Can an antivirus detect a keylogger?

Simply put, can an antivirus program detect if a keylogging program was installed on my device?
Well, I don't think so. My World of Warcraft account was recently hacked and I tried to change the old password, what's worse, I found that my email account was hacked too. I suspected that someone may installed some spy software like keylogger on my computer, and I've run scans with Malwarebytes and SuperAntiSpyware and all have come up lean. At last, I resetted my computer in order to delete the keylogger, I really disappointed with the antivirus program.
 
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