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It has been proposed that some black holes (BHs) in binary black hole (BBH)systems are born from "hierarchical mergers" (HM); i.e. earlier mergers ofsmaller BHs. These HM products have spin magnitudes $\chi \sim 0.7$, and, ifthey are dynamically assembled into BBH systems, their spin orientations willbe sometimes anti-aligned with the binary orbital angular momentum. In fact, asBaibhav et al. (2020) showed, $\sim16\%$ of BBH systems that include HMproducts will have an effective inspiral spin parameter, $\chi_\mathrm{eff} <-0.3$. Nevertheless, the LIGO-Virgo-Kagra (LVK) gravitational-wave (GW)detectors have yet to observe a BBH system with $\chi_\mathrm{eff} \lesssim-0.2$, leading to upper limits on the fraction of HM products in thepopulation. We fit the astrophysical mass and spin distribution of BBH systemsand measure the fraction of BBH systems with $\chi_\mathrm{eff} < -0.3$, whichimplies an upper limit on the HM fraction. We find that fewer than $26\%$ ofsystems in the underlying BBH population include HM products (90\%.credibility). Even among BBH systems with primary masses $m_1=60\,M_\odot$, theHM fraction is less than 69\%, which may constrain the location of thepair-instability mass gap. With 300 GW events (to be expected in the LVK's nextobserving run), if we fail to observe a BBH with $\chi_\mathrm{eff} < -0.3$, wecan conclude that the HM fraction is smaller than $2.5^{+9.1}_{-2.2}\%$.

Limits on hierarchical black hole mergers from the most negative $\chi_\mathrm{eff}$ systems