  The importance of the magnetic (B) field in the formation of infrared dark
clouds (IRDCs) and massive stars is an ongoing topic of investigation. We
studied the plane-of-sky B field for one IRDC, G028.23-00.19, to understand the
interaction between the field and the cloud. We used near-IR background
starlight polarimetry to probe the B field and performed several observational
tests to assess the field importance. The polarimetric data, taken with the
Mimir instrument, consisted of H-band and K-band observations, totaling 17,160
stellar measurements. We traced the plane-of-sky B-field morphology with
respect to the sky-projected cloud elongation. We also found the relationship
between the estimated B-field strength and gas volume density, and we computed
estimates of the normalized mass-to-magnetic flux ratio. The B-field
orientation with respect to the cloud did not show a preferred alignment, but
it did exhibit a large-scale pattern. The plane-of-sky B-field strengths ranged
from 10 to 165 {\mu}G, and the B-field strength dependence on density followed
a power law with an index consistent with 2/3. The mass-to-magnetic flux ratio
also increased as a function of density. The relative orientations and
relationship between the B field and density imply that the B field was not
dynamically important in the formation of the IRDC. The increase in
mass-to-flux ratio as a function of density, though, indicates a dynamically
important B field. Therefore, it is unclear whether the B field influenced the
formation of G28.23. However, it is likely that the presence of the IRDC
changed the local B-field morphology.
