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\documentclass[10pt,oneside]{scrartcl}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{mathtools}
\usepackage{pgfplots}
\pgfplotsset{width=7cm,every tick/.style={black}}
\usepackage{graphicx}
\begin{document}
\begin{center}
\begin{tikzpicture}
\begin{axis}[
scale only axis=true,
width=10cm,
height=2cm,
grid=none,
minor tick num=1,
%xtick align=center,
xlabel=$x$,
ytick=\empty,
title={},
xmin=1.48,
xmax=1.54,
ymin=-1,
ymax=3,
axis x line = bottom,
axis y line = none,
legend style={at={(1, 0.45)},anchor=west,font=\footnotesize,draw=black},
]
\addplot+[color=black,mark options={mark=*,mark size=2pt,fill=gray,scale=1},error bars,x dir=both,x explicit]
coordinates {
(1.51, 1.25) +- (0.02, 0)
};
\addlegendentry{$a$};
\addplot+[color=black,mark options={mark=square*,mark size=2pt,fill=gray,scale=1},error bars,x dir=both,x explicit]
coordinates {
(1.504, 0.25) +- (0.003, 0)
};
\addlegendentry{$b$};
\end{axis}
\end{tikzpicture}
\end{center}
\end{document}