A novel signal-consistency test for gravitational-wave searches of generic black hole binaries

We propose a novel signal-consistency test applicable to a broad search for gravitational waves emitted by generic binary black hole (BBH) systems. The test generalizes the time domain ξ^2 signal-consistency test currently utilized by the GstLAL pipeline, which is restricted to aligned-spin circular orbits and does not account for higher-order modes (HMs). After addressing the mathematical details of the new test, we quantify its advantages in the context of searching for precessing BBHs and/or BBHs with HM content. Our results reveal that for precessing signals, the new test has the potential to diminish ξ^2 by up to two orders of magnitude when compared to the standard test. However, in the case of signals with HM content, only a modest enhancement is observed. Recognizing the computational burden associated with the new test, we also derive an approximated signal-consistency test. This approximation maintains the same computational cost as the standard test while sacrificing only a few percent of accuracy in the low SNR regime. The approximated test can be easily implemented in any matched filtering pipeline aimed at searching for BBH signals with strong precession content.