How to assign the position and size to a half colored circle?

Question

When trying to draw a half colored circle, I cant tell the script where to start to draw, since the custom command uses a coordinate in polar form to start drawing using

    \documentclass{beamer}
\usepackage{tikz}
\begin{document}

\NewDocumentCommand{\statcirc}{ O{#2} m }{
    \begin{tikzpicture}
    \fill[#2] (0,0) circle (1.0ex); 
    \fill[#1] (0,0) -- (90:1.5ex) arc (90:270:1.5ex) -- cycle;
    \end{tikzpicture}
}

\begin{frame}
\frametitle{Frametitle}
    \begin{columns}
        \begin{column}{0.5\textwidth}
        En un diagrama de Venn se vería
                \begin{center}
            \begin{tikzpicture}[scale=0.7]
                \filldraw[fill=blue!20, draw=blue!60] (-2,0) circle (1.5cm);
                \filldraw[fill=red!20, draw=red!60] (2,0) circle (1.5cm);
                \statcirc[orange]{green}
                \node at (-2,1.8) {$D_{f}=R$};
                \node at (2,1.8) {$C_{f}=R_{f}$};
                \node at (0,1.2) {$f$};
                \node at (0,-2) {\textcolor{blue}{some text}};
                \node (x1) at (-1.5,0) {};
                \node (x2) at (-1.15,-0.4) {};
                \node (y1) at (1,0.5) {};
                \node (y3) at (1,-0.5) {};
                \draw[->] (x1) -- (y1);
                
            \end{tikzpicture}
            \end{center}

\begin{document}

I cant adjust the part of

   \fill[#1] (0,0) -- (90:1.5ex) arc (90:270:1.5ex) -- cycle;

since if I use a extra argument (i.e. the circle center must be at (2,0)) the draw overlaps, get ignored or get broke like the next image
When the idea is that the circle half colored be ar right of the arrow and bigger

Answer 1

Here is a pic that does what your command would have done, but can be placed wherever you like. Also this avoids nesting tikzpicture environments. The usage is slightly different, it uses pgf keys, which control the colors and radii of the semicircles.

\documentclass{beamer}
\usepackage{tikz}
\tikzset{pics/statcirc/.style={code={%
 \tikzset{statcirc/.cd,#1}
 \def\myvalue##1{\pgfkeysvalueof{/tikz/statcirc/##1}}
 \fill[color/.expanded=\myvalue{color 1}] (90:\myvalue{r1}) 
    arc[start angle=90,end angle=270,radius=\myvalue{r1}]; 
 \fill[color/.expanded=\myvalue{color 2}] (90:\myvalue{r2}) 
    arc[start angle=90,end angle=-90,radius=\myvalue{r2}]; 
 }},statcirc/.cd,color 1/.initial=orange,color 2/.initial=green,
    r1/.initial=1ex,r2/.initial=1.5ex}
\begin{document}

\NewDocumentCommand{\statcirc}{ O{#2} m }{
    \begin{tikzpicture}
    \fill[#2] (0,0) circle (1.0ex); 
    \fill[#1] (0,0) -- (90:1.5ex) arc (90:270:1.5ex) -- cycle;
    \end{tikzpicture}
}

\begin{frame}
\frametitle{Frametitle}
\begin{columns}[onlytextwidth,t]
  \begin{column}{0.5\textwidth}
   A Venn diagram
   \begin{center}
    \begin{tikzpicture}[scale=0.7]
        \filldraw[fill=blue!20, draw=blue!60] (-2,0) circle[radius=1.5cm];
        \filldraw[fill=red!20, draw=red!60] (2,0) circle[radius=1.5cm];
        \path (2,0) pic[transform shape]{statcirc={r1=1.5cm,r2=1cm}};
        \node at (-2,1.8) {$D_{f}=R$};
        \node at (2,1.8) {$C_{f}=R_{f}$};
        \node at (0,1.2) {$f$};
        \node[text=blue]at (0,-2) {some text};
        \node (x1) at (-1.5,0) {};
        \node (x2) at (-1.15,-0.4) {};
        \node (y1) at (1,0.5) {};
        \node (y3) at (1,-0.5) {};
        \draw[->] (x1) -- (y1);                
    \end{tikzpicture}
   \end{center}
  \end{column}
%
\end{columns}
\end{frame}
\end{document}

Answer 2

This is an alternative for the pic proposed in another answer.

In this case circle paths have been replaced for circular nodes over which half filled circles are drawn with a path picture command.

All additional labels are placed using relative positioning with nodes names as references.

\documentclass{beamer}
\usepackage{tikz}
\usetikzlibrary{positionIning}

\begin{document}
\begin{frame}
\frametitle{Frametitle}
Another Venn diagram

\begin{tikzpicture}
\node[circle, minimum size=2.1cm, fill=blue!20, draw=blue!60, label={$D_f=R$}] (left) {};
\node[circle, minimum size=2.1cm, fill=red!20, draw=red!60, label={$C_f=R_f$}, right=0.7cm of left,
path picture={\fill[red!60] (path picture bounding box.north) rectangle (path picture bounding box.south west); \fill[green] (right.center) --++(90:0.7) arc[start angle=90, end angle=-90, radius=0.7cm]--cycle;}] (right) {};
\draw[->] ([xshift=-7mm]left.east)--([xshift=3mm]right.160);
\path (left.north)--(right.north) node [midway, below] {$f$};
\path (left.south)--(right.south) node [midway, below, blue] {some text};
\end{tikzpicture}
\end{frame}
\end{document}