  We derive the kernels and the Effective Field Theory of Large-Scale Structure
counterterms for the one-loop bispectrum of dark matter and of biased tracers
in real and redshift space. This requires the expansion of biased tracers up to
fourth order in fluctuations. In the process, we encounter several subtleties
related to renormalization. One is the fact that, in renormalizing the
momentum, a local counterterm contributes non-locally. A second subtlety is
related to the renormalization of local products of the velocity fields, which
need to be expressed in terms of the renormalized velocity in order to preserve
Galilean symmetry. We check that the counterterms we identify are necessary and
sufficient to renormalize the one-loop bispectrum at leading and subleading
order in the derivative expansion. The kernels that we originally present here
have already been used for the first analyses of the one-loop bispectrum in
BOSS data [1, 2].
