Alumni-Preis 2024

Betreuer: Prof. Dr. Stefan Dittmaier

Abstract of thesis (english):

As far as we know, there are four fundamental forces of nature: gravitational, electromagnetic, strong, and weak. Rooted in the principles of quantum field theory (QFT), the Standard Model of particle physics (SM) describes the elementary particles and their behavior under the fundamental forces, except for the gravitational force. Since the mid-20th century, numerous experiments conducted in laboratories worldwide have tested the predictions of the SM by performing high-accuracy measurements. These experiments have consistently yielded strong evidence to support the validity of the SM.

Since the discovery of the electron at the end of 19th century, many more elementary particles have been found. The last missing particle described by the SM, the Higgs boson, was finally discovered in 2012. Despite the success of the SM, there are some phenomena that cannot be explained within this model. For instance, it offers no clues about the origin of dark matter or dark energy. Moreover, it does not shed light upon the matter-antimatter asymmetry in the universe or the mechanism that gives mass to neutrinos. Additionally, almost 12 years after the discovery of the Higgs boson, physicists have yet to corroborate if all the couplings of the found Higgs boson align with the values expected from the SM Higgs boson or if it is part of a more comprehensive Higgs sector.

The third and subsequent runs of the LHC will significantly increase the statistics for Higgs boson processes. This will further improve the accuracy of important quantities, such as the coupling of the Higgs boson to the gauge bosons and the third generation of fermions. Moreover, the forthcoming measurements will allow us to study the couplings of the Higgs boson to other generations of fermions and to itself. These measurements are essential to determine the exact structure of the Higgs sector and might provide additional evidence leading to a more complete theory. To match the accuracy of these measurements and improve the corresponding predictions within the SM, it is imperative to derive higher-order corrections for the Higgs-boson decays. The calculation of higher-order corrections to the H → bb decay width, which is the dominant decay channel of the SM Higgs boson, contributes to improving the 1 precision of the total Higgs-boson decay width and, consequently, the precision of all other branching ratios.

The main objectives of this thesis were to compute the next-to-leading-order (NLO) Quantum Chromodynamics (QCD) and Electroweak (EW) corrections to the H → bb decay width in the on-shell renormalization scheme with massive bottom quarks, and the mixed nextto- next-to-leading order (NNLO) QCD×EW correction of order O(Nfαsα) in the on-shell scheme, where Nf stands for the number of fermion flavors. Additionally, the NLO corrections were converted from the on-shell to the modified minimal-subtraction (MS) scheme by applying a reparametrization in terms of a running Yukawa coupling based on the MS mass of the bottom quark.

For comparison purposes, the phase-space integration of the real NLO corrections in the OS scheme was evaluated using both the dipole subtraction method and, alternatively, the slicing method. The relative errors between the NLO corrections computed in this thesis and those obtained from the literature are below 0,0004% for the dipole subtraction method and below 0,09% for the slicing method. Furthermore, the Higgs tadpole contributions to the NLO corrections in the MS scheme were treated within three different tadpole schemes: the Gauge-Invariant Vacuum expectation value Scheme (GIVS), the Parameter Renormalized Tadpole Scheme (PRTS), and the Fleischer–Jegerlehner Tadpole Scheme (FJTS).

The differences between the NLO corrections obtained within these three tadpole schemes were thoroughly discussed, and the results in the PRTS were compared with those reported in the literature under the assumption of massless bottom quarks. The NNLO correction of O(Nfαsα) involves Feynman diagrams at order O(αsα) containing only subdiagrams with closed fermion loops and gluon exchange or radiation. It was found that this correction depends on the NLO QCD correction and the insertions of the one-loop and two-loop renormalization constants in the Hbb vertex at O(Nfα) and O(Nfαsα). Therefore, the renormalization constants for this correction were evaluated using the one-loop and two-loop self-energies of the gauge and Higgs bosons at O(Nfα) and O(Nfαsα), respectively. The NNLO correction to the decay width computed in this thesis is at the per-mille level.