We study the amplitudes of the light quark mediated Higgs boson production via gluon fusion in the high-energy limit. A complete analytic result is obtained for the three-loop $O(m_q^3)$ double-logarithmic term while and the all-order analysis is performed in the large-$N_c$ limit of QCD and in the abelian approximation.

In the first part of the talk, methods for the calculation of two-loop amplitudes with several mass scales, such as HH, HJ or HZ production in gluon fusion, will be discussed. The second part will focus on Higgs boson pair production, in particular the combination of NLO QCD corrections with anomalous couplings in an Effective Field Theory framework. Predictions for the Higgs boson pair...

Kinematic expansions of scattering cross sections provide powerful methods of approximating key LHC observables to a high degree of precision at reduced degree of complexity in comparison to a full computation. I will show several recent advancements and examples in the development and application of collinear expansion techniques.

I critically examine issues that arise when applying modern machine learning techniques in the context of precision collider physics, by specifically considering the case of PDF determinations. Questions that I address include: Can we trust the machine learning model to correctly generalize from known examples? How can we validate results, specifically for uncertainties? Can we detect over-...

I will review novel developments related to an analytic understanding of power corrections to collider processes in the context of renormalon calculus.

We may associate a geometry to a Feynman integral. Understanding the geometry helps in computing the Feynman integral. In this talk I will discuss how Feynman integrals related to non-trivial geometries like Calabi-Yau manifolds can be computed with the help of the method of differential equations. In particular I will discuss an ansatz, which casts the differential equation into an...

In this talk I will describe the construction of local infrared counterterms to remove all infrared singularities in two-loop amplitudes for gluon-fusion processes to colourless final states. The counterterms are given as form-factor integrands whose integrals are known and the number of such counterterms are very small compared to the number of diagrams involved. This procedure is based on...

We will provide a guided tour through the method of calculating high loop order renormalization functions (7 loops $\phi^4$, 6 loops $\phi^3$) with graphical functions. This tour will lead through graphical functions in even dimensions (for calculating primitive Feynman periods, with M. Borinsky), generalized single-valued hyperlogarithms (GSVHs, a suitable function space), and the extension...

In both single top and VBF Higgs production a structure function approximation can be applied to obtain the leading colour contribution. This approximation contains only so-called factorisable diagrams and is exact at NLO. However, at NNLO non-factorisable contributions come into play. A particular challenge for calculations at this order is the evaluation of two-loop diagrams with several...

We will discuss how methods developed in the context of perturbation theory can be applied to the computation of lattice correlation functions, in particular in the non-perturbative regime. The techniques we will consider are integration-by-parts identities and the method of differential equations, cast in the framework of twisted Co-Homology. We will report on calculations of correlation...

Pair production of Z bosons is an essential process at the LHC. It is a significant background to Higgs production, and subsequent decay through the four lepton channel, as well as an important signal process for new physics searches. In this talk, we present our calculation of the next-to-leading order QCD corrections to Z-pair production through gluon fusion with full top quark mass...

The generic 3-loop tetrahedral tadpole, with 6 distinct masses, has elliptic subtructure originating from 12 distinct elliptic curves. I shall show how to evaluate it, at high precision and great speed, by integrating dilogarithms against complete integrals of the third kind, for which there is a proceudre of the arithmetic-geometric mean that is astoundingly fast. The elements of this method...

We propose a Monte Carlo integration algorithm for numerically evaluating Feynman integrals in the physical region of phase space. The algorithm is an extension of the tropical integration algorithm of M. Borinsky. Starting from the projective representation of a Feynman integral, we implement Feynman's i*epsilon prescription via a suitable contour deformation, whereafter tropical sampling is...

We present the first calculation for the production of a W boson in association with massive bottom quarks (Wbb) at hadron colliders at next-to-next-to-leading order (NNLO) in QCD. The use of massive bottom quarks avoids the ambiguities associated with the correct flavour assignment in massless calculations, paving the way to a more realistic comparison with experimental data. The relevant...

I will discuss the use of intersection numbers computed in relative cohomologies for the manipulation of Feynman integrals in Dimensional Regularization. This approach has the potential to revolutionize integral reductions, which with current techniques are a significant bottleneck for phenomenologically relevant scattering amplitude computations.

We compute the two-loop master integrals relevant for the NNLO QCD correction to heavy pseudo-scalar quarkonium production and decay both analytically and numerically. The analytic expressions involve elliptic multiple polylogarithms and iterated integrals of modular forms. We discuss the master integral computation and the form-factors obtained. We briefly discuss their phenomenological importance.

