arXiv subjects

Sven-Olaf Moch

Publications and source records attributed to Sven-Olaf Moch.

At least 19 recordsLinked to original sources

arXiv2026

Graphical Functions by Examples

Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-space integrals, they reveal rich analytic structures and have enabled major advances, including the highest-loop results currently known in several quantum field theories. Their role extends to conformal field theory, and recent algorithmic developments now allow many graphical functions to be computed automatically. This review, based on graduate-level lectures held by O.S. in 2025/26 at the University of Hamburg, introduces the central ideas behind graphical functions, covering periods, Feynman residues, and the treatment of regular and singular cases in both integer and non-integer dimensions. It also discusses connections to momentum space and self-duality, and provides guidance for further study, offering a coherent entry point into a topic not addressed in standard textbooks.

hep-th↗

arXiv2026

HyperFORM -- a FORM package for parametric integration with hyperlogarithms

HyperFORM brings the parametric integration of hyperlogarithms, weighted by rational prefactors, into the symbolic-manipulation system FORM. It ports the capabilities of Erik Panzer's Maple package HyperInt, capitalizing on FORM's speed with bulky algebraic input and on its ability to spread a single calculation across many processor cores. We keep the description of the method brief and concentrate instead on how the package is organized and driven: a fully self-contained program for the three-loop zigzag period serves as a worked illustration, and timing measurements for zigzags through six loops gauge its present reach. HyperFORM is released openly and applies to a broad class of problems, the evaluation of Feynman integrals prominently among them.

hep-ph↗

arXiv2026

Heavy-quark pair-production in DIS at NLO QCD matched to a parton shower

We present theoretical predictions for heavy-quark pair-production in deep-inelastic scattering (DIS) at next-to-leading order (NLO) in quantum chromodynamics (QCD), matched to a parton shower in the POWHEG framework. We revisit the NLO heavy-quark pair-production cross section and implement a consistent matching to parton-shower evolution, with careful treatment of heavy-quark mass effects and the avoidance of double counting between fixed-order and parton-shower radiation. In addition, we compare the virtual NLO corrections available in the literature to one-loop amplitudes obtained through massification in the small-mass limit. This provides an independent validation of the virtual contributions. The study is presently restricted to the gluon-initiated channel, which dominates the kinematic region of interest at the HERA collider and remains important for the future Electron-Ion Collider.

hep-ph↗

arXiv2026

A novel phenomenological approach to total charm cross-section measurements at the LHC

We propose a novel, data-driven method for determining total charm cross sections in proton-proton collisions by extrapolating measured fiducial cross sections without assuming any particular fragmentation model. The recently observed charm fragmentation non-universality at the LHC experimentally establishes strongly increased baryon production fractions and correspondingly decreased meson production fractions compared to electron-positron collisions, with a very significant $p_T$ dependence. The novel method accounts for this non-universality and its $p_T$-dependence through a data-driven extrapolation function called ddFONLL. Applied to $D^0$ production at 5 and 13 TeV, this approach yields total charm cross sections that fully incorporate the fragmentation non-universality and increase significantly compared to the previous measurements still based on fragmentation universality. The results are consistent with NNLO QCD predictions and enable direct comparisons free from fragmentation assumptions. We use this to evaluate the sensitivity of total cross-section measurements to parton distribution functions and the charm-quark mass. An outlook is given on the potential of further expanding the use of the ddFONLL method.

hep-ph↗

arXiv2026

Connecting Supersymmetry to Non-Supersymmetric theories: the Gross-Neveu-Yukawa example

We construct a generalized Lagrangian that unifies the Gross-Neveu-Yukawa, Nambu-Jona-Lasinio-Yukawa, and Wess-Zumino models, allowing for arbitrary scalar and fermion flavors in $D$-dimensional regularization. This framework clarifies how emergent supersymmetry arises at critical points and reveals structural connections between these theories. The unified formulation provides additional supersymmetry Ward identities that simplify loop calculations, even for non-supersymmetric models. As an application, we show how this technique can reduce the computational cost of determining anomalous dimensions of twist-two operators.

hep-th↗

arXiv2026

Threshold Top-Quark Pair-Production: Cross Sections and Key Uncertainties

We study theoretical uncertainties in predicting top-quark pair-production near threshold at the LHC using the non-relativistic QCD framework. We include variations in the top-quark mass and width, the strong coupling $α_s$, renormalization and factorization scales, and parton distribution functions, as well as uncertainties from the color-singlet and octet Green's functions that describe quasi-bound toponium formation. These uncertainties are compared with those from standard fixed-order QCD predictions, and implications for ATLAS and CMS analyses are discussed. For the LHC at 13 TeV center-of-mass energy, the integral of the top-quark pair invariant-mass distribution from 340 to 350 GeV is 11.67 pb with ${}^{+1.43}_{-1.47}$ pb uncertainty. The corresponding excess after subtracting the POWHEG-BOX result is 4.15 pb with the same uncertainties.

