Scalar clockwork and flavor neutrino mass matrix

We study the capability of generating the correct flavor neutrino mass matrix in a scalar clockwork model. First, we assume that the flavor structure is controlled by the Yukawa couplings as in the standard model. In this case, the correct flavor neutrino mass matrix could be obtained by appropriate Yukawa couplings $Y_{{\ell }^{\prime }\ell }$ where ${\ell }^{\prime },\ell =e,\mu ,\tau$. Next, we assume that the Yukawa couplings are extremely democratic: $Y_{{\ell }^{\prime }\ell }=1$. In this case, the model parameters of the scalar clockwork sector, such as the site number of a clockwork gear in a clockwork chain, should have the flavor indices ${\ell }^{\prime }$ and/or $\ell$ to generate the correct flavor neutrino mass matrix. We show some examples of assignments of the flavor indices which can yield the correct flavor neutrino mass matrix.