arXiv subjects

Julia Karlen

Publications and source records attributed to Julia Karlen.

5 recordsLinked to original sources

arXiv2026

Ward identity preserving local ultraviolet counterterms for photoproduction at two loops in QCD

We review the construction of locally finite two-loop amplitude integrands for photoproduction via quark annihilation, presented in arXiv:2509.07805. Building on established techniques for off-shell colorless production, we extend this local subtraction framework to handle transient singularities arising from real outgoing photons. These singularities manifest only at the integrand level, yielding finite contributions upon integration. In these proceedings, we provide the explicit construction of ultraviolet counterterms that satisfy necessary Ward identity cancellations, ensuring that the integrand is rendered integrable. This work provides a locally finite amplitude integrand that is ready for numerical integration in momentum space. Furthermore, it establishes the foundation for extending local subtraction frameworks to processes involving final-state jets.

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arXiv2026

Local finiteness for real-virtual corrections to electroweak production in partonic collisions

We present a local subtraction scheme that enables the combined integration of loop momenta and the final-state parton phase space in real-virtual NNLO QCD corrections to cross sections for hadroproduction of electroweak and other colorless states. All initial- and final-state infrared singularities are subtracted at the integrand level in momentum space, yielding a locally finite integral ready for numerical integration in four dimensions. The subtraction terms are all based on the well-understood process of single-Higgs production. The core of our subtraction scheme relies on achieving local factorization in all infrared limits of real and virtual momenta. This necessitates systematic modifications of the original Feynman integrand for loop amplitudes, enabling gauge symmetry cancellations before performing integrations. Our approach provides an essential step toward NNLO cross-section calculations for hadron collider processes, where both loop and phase-space integrations are carried out numerically.

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arXiv2025

General finite two-loop amplitude integrand for photoproduction in quark annihilation

The construction of integrands free of infrared and ultraviolet singularities may enable the application of numerical methods to evaluate loop amplitudes that are inaccessible with analytic techniques. At two loops, finite amplitude integrands have been constructed for the production of off-shell or massive colorless particles via quark annihilation. In this article, we extend this class of processes to include real photons in the final state. To achieve this, we introduce appropriate momentum flows and counterterms to eliminate singularities that occur because the photons are massless. These singularities arise only locally at the integrand level and do not lead to divergences upon integration. Our treatment also eliminates all power singularities arising from self-energy corrections in the integrand. We extend the analysis to gluon emission from virtual quarks. We believe these new insights will be useful for future extensions of infrared subtraction methods to processes with final-state jets.

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arXiv2024

Locally finite two-loop amplitudes for electroweak production through gluon fusion

The computation of two-loop amplitudes for the production of multiple Higgs and electroweak gauge bosons via gluon fusion with exact dependence on quark masses relies primarily on numerical methods. We propose a framework that enables their numerical evaluation in momentum space. The method is inspired by the factorization of infrared divergences in QCD scattering amplitudes. It extends techniques introduced for electroweak gauge boson production from quark-antiquark annihilation to processes with external gluons. By combining diagrammatic integrands, we make use of local cancellations between diagrams that automatically eliminate most non-factoring infrared singularities. With a limited number of counterterms, we then derive two-loop integrands for which all soft and collinear singularities factorize locally. We hope that the local subtraction techniques presented in this article will play a useful role in extending the local factorization formalism to two-loop amplitudes for arbitrary processes.

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arXiv2023

Tensor reduction of loop integrals

The computational cost associated with reducing tensor integrals to scalar integrals using the Passarino-Veltman method is dominated by the diagonalisation of large systems of equations. These systems of equations are sized according to the number of independent tensor elements that can be constructed using the metric and external momenta. In this article, we present a closed-form solution of this diagonalisation problem in arbitrary tensor integrals. We employ a basis of tensors whose building blocks are the external momentum vectors and a metric tensor transverse to the space of external momenta. The scalar integral coefficients of the basis tensors are obtained by mapping the basis elements to the elements of an orthogonaldual basis. This mapping is succinctly expressed through a formula that resembles the ordering of operators in Wick's theorem. Finally, we provide examples demonstrating the application of our tensor reduction formula to Feynman diagrams in QCD $2 \to 2$ scattering processes, specifically up to three loops.

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