Christoph Frick

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

Abstract 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 + 4w 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 yR 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.

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

Abstract 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 3 24 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.

Numerical simulation of heavy fermions in an SU(2)L ⊗ SU(2)R symmetric Yukawa model

Abstract An exploratory numerical study of the influence of heavy fermion doublets on the mass of the Higgs boson is performed in the decoupling limit of a chiral SU(2) L ⊗ SU(2) R symmetric Yukawa model with mirror fermions. The behaviour of fermion and boson masses is investigated at infinite bare quartic coupling on 4 3 ·8, 6 3 ·12 and 8 3 ·16 lattices. A first estimate of the upper bound on the renormalized quartic coupling as a function of the renormalized Yukawa coupling is given. On the algorithmic side, several standard fermion matrix inversion methods were tried and tuned for better performance.

Spontaneous symmetry breaking on the lattice generated by Yukawa interaction

We study by numerical simulation a lattice Yukawa model with naive fermions at intermediate values of the Yukawa coupling constant y when the nearest-neighbour coupling κ of the scalar field Φ is very weakly ferromagnetic (κ ≈ 0) or even antiferromagnetic (κ < 0) and the non-vanishing value of 〈Φ〉 is generated by the Yukawa interaction. The renormalized Yukawa coupling yR achieves here its maximal value and this y-region is thus of particular importance for lattice investigations of strong Yukawa interaction. However, here the scalar field propagators have a very complex structure caused by fermion loop corrections and by the proximity of phases with antiferromagnetic properties. We develop methods for analyzing these propagators and for extracting the physical observables. We find that going into the negative κ region, the scalar field renormalization constant becomes small and yR does not see, to exceed the unitarity bound, making the existence of a non-trivial fixed point in the investigated Yukawa model quite unlikely.

Mass spectrum and bounds on the couplings in Yukawa models with mirror-fermions

Abstract The SU(2) L ⊗SU(2) R symmetric Yukawa model with mirror-fermions in the limit where the mirror-fermion is decoupled is studied both analytically and numerically. The bare scalar self-coupling λ is fixed at zero and infinity. The phase structure is explored and the relevant phase transition is found to be consistent with a second order one. The fermionic mass spectrum close to that transition is discussed and a first non-perturbative estimate of the influence of fermions on the upper and lower bounds on the renormalized scalar self-coupling is given. Numerical results are confronted with perturbative predictions.

Chiral phase transition in a lattice fermion-gauge-scalar model with U(1) gauge symmetry☆

Abstract The chiral phase transition induced by a charged scalar field is investigated numerically in a lattice fermion-gauge-scalar model with U(1) gauge symmetry, proposed recently as a model for dynamical fermion mass generation. For very strong gauge coupling the transition is of second order and its scaling properties are very similar to those of the Nambu-Jona-Lasinio model. However, in the vicinity of the tricritical point at somewhat weaker coupling, where the transition changes the order, the scaling behavior is different. Therefore it is worthwhile to investigate the continuum limit of the model at this point.

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

Abstract 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.

Scalar sector of an SU(2)L ⊗ SU(2)R Yukawa model

Abstract At intermediate values of the bare Yukawa coupling y, where the SSB is caused by the Yukawa interaction, the scalar propagators show very complex structures which, however, we can explain by the vicinity of phases with antiferromagnetic ordering and by the feedback of the fermion loops. We develop methods for extracting the wave function renormalization constant Zπ and the scalar mass mσ. We present first results on the influence of fermions on mσ. Our results on lattices from 6316 up to 10316 allow a preliminary discussion of the finite-size effects.