To obtain high-quality results from lattice QCD, it is important to use operators that produce good signals for the quantities of interest. Free-form smearing is a powerful tool that helps to accomplish that goal. The present work introduces a new implementation of free-form smearing that maintains its usefulness and reduces its computational time dramatically. Applications to the mass spectrum of B, B s , B c and bottomonium mesons show the effectiveness of the method.Results are compared with other lattice QCD studies and with experimental data where available.The present work includes the first lattice QCD exploration for some of these mesons.

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.

The SUð2Þ-Higgs model, with a single Higgs field in the fundamental representation and a quartic selfinteraction, has a Higgs region and a confinement region which are analytically connected in the parameter space of the theory; these regions thus represent a single phase. The effect of multiple Higgs fields on this phase structure is examined via Monte Carlo lattice simulations. For the case of N ! 2 identical Higgs fields, there is no remaining analytic connection between the Higgs and confinement regions, at least when Lagrangian terms that directly couple different Higgs flavors are omitted. An explanation of this result in terms of enhancement from overlapping phase transitions is explored for N ¼ 2 by introducing an asymmetry in the hopping parameters of the Higgs fields. It is found that an enhancement of the phase transitions can still occur for a moderate (10%) asymmetry in the resulting hopping parameters.

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Free-form smearing was designed as a way to implement source operators of any desired shape.A variation of the method is introduced that reduces the computational cost by reducing the number of link multiplications to its absolute minimum. Practical utility is demonstrated through calculations of bottomonium and B meson masses.

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Gauge-invariant sources with a hydrogen wave function shape are constructed for bottomonium two-point correlation functions using the free-form smearing technique. The bottomonium spectrum, including a first lattice result for the D-wave first-excited state, is extracted from free-form smeared correlation functions. Results are compared with conventional smearing techniques and free-form smearing is found to have the advantage of reduced statistical errors.

Free-form smearing was designed as a way to implement source operators of any desired shape. A variation of the method is introduced that reduces the computational cost by reducing the number of link multiplications to its absolute minimum. Practical utility is demonstrated through calculations of bottomonium and B meson masses.