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Andreas von Manteuffel

Publications and source records attributed to Andreas von Manteuffel.

At least 19 recordsLinked to original sources
arXiv2026

The four-loop quark-to-quark splitting function in QCD

The scale evolution of parton distributions is governed by splitting functions. We compute the four-loop pure-singlet contribution to the quark-to-quark splitting function in perturbative QCD. Together with the known non-singlet contribution, our result completes the quark-to-quark splitting function at this order. We confirm previous partial results and obtain, for the first time, a fully analytic expression valid for all momentum fractions. We examine its behavior at small momentum fractions and provide precise numerical representations suitable for parton evolution.

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arXiv2026

One-loop QCD amplitudes for vector-boson-fusion Higgs-boson production to higher orders in $ε$

We consider one-loop QCD corrections to Higgs-boson production via vector-boson fusion at hadron colliders. As an input for future exact NNLO computations, we derive the one-loop helicity amplitudes to higher orders in the dimensional regulator. We present a direct calculation of the amplitudes with spinor-helicity techniques and different $γ_5$ schemes. In addition, we compare this approach to a projector-based calculation. In order to derive analytical results to higher orders in $ε$, we calculate the pentagon master integrals by the method of $ε$-factorised differential equations and express them in terms of an algebraically independent set of basis functions.

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arXiv2026

Two Feynman integral families for vector boson fusion at NNLO QCD

We consider a planar and a non-planar two-loop Feynman integral family arising in non-factorisable quantum chromodynamics corrections to Higgs-boson production via vector boson fusion. We construct basis integrals which fulfil canonical differential equations with respect to seven variables for the external kinematics and an internal mass. One of the integral families involves nested square roots. We present strategies for deriving canonical master integrals, $\mathrm{d}\log$ forms and analytic continuation for such cases. Including also families with crossed massless legs, we express the $\varepsilon$-expanded integrals in terms of an algebraically independent function basis. For their evaluation, we employ numerical integration of the differential equations.

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arXiv2026

The four-loop non-singlet splitting functions in QCD

The scale evolution of parton distributions is governed by splitting functions. We compute the four-loop splitting functions in perturbative QCD that control the evolution of quark non-singlet distributions. We confirm previous partial results and obtain, for the first time, fully analytic expressions for all non-singlet contributions at this order. These allow us to extract the analytic form of the four-loop virtual and rapidity anomalous dimensions entering logarithmic resummation. We provide precise numerical representations of the splitting functions suitable for parton evolution.

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arXiv2025

Complete Next-to-Leading Order QCD Corrections to $ZZ$ Production in Gluon Fusion

We calculate the complete NLO QCD corrections to loop-induced $gg \rightarrow ZZ$ production including full top-quark mass effects. The two-loop virtual corrections are obtained by combining analytic results for the massless, Higgs-mediated, and one-loop factorizable contributions with numerically computed amplitudes containing the top-quark mass. We show that the choice of subtraction scheme for the virtual contribution impacts the precision with which the virtual contribution must be evaluated in order to obtain sufficiently precise phenomenological predictions. For direct production through a massive top-quark loop, we observe that the relative NLO corrections are large. The direct massive and Higgs-mediated contributions individually increase relative to the massless production at high diboson invariant mass, but interfere destructively with each other. At the Large Hadron Collider, the NLO corrections to the gluon channel give a sizable contribution to the $pp \to ZZ+X$ cross-section at N${}^3$LO.

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arXiv2025

Four-Loop Renormalisation of Chiral Gauge Theories with Non-Anticommuting $γ_5$ in the BMHV Scheme

We present the complete 4-loop renormalisation of an Abelian chiral gauge theory in the Breitenlohner-Maison / `t Hooft-Veltman (BMHV) scheme. Employing a non-anticommuting $γ_5$ in dimensional regularisation, we determine the full set of symmetry restoring counterterms from the quantum action principle. Our calculation represents the highest-order application of the BMHV framework so far, pushing the limits of a self-consistent treatment of $γ_5$ at the multi-loop level. We describe the computational setup that we developed to perform the computations and discuss key implementation aspects, such as the BMHV algebra and tensor reduction. Our work demonstrates the feasibility of applying the BMHV scheme at high loop orders and establishes a solid foundation for future studies of high-precision electroweak physics.

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arXiv2024

The two-loop coefficient functions for double deeply virtual Compton scattering

Making use of conformal symmetry of large-$n_f$ QCD in $d=4-2ε$ dimensions at the Wilson-Fischer fixed point, we calculate the two-loop coefficient functions in the operator product expansion of two electromagnetic currents in general kinematics with two different photon virtualities. This result is necessary for the description of the double deeply virtual Compton scattering to the next-to-next-to-leading order accuracy, but is also interesting for a range of other two-photon processes. We present analytic expression for the coefficient function in momentum fraction space in the $\overline{\text{MS}}$ scheme and study its numerical impact on the Compton form factors for a simple model of the generalized parton distributions. The calculated corrections turn out to be large and are significant for the kinematics of proposed experiments.

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arXiv2024

Three-loop helicity amplitudes for four-quark scattering in massless QCD

We compute the three-loop corrections to the helicity amplitudes for $q\bar{q}\to Q\bar{Q}$ scattering in massless QCD. In the Lorentz decomposition of the scattering amplitude we avoid evanescent Lorentz structures and map the corresponding form factors directly to the physical helicity amplitudes. We reduce the amplitudes to master integrals and express them in terms of harmonic polylogarithms. The renormalised amplitudes exhibit infrared divergences of dipole and quadrupole type, as predicted by previous work on the infrared structure of multileg scattering amplitudes. We derive the finite remainders and present explicit results for all relevant partonic channels, both for equal and different quark flavours.

