\documentclass{book}
\begin{document}

\begin{equation*}
\begin{tikzpicture}[description/.style={fill=white,inner sep=2pt}]
\matrix (m) [matrix of math nodes, row sep=3em,
column sep=3em, text height=1.5ex, text depth=0.25ex]
{  E^{\prime}  \\
 E &  A & B\\ };
\path[->,font=\scriptsize]
(m-1-1) edge node[auto] {$ e^{\prime} $} (m-2-2)
 edge node[auto] [left] {$ \bar{e} $} (m-2-1)
(m-2-1) edge node [auto] [below] {$e$}( m-2-2)
(m-2-2) edge node [r shift  left ] [above] {$p_1$} (m-2-3)
   edge node [auto][below] {$p_2$} (m-2-3)
\end{tikzpicture}
\end{equation*}


\end{document}