  We present a joint likelihood analysis of the real-space power spectrum and
bispectrum measured from a variety of halo and galaxy mock catalogs. A novel
aspect of this work is the inclusion of nonlinear triangle configurations for
the bispectrum, made possible by a complete next-to-leading order ("one-loop")
description of galaxy bias, as is already common practice for the power
spectrum. Based on the goodness-of-fit and the unbiasedness of the parameter
posteriors, we accomplish a stringent validation of this model compared to the
leading order ("tree-level") bispectrum. Using measurement uncertainties that
correspond to an effective survey volume of $6\,(\mathrm{Gpc}/h)^3$, we
determine that the one-loop corrections roughly double the applicable range of
scales, from $\sim 0.17\,h/\mathrm{Mpc}$ (tree-level) to $\sim
0.3\,h/\mathrm{Mpc}$. This converts into a $1.5 - 2$x improvement on
constraints of the linear bias parameter at fixed cosmology, and a $1.5 - 2.4$x
shrinkage of uncertainties on the amplitude of fluctuations $A_s$, which
clearly demonstrates the benefit of extracting information from nonlinear
scales despite having to marginalize over a larger number of bias parameters.
Besides, our precise measurements of galaxy bias parameters up to fourth order
allow for thorough comparisons to coevolution relations, showing excellent
agreement for all contributions generated by the nonlocal action of gravity.
Using these relations in the likelihood analysis does not compromise the model
validity and is crucial for obtaining the quoted improvements on $A_s$. We also
analyzed the impact of higher-derivative and scale-dependent stochastic terms,
finding that for a subset of our tracers the former can boost the performance
of the tree-level model with constraints on $A_s$ that are only slightly
degraded compared to the one-loop model.
