When the engine is running take a volt meter across the battery terminals and see what the voltage is. Should be 13.5-14V. If lower than 13 then check to make sure you have battery voltage at the wire that attaches to the voltage regulator. If battery voltage there, disconnect the wires coming from the alternator under the flywheel and see what the voltage is when going wire to wire, be advised this voltage with be AC not DC. Just guessing AC voltage should be 28-32 volts, but could be higher. If that checks out and have battery voltage at regulator then I would say bad regulator. If voltage from stator under flywheel is excessively low, then most like bad stator.
If you have proper voltage at battery when running, but still discharges battery, I would start looking for something that is draining the battery.