  Scorpius X-1 (Sco X-1) has long been considered one of the most promising
targets for detecting continuous gravitational waves with ground-based
detectors. Observational searches for Sco X-1 have achieved substantial
sensitivity improvements in recent years, to the point of starting to rule out
emission at the torque-balance limit in the low-frequency range \sim 40--180
Hz. In order to further enhance the detection probability, however, there is
still much ground to cover for the full range of plausible signal frequencies
\sim 20--1500 Hz, as well as a wider range of uncertainties in binary orbital
parameters. Motivated by this challenge, we have developed BinaryWeave, a new
search pipeline for continuous waves from a neutron star in a known binary
system such as Sco X-1. This pipeline employs a semi-coherent StackSlide
F-statistic using efficient lattice-based metric template banks, which can
cover wide ranges in frequency and unknown orbital parameters. We present a
detailed timing model and extensive injection-and-recovery simulations that
illustrate that the pipeline can achieve high detection sensitivities over a
significant portion of the parameter space when assuming sufficiently large
(but realistic) computing budgets. Our studies further underline the need for
stricter constraints on the Sco X-1 orbital parameters from electromagnetic
observations, in order to be able to push sensitivity below the torque-balance
limit over the entire range of possible source parameters.
