\begin{tikzpicture}[sketch]

\draw[->](-4,0)--(4.25,0);
\draw[->](0,-2)--(0,2);

\fill[awesome](-2,0) circle(0.1)node[above]{$-E_\text{p}$};
\fill[awesome](2,0) circle(0.1)node[below]{$+E_\text{p}$};
\draw[dodgerblue,postaction={on each segment={mid arrow=dodgerblue}}](-4,0)--(-2.4,0);
\draw[dodgerblue](-2.40,0) arc(-180:-0:0.4);
\draw[dodgerblue,postaction={on each segment={mid arrow=dodgerblue}}](-1.6,0)--(0,0);
\draw[dodgerblue,postaction={on each segment={mid arrow=dodgerblue}}](0,0)--(1.6,0);
\draw[dodgerblue] (1.60,0) arc(180:0:0.4);
\draw[dodgerblue,postaction={on each segment={mid arrow=dodgerblue}}](2.4,0)--(4,0);

%\draw[dodgerblue,postaction={on each segment={mid arrow=dodgerblue}}, out=220, in=290](170:4) to (-4,0);
\draw[dodgerblue,dotted,postaction={on each segment={mid arrow=dodgerblue}}](170:3.75) arc(135:180:0.9);
\draw[dodgerblue,dotted,postaction={on each segment={mid arrow=dodgerblue}}](-170:3.75) arc(-135:-180:0.9);

\draw[dodgerblue,dotted,postaction={on each segment={mid arrow=dodgerblue}}](4,0) arc(0:45:0.9)node[above]{$x^0<y^0$};
\draw[dodgerblue,dotted,postaction={on each segment={mid arrow=dodgerblue}}](4,0) arc(0:-45:0.9)node[below]{$x^0>y^0$};

\draw(4.7,0) node{$=$};

\end{tikzpicture}

%2. Graph:

\begin{tikzpicture}[sketch]

\draw[->](-4,0)--(4.25,0);
\draw[->](0,-2)--(0,2);

\fill[awesome](-2,0.5) circle(0.1)node[above]{$-E_\text{p}+i \varepsilon$};
\fill[awesome](2,-0.5) circle(0.1)node[below]{$E_\text{p}-i\varepsilon$};
\draw[dodgerblue,postaction={on each segment={mid arrow=dodgerblue}}](-4,0)--(-2,0);
%\draw[dodgerblue](-2.25,0) arc(-180:-0:0.25);
\draw[dodgerblue,postaction={on each segment={mid arrow=dodgerblue}}](-2,0)--(0,0);
\draw[dodgerblue,postaction={on each segment={mid arrow=dodgerblue}}](0,0)--(2,0);
%\draw[dodgerblue] (1.75,0) arc(180:0:0.25);
\draw[dodgerblue,postaction={on each segment={mid arrow=dodgerblue}}](2,0)--(4,0);

%\draw[dodgerblue,postaction={on each segment={mid arrow=dodgerblue}}, out=220, in=290](170:4) to (-4,0);
\draw[dodgerblue,dotted,postaction={on each segment={mid arrow=dodgerblue}}](170:3.75) arc(135:180:0.9);
\draw[dodgerblue,dotted,postaction={on each segment={mid arrow=dodgerblue}}](-170:3.75) arc(-135:-180:0.9);

\draw[dodgerblue,dotted,postaction={on each segment={mid arrow=dodgerblue}}](4,0) arc(0:45:0.9)node[above]{$x^0<y^0$};
\draw[dodgerblue,dotted,postaction={on each segment={mid arrow=dodgerblue}}](4,0) arc(0:-45:0.9)node[below]{$x^0>y^0$};

\end{tikzpicture}