hep-ph↗

arXiv2026

NNLO QCD corrections to unpolarized and polarized electroweak structure functions in semi-inclusive deep-inelastic scattering

We present results for unpolarized and polarized semi-inclusive deep-inelastic scattering mediated by electroweak gauge bosons at next-to-next-to-leading order (NNLO) in perturbative quantum chromodynamics. The results include all relevant structure functions arising from both neutral current (NC) and charged current (CC) interactions, incorporating contributions from all partonic channels with full flavor dependence. These corrections are crucial for improving the theoretical precision. A detailed numerical analysis of the NNLO corrections demonstrates their phenomenological importance, revealing sizable effects and a significant reduction in residual scale dependence in the kinematic range probed by the future Electron-Ion-Collider. These results will serve as a critical input for future global extractions of parton distributions functions and fragmentation functions.

hep-ph↗

arXiv2026

HyperFORM -- a FORM package for parametric integration with hyperlogarithms

We present an implementation of algorithms for the symbolic integration of hyperlogarithms multiplied by rational functions in the computer algebra system FORM. This implementation encompasses cases where hyperlogarithms have rational letters or a rational argument. It complements the previous implementation, HyperInt, in MAPLE by Erik Panzer, utilizing the advantages of FORM in the efficient handling of large symbolic expressions. Among a wide range of applications, this approach enables the computation of many Feynman integrals.

hep-ph↗

arXiv2026

Operator Renormalization using Emergent Supersymmetries

We develop a mechanism that enables supersymmetric Ward identities to be applied in non-supersymmetric theories. These identities are then used to streamline calculations in our target theories, potentially including phenomenological models. In these proceedings, we illustrate the method through operator renormalization in the Gross-Neveu-Yukawa model, where it leads to a significant optimization and a substantial reduction in computational effort. This serves as a toy example of the procedure that we ultimately aim to apply to Quantum Chromodynamics.

hep-th↗

arXiv2026

Dimensional Reduction is Supersymmetric at Three Loops

We resolve the long-standing claim that regularisation by dimensional reduction (DR) fails to preserve supersymmetry in Super Yang-Mills (SYM) theories at three loops. Earlier results reported a mismatch between the Yukawa and ghost-gluon $β$ functions in $\mathcal{N}=2$ SYM, suggesting a breakdown of supersymmertry. We show that this discrepancy does not originate from DR itself but from subtleties in the treatment of the Clifford algebra. A corrected three-loop calculation restores full supersymmetric behaviour, and we demonstrate that the same issue would first affect $\mathcal{N}=4$ SYM only at five loops, consistent with existing four-loop results. Our findings confirm that DR preserves supersymmetry for $\mathcal{N}=1, 2$ and $4$ SYM through the loop orders examined.

hep-th↗

arXiv2026

Resummation of small-spin singularities in anomalous dimensions of twist-two operators

Anomalous dimensions of leading-twist operators in QCD play an important role in precision predictions for high-energy processes, since they govern the scale evolution of parton distributions. Their analytic structure as a function of spin is particularly important due to the complexity of higher-loop computations. In these proceedings, we discuss the resummation of the certain type of such singularities that share common features with those appearing in the quark flavor-nonsinglet sector of QCD. Our main focus is on the interplay between Gross-Neveu-Yukawa model in $ε$ expansion and Gross-Neveu in $1/N$ expansion. Such resummation allows one to predict the higher-loop singular behavior and reveals connections with the conformal Regge theory and recent studies of detector operators in QCD and various conformal field theories.

hep-th↗

arXiv2026

Heavy-quark production in deep-inelastic scattering -- Mellin moments of structure functions

We compute Mellin moments of the heavy-quark structure functions in deep-inelastic scattering at next-to-leading order in quantum chromodynamics, retaining their full dependence on the heavy-quark mass. Using the optical theorem and the operator product expansion, we derive analytic results for fixed Mellin moments $N = 2$ to $22$ of the structure functions $F_2$ and $F_L$. Our results reproduce the known expressions in the relevant asymptotic limits, in particular for virtualities of the exchanged photon $Q^2$ much larger than the heavy-quark mass squared $m^2$, and are in agreement with existing parametrisations of the next-to-leading-order coefficient functions. The computational set-up developed in this work also provides a direct pathway toward extending these calculations to next-to-next-to-leading order.

hep-ph↗

arXiv2026

The inclusive Higgs boson cross-section in gluon-gluon fusion in soft-virtual approximation at fourth order in QCD

We present precise results for the inclusive Higgs boson cross-section in gluon-gluon fusion at the LHC considering state-of-the-art fourth-order results in perturbative QCD arising from the dominant soft and virtual gluon emissions. Utilizing four-loop QCD results for the gluon-form factor, the splitting function and related anomalous dimensions, we study the effects of threshold enhanced soft gluon emissions and estimate their impact on the total cross-section at the fourth order. Our study highlights the role of these higher-order contributions in improving the perturbative convergence and in significantly reducing the renormalization and factorization scale uncertainties. The results provide strong evidence for the perturbative stability and reliability of Higgs boson cross-section predictions at the LHC, thereby reinforcing the robustness of theoretical inputs in precision Higgs phenomenology. We also provide cross-section predictions using a large set of available parton distribution functions and show that, together with the value of the strong coupling $α_s(m_Z)$, they cause the largest residual uncertainty for the Higgs boson cross-section in gluon-gluon fusion.