In this talk, we present the mixed QCD-EW two-loop virtual corrections for the charged current Drell-Yan production. The presence of one additional mass compare to the neutral current case makes the computation of the two-loop amplitudes extremely challenging, specially the two-loop Feynman integrals. Our approach to evaluate the relevant two-loop Feynman integrals using semi-analytical...

In this talk, I will introduce new tools towards the evaluation of Feynman integrals, including AMFlow and Blade. AMFlow, based on auxiliary mass flow method, which can numerically evaluate Feynman integrals in an efficient and systematic way, have proved to be very useful in the past year. Another tool named Blade, which is based on block-triangular relations among Feynman integrals, can...

The associated production of a Higgs boson with a top–antitop quark pair is a crucial process at the LHC since it allows for a direct measurement of the top-quark Yukawa coupling. In this talk we will present the computation of the radiative corrections to this process at the next-to-next-to-leading order (NNLO) in QCD perturbation theory. This represents the very first computation for a 2 → 3...

In multiloop computations, choosing an integral basis that minimizes infrared divergences holds the promise of simplifying results. I describe a procedure based on analysis of Landau equations for finding sets of finite integrals. The same technique can also be applied to finding integrals which are manifestly O(ϵ). These integrals can give rise to special relations between integrals beyond...

I will present flow oriented perturbation theory (FOPT), a coordinate space analogue of time-ordered perturbation theory and loop-tree duality. Within this approach, a generic Feynman graph is mapped to a sum of all its possible different energy-flows respecting energy conservation at each vertex (strongly connected directed graphs). In the FOPT framework, the integrals associated with virtual...

Massive form factors in QCD are important building blocks in higher order corrections to various observables like heavy quark production, top quark decays or muon-electron scattering, where they describe the virtual contributions. Furthermore, they show universal infrared behaviour which makes them interesting to study also in the context of the infrared structure of QCD amplitudes. In this...

I will discuss the two-loop computation of massless QCD helicity amplitudes with five external states and full colour dependence.

We present recent analytic results on the 3-loop heavy flavor corrections to deep-inelastic scattering.

Multi-jet rates at hadron colliders provide a unique possibility for probing Quantum Chromodynamics (QCD), the theory of strong interactions. By comparing theory predictions with collider data, one can directly test perturbative QCD, extract fundamental parameters like the strong coupling and search for physics beyond the Standard Model. Recent developments enabled lifting three-jet...

We present recent results on the computation of the splitting functions in quantum chromodynamics at four loops.

I discuss the recent advances in the computation of two-loop scattering amplitudes for five-particle processes. The latter are fundamental ingredients to obtain predictions at the next-to-next-to-leading order (NNLO) in QCD for many interesting LHC processes. I discuss the state-of-the-art technology for computing scattering amplitudes analytically, and present new results relevant for the LHC...

The most general renormalizable quantum field theory one can write down for a finite spectrum of spin-0, 1/2, and 1 particles is a gauge theory, with possible spontaneously broken symmetries. The existence of Lie group structures in such a theory is determined by perturbative unitarity of the on-shell scattering amplitudes. Armed with new tools developed for scattering amplitudes, we...

Multi-loop Feynman integrals are the cornerstone of modern perturbative approaches to quantum field theory and a pillar of precision computations for colliders as well as gravitational wave experiments. It is therefore essential to develop efficient method to evaluate them. A big bottleneck in that direction is the necessity to deal with integrals depending on many scales. In this talk, I will...

I will discuss recent progress concerning the factorization of physical observables and the resummation of large logarithms at next-to-leading power, focusing on the loop calculation of the universal functions in which physical observables factorize.

Amplitude are geometric objects and we have ambitions to classify them. As functions of discrete indices of color, charge, helicity, ..., and spin, they are tensors on the Fock spaces of elementary particles. Linear spaces, like the Fock spaces, they have automorphisms under which a given tensor is transformed into another in the equivalent class. In this sense, equivalent classes of tensors...

The Energy Correlator observables probe the geometric distributions of energy flow in the final states of particle scattering experiments. They provide valuable data for studies ranging from conformal field theories to jet substructure. We present an analytic formula for the three-point energy correlator (EEEC) at leading order (LO) in N = 4 super Yang Mills theory, which exhibits unexplored...

