Lepton Flavour Violating tau and mu decays induced by scalar leptoquark

We show that the scalar leptoquark Yukawa couplings generate a significant lepton flavour violation. We compute the light scalar leptoquark contributions to the branching ratios (Br) of the lepton flavour violating (LFV) decays $\ell \to \ell_i \ell_j \bar{\ell}_j$ and $\ell \rightarrow \ell^{\prime} \gamma$ with (i,j = e,$\mu$). We discuss the role of the relevant input parameters to these decay rates which are the Yukawa couplings ($h_{a\ell}$) with ($a=u,c,t$), the light scalar mass $M_{S_{1}}$ and the mixing angle $\sin2\theta_{LQ}$. We investigate the experimental limits from $(g-2)_\mu$, $\mu-e$ conversion and $\pi \to e \nu_e, \mu \nu_\mu$ to get constraint on the input parameter space. We predict that the upper limits on the branching ratios of $\tau \to \ell_i \ell_j \bar{\ell}_j$ can reach the experimental current limits. We also show that it is possible to accommodate both $\tau \to \ell_i \ell_j \bar{\ell}_j$ and $\tau \to \ell\gamma$ branching ratios for certain choices of LQ parameters.