hep-ph↗

arXiv2025

Soft and Jet functions for SCET at four loops in QCD

Soft-Collinear Effective Theory is a framework for systematically organizing and resumming the logarithmic contributions that occur in high-energy reactions. It provides a factorized description of cross sections in terms of hard, jet, soft, and beam functions. As the latter are universal, they can be obtained from the well-known perturbative results in quantum chromodynamics (QCD) for deep-inelastic scattering, Drell-Yan and Higgs boson productions. Using the recent results ~\cite{Kniehl:2025ttz} on four-loop eikonal $(f^I)$ and collinear anomalous dimensions $(B^I)$ for quarks and gluons, $I=q,g$, as well as perturbative results from previous orders, we present four-loop predictions for the quark and gluon soft and jet functions. They constitute an important component of the $N$-jettiness subtraction method at $\rm{N^4LO}$ accuracy in QCD, which eventually may enable the calculation of fully-differential cross sections at higher orders.

hep-ph↗

arXiv2025

Physics Briefing Book: Input for the 2026 update of the European Strategy for Particle Physics

The European Strategy for Particle Physics (ESPP) reflects the vision and presents concrete plans of the European particle physics community for advancing human knowledge in fundamental physics. The ESPP is updated every five-to-six years through a community-driven process. It commences with the submission of specific proposals and other input from the community at large, outlining projects envisioned for the near-, mid-, and long-term future. All submitted contributions are evaluated by the Physics Preparatory Group (PPG), and a preliminary analysis is presented at a Symposium meant to foster a broad community discussion on the scientific value and feasibility of the various ideas proposed. The outcomes of the analysis and the deliberations at the Symposium are synthesized in the current Briefing Book, which provides an important input in the deliberations of the Strategy recommendations by the European Strategy Group (ESG).

hep-ex↗

arXiv2025

NNLO QCD corrections to unpolarized and polarized SIDIS

The semi-inclusive deep-inelastic scattering (SIDIS) process requires the presence of an identified hadron H$'$ in the final state, which arises from the scattering of a lepton with an initial hadron P. By employing factorization in quantum chromodynamics (QCD), SIDIS provides essential knowledge on the hadron structure, enabling the exploration of parton distribution functions (PDFs) and fragmentation functions (FFs). The coefficient functions for SIDIS can be calculated in perturbative QCD and are currently known to the next-to-next-to-leading order (NNLO) for the cases, where the incoming lepton and the hadron P are either both polarized or unpolarized. We present a detailed description of these NNLO computations, including a thorough discussion of all the partonic channels, the calculation of the amplitudes and master integrals for the phase-space integration as well as the renormalization of ultraviolet divergences and mass factorization of infrared divergences in dimensional regularization through NNLO. We provide an extensive phenomenological analysis of the effects of NNLO corrections on SIDIS cross sections for different PDFs and FFs and various kinematics, including those of the future Electron-Ion Collider (EIC). We find that these corrections are not only significant but also crucial for reducing the dependence on the renormalization and factorization scales $μ_R$ and $μ_F$ to obtain stable predictions.

hep-ph↗

arXiv2025

Next-to-Next-to-Leading Order QCD Corrections to Polarized Semi-Inclusive Deep-Inelastic Scattering

Polarized semi-inclusive deep-inelastic scattering (SIDIS) is a key process in the quest for a resolution of the proton spin puzzle. We present the complete results for the polarized SIDIS process at next-to-next-to-leading order (NNLO) in perturbative quantum chromodynamics. Our analytical results include all partonic channels for the scattering of polarized leptons off hadrons and a spin-averaged hadron identified in the final state. A numerical analysis of the NNLO corrections illustrates their significance and the reduced residual scale dependence in the kinematic range probed by the future Electron-Ion-Collider EIC.

hep-ph↗

arXiv2025

NNLO QCD$\otimes$QED corrections to unpolarized and polarized SIDIS

We present the first computation of next-to-next-to-leading order (NNLO) pure QED and mixed QCD$\otimes$QED corrections to unpolarized and polarized semi-inclusive deep-inelastic scattering (SIDIS). Building on our previous NNLO QCD results, these corrections are crucial for improving the theoretical precision. The coefficient functions are derived within the QCD factorization framework using dimensional regularization, with consistent renormalization and mass factorization. A detailed phenomenological analysis shows that the NNLO QED and QCD$\otimes$QED terms enhance perturbative stability and reduce scale uncertainties. These results are essential for high-precision SIDIS predictions at future facilities such as the Electron-Ion Collider.

hep-ph↗