We study a chirally invariant Higgs-Yukawa model regulated on a space-time lattice. We calculate Higgs boson resonance parameters and mass bounds for various values of the mass of the degenerate fermion doublet. Also, first results on the phase transition temperature are presented. In general, this model may be relevant for BSM scenarios with a heavy fourth generation of quarks.
We discuss the non-thermal phase structure of a chirally invariant Higgs-Yukawa model on the lattice in the presence of a higher dimensional $Φ^6$-term. For the exploration of the phase diagram we use analytical, lattice perturbative calculations of the constraint effectice potential as well as numerical simulations. We also present first results of the effects of the $Φ^6$-term on the lower Higgs boson mass bounds.
We establish the cutoff-dependent upper Higgs boson mass bound by means of direct lattice computations in the framework of a chirally invariant lattice Higgs-Yukawa model emulating the same chiral Yukawa coupling structure as in the Higgs-fermion sector of the Standard Model. As expected from the triviality picture of the Higgs sector, we observe the upper mass bound to decrease with rising cutoff parameter $Λ$. Moreover, the strength of the fermionic contribution to the upper mass bound is explored by comparing to the corresponding analysis in the pure $Φ^4$-theory.
Non-perturbative numerical lattice studies of the Higgs-Yukawa sector of the standard model with exact chiral symmetry are reviewed. In particular, we discuss bounds on the Higgs boson mass at the standard model top quark mass, and in the presence of heavy fermions. We present a comprehensive study of the phase structure of the theory at weak and very strong values of the Yukawa coupling as well as at non-zero temperature.
We present new results of our ongoing project on the investigation of the phase structure of the Higgs-Yukawa model at small and large bare Yukawa couplings. The critical exponents of the second order bulk phase transitions of this model are determined from finite-size analyses and compared to the pure O(4)-model to test for triviality and the possibility of having a non-Gaussian fixed point. In addition, we will present a first study of Higgs boson masses and fermion correlation functions.
We present new data on our ongoing project on the investigation of the phase structure of the Higgs-Yukawa model at large bare Yukawa couplings. The data presented last year are extended in terms of statistics, the number of bare Yukawa couplings at existing, and new larger volumes. In addition, this study is extended by a finite temperature project at the physical top quark mass m_t =175 GeV and a hypothetical fourth generation top quark with a mass of m_t' =700 GeV .
Motivated by the advent of the Large Hadron Collider the aim of the present work is the non-perturbative determination of the cutoff-dependent upper and lower mass bounds of the Standard Model Higgs boson based on first principle calculations, in particular not relying on additional information such as the triviality property of the Higgs-Yukawa sector or indirect arguments like vacuum stability considerations. For that purpose the lattice approach is employed to allow for a non-perturbative investigation of a chirally invariant lattice Higgs-Yukawa model, serving here as a reasonable simplifi…
In this article, we present an ongoing lattice study of the Higgs-Yukawa model, in the regime of strong-Yukawa coupling, using overlap fermions. We investigated the phase structure in this regime by computing the Higgs vacuum expectation value, and by exploring the finite-size scaling behaviour of the susceptibility corresponding to the magnetisation. Our preliminary results indicate the existence of a second-order phase transition when the Yukawa coupling becomes large enough, at which the Higgs vacuum expectation value vanishes and the susceptibility diverges.
