The matrix elements of the electro-weak mixing matrix, the Cabibbo-Kobayashi-Maskawa matrix, are of importance to many experimental and phenomenological applications in flavour physics. We will address the particular matrix element V(us), which can be extracted from experimental measurements once the kaon semi-leptonic form factors for the K(l3) decay is known. Therefore, we will provide quantitative results for that form factor using numerical simulations of Quantum Chromodynamics on the lattice, i.e. lattice QCD.
The hadronic matrix element for the K to pi decay will be measured on gauge configurations produced by the QCDSF collaboration. Those lattice QCD simulations are performed with 2 and 2+1 quark flavours of various masses, where the light quark masses eventually will approach the physical point realized in Nature. The non-perturbative clover improved fermion action is used to simulate the dynamical quark effects. Results for the kaon semi-leptonic form factor at different simulated quark masses will be compared with predictions from chiral perturbation theory.
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