational poles by transcendental functions. Agreement between all three partonic channels, as well agreement of the maximal weight contributions with the super Yang-Mills Lipatov vertex provide robust checks of the result.

Scattering amplitudes in the high-energy limit can be described in terms of their singularity structure in the complex angular momentum plane, consisting of Regge poles and cuts. In QCD, gluon Reggeization has long been understood as a manifestation of a Regge pole, but until recently Reggeization violation remained largely obscure. New methods, based on iterative solution of rapidity evolution equations, facilitate direct computation of components of the amplitude which are mediated by multi-Reggeon exchange, a manifestation of Regge cuts. Upon disentangling the Regge cut from the pole we are now able to extract the pole parameters from state-of-the-art fixed-order computations (3 loops) and make predictions regarding certain components of the amplitude to higher loop orders. In this talk I review the key ideas which led to this progress, describe where we stand in exploring the structure of 2 -> 2 and 2 -> 3 amplitudes in the (multi-) Regge limit, and comment on the interplay between this research and the study of infrared factorization.

Scattering amplitudes in the high-energy limit can be described in terms of their singularity structure in the complex angular momentum plane, consisting of Regge poles and cuts. In QCD, gluon Reggeization has long been understood as a manifestation of a Regge pole, but until recently Reggeization violation remained largely obscure. New methods, based on iterative solution of rapidity evolution equations, facilitate direct computation of components of the amplitude which are mediated by multi-Reggeon exchange, a manifestation of Regge cuts. Upon disentangling the Regge cut from the pole we are now able to extract the pole parameters from state-of-the-art fixed- order computations (3 loops) and make predictions regarding certain components of the amplitude to higher loop orders. In this talk I review the key ideas which led to this progress, describe where we stand in exploring the structure of 2 → 2 and 2 → 3 amplitudes in the (multi-) Regge limit, and comment on the interplay between this research and the study of infrared factorization.

In this paper, we show that multiple maximally soft (anti-)quark and gluon emissions exponentiate at the level of either the amplitude or cross-section. We first show that such emissions can be captured by introducing new soft emission operators, which serve to generalise the well-known Wilson lines describing emissions of maximally soft gluons. Next, we prove that vacuum expectation values of these operators exponentiate using the replica trick, a statistical-physics argument that has previously been used to demonstrate soft-gluon exponentiation properties in QCD. The obtained results are general, i.e. not tied to a particular scattering process. We illustrate our arguments by demonstrating the exponentiation of certain real and virtual corrections affecting subleading partonic channels in deep-inelastic scattering.

We discuss recent progress concerning the resummation of large logarithms at next-to-leading power (NLP) in scattering processes such as Drell-Yan and deep inelastic scattering near threshold, and thrust in the two-jet limit. We start by reviewing the approach based on soft-collinear effective field theory and show that the standard factorization into short distance coefficients, collinear and soft functions at NLP leads in general to the appearance of endpoint divergences, which prevent the naive application of resummation techniques based on the renormalization group. Taking thrust as a case study, we then show that these singularities are indeed an artifact of the effective theory, and discuss how they can be removed to recover a finite factorization theorem and achieve resummation at NLP, at LL accuracy. Last, we discuss recent work concerning the calculation of all collinear and soft functions necessary to reproduce Drell-Yan near threshold up to NNLO in perturbation theory. This calculation provides useful data to extend resummation at NLP beyond LL accuracy.

We perform an analysis of the one- and two-loop massive quark form factor in QED in a region expansion, up to next-to-leading power in the quark mass. This yields an extensive set of regional integrals, categorized into three topologies, against which factorization theorems at next-to-leading power could be tested. Our analysis reveals a number of subtle aspects involving rapidity regulators, as well as additional regions that manifest themselves only beyond one loop, at the level of single diagrams, but which cancel in the form factor.