We report on recent progress for the QCD corrections to top-quark pair plus jet production. In particular, we discuss a recent computation for the two-loop master integrals associated to a two-loop five-point pentagon-box integral configuration with one internal massive propagator, that contributes to top-quark pair production in association with a jet in the QCD planar limit.

In this talk we present the calculation of NLO QCD corrections to $pp \to t\bar{t}jj$ in the dilepton decay channel. The narrow width approximation is used to model the decays of the top quark pair preserving spin correlations. Jet radiation and QCD corrections are consistently included in the production and decay of the top quarks. We discuss the size of NLO QCD corrections and the main...

The associated production of a single top quark with a Z boson (tZj) represents an important probe of the EW sector of the Standard Model. Since differential measurements of tZj are expected to enhance the sensitivity to new-physics effects, and the experimental interest in this direction is growing in the light of upcoming LHC runs, it is crucial to improve the off-shell modelling of this...

Scattering amplitudes are the fundamental building blocks of collider observables. Comparing high precision measurements with theory predictions requires computing them to high perturbative order. The growth in the number of loops significantly increases the complexity of the problem. Using novel methods allowed us to compute QCD corrections to four-point massless processes at the...

I discuss a new observable for the determination of the W mass at hadron colliders

The method of regions (MoR), a systematic way to compute Feynman integrals involving multiple kinematic scales, states that a Feynman integral can be approximated, and even reproduced, by summing over integrals that are expanded in certain regions. A modern perspective of the MoR is to consider any given Feynman integral as a certain Newton polytope, which is defined as the convex hull of the...

In this talk, I will present a calculation of the NNLO mixed QCD-EW corrections to the neutral-current Drell-Yan production of a pair of massless leptons in the high invariant-mass region. Our computation is fully differential with respect to the final state particles.

We find that the mixed corrections corrections are larger than what one would expect based on the magnitude of the coupling...

As one of the primary sources of QCD background to $pp \to t\bar{t}H(H\to b\bar{b})$ at the LHC, the $t\bar{t}b\bar{b}$ production process demands precise theoretical predictions and estimates of the dominant uncertainties. On top of that, the capacity of properly disentangling the prompt b-jets and the b-jets from top-quark decays has important phenomenological consequences. In this talk we...

Following up on some distant and little-known papers by Tullio Regge and collaborators, I will present an approach to integration-by-parts identities and differential equations for Feynman integrals, based on the Feynman parameter representation, and relying upon the projective nature of parameter integrands. A very general identity connecting projective forms allows to move across families of...

Landau analysis aims to predict the singularity structure of Feynman integrals without their explicit evaluation. We point out a number of errors in its textbook formulation that prevented applications to the Standard Model processes in the past. After resolving these issues, we use a combination of tropical analysis and numerical algebraic geometry to implement an algorithm that classifies...

Dynamics of high energy scattering in QCD are primarily probed through detector energy flow correlations. One important IRC safe energy-flow observable is the Energy-Energy Correlator (EEC). At leading power approximation in the back-to-back limit, EEC enjoys a factorization formula similar to the Drell-Yan production at small transverse momentum. Therefor studying the power corrections to EEC...

We subtract the gluon-condensate renormalon singularity in the Adler function, which causes the discrepancy between fixed-order (FOPT) and contour-improved perturbation theory (CIPT), employing the gradient flow action density. The scheme leads to automatic subtraction, does not require knowledge of the Stokes constant (renormalon residue), and relates to a non-perturbatively defined cut-off...

In my talk, I will present the calculation of the two-loop soft and beam functions for the transverse-momentum distribution of the leading jet in the production of a colour-singlet system such as a Higgs or Z boson. This calculation constitutes a vital component for the resummation of the transverse-momentum distribution and the jet-vetoed cross-section at next-to-next-to-next-to-leading...

I will present recently published as well as yet unpublished results on multi-photon and multi-jet cross sections obtained with next-to-next-to-leading and possibly higher order in perturbative QCD.

In a recent work by Hoang, Plätzer and Samitz is has been shown at the parton level that the relation top quark mass in MC event generators to a well-defined renormalization scheme depends on the parton shower cutoff. Still, it has not been known to which extent the hadronization model may affect this relation and how much this relation depends on the MC event generator and the NLO matching...

We present an extension of HELAC for two-loop amplitudes. All basic two-loop topologies (Theta, Infinity, Dumbbell) are included in the skeleton construction. For colored particles, the color-connection representation is extended to two loops offering a unified framework for tree-order, one- and two-loop amplitudes. HELAC-2LOOP provides, at the moment, an automated algorithm capable to compute...

