Implications for Pulsar Timing Arrays of Sub-solar Black Hole Detections: From LVK to Einstein Telescope and Cosmic Explorer

The detection of compact binary mergers with sub-solar masses at gravitational-wave observatories could mark the groundbreaking discovery of primordial black holes (PBHs). Concurrently, evidence for a nHz stochastic gravitational wave background observed by pulsar timing arrays (PTAs) could suggest a non-astrophysical origin, potentially arising from scalar-induced gravitational waves (SIGW). In this work, we analyze the connection between the two phenomena in the case where they share a common origin: the collapse of large primordial curvature perturbations in the early universe. We focus on sub-solar PBH populations within reach of upcoming experiments, including the current and future runs of LIGO-Virgo-KAGRA as well as the third generation observatories such as the Einstein Telescope and Cosmic Explorer. Using a Bayesian framework with physically motivated priors, we perform a consistent model comparison that incorporates existing astrophysical bounds together with the discovery potential of future detectors. Our analysis lends stronger support for the SIGW interpretation over the astrophysical one, as the narrowed priors place greater weight on the region of highest likelihood. Ultimately, we illustrate that combining PTA data with interferometer searches can deliver correlated evidence for new physics across multiple gravitational-wave bands.