Taming ${\epsilon }_K$ in little Randall-Sundrum models

The Randall Sundrum models receive significant constraints from the neutral kaon system. The $CP$ violating observable ${\epsilon }_K$, in the Randall Sundrum scenario, requires the lightest $KK$ gluon to be heavier than $\sim 24\mathrm{TeV}$. The constraint is even stronger in the little Randall Sundrum (LRS) models, $\gtrsim 32\mathrm{TeV}$. 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 à la minimal flavor protection.

Figure 1

A comparison of coupling of first $KK$ gluon with light fermions as a function of the $c$ values in RS (blue/dotted) and little RS (red/solid).

Figure 2

The observed cross section 95% C.L. upper limit [23] on the $g_1$ signal and the theoretical prediction for the production cross-section times branching ratio of $g_1\to t\overline{t}$ at corresponding masses.

Figure 3

CDF for $M_g$ from ${\epsilon }_K$ (analysis performed from the dominant $|\mathrm{Im}{C}_4^{sd}|$) for RS and LRS model. Dashed lines correspond to the RS and dash-dot to LRS.

Figure 4

(a) The behavior of the first root as function of $l_{\mathrm{IR}}$ and $l_{\mathrm{UV}}$. We have considered four cases: (i) $k{l}_{\mathrm{UV}}=0$ (black dashed), (ii) $k{l}_{\mathrm{IR}}=0$ (blue dot-dashed), (iii) $k{l}_{\mathrm{IR}}=k{l}_{\mathrm{UV}}$ (red solid), and (iv) $k{l}_{\mathrm{IR}}=-k{l}_{\mathrm{UV}}$ (green dotted) (b) The difference in $KK-1$ gluon-gauge couplings, $|\mathrm{\Delta }{g}_1/g_0|$, with fermions with bulk-mass parameters $c=0.8$ and $c=1.2$ as a function of $k{l}_{\mathrm{UV}}$ [assuming $k{l}_{\mathrm{IR}}=0$ (red solid)] and $k{l}_{\mathrm{IR}}$ [assuming $k{l}_{\mathrm{UV}}=0$ (black dashed)].

Figure 5

Cumulative distribution function and probability distribution function satisfying the constraint on $\mathrm{Im}(C_4)$ for three different scenarios: (a) $k{l}_{\mathrm{IR}}=k{l}_{\mathrm{UV}}=0$ (red dash), (b) $k{l}_{\mathrm{UV}}=0,k{l}_{\mathrm{IR}}=-5.0$ (blue dot-dash), and (c) $k{l}_{\mathrm{IR}}=0,k{l}_{\mathrm{UV}}=-5$. (black solid).

Figure 6

Cumulative distribution function (a) and probability distribution function (b) regions satisfying the constraint on $\mathrm{Im}(C_1)$ [for the cases of unbroken U(3) flavor symmetry (red dashed)], and $\mathrm{Im}(C_4)$ [for the cases of unbroken U(2) flavor symmetry (blue dot-dash)] as a function of $M_g$.