Taming ε K in little Randall-Sundrum models

The Randall Sundrum models receive significant constraints from the neutral kaon system. The $CP$ violating observable ${\ensuremath{\epsilon}}_{K}$, in the Randall Sundrum scenario, requires the lightest $KK$ gluon to be heavier than $\ensuremath{\sim}24\text{ }\text{ }\mathrm{TeV}$. The constraint is even stronger in the little Randall Sundrum (LRS) models, $\ensuremath{\gtrsim}32\text{ }\text{ }\mathrm{TeV}$. The LRS models are motivated for their possible visibility at the LHC. We show that the stringent constraints from $K$ physics can be relaxed in the LRS models, in the presence of the brane localized kinetic terms (BLKT). In particular, for a range of values, a UV BLKT could significantly modify the lightest $KK$ gluon wave function such that the limit can reduces to 5 TeV. We also show that such a relaxation of the constraints can also be achieved by imposing flavor symmetries \`a la minimal flavor protection.