Composite Higgs models must exhibit very different dynamics from quantum chromodynamics (QCD) regardless whether they describe the Higgs boson as a dilatonlike state or a pseudo-Nambu-Goldstone boson. Large separation of scales and large anomalous dimensions are frequently desired by phenomenological models. Mass-split systems are well-suited for composite Higgs models because they are governed by a conformal fixed point in the ultraviolet but are chirally broken in the infrared. In this work we use lattice field theory calculations with domain wall fermions to investigate a system with four l…
The Higgs boson is a central part of the electroweak theory and is crucial to generate masses for quarks, leptons and the weak gauge bosons. We use a 4-dimensional Euclidean lattice formulation of the Higgs-Yukawa sector of the electroweak model to compute physical quantities in the path integral approach which is evaluated by means of Monte Carlo simulations thus allowing for fully non perturbative calculations. The chiral symmetry of the model is incorporated by using the Neuberger overlap Dirac operator. The here considered Higgs-Yukawa model does not involve the weak gauge bosons and furth…
We present results from two projects on lattice calculations for the Higgs-Yukawa model. First we report progress on the search of first-order thermal phase transitions in the presence of a dimension-six operator, with the choices of bare couplings that lead to viable phenomenological predictions. In this project the simulations are performed using overlap fermions to implement the required chiral symmetry. Secondly, our study for applying finite-size scaling techniques near the Gaussian fixed point of the Higgs-Yukawa model is presented. We discuss the analytical formulae for the Higgs Yukawa…
We investigate the impact of a $λ_6 φ^6$ term included in a chirally invariant lattice Higgs-Yukawa model. Such a term could emerge from BSM physics at some larger energy scale. We map out the phase structure of the Higgs-Yukawa model with positive $λ_6$ and negative quartic self coupling of the scalar fields. To this end, we evaluate the constraint effective potential in lattice perturbation theory and also determine the magnetization of the model via numerical simulations which allow us to reach also non-perturbative values of the couplings. As a result, we find a complex phase structure wit…
We study the scaling properties of Higgs-Yukawa models. Using the technique of Finite-Size Scaling, we are able to derive scaling functions that describe the observables of the model in the vicinity of a Gaussian fixed point. A feasibility study of our strategy is performed for the pure scalar theory in the weak-coupling regime. Choosing the on-shell renormalisation scheme gives us an advantage to fit the scaling functions against lattice data with only a small number of fit parameters. These formulae can be used to determine the universality of the observed phase transitions, and thus play an…
We derive finite-size scaling formulae for four-dimensional Higgs-Yukawa models near the Gaussian fixed point. These formulae will play an essential role in future, detailed investigation of such models. In particular, they can be used to determine the nature of the observed phase transitions, and confirm or rule out the possibility of having non-trivial fixed points in the Higgs-Yukawa models. Our scaling formula for Binder's cumulant is tested against lattice simulations carried out at weak couplings, and good agreement is found. As a separate project, we also present preliminary results fro…
We analyse finite-size scaling behaviour of a four-dimensional Higgs-Yukawa model near the Gaussian infrared fixed point. Through improving the mean-field scaling laws by solving one-loop renormalisation group equations, the triviality property of this model can be manifested in the volume-dependence of moments of the scalar-field zero mode. The scaling formulae for the moments are derived in this work with the inclusion of the leading-logarithmic corrections. To test these formulae, we confront them with data from lattice simulations in a simpler model, namely the O(4) pure scalar theory, and…
Using extended mean field theory (EMFT) on the lattice, we study properties of the Higgs-Yukawa model as an approximation of the standard model Higgs sector, and the effect of higher dimension operators. We note that the discussion of vacuum stability is completely modified in the presence of a $ϕ^6$ term, and that the Higgs mass no longer appears fine tuned. We also study the finite temperature transition. Without higher dimension operators the transition is found to be second order (crossover with gauge fields) for the experimental value of the Higgs mass $M_h=125$ GeV. By taking a $ϕ^6$ int…
We study a lattice Higgs-Yukawa model emulating the same Higgs-fermion coupling structure as in the Higgs sector of the electroweak Standard Model, in particular, obeying a Ginsparg-Wilson version of the underlying SU(2) x U(1) symmetry, being a global symmetry here due to the neglection of gauge fields in this model. In this paper we present our results on the cutoff-dependent upper Higgs boson mass bound at several selected values of the cutoff parameter.
We study the functional renormalization group flow of a Higgs-Yukawa toy model mimicking the top-Higgs sector of the standard model. This approach allows for treating arbitrary bare couplings. For the class of standard bare potentials of ϕ^4-type at a given ultraviolet cut-off, we show that a finite infrared Higgs mass range emerges naturally from the renormalization group flow itself. Higgs masses outside the resulting bounds cannot be connected to any conceivable set of bare parameters in this standard-model ϕ^4 class. By contrast, more general bare potentials allow to diminish the lower bou…
We investigate the phase structure of a four dimensional SO(4) invariant lattice Higgs-Yukawa model comprising four reduced staggered fermions interacting with a real scalar field. The fermions belong to the fundamental representation of the symmetry group while the three scalar field components transform in the self-dual representation of SO(4). We explore the phase diagram and find evidence of a continuous transition between a phase where the fermions are massless to one where the fermions acquire mass. This transition is not associated with symmetry breaking and there is no obvious local or…
A non perturbative proof of the mass generation of fermions via the Higgs mechanism is given. This is done by showing exponential decay of the two point fermionic correlation function in a weakly coupled U(1) Higgs-Yukawa theory on a unit lattice in $d=4$. This decay implies that the Higgs boson, the photon and the fermion all have a non zero physical mass and the theory is said to have a mass gap.
