problem with tilde and squaring overlined symbols, stix2

Question

I have problem with the following math text:

As you can see, the tilde over S is not actually wide, but it's squared nicely. On the other hand, the overline over the X is okay, but the deuce is placed ugly.

Im using Stix 2.0. I'd like to have tilde as wide as overline over the X and the square of X be positioned properly.

How to achieve it without changing math font?

I use XeLaTex. Stix2 is loaded as in MWE:

MWE:

\documentclass[11pt]{article}
\usepackage{fontspec}
\usepackage{xunicode}
\usepackage{unicode-math}
\setmathfont{STIX2Math.otf}[StylisticSet=02]
\begin{document}
$$\widetilde{S}^2 = \int x^2 dF_n - \left(\int x dF_n\right)^2 
     = \frac{1}{n}\sum X_i^2 - \overline{X}^2$$
\end{document}

Answer 1

You can use \wideoverbar instead of \overline.

For the tilde, you can substitute it with the one from TeX Gyre Termes, but some low level tricks are necessary.

\documentclass[11pt]{article}

\usepackage{amsmath}
\usepackage{fontspec}
\usepackage{unicode-math}

\setmainfont{TeX Gyre Termes}
\setmathfont{STIX2Math.otf}[StylisticSet=02]

\newfontface{\termesmath}{texgyretermes-math.otf}[NFSSFamily=termesmath]
\DeclareSymbolFont{termesmath}{TU}{termesmath}{m}{n}

\AtBeginDocument{%
  \protected\def\widetilde{\Umathaccent 7 \symtermesmath "00303\relax}%
}

\begin{document}

\[
\widetilde{S}^2
= \int x^2 \,dF_n - \left(\,\int x \,dF_n\right)^{\!2}
= \frac{1}{n}\sum X_i^2 - \wideoverbar{X}^2
\]

\end{document}