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Maximilian Delto

Publications and source records attributed to Maximilian Delto.

17 recordsLinked to original sources
arXiv2026

Two-loop QCD amplitudes for $t\bar{t}W$ production at the LHC in the leading-colour approximation

We present a numerical computation of the two-loop QCD scattering amplitudes for the production of a top-antitop quark pair in association with a $W$ boson ($t\bar{t}W$) at the LHC in the generalised leading-colour approximation, retaining the exact dependence on the top-quark and $W$-boson masses. Rather than pursuing a fully analytic calculation, we employ a hybrid framework that combines numerical evaluation with strong algebraic and analytic control, allowing ultraviolet and infrared singularities as well as large intermediate cancellations to be treated exactly. This is achieved by expressing the finite remainder in terms of a set of special functions with rational coefficients. The special functions are evaluated numerically by solving differential equations through power-series expansions, while the values of the rational coefficients are reconstructed, point by point, from finite-field evaluations. The calculation is performed in the 't Hooft-Veltman scheme and validated against an independent implementation in conventional dimensional regularisation employing a substantially different computational strategy. We finally provide the colour- and polarisation-summed hard functions evaluated on the phase-space grid used in a previous computation of the next-to-next-to-leading-order QCD corrections to the $t\bar{t}W$ cross section.

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arXiv2026

NNLO QCD predictions for $t\bar t W$ production at hadron colliders

The production of a top-antitop quark pair in association with a $W$ boson constitutes one of the heaviest final states currently studied at the Large Hadron Collider (LHC) at CERN. Measurements of its production rate have consistently exceeded Standard Model predictions. Owing to the complexity of the two-loop amplitudes entering the double-virtual correction, next-to-next-to-leading-order (NNLO) QCD calculations for this process have so far employed dynamical approximations for the two-loop contribution. We present NNLO QCD predictions based, for the first time, on a direct computation of the required two-loop amplitudes in the generalised leading-colour limit.

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arXiv2026

$N$-Jettiness Soft Functions Made Simple

We present a new method to compute the soft function for the $N$-Jettiness variable for arbitrary $N$ at high perturbative orders in QCD. It is based on the observation that the most singular part of the soft function, the dipole contribution, can be represented by a sum of an analytically calculable inclusive soft function and a remainder. The latter is absent at NLO, is immediately finite at NNLO and can be made finite with the help of simple NLO-like infrared subtractions at N$^3$LO. As a byproduct of this approach, we derive a very simple formula for the tripole contribution to the $N$-Jettiness NNLO soft function, which results in a fast numerical evaluation. We apply this method to compute the $N$-Jettiness soft function at NNLO, and report numerical results for up to five jets for the hadron-collider soft function. We finally outline the prospects for applications at N$^3$LO.

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arXiv2025

High-Energy Evolution of Power-Suppressed Amplitudes

We present a new class of evolution equations which govern the high-energy behavior of power-suppressed scattering amplitudes. The equations can be viewed as a renormalization group flow with respect to the relevant effective field theory cutoff. A distinct feature of the method is in the use of a multidimensional cutoff to separate the relevant scales in problems characterized by a complex factorization structure. By adjusting the renormalization group variables to the geometry of the effective theory modes, our method naturally extends to a broad spectrum of physical problems including massive, massless, small, and wide angle scattering. We present applications to the benchmark processes of electron-positron forward annihilation and light quark mediated Higgs boson production/decays.

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arXiv2025

One-Loop QCD Corrections to $\bar{u}d \rightarrow t\bar{t}W$ at $\mathcal{O}(\varepsilon^2)$

We present a computation of the one-loop QCD corrections to top-quark pair production in association with a $W$ boson, including terms up to order $\varepsilon^2$ in dimensional regularization. Providing a first glimpse into the complexity of the corresponding two-loop amplitude, this result is a first step towards a description of this process at next-to-next-to-leading order (NNLO) in QCD. We perform a tensor decomposition and express the corresponding form factors in terms of a basis of independent special functions with compact rational coefficients, providing a structured framework for future developments. In addition, we derive an explicit analytic representation of the form factors, valid up to order $\varepsilon^0$, expressed in terms of logarithms and dilogarithms. For the complete set of special functions required, we obtain a semi-numerical solution based on generalized power series expansion.

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arXiv2024

Triple real-emission contribution to the zero-jettiness soft function at N3LO in QCD

Recently, we have presented the result for the zero-jettiness soft function at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD [arXiv:2409.11042], without providing technical details of the calculation. The goal of this paper is to describe the most important element of that computation, the triple real-emission contribution. We present a detailed discussion of the many technical aspects of the calculation, for which a number of methodological innovations was required. Although some elements of the calculation were discussed earlier [arXiv:2004.03285,arXiv:2206.12323,arXiv:2111.13594,arXiv:2204.09459,arXiv:2401.05245], this paper is intended to provide a complete summary of the methods used in the computation of the triple real-emission contribution to the soft function.

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arXiv2024

Zero-jettiness soft function to third order in perturbative QCD

We present the high-precision result for the zero-jettiness soft function at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. At this perturbative order, the soft function is the last missing ingredient required for the computation of a hadronic colour singlet production or a colour singlet decay into two jets using the zero-jettiness variable as the slicing parameter. Furthermore, the knowledge of the N3LO soft function enables the re-summed description of the thrust distribution in the process $e^+ e^- \to \textrm{hadrons}$ through next-to-next-to-next-to-leading logarithmic order, which is important for the extraction of the strong coupling constant using this shape variable. On the methodological side, the complexity of the zero-jettiness variable forced us to develop a new semi-analytic method for phase-space integration in the presence of constraints parameterized through Heaviside functions which, hopefully, will be useful for further development of the $N$-jettiness slicing scheme.

