Battery would have been my first thought since I just had the same issue, but I see you already did that. Do you know for certain this is a brand new, unused, battery? Even if it is, it seems batteries are prone to defects from the factory. Mostly aftermarket ones, but I've seen a fair few OEM ones reported DOA too.
How's your in home signal? Is it pretty strong? What about 3/4G coverage? If something happened that has causes the signal to drop a lot, the phone could simply be expending more power to maintain reception.
Another big drain is the GPS, so look for any apps that may be turning it on more often than you need. Anything using location tracking could be suspect.
If using wifi, are you turning mobile data off? That saves a fair bit of power, and easy to setup a Smart Action to automate the change.
The vibrate function uses a lot more power relative to audible notifications. If you have been doing a lot of texting and such, turn the vibration off for notifications and use sounds only if you can get away with it.
And for reference if nothing else works, an extended battery is awesome. I got the OEM one (there are larger ones out there, but reviews were iffy), and I'm blown away. If I leave 4G turned on with no display timeout, I think I get about 5-6 hrs with light to moderate use. Turning 4G off and going 3G only (get the LTE On/Off app in play to easily set to "CDMA (auto PRL)" for 3G only) and using a 2 min display timeout gets me about 10-14 hrs. Then today I hardly used it except for minor texting and browsing, with the display mostly off, and I was on track to get 18 hrs off the charge. In fact, I really don't see much of a speed difference between 3 and 4G for simple browsing and stuff. Even YouTube loads fast enough to not need to buffer on standard definition most of the time. So unless I'm about to download a really big file or need to browse while on the phone, I typically leave 4G off all together to save on battery life.