参考答案：B

解析：句中which的先行词是grounds，不定式to base的逻辑主语是the professor，base是及物动词，全句相当于The professor can hardly find sufficient grounds on which he bases his argument in favor of the new theory. base...on(the)grounds“以……为依据建立……”。因此，无论从逻辑上还是从语义上讲，A、C、D都是不通的。另外，which是介词on的宾语，应紧跟该介词，从这个意义上讲，也应选B。