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

We consider a chirally invariant lattice Higgs-Yukawa model based on the Neuberger overlap operator. As a first step towards the eventual determination of Higgs mass bounds we study the phase diagram of the model analytically in the large Nf-limit. We present an expression for the effective potential at tree-level in the regime of small Yukawa and quartic coupling constants and determine the order of the phase transitions. In the case of strong Yukawa couplings the model effectively becomes an O(4)-symmetric non-linear sigma-model for all values of the quartic coupling constant. This leads to the existence of a symmetric phase also in the regime of large values of the Yukawa coupling constant. On finite and small lattices, however, strong finite volume effects prevent the expectation value of the Higgs field from vanishing thus obscuring the existence of the symmetric phase at strong Yukawa couplings.