Lepton Flavour Violation via the K\"ahler Potential in Compactified M-Theory

We use lepton-flavour violating (LFV) processes as a probe of higher-order corrections to the K\"ahler potential in compactified M-theory. We consider a generic K\"ahler potential with higher-order terms coupling visible sector fields to fields in the hidden sector of the compactified theory. Such terms generally give rise to potentially large flavour-violating effects. Unless there are suppressions, the size of the resulting off-diagonal terms in the K\"ahler potential may be at odds with experimental results. The rare decay $\mu \to e \gamma$ and $\mu \to e$ conversion in nuclei probe the size of the potential flavour non-diagonality of the higher-order terms for realistic spectra in the M-theory compactification. We consider a parameterisation of the higher-order corrections in terms of a small parameter $\epsilon$. By analysing various textures for the higher-order corrections, we find current bounds on $\epsilon$ from the LFV processes. The constraint from the neutral kaon mass difference $\Delta m_K$ is currently similar to that from $\mu \to e \gamma$. Measurement or new limits on the process $\mu \to e \gamma$ and, in the future, $\mu \to e$ conversion in Aluminium, will be an effective probe of the form of the higher-order K\"ahler potential terms. For the preferred range of gravitino masses, unless the K\"ahler potential is strikingly flavour-diagonal, improvement in experimental sensitivity of LFV processes should give a non-zero signal.