According to our current understanding of nature, there are four fundamental forces: gravitation, electro-magnetism, weak and strong force. The Standard Model (SM) of elementary particle physics provides a very successfully description of electro-magnetism, weak, and strong interactions. It contains elementary particles (leptons and quarks) and the force carriers (W/Z boson, photons, and gluons) as well as the 2012 discovered Higgs particle, which plays a key role in the generation of mass. The strong interactions are responsible for confining quarks into bound states either formed of quark-antiquark pairs (mesons) or three quark bound states (baryons). The theory of the strong interactions is named quantum chromodynamics (QCD) and is, unlike the electro-magnetism or the weak force, of nonperturbative nature. Thus to calculate strong interactions contributing to SM processes special concepts, like lattice field theory simulations, have to be used.
Out of the six known quarks, the b-quarks play a special role: due to their large mass of 4.18 GeV [PDG] they allow to explore processes at otherwise not accessible energies and couple more strongly to the Higgs boson than the lighter quarks. Of particular interest are weak decays of b-quarks to another lighter quark where in addition a pair of leptons (electron, muon, tau or neutrino) is emitted. If the b-quark is bound as a quark-antiquark pair, the particle is named B-meson and such decays are classified as semileptonic. Lately, such semileptonic B decays have received much attention because several experiments (BaBar, Belle, and LHCb) see indications for violations of lepton flavor universality i.e. results exhibit an unexpected dependence whether the lepton is e.g. an electron or a tau. When combined these results amount to the strongest indications of new physics seen so far. However, improvements of the SM predictions are highly desirable which include predictions for so called form factors based on lattice field theory calculations. These form factors parametrize contributions from the strong force and the calculation faces the challenge to simulate b-quarks carrying a mass larger than the lattice cut-off currently possible to simulate.
The emphasis of this project is to improve simulations involving such heavy quarks and calculate quantities relevant to the experimental research program. First we explored using so called domain-wall fermions for simulations of heavy quarks and found them suitable for quark masses in the range of c-quarks (1.28 GeV [PDG]). With a modification (link smearing), up to half the mass of b-quarks can be simulated and the results extrapolated to the physical b-quark mass. In addition concepts to nonperturbatively renormalize heavy-light operators have been investigated. While such extrapolations are promising to determine simple quantities (decay constants, neutral meson mixing parameters), the application to a form factor calculations is more difficult. To explore improvements for the most timely form factor calculations involving the decay of a b-quark to a c-quark, we therefore chose to study B_(s) -> D_(s)^(*) l nu semileptonic decays using a different, effective action to simulate b-quarks at their physical mass but use the newly established concept of heavy domain-wall fermions to simulate c-quarks. We have completed the massive scale numerical simulations and implemented all parts of the analysis required for the different projects. Preliminary results have been presented at workshops and conferences and work is in progress to prepare a manuscript for submission to a peer-reviewed journal.
