Lepton flavour violation in the MSSM

We derive new constraints on the quantities δ^ijXY, X,Y = L,R, which parametrise the flavour-off-diagonal terms of the charged slepton mass matrix in the MSSM. Considering mass and anomalous magnetic moment of the electron we obtain the bound |_δ^{1 3} _Lδ_R^{1 3}_R| ≲5 0.1 for tanβ = 50, which involves the poorly constrained element β_R^{1 3}_R. We improve the predictions for the decays ι→ μγ ι → eγ and μ → eγ by including two-loop corrections which are enhanced if tan β is large. The finite renormalisation of the PMNS matrix from soft SUSY-breaking terms is derived and applied to the charged-Higgs-lepton vertex. We find that the experimental bound on BR(ι→ eγ) severely limits the size of the MSSM loop correction to the PMNS element U_e3, which is important for the proper interpretation of a future U_e3 measurement. Subsequently we confront our new values for β_ijLL with a GUT analysis. Further, we include the effects of dimension-5 Yukawa terms, which are needed to fix the Yukawa unification of the first two generations. If universal supersymmetry breaking occurs above the GUT scale, we find the flavour structure of the dimension-5 Yukawa couplings tightly constrained by μ → eγ.