In this talk I investigate the interplay of NLO matching and next-to-leading-logarithmic (NLL) parton showers in the context of two-body decays. Three matching schemes have been implemented in the NLL-accurate PanScales showers: a multiplicative scheme, MC@NLO and POWHEG. By means of both analytic and numerical arguments, I show how these retain the shower’s NLL accuracy, and (under certain...

In this talk I will present an automated framework calculating NLO corrections in the full SM for arbitrary processes at hadron and lepton colliders. This framework is an element of the Monte-Carlo program WHIZARD simulating cross sections and differential distributions. The generalization of the implemented FKS scheme to systematically subtract QED and QCD infrared divergences in mixed...

In this talk, I will discuss a framework that resums soft (logarithms ln^k(N) in Mellin space) and next-to-soft (power-suppressed terms ln^k(N)/N in Mellin space) logarithms to all orders in perturbative QCD. We use the concepts of collinear factorisation and renormalisation group invariance to achieve this. The former allows one to define a soft-collinear (SC) function that encapsulates soft...

I will describe recent progress on sector showers that consistently incorporate second-order "direct" 2->4 branchings. These showers are able to reproduce the full singularity structure of QCD through NNLO and can be matched in a very natural and fully differential way to calculations at this accuracy, provided that consistent "Born-local" K-factors can be defined. The method appears...

Double parton scattering (DPS) is the process in which one has two hard scatterings in an individual proton-proton collision. It can compete in rate with single scattering in certain kinematic regions and/or for certain processes, and reveals information on nucleon structure not accessible in single parton scattering: spatial, spin, and colour correlations between the partons inside the...

In view of the increasing level of precision of current and future experimental measurements, matching NNLO QCD and NLO EW corrections represents a crucial step for LHC phenomenology. Furthermore, complementing fixed-order perturbative computations with parton-shower effects is indispensable for a realistic description of LHC processes. In this talk we present the computation of WZ production...

Precision physics in the Higgs sector has been one of the main challenges in recent years. The pure fixed-order calculations entering in the \textit{collinear factorization} framework, which have been pushed up to N3LO, are not able to describe the entire kinematic spectrum. In particular conditions, they must be necessarily supplemented by all-order \textit{resummations}; for instance, in the...

We discuss new observables for probing physics beyond the SM within the framework of the Standard Model Effective Field Theory (SMEFT). We consider both existing measurements at the LHC, and potential future ones at upcoming colliders such as the Electron-Ion Collider (EIC).

Using diagrammatic resummation techniques, I discuss the double logarithmic series of B_c to eta_c form factors at large hadronic recoil. In the non-relativistic limit, mb >> mc >> LambdaQCD, this process provides one of the simplest setups to study the problem of endpoint singularities appearing in the SCET factorization of exclusive B decay amplitudes in a perturbative framework. The leading...

Quantum computers offer major speed-ups for problems like prime factorisation, searching, and quantum simulation. Recent years have seen the emergence of quantum algorithms for simulating lattice QCD and parton showers, but the quantum simulation of generic perturbative QCD processes has largely remained unexplored. As a first non-trivial step, I will discuss the quantum simulation of colour...

The renormalization scale setting in QCD is a fundamental problem for high precision tests of the Standard Model (SM). It is considered a conventional practice to set the renormalization scale to the typical scale of a process Q, namely to the momentum transfer and to determine theoretical errors by varying it in a range of two. According to the Conventional Scale Setting (C.S.S.),...

Scattering amplitudes greatly simplify in the Regge limit, and yet exhibit a very interesting structure, which is far richer in the full gauge theory than in the planar limit. Prior to the development of QCD, Regge and others showed that the asymptotic high-energy behaviour of amplitudes is governed by poles and cuts in the complex angular momentum plane. It was also shown (Mandelstam, 1963)...

I'd like to present the new developments and talk about the current status of numerical evaluation of multi-loop integrals and amplitudes using the new release of pySecDec (v1.6), particularly concentrating on significant integration performance improvements and automation related to expansion-by-regions.

This talk presents the construction of the NNLO subtraction formula for the cancellation of IR singularities obtained within the framework of Local Analytic Sector Subtraction. Such general program has been (so far) completed for the treatment of unresolved radiation in processes featuring any partonic final state in massless QCD. The outcome of the subtraction is a compact and analytic...

