\fill(-\xr/2, 0) circle (2pt) node[above] (l_branch) {$-\sqrt{\vec{p}^2}$} (\xr/2, 0) circle (2pt) node[above] (r_branch) {$\sqrt{\vec{p}^2}$}; ...

\addplot[color=red,domain = 1:9]{1/(sqrt(x)+2)}; \addplot[color=red,domain = 1:9]{1/(x+2) + 1/3}; \addplot[color=blue,domain = 1:9]{-1/(sqrt(x)+2)}; \addplot[color ...

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