You can find some studies, but they are not all that helpful. Dana has one using Porites from Hawaii and he readily admits that it will not scale to other types of corals - people were able to grow porites under incandescent light bulbs in fuges back in the day. If you do read them, pay attention to if they are peer reviewed and every detail - they might not be all that telling of what you will see in a tank.
He has another article that discusses TLI - Total Light Index. I could be getting that slightly wrong. Basically said that the light multiplied by the duration is just as effective in most scenarios... so 10 hours at 200 PAR is as good as 8 hours at 160... or so.
What I have found is that 10 hours of as much light as I can give acropora yields the best color and growth combined with low, but not too low building blocks, heavy fish feeding and constant element supply with CaRx. I have no doubt that all of these are linked... but I also believe that light is the most important factor since that is what truly feeds the coral.
