Abstract
The forthcoming precision data on lepton flavour violating (LFV) decays require precise and efficient calculations in New Physics models. In this article lepton flavour violating processes within the Minimal Supersymmetric Standard Model (MSSM) are calculated using the method based on the Flavour Expansion Theorem, a recently developed technique performing a purely algebraic mass-insertion expansion of the amplitudes. The expansion in both flavour-violating and flavour-conserving off-diagonal terms of sfermion and supersymmetric fermion mass matrices is considered. In this way the relevant processes are expressed directly in terms of the parameters of the MSSM Lagrangian. We also study the decoupling properties of the amplitudes. The results are compared to the corresponding calculations in the mass eigenbasis (i.e. using the exact diagonalization of the mass matrices). Using these methods, we consider the following processes: ℓ → ℓ′γ, ℓ→3ℓ′, ℓ→2ℓ′ℓ′′, h→ℓℓ′ as well as μ→e conversion in nuclei. In the numerical analysis we update the bounds on the flavour changing parameters of the MSSM and examine the sensitivity to the forthcoming experimental results. We find that flavour violating muon decays provide the most stringent bounds on supersymmetric effects and will continue to do so in the future. Radiative ℓ → ℓ′γ decays and leptonic three-body decays ℓ → 3ℓ′ show an interesting complementarity in eliminating “blind spots” in the parameter space. In our analysis we also include the effects of non-holomorphic A-terms which are important for the study of LFV Higgs decays.
Highlights
The LHC did not observe any particles beyond those of the Standard Model (SM)
In this article lepton flavour violating processes within the Minimal Supersymmetric Standard Model (MSSM) are calculated using the method based on the Flavour Expansion Theorem, a recently developed technique performing a purely algebraic mass-insertion expansion of the amplitudes
A promising approach is the search for processes which are absent — or extremely suppressed — in the SM such as lepton flavour violation (LFV) which is forbidden in the SM in the limit of vanishing neutrino masses
Summary
The LHC did not observe any particles beyond those of the Standard Model (SM). In this article we revisit this subject in the light of the new calculational methods which have been recently developed [31, 32] These methods allow for a systematic expansion of the amplitudes of the LFV processes in terms of mass insertions (MI), i.e. in terms of off-diagonal elements of the mass matrices. We show that a transparent qualitative behaviour of the amplitudes of the LFV processes is obtained by expanding them in the flavour-violating off-diagonal terms in the sfermion mass matrices and in the flavour conserving but chirality violating entries related to the tri-linear A-terms as well as in the off-diagonal terms of the gaugino and higgsino mass matrices This procedure is useful because in the MI approximation we work directly with the parameters of the Lagrangian and can put experimental bounds on them. The expression for the 4-lepton box diagrams and for the MI-expanded expression of the amplitudes are given in the appendices D and E, respectively
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