There is no "authoritative document" like you ask for. The FDA doesn't set concrete standards for efficacy and safety; rather, they review applications for vaccines and other drugs on a case-by-case basis according to safety, efficacy, other available treatments, and severity of the condition.
The FDA has issued guidance to industry about how they expect to review vaccines and consider data (they issue these sorts of guidance documents for all sorts of things), but none of it is binding. Most of it is pretty vague, for example on efficacy:
To generate sufficient data to meet the BLA approval standard, late phase clinical
trials to demonstrate vaccine efficacy with formal hypothesis testing will likely
need to enroll many thousands of participants, including many with medical
comorbidities for trials seeking to assess protection against severe COVID-19
And for safety:
The pre-licensure safety database for preventive vaccines for infectious diseases
typically consists of at least 3,000 study participants vaccinated with the dosing
regimen intended for licensure. FDA anticipates that adequately powered efficacy
trials for COVID-19 vaccines will be of sufficient size to provide an acceptable
safety database for each of younger adult and elderly populations, provided that no
significant safety concerns arise during clinical development that would warrant
further pre-licensure evaluation.
This isn't saying anything about requirements, it's saying "hey, here's what people usually do to convince us, so you know what the rough expectations are".
Other guidance seems to be more specific:
To ensure that a widely deployed COVID-19 vaccine is effective, the primary
efficacy endpoint point estimate for a placebo-controlled efficacy trial should be at
least 50%, and the statistical success criterion should be that the lower bound of
the appropriately alpha-adjusted confidence interval around the primary efficacy
endpoint point estimate is >30%.
The same statistical success criterion should be used for any interim analysis
designed for early detection of efficacy.
A lower bound ≤30% but >0% may be acceptable as a statistical success
criterion for a secondary efficacy endpoint, provided that secondary endpoint
hypothesis testing is dependent on success on the primary endpoint.
but note this is about trial design, not bounds for acceptance.