I have refereed and taught referees for 20+ years. I am talking about US rules interpretation - albeit I don't think international rules/standards are different.
You should not raise one arm as a referee on a 3-point attempt.
- raising one arm signifies to start or stop the clock. The scorer's table could be confused.
- raising one arm also could mean the player was fouled while shooting. If there was a close play were a foul might have happened and I drew up my right arm hard on the three point shot attempt a good coach would correctly hassle me and say "where is the whistle?"
Why do some refs raise an arm up on an attempt?
- laziness - does this to remind himself that it was a 3-pointer so that he raises both arms after shot
- in some cases when it is a close call a referee may do so to indicate that it is a three point attaempt. In my opinion this is the only suitable situation to do it although I do not agree with its application.
What should a referee do?
Raise two hands after a successful three point shot. This tells the scorers table to put a three in. The scorer's table will automatically count a made basket as two without the raised arms - even if a player is 10 feet beyond the line, if the scorer's table counts that as a 3 without a referee signaling with two arms or verbally saying "3" to them then the scorer's table is not doing their job.
Why I do not like to teach ref's to hold up an arm on a "close 3 point attempt"?
This is simply because it is a distraction of a possible foul call. Also when doing high school and lower games or even small college games you want to be clear to everyone. The best approach to this, and what is taught to ref's in the US if they want to communicate to the crowd/benches is that hold your arm down with two fingers to indicate that a player stepped over the line on a close attempt and holding three fingers with an arm in a more outstretched position (not straight out but I would say maybe 45 degrees) gives a good preface for a three point attempt. These are not in the basketball rulebook but would be taught locally to referees as best practices (referees are not required to do this).