We present high energy next-to-leading logarithmic corrections, their inclusion within the framework of High Energy Jets, and their impact on the stabilisation of the perturbative prediction of R32 for large rapidity separations.

In the past decade the antenna subtraction method has been successfully implemented to compute Next-to-Next-to-Leading Order (NNLO) corrections in QCD for a series of relevant processes. In this talk we discuss the first steps towards the extension of this method at Next-to-Next-to-Next-to-Leading Order (N3LO). In particular, the calculation of N3LO antenna functions for final state radiation...

In this talk, I will present recent progress in the generalisation of the nested soft-collinear subtraction scheme to multi-parton final state processes. The scheme has already been successfully applied to scatterings involving a limited number of coloured partons, and it has shown remarkable flexibility and good numerical performances. I will discuss how to overcome the difficulties that...

Recent analyses on high-energy inclusive Higgs-boson rates in proton collisions via the gluon fusion channel, matched with the state of-the-art fixed-order N3LO accuracy, have shown that the impact of high-energy resummation corrections reaches 10% at the FCC nominal energies. This supports the statement that electroweak physics at 100 TeV is expected to receive relevant contributions from...

In this talk I will present the method to merge the resummation of high energy logarithms implemented in High Energy Jets (HEJ) partonic Monte Carlo framework with the soft-collinear effects described by the Pythia parton shower. The method preserves the accuracy of the leading order cross sections and the logarithmic accuracy of both resummation schemes across all of phase space. I will show...

Low-energy experiments allow for some of the most precise measurements in particle physics, such as g-2. To make the most of these experiments, theory needs to match the experimental precision. Over the last decade, this meant that even in QED next-to-next-to-leading order calculations (or even more in some cases) became necessary. I will discuss some of the challenges faced when dealing with...

A recently proposed experiment, MUonE, aims to extract the hadronic vacuum polarisation contribution to the muon g-2 from muon-electron scattering at low energy. The extrapolation requires that both experimental and theoretical uncertainties do not exceed 10 ppm. This corresponds, at least, to next-to-next-to leading order QED corrections to $e\mu \to e\mu$. I will discuss the implementation...

This talk will present radiative corrections and their interpretation for the so-called D-term. This is related to the Electron-Ion Collider project, where Generalized Parton Distributions (GPD) will be measured. GPD give access to matrix elements of the energy-momentum tensor of a nucleon. The D-term is sometimes roughly interpreted as characterizing pressure distribution. Calculated it in...

The antenna subtraction method has been successfully applied to a wide range of processes relevant for the Large Hadron Collider at next-to-next-to-leading order in $\alpha_s$ (NNLO). We propose an algorithm for building antenna functions for any number of real emissions directly out of the unresolved limits we require. Antenna functions of this kind always identify two hard radiators. We then...

The anomalous excess of soft photons radiated in inelastic hadronic collisions, has been challenging the physics community over four decades, but no solution was proposed so far. We argue that the problem is rooted in comparison with an incorrect model for radiative corrections, usually called bremsstrahlung model. It is based on an illegitimate extension of the Low theorem to radiative...

There is a continuing effort to support and prepare the precision physics programs for the present and planned future colliders such as HL-LHC, FCC, CLIC, CEPC, and CPPC. We discuss new results from IR-improved amplitude-based resummation in quantum field theory relevant to such support and preparation with some emphasis on the interplay between soft and collinear resummation algebras.

We consider two-loop corrections to $2\to 2$ scattering processes with massive particles in the final state and massive particles in the loop. We discuss the combination of analytic expansions in the high-energy limit and for small Mandelstam variable~$t$. For the example of double Higgs boson production we show that the whole phase space can be covered and time-consuming numerical...

In this talk we present the analytic results for two-loop QCD as well as QED corrections to light-by-light scattering including contributions due to massive internal fermions.

One-loop integrands can be written in terms of a simple, process-independent basis. A similar basis exists for integrands of phase-space integrals for the real-emission contribution at next-to-leading order. The demonstration deploys techniques from computational algebraic geometry in order to partial-fraction integrands in a systematic way. This provides the first step towards a decomposition...

Shower Monte Carlo generators simulate fully realistic collider events, and reproduce much of the data from the LHC and its predecessors. Their core is represented by Parton Shower~(PS) algorithms, which provide the inclusion of soft radiation and enable us to mimic a realistic high-multiplicity collider event. The flexibility of these tools comes at a cost of a lower accuracy, which can lead...