Hello,
The payment log is used by the plugins to store their debug data ; it is purely plugin related.
The only thing that HikaShop can store in that log is the content return by the "payment notification", but once again, it depends on the content returned by the plugin for that function.
So, the fact that you have an empty log is not a problem in HikaShop ; but it is something that your payment plugin should do.
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.