Flavour Physics in the Soft Wall Model

TL;DR

This paper extends flavour physics models from the Randall-Sundrum framework to the soft wall model, analyzing fermion mass hierarchies, gauge propagators, and flavor-changing neutral currents with notable differences and reductions in certain observables.

Contribution

It introduces a soft wall model extension for flavour physics, highlighting differences in fermion mass scaling, a minimum fermion mass, and reduced FCNC contributions compared to the RS model.

Findings

Fermion masses scale less steeply in the soft wall model.

A minimum fermion mass exists for UV-localized fermions.

FCNC contributions are significantly reduced due to more universal gauge-fermion couplings.

Abstract

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.