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We consider a chirally invariant lattice Higgs-Yukawa model based on theNeuberger overlap operator. As a first step towards the eventual determinationof Higgs mass bounds we study the phase diagram of the model analytically inthe large Nf-limit. We present an expression for the effective potential attree-level in the regime of small Yukawa and quartic coupling constants anddetermine the order of the phase transitions. In the case of strong Yukawacouplings the model effectively becomes an O(4)-symmetric non-linearsigma-model for all values of the quartic coupling constant. This leads to theexistence of a symmetric phase also in the regime of large values of the Yukawacoupling constant. On finite and small lattices, however, strong finite volumeeffects prevent the expectation value of the Higgs field from vanishing thusobscuring the existence of the symmetric phase at strong Yukawa couplings.

The phase structure of a chirally invariant lattice Higgs-Yukawa model for small and for large values of the Yukawa coupling constant