Revisiting neutrino masses from Planck scale operators

Planck scale lepton number violation is an interesting and natural possibility to explain nonzero neutrino masses. We consider such operators in the context of Randall-Sundrum (RS1) scenarios. Implementation of this scenario with a single Higgs localized on the IR brane (standard RS1) is not phenomenologically viable as they lead to inconsistencies in the charged lepton mass fits. In this paper we propose a setup with two Higgs doublets. We present a detailed numerical analysis of the fits to fermion masses and mixing angles. This model solves the issues regarding the fermion mass fits but solutions with consistent electroweak symmetry breaking are highly fine-tuned. A simple resolution is to consider supersymmetry in the bulk and a detailed discussion of which is provided. Constraints from flavor are found to be strong and minimal flavor violation (MFV) is imposed to alleviate them.

Figure 1

The four different configurations which depict the localization of the zero mode of the Higgs doublet in the bulk.

Figure 2

Green region depicts total available parameter space of $c_E$ which fit charged lepton masses for configuration A. The black points represent the available parameter space after the constraints from tree level processes ($l_i\to l_j{l}_k{l}_k$) are imposed for $M_{KK}=2\mathrm{TeV}$.

Figure 3

The figure shows the contribution to process $j\to i\gamma$ due to exchange of neutral scalar mass eigenstates ($h,H,A$) on the left and charged Higgs on the right.

Figure 4

The figure shows the overlap between two fermion KK fields and the vev in the mass insertion approximation.

Figure 5

The figure shows the overlap ($Y_d^{011}$) between a zero mode fermion with the first KK state of $L$ and $H_d$. $c_L=0.86$ is chosen for the first KK state of $L$.

Figure 6

The figure shows the coupling $Y_d^{010}$ between a zero mode lepton, KK fermion and scalar mass eigenstate for two specific values of the brane mass parameter $b$. The left panel corresponds to the case where the Higgs field $H_a$ is localized near the IR brane $b>1$ while the right panel corresponds to the case where it is localized towards the UV brane $b<1$.

Figure 7

The dominant contribution to $l_j\to l_i+\gamma$ decay due to exchange of ${\varphi }^{+(n)}$. The dot denotes mass insertion. The localization of the first two generation charged singlets close to the IR brane ($c<0.5$) results in $\mathcal{O}(1)$ overlap with the KK states as shown in Fig. 5.

Figure 8

Parameter space of bulk masses for configuration A. The graphs in the upper row show the parameter space for the bulk masses for doublets ($c_{L_i}$) while the lower row shows the corresponding parameter space for the charged singlets $c_{E_i}$. All points satisfy $0<{\chi }^2<10$.

Figure 9

Parameter space of bulk masses for configuration B.

Figure 10

Parameter space of bulk masses for configuration C.

Figure 11

Parameter space of bulk masses for configuration D.

Figure 12

The overlap integral $H^{0001}$ as a function of $b$ parameter of the scalar field.