How to enter/render d-hat in emacs and latex export

Question

I want to be able to use d-hat (d with a caret (^) above it) in emacs to indicate an estimate of Cohen's 'd' (an effect size statistic).

How can I enter this in org-mode in a way that it renders within emacs, and also how can I make sure it exports out to latex/PDF?

Thanks

EDIT: Below are a tex file that resulted from a LaTeX export of a one-line org file, with the latex output

% Created 2020-09-17 Thu 16:09
% Intended LaTeX compiler: pdflatex
\documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{graphicx}
\usepackage{grffile}
\usepackage{longtable}
\usepackage{wrapfig}
\usepackage{rotating}
\usepackage[normalem]{ulem}
\usepackage{amsmath}
\usepackage{textcomp}
\usepackage{amssymb}
\usepackage{capt-of}
\usepackage[colorlinks=true]{hyperref}
\author{U-BRXPS\brett}
\date{\today}
\title{}
\hypersetup{
 pdfauthor={U-BRXPS\brett},
 pdftitle={},
 pdfkeywords={},
 pdfsubject={},
 pdfcreator={Emacs 26.3 (Org mode 9.1.9)},
 pdflang={English}}
\begin{document}

\tableofcontents

This is a d-hat: \(\hat{d}\)
\end{document}

$ latex test.tex
This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 20.6.29)
entering extended mode
(test.tex
LaTeX2e <2020-02-02> patch level 5
L3 programming layer <2020-07-17>
("C:\Program Files\MiKTeX\tex/latex/base\article.cls"
Document Class: article 2019/12/20 v1.4l Standard LaTeX document class
("C:\Program Files\MiKTeX\tex/latex/base\size11.clo"))
("C:\Program Files\MiKTeX\tex/latex/base\inputenc.sty")
("C:\Program Files\MiKTeX\tex/latex/base\fontenc.sty")
("C:\Program Files\MiKTeX\tex/latex/graphics\graphicx.sty"
("C:\Program Files\MiKTeX\tex/latex/graphics\keyval.sty")
("C:\Program Files\MiKTeX\tex/latex/graphics\graphics.sty"
("C:\Program Files\MiKTeX\tex/latex/graphics\trig.sty")
("C:\Program Files\MiKTeX\tex/latex/graphics-cfg\graphics.cfg")
("C:\Program Files\MiKTeX\tex/latex/graphics-def\dvips.def")))
(C:\Users\brett\AppData\Roaming\MiKTeX\tex/latex/grffile\grffile.sty)
y) (C:\Users\brett\AppData\Roaming\MiKTeX\tex/generic/pdfescape\pdfescape.sty)
(C:\Users\brett\AppData\Roaming\MiKTeX\tex/latex/hycolor\hycolor.sty)
(C:\Users\brett\AppData\Roaming\MiKTeX\tex/latex/letltxmacro\letltxmacro.sty)
(C:\Users\brett\AppData\Roaming\MiKTeX\tex/latex/auxhook\auxhook.sty)
(C:\Users\brett\AppData\Roaming\MiKTeX\tex/latex/kvoptions\kvoptions.sty)
("C:\Program Files\MiKTeX\tex/latex/hyperref\pd1enc.def")
(C:\Users\brett\AppData\Roaming\MiKTeX\tex/generic/intcalc\intcalc.sty)
(C:\Users\brett\AppData\Roaming\MiKTeX\tex/generic/etexcmds\etexcmds.sty)
("C:\Program Files\MiKTeX\tex/latex/url\url.sty")
(C:\Users\brett\AppData\Roaming\MiKTeX\tex/generic/bitset\bitset.sty
(C:\Users\brett\AppData\Roaming\MiKTeX\tex/generic/bigintcalc\bigintcalc.sty))
(C:\Users\brett\AppData\Roaming\MiKTeX\tex/generic/atbegshi\atbegshi.sty))
("C:\Program Files\MiKTeX\tex/latex/hyperref\hdvips.def"
("C:\Program Files\MiKTeX\tex/latex/hyperref\pdfmark.def"
(C:\Users\brett\AppData\Roaming\MiKTeX\tex/latex/rerunfilecheck\rerunfilecheck.
sty (C:\Users\brett\AppData\Roaming\MiKTeX\tex/latex/atveryend\atveryend.sty)
(C:\Users\brett\AppData\Roaming\MiKTeX\tex/generic/uniquecounter\uniquecounter.
sty))))
! Undefined control sequence.
<argument> U-BRXPS\brett

l.26  pdflang={English}}

? 

Answer 1

If there is a Unicode d-hat, then using that should take care of it both in the buffer and in the PDF produced through LaTeX (assuming your LaTeX tool chain can handle Unicode, which should be no problem nowadays).

Unfortunately, I can't find such a Unicode character. In the absence of that, I would suggest you use a LaTeX math expression:

\(\hat{d}\)

which will produce a d-hat in the output. But it's not going to look like a d-hat in the buffer, unless you preview the LaTeX fragment with M-x org-latex-fragment (usually bound to C-c C-x C-l) - this is a toggle, so repeating it will eliminate the overlay and show you the LaTeX fragment again. You can preview all the LaTeX fragments in your buffer with C-u C-u C-c C-x C-l and if you want that to happen whenever you open the file, you can add a Local File Variables section at the end of your file:

# Local Variables:
# eval: (org-latex-fragment '(16))
# End:

This last trick is a general Emacs customization trick, applicable generally, not just for Org mode stuff.

See Embedded LaTeX in the manual. In the long run, if you have to do a lot of math, then learning some LaTeX and using this embedding is likely to be a more productive way to produce your documents.