Higgs andWboson spectrum from lattice simulations

Abstract

The spectrum of energy levels is computed for all available angular momentum and parity quantum numbers in the SU(2)-Higgs model, with parameters chosen to match experimental data from the Higgs-W boson sector of the standard model. Several multiboson states are observed, with and without linear momentum, and all are consistent with weakly interacting Higgs and W bosons. The creation operators used in this study are gauge-invariant so, for example, the Higgs operator is quadratic rather than linear in the Lagrangian's scalar field.

Two- and three-point functions in Landau gauge Yang-Mills-Higgs theory

“…Moreover, the running gauge coupling, as will be seen below, runs much faster in the present theory as in the standard model, due to the lack of fermions and therefore a much larger β 0 [36]. Hence a quantitative comparison to the standard model is at the current time anyhow only of limited reliability, a problem recognized also in other investigations [55].…”

Gauge invariance and the physical spectrum in the two-Higgs-doublet model

“…Of course, it is possible to doubt the correctness of the expansion 7 . But the prediction has been confirmed non-perturbatively in various lattice calculations for the weak-Higgs theory with one doublet [25,26,35,36]. Thus, the FMS mechanism appears to be indeed the correct description of the electroweak theory.…”

“…tr(U (x, x, C ′ )) with C ′ a closed path [24] (in classical field theory it is proved, in quantum field theory it is believed). Non-perturbatively, these operators also carry all the information about the bound-state spectrum, if they have non-zero overlap with all states [25,26]. SU (2) L matrix (with no Higgs flavor indices) and so it satisfies…”

“…• the binding energy of the interactions from the Higgs potential is extremely weak when it exists at all [32][33][34] (for the parameters' scale around the Standard Model) and so the energy spectrum starts at ∼ 2mH. Moreover no evidence that such bound states exist have yet been found for the Standard Model [25,26].…”

“…Lattice simulations are a possible tool, and 2HDM are accessible in such simulations [19,20]. Calculating the spectrum and testing the FMS mechanism is a straightforward extension of [25,26,36], and should not pose a conceptual problem, though especially correlators of scalars are numerically expensive.…”