\documentclass{standalone}

\usepackage{siunitx}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usepackage{pgfplots}
\usetikzlibrary{positioning,shapes,arrows}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.markings}

\begin{document}
\newcommand*{\fcsone}{\ensuremath{f(c \rightarrow D_{s 1}^+)}}
\newcommand*{\BranStrangeLOW}{\ensuremath{%
    \mathcal{B}_{D_{s1}^{+} \rightarrow D^{*+} K^0_S}/
    \mathcal{B}_{D_{s1}^{+} \rightarrow D^{*0} K^+}}}
\sisetup{retain-explicit-plus}
\begin{tikzpicture}
  \begin{axis}[width=0.98\textwidth,height=0.38\textwidth,
    major grid style={color=red},
    xmin=-0.4,xmax=57.4,
    xticklabels={},xtick=data,name=pic1,ylabel=$\BranStrangeLOW$,
    ylabel shift ={-1cm,0 },
    extra x ticks={0.5,40.5,44.5,49.5,53.5},
    extra x tick style={grid=major,
      tick label style={rotate=-90,anchor=east}},
    extra x tick labels={},
    clip=false]
    \addplot+[only marks,mark size=1.5pt,error bars/.cd,y dir=both,y explicit]
    table[x=x, y=y, x error=errorx, y error=errory
    ]{../tikz/BRANCHINGSTRANGE0.dat}  ;%node [pos=0] {$R=2$};
    \node at (axis cs:22,  2.795)    {{\Large $\delta_1$}};
    \node at (axis cs:42.5,  2.795)   {{\Large $\delta_2$}};
    \node at (axis cs:47.5,2.795) {{\Large $\delta_3$}};
    \node at (axis cs:51,  2.795)   {{\Large $\delta_4$}};
    \node at (axis cs:55,  2.795)   {{\Large $\delta_5$}};
    \addplot [const plot,draw=blue] coordinates {(0,1.60) (57.4,1.60)};
  \end{axis}
  \begin{axis}[width=0.98\textwidth,height=0.38\textwidth,
    major grid style={color=red},
    xmin=-0.4,xmax=57.4,
    xticklabels from table={../tikz/BRANCHINGSTRANGE_titles.dat}{label},
    x tick label style={rotate=90,anchor=east,font=\tiny},xtick=data,
    name=pic3,at={($(pic1.south)-(pic1.north)$)},
    ylabel=$f(c \rightarrow D_{s 1}^+)$,
    extra x ticks={0.5,40.5,44.5,49.5,53.5},
    extra x tick style={grid=major,
      tick label style={rotate=-90,anchor=east}},
    extra x tick labels={}]
    \addplot+[only marks,mark size=1.5pt,error bars/.cd,y dir=both,y explicit]
    table[x=x,y=y,x error= errorx,y error=errory]{../tikz/BRANCHINGSTRANGE1.dat};
    \addplot [const plot,draw=blue] coordinates {(0,0.76) (100,0.76)};
  \end{axis}
\end{tikzpicture}
\end{document}
