Local Unitarity

Local Unitarity provides an order-by-order representation of perturbative cross-sections that realises at the local level the cancellation of final-state collinear and soft singularities predicted by the KLN theorem. The representation is obtained by manipulating the real and virtual interference diagrams contributing to transition probabilities using general local identities. As a consequence, the Local Unitarity representation can be directly integrated using Monte Carlo methods and without the need of infrared counter-terms. I will start by presenting the Cross-Free Family representation of loop integrals, a close relative of the Time-Ordered Perturbation Theory and Loop-Tree Duality representations, which reveals with unmatched clarity the singularity structure of Feynman diagrams. I will use this representation and the causal flow, a construct that allows to bypass the mappings common to subtraction methods, to obtain the Local Unitarity representation. Finally, I will show first results from this new approach with examples up to N3LO accuracy. I will conclude by giving an outlook on future generalisations of the method applicable to hadronic collisions.

*Wednesday, 14th December 2022, 14:30 — Sala Wataghin *

A New Amplitude/Form Factor Duality

Traditional methods for computing quantities such as scattering amplitudes and form factors in quantum field theory become intractable at high perturbative orders. However, a great deal is now known about the mathematical properties of these quantities, especially in supersymmetric gauge theories. In this talk, I will describe how this knowledge can be leveraged to 'bootstrap' amplitudes and form factors directly, by constructing an ansatz with the appropriate mathematical structure and requiring it to have certain expected behavior in special kinematic limits. I will focus on the example of three-point form factors in maximally supersymmetric gauge theory, which have recently been bootstrapped through eight loops. I will then describe a remarkable new duality between this form factor and certain six-particle amplitudes in the same theory, which holds order by order in perturbation theory.

*Wednesday, 30th Novemeber 2022, 14:30 — Sala Wataghin *

Strange Symbol Structures for a Sufficiently Supplemented Sunrise

The symbol is a powerful formalism used to manipulate and understand certain classes of Feynman diagrams. It can dramatically simplify expressions, reveal analytic structure, and even allow perturbative amplitudes to be bootstrapped from first principles to high loop orders. However, many classes of diagrams involve functions for which an appropriate symbol formalism is not known. The simplest such class, the sunrise diagrams, consist of a family of massive propagator corrections that can be thought of as integrals over the Calabi-Yau manifolds coincidentally explored by string theorists. We explore an extension of the symbol formalism to this class of diagrams. There are many choices involved in setting up such a formalism, and we comment on the challenge of finding ways to make those choices that achieve the amplitudes community's aims.

*Tuesday, 29th Novemeber 2022, 14:30 — Sala Wataghin *

Jets for LHC Run3

In this talk I review some recent developments in the context of jet physics and their structure. In particular, I focus on applications of ideas developed by the jet substructure community to the wider phenomenology program of the LHC, such as precision studies and heavy flavours. I also discuss how first-principle understanding reached in the context of jets, can help us confronting complex analysis strategies based on machine-learning techniques.

*Friday, 4th Novemeber 2022, 14:00 — Sala Fubini *

Handling Linear Power Corrections in Collider Processes

Understanding leading non-perturbative corrections, showing up as linear power corrections, is crucial to properly describe observables both at lepton and hadron colliders. Using an abelian model, we examine these effects for the transverse momentum distribution of a Z boson produced in association with a jet in hadronic collisions, that is one of the cleanest LHC observables, where the presence of leading non-perturbative corrections would spoil the chance to reach the current experimental accuracy, even considering higher orders in the perturbative expansion. As we did not find any such corrections exploiting numeric techniques, we looked for a rigorous field-theoretical derivation of them, and explain under which circumstances linear power corrections can arise. We apply our theoretical understanding to the study of event-shape observables in e+e- annihilation, focusing in particular on C-parameter and thrust, and obtaining for them an estimate of non-perturbative corrections in the three-jet region for the first time. We also derived a factorisation formula for non-perturbative corrections, with a term describing the change of the shape variable when a soft parton is emitted, and a universal factor, proportional to the so-called Milan factor. These observables are routinely used to extract the strong coupling constant alpha_s and they constitute an environment to test perturbative QCD. It is then extremely important to obtain reliable estimates of non-perturbative corrections in the whole kinematic region relevant for the alpha_s fits.

*Wednesday, 19th October 2022, 15:30 — Sala Wataghin *

Phenomenology of Padé approximants: the case of |Vub| from B to pi and B_s to K

Padé approximants provide an excellent toolkit for studying hadronic form factors. They are not only user-friendly but also provide a handle on the approximation error. We will exemplify their use by revisiting the determination of the Cabibbo-Kobayashi-Maskawa parameter from exclusive semileptonic -meson decays. A brief outlook on extensions to that method will also be discussed.

*Wednesday, 22nd June 2022, 14:30 — Sala Wataghin *

Gravitational Physics and Scattering Amplitudes

Scattering amplitudes have recently found a new application to classical gravitational-wave physics. In this talk I will discuss why amplitudes can be useful in this area, and outline how to extract classical observables from the amplitudes. We will see that the basic aspects of classical physics in turn yields interesting new constraints on the structure of multiloop, multileg amplitudes.

*Wednesday, 7th June 2022, 14:30 — Sala Wataghin *

Feynman Integral: Harnessing it through Intersection Theory

Abstract: Feynman integrals are an integral part of the computation of scattering amplitudes and related quantities. The Feynman integrals obey linear relations, which are exploited by employing the standard Integration-by-parts identities to simplify the evaluation of scattering amplitudes: they can be used both for decomposing the scattering amplitudes in terms of a basis of functions, referred to as master integrals (MIs) and for the evaluation of the latter using the differential equation. I will show that they are better understood by using the Intersection Numbers, which act as scalar products between the vector spaces of the Feynman Integrals. Application to few Feynman integrals at one- and two-loops will be shown, thereby sketching various direct decomposition of Feynman integrals using multivariate Intersection numbers.

*Wednesday, 24th May 2022, 14:30 — Sala Wataghin *

Two-loop tensor integral coefficients in OpenLoops

The development of a fully automated tool for the numerical calculation of NNLO corrections to scattering amplitudes is a highly desirable goal for the LHC era. Two-loop amplitudes can be expressed in terms of tensor integrals over two loop momenta with coefficients derived from the Feynman diagrams of a given scattering process. Hence, the calculation can be structured into the computation of the tensor coefficients, the reduction of the tensor integrals and the evaluation of the resulting master integrals.

In this talk, we present a new algorithm to numerically construct the tensor coefficients for two-loop amplitudes in the OpenLoops framework. Exploiting the factorisation of Feynman diagrams into universal building blocks, we construct these coefficients in a highly efficient way. The algorithm is completely general and has been fully implemented and tested for QED and QCD corrections to the Standard Model. We will discuss the structure of the algorithm and present studies on its CPU efficiency and numerical stability.

*Wednesday, 22nd April 2022, 14:30 — Zoom Seminar *

Numerical evaluation of multi-loop integrals without contour deformation

We propose a method to produce precise Monte Carlo estimates of multi-scale multi-loop integrals directly in Minkowski space. The validity of our strategy is corroborated by presenting several examples ranging from one to three loops. When used in connection with four-dimensional regularization techniques, our treatment can be extended to ultraviolet and infrared divergent integrals.

*Wednesday, 12th April 2022, 14:30 — Sala Wataghin *