Search for Sub-Solar Mass Binaries in the First Part of LIGO's Fourth Observing Run

We report the first results of a sub-solar mass compact binary search using the data from the first part of the fourth observing run (O4a) of the Advanced LIGO detectors. Sub-solar mass neutron stars and black holes are not expected to form via standard stellar evolution, and their observation would signify a new class of astrophysical objects or the discovery of a component of dark matter. Our search covers binaries with primary masses 0.1 to 2 $M_\odot$ and secondary masses 0.1 to 1 $M_\odot$. We explicitly incorporate tidal effects up to $7\times10^5$ for extremely low mass neutron stars. Due to the recent development of efficient ratio filter de-chirping frameworks, this search consisting of 25 million templates is now computationally feasible. No statistically significant candidates are identified. We place a $90\%$ confidence upper limit on the merger rate $\mathcal{R}_{90}$ for sub-solar mass black holes to be $< 2.5\times10^4\,\textrm{Gpc}^{-3} \textrm{yr}^{-1}$ for a chirp mass of 0.2 $M_\odot$. We place the first constraints for binary neutron stars with tidal deformabilities up to $\sim 7\times10^5$ and improve the merger rate estimate by a factor $\sim 3$ in comparison to previous O3 tidal searches for tidal deformabilities $< 10^4$. The advanced sensitivity of the O4a run enables an improvement in the sub-solar mass black hole merger rate limits by more than $2 \times$ over the previous three observing runs (O1-O3) combined. We constrain the effective local dark matter fraction to be $\tilde{f}_\textrm{PBH}