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arXiv2024

Leading Twist-Two Gauge-Variant Counterterms

Anomalous dimensions of twist-two operators govern the scale evolution of parton distribution functions. For off-shell external states, the physical twist-two operators mix with unknown gauge-variant operators under renormalization. In this talk, we apply the method proposed by us in~\cite{Gehrmann:2023ksf} to compute all gauge-variant one-loop counterterm Feynman rules with five legs, which enter the determination of the four-loop splitting functions in QCD.

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arXiv2024

Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions

The scale evolution of parton distributions is determined by universal splitting functions. As a milestone towards the computation of these functions to four-loop order in QCD, we compute all contributions to the pure-singlet quark-quark splitting functions that involve two closed fermion loops. The splitting functions are extracted from the pole terms of off-shell operator matrix elements, and the workflow for their calculation is outlined. We reproduce known results for the non-singlet four-loop splitting functions and validate our new pure-singlet results against fixed Mellin moments.

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arXiv2024

The $N_f \,C_F^3$ contribution to the non-singlet splitting function at four-loop order

We report a new result for the $N_f \,C_F^3$ contribution to the four-loop anomalous dimensions of non-singlet, twist-two operators in Quantum Chromodynamics. This result is obtained through computations of off-shell operator matrix elements. Employing integration-by-parts reductions and differential equations with respect to a tracing parameter allowed us to derive analytic results valid for arbitrary Mellin moment $n$.

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arXiv2023

Five-Parton Scattering in QCD at Two Loops

We compute all helicity amplitudes for the scattering of five partons in two-loop QCD in all the relevant flavor configurations, retaining all contributing color structures. We employ tensor projection to obtain helicity amplitudes in the 't Hooft-Veltman scheme starting from a set of primitive amplitudes. Our analytic results are expressed in terms of massless pentagon functions, and are easy to evaluate numerically. These amplitudes provide important input to investigations of collinear-factorization breaking and to studies of the multi-Regge kinematics regime.

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arXiv2023

Three-loop gluon scattering in QCD and the gluon Regge trajectory

We compute the three-loop helicity amplitudes for the scattering of four gluons in QCD. We employ projectors in the 't Hooft-Veltman scheme and construct the amplitudes from a minimal set of physical building blocks, which allows us to keep the computational complexity under control. We obtain relatively compact results that can be expressed in terms of harmonic polylogarithms. In addition, we consider the Regge limit of our amplitude and extract the gluon Regge trajectory in full three-loop QCD. This is the last missing ingredient required for studying single-Reggeon exchanges at next-to-next-to-leading logarithmic accuracy.

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arXiv2023

Master Integrals for Four-Loop Massless Form Factors

We present analytical results for all master integrals for massless three-point functions, with one off-shell leg, at four loops. Our solutions were obtained using differential equations and direct integration techniques. We review the methods and provide additional details.

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arXiv2023

Renormalization of twist-two operators in covariant gauge to three loops in QCD

The leading short-distance contributions to hadronic hard-scattering cross sections in the operator product expansion are described by twist-two quark and gluon operators. The anomalous dimensions of these operators determine the splitting functions that govern the scale evolution of parton distribution functions. In massless QCD, these anomalous dimensions can be determined through the calculation of off-shell operator matrix elements, typically performed in a covariant gauge, where the physical operators mix with gauge-variant operators of the same quantum numbers. We derive a new method to systematically extract the counterterm Feynman rules resulting from these gauge-variant operators. As a first application of the new method, we rederive the unpolarized three-loop singlet anomalous dimensions, independently confirming previous results obtained with other methods. Employing a general covariant gauge, we observe the explicit cancellation of the gauge parameter dependence in these results.

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arXiv2022

Signal-background interference effects in Higgs-mediated diphoton production beyond NLO

In this paper we consider signal-background interference effects in Higgs-mediated diphoton production at the LHC. After reviewing earlier works that show how to use these effects to constrain the Higgs boson total decay width, we provide predictions beyond NLO accuracy for the interference and related observables, and study the impact of QCD radiative corrections on the Higgs width determination. In particular, we use the so-called soft-virtual approximation to estimate interference effects at NNLO in QCD. The inclusion of these effects reduce the NNLO prediction for the total Higgs cross-section in the diphoton channel by about 1.7%. We study in detail the impact of QCD corrections on the Higgs-boson line-shape and its implications for the Higgs width extraction. Assuming an experimental resolution of about 150~MeV on interference-induced modifications of the Higgs-boson line-shape, our NNLO analysis shows that one could constrain the Higgs-boson total width to about 10-20 times its Standard Model value.

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arXiv2022

Renormalization of twist-two operators in QCD and its application to singlet splitting functions

Splitting functions govern the scale evolution of parton distribution functions. Through a Mellin transformation, they are related to anomalous dimensions of twist-two operators in the operator product expansion. We study off-shell operator matrix element, where the physical operators mix under renormalization with other gauge-variant operators of the same quantum numbers. We devise a new method to systematically extract the Feynman rules resulting from those operators without knowing the operators themselves. As a first application of the new approach, we independently reproduce the well-known three-loop singlet splitting functions obtained from computations of on-shell quantities.

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