In my state (OK), it is illegal to carry any firearm while afield during an archery season. This includes those with carry licenses & those carrying under “Constitutional Carry”. BTW - “afield” means to be hunting game with the designated mode of taking said game, in this case using archery equipment.
Can a hunter who possesses a concealed weapons permit carry a concealed weapon while hunting? Individuals who possess a valid concealed carrying permit may carry a concealed handgun while hunting for the purposes of self defense only.
I expect that shooting a mountain lion (when obviously bow-hunting for deer) would be considered self defense.
https://forums.bowhunting.com/threads/carrying-a-sidearm-during-archery-hunting-seasons.100427/
"Here is an answer from Mr. Erdman of the ODWC (Oklahoma state game agency) regarding handgun carry during archery seasons: "Yes, you can carry a pistol for personal defense only. It can not be used in the hunt in any way. If hunting on any federally owned lands check with them first. If you have any other questions please let me know. Thank you."