How to make RevTeX4-2 use different section name in the table of contents?

Question

I am using RevTeX4-2. I have a math expression in the name of a section. I would like it to be in the same font weight as the surrounding text: bold in the body of the text, and regular in the table of contents. The usual way to do this, \section[toc version]{doc version}, doesn't work, as shown by the following MWE

\documentclass[aps,reprint,superscriptaddress]{revtex4-2}
\usepackage{bm}
\begin{document}
\title{This is the title}
\author{Bob Author}
\affiliation{L.A. Tex University}
\date{\today}
\begin{abstract}
 Revtex doesn't seem to allow the section titles to have a different name in the table of contents.
\end{abstract}
\maketitle
\tableofcontents
\section[Case $\alpha>1$]{Case $\alpha>1$}
Note that $\alpha>1$ is not boldfaced in the section title.
\section[Case $\beta>1$]{Case \bm{$\beta>1$}}
In contrast, $\beta>1$ is indeed boldfaced in the section title. 
Unfortunately, it is also boldfaced in the Table of Contents.
\vfill
\end{document}

Output:

---

Switching to memoir class (though report would also work), the usual way does work:

\documentclass{memoir}
% The `report` class would also work.
\usepackage{bm}
\begin{document}
\tableofcontents
\section[Case $\alpha>1$]{Case $\alpha>1$}
This uses the memoir class, but report would also work.
As before, $\alpha>1$ is not boldfaced in the section title.
\section[Case $\beta>1$]{Case \bm{$\beta>1$}}
Again, $\beta>1$ is indeed boldfaced in the section title. 
However, this time around, it is \emph{not} boldfaced in 
the Table of Contents.
\end{document}

Is there a way to make RevTex4-2 use the 'toc version' of the section name (which has non-bold math) in the Table of Contents?

Answer 1

As you discovered, revtex4-2 does not use the optional \section argument to write the ToC.

This can be fixed by changing a single line in the \@sect@ltx macro. I don't know how to patch this long command, but by redefining it in the document, the bold face is removed from the ToC.

Try this code. It needs to be compiled twice.

\documentclass[aps,reprint,superscriptaddress]{revtex4-2}
\usepackage{bm}
\usepackage{showframe} % show margins
%********************************added <<<<<<<<<<<<<<<<<<<<<<
\makeatletter
\def@sect@ltx#1#2#3#4#5#6[#7]#8{%
    @ifnum{#2>\c@secnumdepth}{%
        \def\H@svsec{\phantomsection}%
        \let@svsec@empty
    }{%
        \H@refstepcounter{#1}%
        \def\H@svsec{%
            \phantomsection
        }%
        \protected@edef@svsec{{#1}}%
        @ifundefined{@#1cntformat}{%
            \prepdef@svsec@seccntformat
        }{%
            \expandafter\prepdef
            \expandafter@svsec
            \csname @#1cntformat\endcsname
        }%
    }%
    @tempskipa #5\relax
    @ifdim{@tempskipa>\z@}{%
        \begingroup
        \interlinepenalty @M
        #6{%
            @ifundefined{@hangfrom@#1}{@hang@from}{\csname @hangfrom@#1\endcsname}%
            {\hskip#3\relax\H@svsec}{@svsec}{#8}%
        }%
        @@par
        \endgroup
        @ifundefined{#1mark}{@gobble}{\csname #1mark\endcsname}{#7}%
        \addcontentsline{toc}{#1}{%
            @ifnum{#2>\c@secnumdepth}{%
                \protect\numberline{}%
            }{%
                \protect\numberline{\csname the#1\endcsname}%
            }%
            #7}% <<<<<<<<<<<<<<<<<<<<<<<< changed from #8
    }{%
        \def@svsechd{%
            #6{%
                @ifundefined{@runin@to@#1}{@runin@to}{\csname @runin@to@#1\endcsname}%
                {\hskip#3\relax\H@svsec}{@svsec}{#8}%
            }%
            @ifundefined{#1mark}{@gobble}{\csname #1mark\endcsname}{#7}%
            \addcontentsline{toc}{#1}{%
                @ifnum{#2>\c@secnumdepth}{%
                    \protect\numberline{}%
                }{%
                    \protect\numberline{\csname the#1\endcsname}%
                }%
                #8}%
        }%
    }%
    @xsect{#5}}%
\makeatother
%*******************************
\begin{document}
    \title{This is the title}
\author{Bob Author}
\affiliation{L.A. Tex University}

\date{\today}


\begin{abstract}
    Revtex doesn't seem to allow the section titles to have a different name in the table of contents.
\end{abstract}

\maketitle

\tableofcontents

\section[Case $\alpha&gt;1$]{Case $\alpha&gt;1$}

Note that $\alpha&gt;1$ is not boldfaced in the section title.

\section[Case $\beta&gt;1$]{Case \bm{$\beta&gt;1$}}

In contrast, $\beta&gt;1$ is indeed boldfaced in the section title. 
Unfortunately, it is also boldfaced in the Table of Contents.
\vfill

\end{document}