Flavor-violating charged lepton decays in the little Randall-Sundrum model

The little Randall-Sundrum (little RS) model receives significantly stronger constraints from the flavor observables in comparison to the Randall-Sundrum (RS) model. In this paper, we analyze the effect of the electroweak sector in little RS on flavor-changing decays of charged leptons. We compare the predictions of the model with the current limits on the flavor-violating branching ratios of $\mu \to eee$, $\tau \to eee$, $\tau \to \mu \mu \mu$, $\tau \to \mu ee$, $\tau \to e\mu \mu$, $\mu \to e\gamma$, and $\mu Ti\to eTi$, and we show that the dominant constraint arises from the $\mu Ti\to eTi$ process which strongly limits the KK-1 gauge boson mass ($M_{KK}$) to be $\gtrsim 30.7\mathrm{TeV}$. We then derive and show that generalizing the electroweak gauge sector to include the brane localized kinetic term relaxes this constraint to $\gtrsim 12\mathrm{TeV}$. Toward the conclusion, we comment on the possibility that the large flavor-violating currents can be mitigated by relaxing the assumption regarding the unnatural thinness and rigidity of the UV brane and discuss the possibility of suppression of these currents in the presence of fat fluctuating branes.

Figure 1

The diagram that generates the process $\mu \to e\gamma$.

Figure 2

(a) The coupling of KK-$1Z$ boson, $|g_1/g_0|$, with leptons having bulk mass parameters $c=0.8$ (red solid line) and $c=0.7$ (black dotted line) as a function of $k{l}_{\mathrm{IR}}$ (assuming $k{l}_{\mathrm{UV}}=0$). (b) The coupling of KK-$1Z$ boson, $|g_1/g_0|$,with fermions having bulk mass parameters $c=0.8$ (red solid line) and $c=0.7$ (black dotted line) as a function of $k{l}_{\mathrm{UV}}$ (assuming $k{l}_{\mathrm{IR}}=0$).

Figure 3

Probability distribution function satisfying (a) the experimental branching ratio for the process $\mu \to eee$ with $k{l}_{\mathrm{IR}}=5,k{l}_{\mathrm{UV}}=-5$ (black solid line) and $k{l}_{\mathrm{UV}}=0,k{l}_{\mathrm{IR}}=0$ (red dashed line) and (b) the experimental $\mu Ti\to eTi$ conversion rate $k{l}_{\mathrm{IR}}=5,k{l}_{\mathrm{UV}}=-5$ (black solid line) and $k{l}_{\mathrm{UV}}=0,k{l}_{\mathrm{IR}}=0$ (red dashed line).

Figure 4

Probability distribution function satisfying (a) constraints on the branching ratio of $\mu \to eee$ with a fat brane of size ratio 0.2 (black solid line) and 0.1 (blue dot-dashed line) and a thin brane (red dashed line) and (b) constraints on the $\mu -e$ conversion with a fat brane of size ratio 0.2 (black solid line) and 0.1 (blue dot-dashed line) and a thin brane (red dashed line).