Lepton Flavour Violating Decays tau to lll and mu to e gamma in the Higgs Triplet Model

Singly and doubly charged Higgs bosons in the Higgs Triplet Model mediate the lepton flavour violating (LFV) decays tau to \bar{l}ll and mu to e gamma. The LFV decay rates are proportional to products of two triplet Yukawa couplings (h_{ij}) which can be expressed in terms of the parameters of the neutrino mass matrix and an unknown triplet vacuum expectation value. We determine the parameter space of the neutrino mass matrix in which a signal for tau to \bar{l}ll and/or mu to e gamma is possible at ongoing and planned experiments. The conditions for respecting the stringent upper limit for mu to eee are studied in detail, with emphasis given to the possibility of |h_{ee}|\simeq 0 which can only be realized if Majorana phases are present.