Flavour Physics in the Soft Wall Model

We extend the description of flavour that exists in the Randall-Sundrum (RS) model to the soft wall (SW) model in which the IR brane is removed and the Higgs is free to propagate in the bulk. It is demonstrated that, like the RS model, one can generate the hierarchy of fermion masses by localising the fermions at different locations throughout the space. However, there are two significant differences. Firstly the possible fermion masses scale down, from the electroweak scale, less steeply than in the RS model and secondly there now exists a minimum fermion mass for fermions sitting towards the UV brane. With a quadratic Higgs VEV, this minimum mass is about fifteen orders of magnitude lower than the electroweak scale. We derive the gauge propagator and despite the KK masses scaling as $m_n^2\sim n$, it is demonstrated that the coefficients of four fermion operators are not divergent at tree level. FCNC's amongst kaons and leptons are considered and compared to calculations in the RS model, with a brane localised Higgs and equivalent levels of tuning. It is found that since the gauge fermion couplings are slightly more universal and the SM fermions typically sit slightly further towards the UV brane, the contributions to observables such as $\epsilon_K$ and $\Delta m_K$, from the exchange of KK gauge fields, are significantly reduced.