Let's first state for the record that I am well aware of Rule 0 and am in no way asking a practical question. The DM's job is to make the game fun for everyone and in this regard his power is truly absolute and, when the situation calls for it, he can and should break any rule.
That being said, another DM and I have been having a bit of a discussion concerning where the DM's power "officially" ends and the players power begins. We both DM D&D 5e games with moderate levels of success but handle this specific issue vastly differently. My opinion has long been that players are completely in charge of their characters; their actions as well as their emotions. In other-words the DM only has control over factors EXTERNAL to the characters. Consequently, I would (ideally) never presume to describe the emotion a character was feeling, for example "you feel a sense of dread come over you." I would describe the situation and leave it up to the players to decide how their characters would feel about it.
My friend, on the other hand, will often describe the emotions PCs are feeling. If its a situation he feels like the PCs would feel sad he describes them as such, even going so far as to say something along the lines of "you feel tears begin to well up in your eyes." To me this seems like he's overreaching his power, if a PC is an apathetic robot that should be up to the player.
Is there a RAW limitation to the DM's power over Player Characters, especially regarding their emotions, and if so what is it?
Edit: To clarify spells/potions/conditions/etc that explicitly and/or directly affect the PCs feelings/emotions would fall into the External category.
Best Answer
Mostly, DMs control everything except the player characters: there are exceptions
Overall, I'd agree with the OP's position that a good DM will describe situations purely "external to the characters." A player has control of one aspect of the game: their character. As much as possible, they should retain autonomy in this control, including the actions, motivations, and emotions of their character.
The most "RAW" support for this position is the PHB's descriptions of the roles of players and DMs on page 6.
A DM might use emotional language as a shorthand to describe an environment or creature (a creature might be "terrifyingly ugly", or a house "unsettlingly quiet"), but such a description is still a description of the environment (things external to the character): not a description of a character's reaction. Also, it is worth noting that emotions are inexorably tied up in sentient motivation and decisions: what you feel in large part informs what you want. If the DM were to define the emotions of the player characters, it could reduce the players' role in step #2 (debatably, their main role in the game): deciding and describing what they want to do.
There are exceptions
That being said, in D&D (and some other systems as well) a character's emotional state can be a measurable game mechanic, that has a tactical implication in play. Take, for example, the "Frightened" condition in the PHB (p. 290):
Certain creatures in the game (like Ancient Dragons) can impose the Frightened condition on creatures that fail saving throws: their ability to do this is written into their stat-block, and this emotional reaction is not subject to player veto. A player cannot simply say "my character isn't Frightened of the Ancient Red Dragon because he's really brave." Being Frightened is a condition that confers specific game effects, is decided by dice rolls, and has starting and ending conditions that are well defined in RAW. As such, a DM can override a player's decision on whether or not their character is emotionally "Frightened". So RAW, DMs have some say in defining or setting the emotional state of player characters.
Similarly, the role of fear, madness, sorrow, or feelings of triumph may sometimes be up to DM discretion in specific situations where the rules define them, or in stories where these emotions will take center stage. The DMG gives rules (p. 266) for a "Fear" or "Horror" check, that applies to games where such emotions are a focus of the story (such as Ravenloft campaigns). And it's worth noting that even something as commonly used as Hit Points can be a measure of a character's mental state.
Overall
That said, in general, the division of labor is clear. In most cases, where RAW does not directly state otherwise (or the agreed upon nature of the story does not require otherwise), the players control the player characters, and the DM controls the rest of the world.