The "coupling constant" αs is not a constant at all - it decreases with increasing momentum. Moreover, it lies in the range 0.1 - 0.3 at values of Q that can be probed in experiment, which means that it's about 50 times larger than the fine structure constant of electrodynamics - that's why the "strong interactions" are strong -, and the factor g² = 4παs is on the order of 1, and bigger than 1 for small momenta