arXiv subjects

Dhimiter Canko

Publications and source records attributed to Dhimiter Canko.

8 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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arXiv2025

All planar three-loop Feynman integrals for the production of two vector bosons at hadron colliders

We compute all the planar three-loop master integrals relevant for the leading colour N3LO QCD corrections to the production of two massive or off-shell vector bosons at hadron colliders. These integrals are organised into nine four-point integral families with massless internal propagators and two external massive legs. For each family, we construct a basis of pure master integrals and we reconstruct the corresponding canonical differential equations using finite field techniques. We evaluate the master integrals by solving the differential equations using generalised power series expansions.

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arXiv2025

Towards numerical two-loop integrand reduction

We present a method for the integrand-level reduction of two-loop helicity amplitudes in both $d=4-2\epsilon$ and $d=4$ dimensions. The amplitude is expressed in terms of a set of Feynman integrals and their coefficients that depend on the external kinematics. The analysis presented in this paper, in conjunction with the ongoing development of the computational framework $\text{HELAC-2LOOP}$, paves the road for the construction of an automated program for two-loop amplitude calculations for arbitrary scattering processes.

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arXiv2025

One-loop amplitudes for $t\bar{t}j$ and $t\bar{t}\gamma$ productions at the LHC through $\mathcal{O}(\epsilon^2)$

We present analytic expressions for the one-loop QCD helicity amplitudes contributing to top-quark pair production in association with a photon or a jet at the Large Hadron Collider (LHC), evaluated through $\mathcal{O}(\epsilon^2)$ in the dimensional regularisation parameter, $\epsilon$. These amplitudes are required to construct the two-loop hard functions that enter the NNLO QCD computation. The helicity amplitudes are expressed as linear combinations of algebraically independent components of the $\epsilon$-expanded master integrals--known as pentagon function--with the corresponding rational coefficients written in terms of momentum-twistor variables. We derive differential equations for the pentagon functions and solve them numerically using the generalised power series expansion method.

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arXiv2025

Two-loop Feynman integrals for leading colour $t\bar{t}W$ production at hadron colliders

We compute a complete set of the two-loop Feynman integrals that are required for the next-to-next-to-leading order QCD corrections to on-shell top-pair production in association with a $W$ boson at hadron colliders in the leading colour approximation. These Feynman integrals also contribute to Higgs or $Z$-boson production in association with a top pair. We employ the method of differential equations (DEs), facilitated by the use of finite field methods to handle the algebraic complexity stemming from the seven-scale kinematics. The presence of the top quark in the virtual propagators, in addition to the mass of the external $W$ boson, gives rise to nested square roots and three elliptic curves. We obtain DEs that depend at most quadratically on the dimensional regulator $\epsilon$ for sectors where these analytic structures appear, and are $\epsilon$-factorised otherwise. We express the DEs in terms of a minimal set of differential one-forms, separating the logarithmic ones. We solve the DEs numerically in the physical kinematic region, with the method of generalised power series expansions.

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arXiv2024

A first computation of three-loop master integrals for the production of two off-shell vector bosons with different masses

We present analytic results on physical kinematics for four integral families that are relevant to the production of two off-shell vector bosons with different masses. Our study consists of a ladder-box, a tennis-court, and two reducible ladder-box-like families. The results for the master integrals of these families are expressed up to order six in the dimensional regulator in terms of real-valued multiple polylogarithms. Furthermore, a semi-numeric solution is provided, employing generalized power series expansions using the package DiffExp.

hep-ph↗

arXiv2024

Two-Loop Amplitude Reduction with HELAC

We discuss recent progress towards extending the Helac framework to the calculation of two-loop amplitudes. A general algorithm for the automated computation of two-loop integrands is described. The algorithm covers all the steps of the computation, from the generation of loop topologies up to the construction of recursion relations for two loop integrands. Finally, first steps towards the formulation of a new approach for reducing two-loop amplitudes to a basis of master integrals are discussed.

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