## Final Report Summary - LATTICE FLAVOUR QCD (Flavour physics from lattice QCD at the physical point)

The project "Lattice Flavour QCD" aimed at obtaining quantities relevant for the phenomenology of Quantum Chromodynamics (QCD) from simulating this theory on a lattice. QCD is the theory of the strong interactions between elementary particles and is, along with the electro-weak interactions, a component of the Standard Model of Particle Physics. Due to its nature, QCD interactions at low energies have to be studied non-perturbatively, which can be done by numerical simulations of QCD. From such simulations properties like masses, decay rates etc. of bound states of elementary particles, e.g. mesons or baryons, can be computed, which are directly accessible in experiments like the LHC at CERN. An important aspect of such lattice simulations of QCD is that the obtained results can provide valuable input for hadronic observables in phenomenological models like chiral effective models.

In this project we aimed at calculations for form factors and decay constants to extract certain elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix from experimental measurements. The CKM matrix elements are a further ingredient of the Standard Model, describing the mixing between the eigenstates of the electro-weak and strong theory. By testing for unitarity violations of the CKM-matrix, one might be able to identify possible extensions of the Standard Model or rule them out. One approach was to calculate the kaon semi-leptonic form factor from lattice QCD simulations. In another approach we examined the ratio of the kaon and pion decay constants, which allows to extract the ratio of CKM elements |V_us/V_ud| from the experimentally measured decay rates. A publication concerning results from the latter approach is under preparation. In a second part of this research project, we determined low-energy constants of Chiral Perturbation Theory (ChPT) from lattice simulations. ChPT is an effective field theory for low energies, resulting from an expansion in pion masses and momenta. Since in lattice simulations - in contrast to experiments - one can within a certain range freely vary the masses of the simulated quarks, an ideal testbed for the predictions of ChPT is provided by such simulations. Eventually, they allow to determine the parameters of ChPT, the low-energy constants, from a first-principle approach. Results have been published together with collaborators in S. Borsanyi et al., Phys. Rev. D88 (2013) 014513 and in several conference proceedings.

In this project we aimed at calculations for form factors and decay constants to extract certain elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix from experimental measurements. The CKM matrix elements are a further ingredient of the Standard Model, describing the mixing between the eigenstates of the electro-weak and strong theory. By testing for unitarity violations of the CKM-matrix, one might be able to identify possible extensions of the Standard Model or rule them out. One approach was to calculate the kaon semi-leptonic form factor from lattice QCD simulations. In another approach we examined the ratio of the kaon and pion decay constants, which allows to extract the ratio of CKM elements |V_us/V_ud| from the experimentally measured decay rates. A publication concerning results from the latter approach is under preparation. In a second part of this research project, we determined low-energy constants of Chiral Perturbation Theory (ChPT) from lattice simulations. ChPT is an effective field theory for low energies, resulting from an expansion in pion masses and momenta. Since in lattice simulations - in contrast to experiments - one can within a certain range freely vary the masses of the simulated quarks, an ideal testbed for the predictions of ChPT is provided by such simulations. Eventually, they allow to determine the parameters of ChPT, the low-energy constants, from a first-principle approach. Results have been published together with collaborators in S. Borsanyi et al., Phys. Rev. D88 (2013) 014513 and in several conference proceedings.