Ehsan,

there is something wrong with the power symbols you are using, e.g. $\chi 1$ (in FullForm) contains TextCell["2"]. Instead try this:

\[Chi]1 = -((4 \[Beta] (\[CapitalDelta]c - \[CapitalDelta]p\
) (\[CapitalDelta]p (\[CapitalDelta]c - \[CapitalDelta]p) + \
\[CapitalOmega]c^2))/((\[CapitalDelta]c - \[CapitalDelta]p)^2\
 (\[CapitalGamma]c^2 + 4 \[CapitalDelta]p^2) + \[Zeta]d + 
       4 \[CapitalOmega]c^4));
\[Chi]2 = ((2 \[Beta] \[CapitalGamma]c (\[CapitalDelta]c - \
\[CapitalDelta]p)^2)/((\[CapitalDelta]c - \[CapitalDelta]p)^2\
 (\[CapitalGamma]c^2 + 4 \[CapitalDelta]p^2) + \[Zeta]d + 
      4 \[CapitalOmega]c^4));