tikzpicture, feynman, equation

Did you meant the equation into the center? You could make it a simple node ike this:

documentclass{article}
usepackage{tikz}
usepackage[compat=1.0.0]{tikz-feynman}
usepackage{amsmath}

begin{document}
    
    
    begin{equation}
        begin{tikzpicture}[baseline=(a1.base)]         
            node at (7,-1) {( begin{split}equiv <Q_i>(alpha_s^0)=Q_i,quad text{for}quad Q_i=Q_1,Q_2,E_1,E_2 end{split} )};
            large
            begin{feynman}[inline=(a1.base)]
                vertex (a1) {(d)};
                vertex[right=2cm of a1] (a2);
                vertex[right=2cm of a2] (a3) {(s)};
                vertex[below=4em of a1] (b1) {(overline s)};
                vertex[right=2cm of b1] (b2);
                vertex[right=2cm of b2] (b3) {(overline d)};                
                diagram* {
                    {[edges=fermion]
                        (a1) -- (a2) -- (a3) 
                    },
                    {[edges= anti fermion]
                        (b1) -- (b2) -- (b3)
                    },
                    (a2) -- [dashed, edge label=(Q_i)] (b2),              
                };
            end{feynman}
        end{tikzpicture}
        %equiv <Q_i>(alpha_s^0)=Q_i,quad text{for}quad Q_i=Q_1,Q_2,E_1,E_2 .
    end{equation}
end{document}