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arXiv2024

One-loop corrections to the double-real emission contribution to the zero-jettiness soft function at N3LO in QCD

We present an analytic calculation of the one-loop correction to the double-real emission contribution to the zero-jettiness soft function at N3LO in QCD, accounting for both gluon-gluon and quark-antiquark soft final-state partons. We explain all the relevant steps of the computation including the reduction of phase-space integrals to master integrals in the presence of Heaviside functions, and the methods we employed to compute them.

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arXiv2023

Two-loop QED corrections to the scattering of four massive leptons

We study two-loop corrections to the scattering amplitude of four massive leptons in quantum electrodynamics. These amplitudes involve previously unknown elliptic Feynman integrals, which we compute analytically using the differential equation method. In doing so, we uncover the details of the elliptic geometry underlying this scattering amplitude and show how to exploit its properties to obtain compact, easy-to-evaluate series expansions that describe the scattering of four massive leptons in QED in the kinematical regions relevant for Bhabha and Møller scattering processes.

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arXiv2021

On phase-space integrals with Heaviside functions

We discuss peculiarities that arise in the computation of real-emission contributions to observables that contain Heaviside functions. A prominent example of such a case is the zero-jettiness soft function in SCET, whose calculation at next-to-next-to-next-to-leading order in perturbative QCD is an interesting problem. Since the zero-jettiness soft function distinguishes between emissions into different hemispheres, its definition involves $θ$-functions of light-cone components of emitted soft partons. This prevents a direct use of multi-loop methods, based on reverse unitarity, for computing the zero-jettiness soft function in high orders of perturbation theory. We propose a way to bypass this problem and illustrate its effectiveness by computing various non-trivial contrbutions to the zero-jettiness soft function at NNLO and N3LO in perturbative QCD.

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arXiv2021

Estimating the impact of mixed QCD-electroweak corrections on the $W$-mass determination at the LHC

We study the impact of the recently computed mixed QCD-electroweak corrections to the production of $W$ and $Z$ bosons at the LHC on the value of the $W$ mass extracted from the transverse momentum distribution of charged leptons from $W$ decays. Using the average lepton transverse momenta in $W$ and $Z$ decays as simplified observables for the determination of the $W$ mass, we estimate that mixed QCD-electroweak corrections can shift the extracted value of the $W$ mass by up to ${\cal O}(20)~{\rm MeV}$, depending on the kinematic cuts employed to define fiducial cross sections for $Z$ and $W$ production. Since the target precision of the $W$-mass measurement at the LHC is ${\cal O}(10)~{\rm MeV}$, our results emphasize the need for fully-differential computations of mixed QCD-electroweak corrections and a careful analysis of their potential impact on the determination of the $W$ mass.

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arXiv2020

Mixed QCD-electroweak corrections to on-shell Z production at the LHC

We present the first complete calculation of mixed QCD-electroweak corrections to the production of on-shell $Z$ bosons in hadron collisions and their decays to massless charged leptons. Our computation is fully differential with respect to final state QCD partons and resolved photons, allowing us to compute any infra-red safe observable pertinent to the $pp \to Z \to l^+ l^-$ process in the approximation that the $Z$ boson is on shell. Although mixed QCD-electroweak corrections are small, at about the per mill level, we observe that the interplay between QCD-QED and QCD-weak contributions is subtle and observable-dependent. It is therefore not possible to avoid computing one or the other if ${\cal O}(α_{EW} α_s)$ precision is desired.

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arXiv2020

Analytic double-soft integrated subtraction terms for two massive emitters in a back-to-back kinematics

We consider the double-soft limit of QCD amplitudes with two massive quarks in a back-to-back kinematics accompanied by two soft partons. We integrate analytically the respective double-soft eikonal functions over the phase space of the two soft partons. Within the context of the nested soft-collinear subtraction scheme, our results may serve as one of the integrated subtraction terms needed for the analytic and fully-differential description of next-to-next-to-leading order (NNLO) QCD corrections to colour-singlet decay into massive partons or to heavy-quark pair production.

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arXiv2019

Mixed QCD$\otimes$QED corrections to on-shell $Z$ boson production at the LHC

We compute the mixed QCD$\otimes$QED corrections to the production of on-shell $Z$ bosons at the LHC at a fully-exclusive level. We also include the factorised NLO QCD correction to $Z$ boson production and NLO QED correction to $Z$ boson decay into two leptons. We make use of an abelianised version of the nested soft-collinear subtraction formalism to perform this computation. We study the phenomenological impact of the mixed QCD$\otimes$QED corrections for a number of observables relevant for LHC phenomenology.

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arXiv2019

Integrated triple-collinear counter-terms for the nested soft-collinear subtraction scheme

We obtain analytic results for integrated triple-collinear splitting functions that emerge as collinear counter-terms in the context of the nested soft-collinear subtraction scheme arXiv:1702.01352 . With these results, all integrated subtraction terms required for NNLO QCD computations within this scheme are known analytically. In addition to improving efficiency and numerical stability of practical computations, the availability of these results will contribute towards establishing a general NNLO QCD subtraction formula for generic hard scattering processes in hadron collisions, similar to Catani-Seymour and FKS subtractions at NLO.

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arXiv2018

The double-soft integral for an arbitrary angle between hard radiators

We consider the double-soft limit of a generic QCD process involving massless partons and integrate analytically the double-soft eikonal functions over the phase-space of soft partons (gluons or quarks) allowing for an arbitrary relative angle between the three-momenta of two hard massless radiators. This result provides one of the missing ingredients for a fully analytic formulation of the nested soft-collinear subtraction scheme recently proposed by some of us.

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