Huber, Tobias
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Publication Feynman integral reduction using Gröbner bases(2023); ; ; ; Piclum, JanWe investigate the reduction of Feynman integrals to master integrals using Gröbner bases in a rational double-shift algebra Y in which the integration-by-parts (IBP) relations form a left ideal. The problem of reducing a given family of integrals to master integrals can then be solved once and for all by computing the Gröbner basis of the left ideal formed by the IBP relations. We demonstrate this explicitly for several examples. We introduce so-called first-order normal-form IBP relations which we obtain by reducing the shift operators in Y modulo the Gröbner basis of the left ideal of IBP relations. For more complicated cases, where the Gröbner basis is computationally expensive, we develop an ansatz based on linear algebra over a function field to obtain the normal-form IBP relations.Source Type:Article1 - Some of the metrics are blocked by yourconsent settings
Publication Access status: Open Access , Higher-order corrections in perturbative quantum field theory : concepts, techniques, and applications : Habilitationsschrift(2016)The present thesis consists of three parts and accumulates a total of twelve scientific articles. The first part contains work that is related to the quark flavour sector of the Standard Model of particle physics. It contains papers from two sub-areas of this field of research: rare and radiative decays of B mesons, as well as non-leptonic decays of B mesons. Representatives of the former type are inclusive transitions of a bottom quark into a strange quark. These processes typically have tiny branching ratios and are therefore sensitive to contributions from particles beyond the Standard Model. Precise predictions from theoretical physics are required and are obtained by computing and including higher-order corrections (so-called loop corrections) in the perturbative expansion of the underlying quantum field theory, most prominently quantum chromodynamics (QCD) and quantum electrodynamics (QED). We evaluate loop corrections to two particular bottom-to-strange decays and provide updated theory predictions to many physical observables. Non-leptonic decays of B mesons on the other hand are of particular interest because they are sensitive to the phenomenon of CP violation. After including higher-order QCD corrections we give predictions for direct CP asymmetries to numerous decay channels in the framework of QCD factorisation. The second part deals with higher-order corrections in perturbative (QCD) to two particular quantities which have numerous applications in collider physics, namely the quark and gluon form factors. These form factors are the simplest objects containing infrared divergences at higher orders in massless quantum field theory, and therefore are of particular interest in many respects. They appear, for instance, as virtual higher-order corrections in coefficient functions for the inclusive Drell-Yan process, in deep-inelastic scattering, and in the inclusive Higgs production cross section. The quark and gluon form factors are evaluated analytically to three-loop accuracy in QCD. All terms to perform renormalisation at the four-loop level are also provided. Finally, the third part of the thesis is devoted to multi-loop calculations in supersymmetric gauge theories, in particular N=4 super Yang-Mills (SYM) theory. The quantities that we consider here are the Sudakov form factor and the angle-dependent cusp anomalous dimension. The Sudakov form factor is constructed to three-loop order from unitarity cuts, and assumes a particularly simple form if a suitable integral basis (called homogeneous basis) is chosen. Moreover, an interesting connection to the QCD quark and gluon form factors (see second part of the thesis) is revealed, which is called the leading transcendentality principle. The angle-dependent cusp anomalous dimension is first investigated in a particular limit, the scaling limit, in which ladder diagrams dominate. We give an algorithm to compute the solution in this limit at any loop order, and give explicit results to six loops. Next, we compute the complete planar (i.e. leading in colour) contribution to the angle-dependent cusp anomalous dimension at four loops in N=4 SYM theory, and the non-planar (sub-leading in colour) contribution in the aforementioned scaling limit.Source Type:Habilitation580 202 - Some of the metrics are blocked by yourconsent settings
Publication Inclusive $$\overline{B}\to {X}_s{\ell}^{+}{\ell}^{-}$$ at the LHC: theory predictions and new-physics reach(2024); 2
