I have been trying to do a paper on Capital punishment for a few days and have researched for hours and hours?

but I can not seem to find basic facts. Some "authoritative" studies seem to say that capital punishment costs more and yet when I search on google I can't find the original source. Some say that the cost is more for capital punishment than LWOP but then others give studies saying the opposite and each side picks flaws at eachother's statistic gathering. The same thing with deterrance. Some say it's undeniable that it deters and point to numerous studies and then others point to an attorney general and other studies that it doesn't deter. I'm not a statistician or anything and so I can't really yze these studies myself but when I can't find any concrete basic facts because both sides have "authoritative" sources or unnamed sources that contradict eachother, it's hard to write a paper on it. Anyone have suggestions?