β=1;Ωc=1;Γc=1;Δc=0;ζd=8Δp(Δc-Δp);
2
Ωc
χ1=-(+4)+ζd+4;
4β(Δc-Δp)(Δp(Δc-Δp)+)
2
Ωc
2
(Δc-Δp)
2
Γc
2
Δp
4
Ωc
χ2=(+4)+ζd+4;
2βΓc
2
(Δc-Δp)
2
(Δc-Δp)
2
Γc
2
Δp
4
Ωc
Plot[{χ1,χ2},{Δp,-0.5,0.5},PlotLegends{"Re[χ]","Im[χ]"},PlotStyle{Blue,Red},PlotRangeAll]