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The distance between the superscript and the subscript for the character of parenthesis, for example, grows in group mode, while the equivalent behavior does not occur for the character of "x", for example, and the distance remains the same! Why is that?

I suppose it's possibly related to the character itself, but I want a convincing reason.

${)}^{a}_{b}$\quad $)^{a}_{b}$\\
${x}^{a}_{b}$\quad $x^{a}_{b}$

my example

The output produced using the report class with no options.

my example with border around boxes

I've depicted my investigations on the matter through the figure. The boxes for each character are drawn in red, and the blue lines are the baselines to the sub- and superscripts, and the green lines are the baselines.

Since the non-paired case, the following:

x^{a}_{b}

doesn't differ with the followings:

^{a}_{b}
{}^{a}_{b}

then, which one is more preferable to use?

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    The height (and depth) of ) is greater than those of x. You can achieve the same spacing for x if you use {x\mathstrut}^a_b. \mathstrut has the height and depth of ) without taking any horizontal space. On the other hand you can do something like {\smash{)}\vphantom{x}}^a_b to get the spacing of x after a closing parenthesis. The last version looks quite odd which is why latex increases the spacing for larger letters. – nox Dec 8 '19 at 13:35
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    @nox That's not the entire story. There is a difference in how TeX handles superscripts after \mathord and \mathclose. – campa Dec 8 '19 at 13:37
  • @campa Oh, you're right. Didn't have this in mind. – nox Dec 8 '19 at 13:40
  • I found this link useful (but the title is very bad!) tex.stackexchange.com/questions/104004/xy2-or-xy2 – Qaher Dec 8 '19 at 13:57