Volume 171, number 4 PHYSICS LETTERS B 1 May 1986 LEPTON AND FLAVOR VIOLATION IN SUSY MODELS G.K. LEONTARIS, K. TAMVAKIS and J.D. VERGADOS Physics Department, University of loannina, loannina, Greece Received 13 December 1985 Lepton and flavor violating processes resulting from neutral scalar-lepton mixing are examined in the context of supersymmetric models. Contributions arising at the one-loop level for # --* e~,, # ---, 3e, #p ~ ee as well as for neutrinoless tiff-decay are found to be suppressed for a general class of supersymmetry breaking parameters. 1. Introduction: Lepton number (L) and lepton flavour (F) violating processes have not yet been observed tn nature ,1. Even though lepton and flavour non-conservation is automatically conserved in the standard model [5], there is no satisfactory explanation for the existence of such global symmetries. F and L violating processes could arise in the context of the standard SUe(3 ) X SUL(2 ) X U(1) gauge group or its minimal parity-conserving SUe(3 ) × SUR(2 ) × SUL(2 ) X U(1) extension [6] with a suitably enlarged fermionic or scalar sector. One of the available possibilities is the extension of the fermionic sector by introducing a gauge singlet field N, the well-known right-handed neutrino [7]. An analogous extension of the bosonic sector could in- volve the introduction of flavour mixing isodoublets or couplings to other representations which are compatible with renormalizability and gauge symmetry [8]. In this letter we will examine the implications on L and F con- servation of supersymmetric extensions of the standard model. In the supersymmetric generalizations of the standard model ,2 one writes the Yukawa couplings (for notation see table 1) V = QHU c + LHE e + QHD e. (1.1) These, however, are not the most general trilinear couplings which are consistent with the SU(3) X SU(2) X U(1) gauge symmetry. The following trilinear Yukawa couplings which violate lepton number are also possible QLD + LECL. (1.2) The naive inclusion of these terms into the superpotential (1.1) will lead to disastrous consequences. More precisely, with such terms we have to face L violation ,3 at the level of renormalizable interactions unless we impose sym- metries by hand, to prevent them. The usual symmetries one imposes to avoid problems like those mentioned above, are the so-called R-symmetries [10]. These symmetries unlike the case with the usual global symmetries do not necessarily commute with the supersymmetry generators. Nevertheless, one could imagine special kinds of those symmetries that might allow explicit lepton violating terms which under special combinations of leptons and higgses would lead to L violation [11 ] in accordance with the experimental limits. Other possibilities related either with the spontaneous violation of R-symmetry [ 12], or with other mechanisms [ 13] ,4, of course, could lead to lepton-number violation. ~1 For limits on the branching ratios of the various L and F violating processes see ref. [1 ] for u ~ 3e, R < 2.4 X 10 -11 , ref. [2] for ~ ~ e, R < 1.7 X 10 -12 , ref. [3] for t~- ~ e- conversion, R < 1.6 X 10 -it, and ref. [4] for t~- ~ e ÷, R < 9 X 10 -10. ,2 For a review of supersymmetric models see ref. [9]. ,3 We may also have baryon-number violation if we include the term UCDCD e. Combining this term with the LECL we have fast proton decay [9]. ,4 For a review on L violation in SUSY see ref. [14]. 412 0370-2693/86/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)