  Strong gravitationally lensed arcs produced by galaxy clusters have been
observationally detected for several decades now. These strong lensing
constraints provided high-fidelity mass models for cluster lenses that include
substructure down to $10^{9-10}\,\mathrm{M}_\odot$. Optimizing lens models,
where the cluster mass distribution is modeled by a smooth component and
subhalos associated with the locations of individual cluster galaxies, has
enabled deriving the subhalo mass function, providing important constraints on
the nature and granularity of dark matter. In this work, we explore and present
a novel method to detect and measure individual perturbers (subhalos,
line-of-sight halos, and wandering supermassive black holes) by exploiting
their proximity to highly distorted lensed arcs in galaxy clusters, and by
modeling the local lensing distortions with curved arc bases. This method
offers the possibility of detecting individual low-mass perturber subhalos in
clusters and halos along the line-of-sight down to a mass resolution of
$10^8\,\mathrm{M}_\odot$. We quantify our sensitivity to low-mass perturbers
($M\sim 10^{7-9}\,\mathrm{M}_\odot$) in clusters ($M\sim
10^{14-15}\mathrm{M}_\odot$), by creating realistic mock data. Using three
lensed images of a background galaxy in the cluster SMACS J0723, taken by the
$\textit{James Webb Space Telescope}$, we study the retrieval of the properties
of potential perturbers with masses $M=10^{7-9}\,\mathrm{M}_\odot$. From the
derived posterior probability distributions for the perturber, we constrain its
concentration, redshift, and ellipticity. By allowing us to probe lower-mass
substructures, the use of curved arc bases can lead to powerful constraints on
the nature of dark matter as discrimination between dark matter models appears
on smaller scales.
