We present results for the $I=2$ $pipi$ scattering length using $N_f=2+1+1$ twisted mass lattice QCD for three values of the lattice spacing and a range of pion mass values. Due to the use of Laplacian Heaviside smearing our statistical errors are re
duced compared to previous lattice studies. A detailed investigation of systematic effects such as discretisation effects, volume effects, and pollution of excited and thermal states is performed. After extrapolation to the physical point using chiral perturbation theory at NLO we obtain $M_pi a_0=-0.0442(2)_mathrm{stat}(^{+4}_{-0})_mathrm{sys}$.
Pi-Pi scattering is investigated for the first time for Nf=2+1+1 dynamical quark flavours using Wilson twisted mass fermions. Luschers finite size method is used to relate energy shifts in finite volume to scattering quantities like the scattering le
ngth in the I=2 channel. The computation is performed at several pion masses and lattice spacings utilising the stochastic LapH method.
We present new results of our ongoing project on the investigation of the phase structure of the Higgs-Yukawa model at small and large bare Yukawa couplings. The critical exponents of the second order bulk phase transitions of this model are determin
ed from finite-size analyses and compared to the pure O(4)-model to test for triviality and the possibility of having a non-Gaussian fixed point. In addition, we will present a first study of Higgs boson masses and fermion correlation functions.
We present new data on our ongoing project on the investigation of the phase structure of the Higgs-Yukawa model at large bare Yukawa couplings. The data presented last year are extended in terms of statistics, the number of bare Yukawa couplings at
existing, and new larger volumes. In addition, this study is extended by a finite temperature project at the physical top quark mass m_t =175 GeV and a hypothetical fourth generation top quark with a mass of m_t =700 GeV .
Form factors of the nucleon have been extracted from experiment with high precision. However, lattice calculations have failed so far to reproduce the observed dependence of form factors on the momentum transfer. We have embarked on a program to thor
oughly investigate systematic effects in lattice calculation of the required three-point correlation functions. Here we focus on the possible contamination from higher excited states and present a method which is designed to suppress them. Its effectiveness is tested for several baryonic matrix elements, different lattice sizes and pion masses.
