TikZ: Centering dash pattern between two nodes

There are standard answers, but all of them are very advanced and hard to understand. However, with markings one can "mirror" a half of the curve like this.

\documentclass[tikz]{standalone}
\usetikzlibrary{shapes,decorations,circuits.logic.US,circuits.logic.IEC,fit,external}
\tikzstyle{loosely dashed}=[dash pattern=on 4pt off 8pt]
\tikzstyle{loosely dashed2}=[dash pattern=on 4pt off 8pt]

\begin{document}
    \begin{tikzpicture}[every node/.style = {draw=none, text=black, circle, minimum size = 13mm, fill=gray!25}]
        \path
        (0,3) node(y) {$Y$}
        (-1.5,0) node[draw, line width=1pt](x1) {$X_1$}
        (1.5,0) node[draw, line width=1pt](x2) {$X_2$};
        \draw [line width=1pt,-,black] (y) -- (x1);
        \draw [line width=1pt,-,black] (y) -- (x2);
        %\draw [line width=3pt,-,loosely dashed,black] (x1.south east) to[bend right=40] (x2.south west);
        \path [postaction={
            decorate,
            decoration={
                markings,
                mark=at position 0.5 with \coordinate (mid);
            }
        }] (x1) to[bend right=40] (x2);
        \draw[line width=3pt,-,loosely dashed] ([xshift=-4pt]mid) to[out=180,in=-40] (x1);
        \draw[line width=3pt,-,loosely dashed] ([xshift=4pt]mid) to[out=0,in=-140] (x2);
    \end{tikzpicture}
\end{document}

Another way is to measure the path and then stretch the dash length a bit in such a way that the path ends with a full on. Please also note that \tikzstyle is deprecated.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\tikzset{
    full dash/.style args={on #1 off #2}{
    decoration={
    markings,
    mark=at position 0 with {
      \pgfmathsetmacro{\mystretch}{((\pgfdecoratedpathlength-#1)/(#1+#2))/int((\pgfdecoratedpathlength-#1)/(#1+#2))}
      \pgfmathsetmacro{\myon}{#1*\mystretch}
      \xdef\myon{\myon}
      \pgfmathsetmacro{\myoff}{#2*\mystretch}
      \xdef\myoff{\myoff}
    },
  },
  preaction={decorate},draw=none,
  postaction={draw,dash pattern=on \myon pt off \myoff pt}
  },
}
\begin{document}

\begin{figure}
    \centering
    \begin{tikzpicture}[every node/.style = {draw=none, text=black, circle, minimum size = 13mm, fill=gray!25}]
        \path
        (0,3) node(y) {$Y$}
        (-1.5,0) node[draw, line width=1pt](x1) {$X_1$}
        (1.5,0) node[draw, line width=1pt](x2) {$X_2$};
        \draw [line width=1pt,-,black] (y) -- (x1);
        \draw [line width=1pt,-,black] (y) -- (x2);
        \draw [line width=3pt,-,full dash=on 3pt off 6pt,black] (x1) to[bend right=40] (x2);
    \end{tikzpicture}
\end{figure}

\end{document}