arXiv subjects

Sara Ditsch

Publications and source records attributed to Sara Ditsch.

6 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.

hep-ph↗

arXiv2026

Approximating Feynman integrals using complete monotonicity and Stieltjes properties

We present two novel approaches for the numerical evaluation of Feynman integrals based on their universal analytic properties related to positivity, namely complete monotonicity (CM) and Stieltjes properties. Building on recent results, we exploit the fact that scalar Feynman integrals in the Euclidean region are completely monotonic functions, meaning that all their derivatives have a fixed sign. Building on this observation, the CM bootstrap allows one to reconstruct integrals from differential equations without explicit boundary data, yielding rigorous bounds. The second method is based on a refinement of CM. We prove that Feynman integrals, within a certain range of parameters, are not only CM but in fact Stieltjes functions. This enables the use of Pad\'e approximants with provable convergence properties in the cut complex plane, providing an efficient method for analytic continuation and fast numerical evaluation. We illustrate the method with simple examples such as the massive bubble integral and discuss applications to multi-loop integrals, including the 20-loop banana integral. Finally, we comment on a number of extensions of these novel avenues for computing Feynman integrals.

hep-th↗

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.

hep-ph↗

arXiv2025

Approximating Feynman Integrals Using Complete Monotonicity and Stieltjes Properties

We introduce two novel numerical approaches for computing Feynman integrals based on their complete monotonicity (CM) and Stieltjes properties. The first method uses that scalar Feynman integrals are CM, meaning that all their derivatives have a fixed sign, in the Euclidean kinematic region. This imposes strong constraints on the function space. Simultaneously, these integrals obey systems of linear differential equations with respect to kinematic parameters. By imposing that the solutions to these differential equations satisfy complete monotonicity across the Euclidean region, we develop an efficient and highly constraining numerical bootstrap method. We provide a proof of principle of the power of our approach by applying it to a class of multi-loop Feynman integrals with internal masses. The second method is based on a refinement of CM. We prove that Feynman integrals, within a certain range of parameters, such as dimension and propagator exponents, are not only CM but in fact Stieltjes functions. The latter can be described efficiently by Pad\'e approximants that are known to converge in the cut complex plane. This means that these representations are valid also in analytically continued kinematics, such as physical scattering regions. These insights allow us to obtain rational approximations to Feynman integrals from minimal information, such as a Taylor expansion about a soft limit. We demonstrate the effectiveness of this method by applying it to a 20-loop banana-type Feynman integral. Finally, we comment on a number of extensions of these novel avenues for computing Feynman integrals.

hep-th↗

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.

hep-ph↗

arXiv2023

Entropic distinguishability of quantum fields in phase space

We present a general way of quantifying the entropic uncertainty of quantum field configurations in phase space in terms of entropic distinguishability with respect to the vacuum. Our approach is based on the functional Husimi $Q$-distribution and a suitably chosen relative entropy, which we show to be non-trivially bounded from above by the uncertainty principle. The resulting relative entropic uncertainty relation is as general as the concept of coherent states and thus holds for quantum fields of bosonic and fermionic type. Its simple form enables diverse applications, among which we present a complete characterization of the uncertainty surplus of arbitrary states in terms of the total particle number for a scalar field and the fermionic description of the Ising model. Moreover, we provide a quantitative interpretation of the role of the uncertainty principle for quantum phase transitions.

quant-ph↗