fermion-Higgs Model Research Articles

Δ ρ in an SU(2)×U(1) chiral Yukawa model

We report on a simulation in progress of an SU(2) X U(1) fermion-Higgs model with two *non-degenerate* fermion doublets. The Zaragoza proposal for chiral lattice fermions is used; naive fermions are studied for comparison. The aims of this simulation are a non-perturbative study of the decoupling of species doublers, of triviality bounds on the Higgs and fermion masses and of the phenomenological quantity Delta-rho.

Fermion-Higgs model with strong Wilson-Yukawa coupling in two dimensions

The fermion mass spectrum is studied in the quenched approximation in the strong-coupling vortex phase (VXS) of a globally U(1) L⊗U(1) R symmetric scalar-fermion model in two dimensions. In this phase fermion doublers can be completely removed from the physical spectrum by means of a strong Wilson-Yukawa coupling. The lowest lying fermion spectrum in this phase consists most probably only of a massive Dirac fermion which has charge zero with respect to the U(1) L group. We give evidence that the fermion which is charged with respect to that subgroup is absent in the VXS phase. When the U(1) L gauge fields are turned on, the neutral fermion may couple chirally to the massive vector boson state in the confinement phase. The outcome is very similar to our findings in the strong-coupling symmetric phase (PMS) of fermion-Higgs models with Wilson-Yukawa coupling in four dimensions, with the exception that in four dimensions the neutral fermion does most probably decouple from the bosonic bound states.

Can the couplings in the fermion-Higgs sector of the standard model be strong?

We present results for the renormalized quartic self-coupling λ R and the Yukawa coupling y R in a lattice fermion-Higgs model with two SU(2) L doublets, mostly for large values of the bare couplings. One-component (“reduced”) staggered fermions are used in a numerical simulation with the Hybrid Monte Carlo algorithm. The fermion and Higgs masses and the renormalized scalar field expectation value are computed on L 324 lattices where L ranges from 6 to 16. In the scaling region these quantities are found to have a 1 L 2 dependence, which is used to determine their values in the infinite-volume limit. We then calculate the y R and λ R from their tree-level definitions in terms of the masses and renormalized scalar field expectation value, extrapolated to infinite volume. The scalar field propagators can be described momenta up to the cut-off by one-fermion-loop renormalized perturbation theory and the results for λ R and y R come out to be close to the tree-level unitarity bounds. There are no signs that are in contradiction with the triviality of the Yukawa and quartic self-coupling.

No strong coupling regime in the fermion-Higgs sector of the standard model

We present results for the renormalized quartic self-coupling λ R ̧ and the renormalized Yukawa coupling y R ̧ in a fermion-Higgs model with two SU(2) doublets, indicating that these couplings are not very strong.

Fermion-Higgs model with reduced staggered fermions

We introduce a lattice fermion-Higgs model with one component ‘reduced staggered’ fermions. In order to use the fermion field as efficiently as possible we couple the two staggered flavors to the O(4) Higgs field leading to a model with only one SU(2) doublet in the scaling region. The number of fermions is doubled in a numerical investigation of the model with the hybrid Monte Carlo algorithm. We present results for the phase diagram, particle masses and renormalized couplings on lattices ranging in size from 6 324 to 16 324.

Search for an upper bound of the renormalized Yukawa coupling in a lattice fermion-Higgs model

We study the scaling laws for the fermion mass and the scalar field expectation value in the weak coupling region of the broken phase of a lattice regularized chiral-invariant SU(2) L ⊗ SU(2) R fermion-Higgs model with bare Yukawa coupling y and Wilson-Yukawa coupling w. In particular we concentrate on the region in the vicinity of the line A, which is the line of maximal values of y + 4 w on the critical surface containing the gaussian fixed point. We have not found any indication for the existence of a nontrivial fixed point on that line or anywhere else in the weak coupling region. The renormalized Yukawa coupling y R as a function of the fermionic correlation length appears to be bounded from above. The upper bound obtained from the numerical data at w = 0 is compatible with the perturbative unitarity bound. Furthermore, in the weak coupling region, including the line A, it is not possible to choose w such that the unwanted fermion doublers would be removed from the physical particle pectrum.

The eigenvalue spectra in Z(2) ⊗ Z(2) and SU(2) ⊗ SU(2) fermion-Higgs models

We present an analysis of the eigenvalue spectra of the Dirac operator M and related operators M′ and M†M in an SU(2) ⊗ SU(2) and a Z(2) ⊗ Z(2) fermion-Higgs model in the quenched approximation. We especially study the spectra in the symmetric and broken symmetry phases along the crossover line which was recently discovered in these models in numerical simulations. It turns out that in the symmetric phases of both models zero modes emerge along the crossover line. In the case of the Z(2) model the zero modes follow the crossover line into the broken symmetry phase whereas in the case of the SU(2) model they appear to stop at the phase transition line between the symmetric and the broken phases.

Unquenched investigation of fermion masses in the SU(2) L⊗ SU(2) R Fermion-Higgs model

The fermion masses were studied in the broken phase of the chiral SU(2) L ⊗ SU(2) R model with dynamical fermions. In our work we follow the proposal by Smit and Swift adding a manifestly chiral gauge invariant Wilson-Yukawa term with strength ω to the action of this model in the hope of rendering the unwanted doubler fermions heavy dynamically. In the case of naive fermions ( ω = 0) a strong and weak coupling region were established in the broken phase. The scaling behaviour of the fermion masses and the lines of constant fermion mass were investigated close to the quadruple point A in the broken phase. We show that for large ω doublers can be easily decoupled in the strong coupling region of the broken phase while the physical fermion mass and the electroweak scale can be made arbitrarily small.

The eigenvalue spectra in Z(2)⊗Z(2) and SU(2)⊗SU(2) fermion-Higgs models

We present an analysis of the eigenvalue spectra of the Dirac operator M and related operators M 1 and M †M in an SU(2)⊗SU(2) and in aZ(2)⊗Z(2) fermion-Higgs model. We see different behaviour in different regions of the phase diagram and for local vs hypercubic Yukawa coupling. A Wilson-Yukawa coupling is also studied in the SU(2) model. The troublesome crossover region in the quenched approximation for models with local Yukawa coupling is shown to be associated with the development of zero modes in M. This occurs in the symmetric phase for both SU(2) and Z(2) models, but persists into the broken (ferromagnetic) phase for the Z(2) model. As expected, the zero modes are suppressed, at least on small volumes, when dynamical fermions are included.

Decoupling of doublers and the phase diagram of lattice chiral fermions for strong Wilson-Yukawa coupling

A systematic expansion in 1 d around the mean field saddle point is used to calculate the critical value of the boson hopping parameter in a chiral fermion-Higgs model to two non-leading orders. The expansion is valid for strong Wilson-Yukawa coupling. The fermion propagator is also calculated in the broken phase, and the fermion doublers are seen to decouple as the critical line is approached, while one fermion species remains light.

Decoupling doublers of chiral lattice fermions in a quenched fermion-Higgs model

We study in the quenched approximation the fermion-scalar sector of a lattice version of the standard model in the broken symmetry phase using a Wilson-Yukawa coupling to deal with the fermion doubling. For relatively strong but fixed Wilson-Yukawa coupling the fermion doublers can be easily decoupled as the critical point is approached by giving them masses of the order of the cutoff.