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

Abstract

We consider a chirally invariant lattice Higgs-Yukawa model based on the Neuberger overlap operator D (ov) . As a first step towards the eventual determination of Higgs mass bounds we study the phase diagram of the model analytically in the large N flimit. 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 nonlinear σ-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.

The phase structure of a chirally invariant lattice Higgs-Yukawa model—numerical simulations

“…m > 0 and s > 0. It was found that such a ferrimagnetic phase should exist deeply inside the anti-ferromagnetic phase [25]. In figure 4 we provide evidence for the existence of this ferrimagnetic phase.…”

“…The anticipated structure of the phase diagram can be inferred from our large N f computation in ref. [25]. In that large N f approach the Higgs field and the coupling constants are scaled according to…”

“…In [25] we have studied the phase structure of this chirally invariant Higgs-Yukawa model by means of a large N f computation, where N f denotes the number of fermion generations. We found a complex phase structure that resembles qualitatively the one of earlier lattice Higgs-Yukawa models, see e.g.…”

“…We remark that in the present work, as in ref. [25], we neglect the gauge degrees of freedom and consider the pure scalar-fermion sector of the electroweak standard model.…”

“…[25]. Since we focus here on checking the validity of our earlier analytical investigation of the phase structure, which was determined in the large N f -limit, we will only consider even values for N f , allowing to rewrite the effective action according to…”