I would personally consider the IEEE Standard Definitions of Terms for Antennas (145-1983) the most authoritative source for definitions of antenna parameters.
IEEE Xplore - IEEE Standard Definitions of Terms for Antennas
I doubt you will find a definition of broadband in the IEEE standard, but I might be wrong.
You will find a definition of bandwidth in the IEEE standard. In that standard it defines bandwidth as something like "The frequency range over which one or more parameters are within a given specification". Note that is NOT the exact wording in the IEEE standard, but my interpretation of it.
So (my examples) an antenna can have a bandwidth set by
1) The SWR is less than x:1
2) The gain is greater than y.
3) The SWR is less than x:1 and the gain is greater than y.
4) The antenna can withstand a continuous power of at least z Watts.
etc etc
you can specify any number of parameters making up the bandwidth - frequency, return loss, radiation pattern, axial ratio for polarization, power handling .... etc.
Anyway, I would refer you to that standard.