(* ::Package:: *)

(* ::Input:: *)
(*(*FIELD REDEFINITIONS*)*)
(**)


(* ::Input::Closed:: *)
(*(*INITIAL SETTINGS*)*)


(* ::Input:: *)
(*SetAttributes[\[Eta],Orderless]*)
(*SetAttributes[f1, Orderless]*)
(*SetAttributes[f2, Orderless]*)
(*SetAttributes[f3, Orderless]*)
(*SetAttributes[f4, Orderless]*)
(*Unprotect[Power,Plus,Times];*)
(*\[Eta][\[Mu]_,\[Nu]_]\[Eta][\[Nu]_,\[Rho]_]:=\[Eta][\[Mu],\[Rho]]*)
(*\[Eta][\[Mu]_,\[Mu]_]:=4*)
(*\[Eta][\[Mu]_,\[Nu]_]^2:=4*)
(*\[Eta][\[Mu]_,\[Nu]_]p[\[Nu]_]:=p[\[Mu]]*)
(*\[Eta][\[Mu]_,\[Nu]_]k[\[Nu]_]:=k[\[Mu]]*)
(*\[Eta][\[Mu]_,\[Nu]_]q[\[Nu]_]:=q[\[Mu]]*)
(*\[Eta][\[Mu]_,\[Nu]_]l[\[Nu]_]:=l[\[Mu]]*)
(*p[\[Mu]_]^2:=p2*)
(*k[\[Mu]_]^2:=k2*)
(*q[\[Mu]_]^2:=q2*)
(*l[\[Mu]_]^2:=l2*)
(*p[m_] q[m_]:=pq*)
(*p[m_] k[m_]:=pk*)
(*q[m_] k[m_]:=qk*)
(*l[m_]p[m_]:=lp*)
(*l[m_]q[m_]:=lq*)
(*l[m_]k[m_]:=lk*)
(*(2p_)[m_]:=2(p[m])*)
(*(-2p_)[m_]:=-2(p[m])*)
(*(p_+q_)[m_]:= p[m]+ q[m]*)
(*(-p_)[m_]:=-(p[m])*)
(*pk:=0*)
(*p[m_]p[n_]:=0*)
(*k[m_]k[n_]:=0*)
(*p[m_]k[n_]:=0*)
(*qk p[m_]:=0*)
(*pq k[m_]:=0*)
(*pq p[m_]:=0*)
(*qk k[m_]:=0*)
(*pq^2:=0*)
(*qk^2:=0*)
(*pq^3:=0*)
(*qk^3:=0*)
(*pq^4:=0*)
(*qk^4:=0*)
(*\[CapitalLambda]=0;*)
(*Cc=0;*)


(* ::Input::Closed:: *)
(*(*SUBSTITUTION RULES FOR SYMMETRIC INTEGRATION*)*)


(* ::Input::Closed:: *)
(*	(*Function used to construct the rules*)*)


(* ::Input:: *)
(*F[m_]:=2/\[Pi] ((1+(-1)^m) Sqrt[\[Pi]] Gamma[(1+m)/2])/(4 Gamma[2+m/2])*)


(* ::Input::Closed:: *)
(*	(*Functions used for the rules up to the 4-tensor case, p external, q integrated, m integer  *)*)


(* ::Input:: *)
(**)
(*F0[m_,p2_,q2_]:=p2^(m/2)q2^(m/2)F[m]*)
(*F1[m_,r_,p_,p2_,q2_]:=p2^((m+1)/2-1)q2^((m+1)/2)F[m+1]p[r]*)
(*F2[m_,r_,s_,p_,p2_,q2_]:=Expand[p2^((m+2)/2-2)q2^((m+2)/2) F[m+2]/(m+1) (p2 \[Eta][r,s]+m p[r]p[s])]*)
(*F3[m_,r_,s_,t_,p_,p2_,q2_]:=Expand[p2^((m+3)/2-3)q2^((m+3)/2) F[m+3]/(m+2) (p2 (p[t] \[Eta][r,s]+p[r] \[Eta][t,s]+p[s] \[Eta][r,t])+(m-1)p[r]p[s]p[t])]*)
(*F4[m_,r_,s_,t_,u_,p_,p2_,q2_]:=Expand[-(((1+(-1)^m) p2^(-2+m/2) q2^(2+m/2) (3 p[r] (-p2 ((1+2 m) Gamma[4+m/2] Gamma[(3+m)/2]-2 (1+m) Gamma[3+m/2] Gamma[(5+m)/2]) (p[u] \[Eta][s,t]+p[t] \[Eta][s,u])+p[s] (((8+11 m) Gamma[4+m/2] Gamma[(3+m)/2]-16 (1+m) Gamma[3+m/2] Gamma[(5+m)/2]) p[t] p[u]+p2 (-(1+2 m) Gamma[4+m/2] Gamma[(3+m)/2]+2 (1+m) Gamma[3+m/2] Gamma[(5+m)/2]) \[Eta][t,u]))+p2 (-3 ((1+2 m) Gamma[4+m/2] Gamma[(3+m)/2]-2 (1+m) Gamma[3+m/2] Gamma[(5+m)/2]) p[s] p[u] \[Eta][r,t]-3 ((1+2 m) Gamma[4+m/2] Gamma[(3+m)/2]-2 (1+m) Gamma[3+m/2] Gamma[(5+m)/2]) p[t] (p[u] \[Eta][r,s]+p[s] \[Eta][r,u])+p2 ((-2+m) Gamma[4+m/2] Gamma[(3+m)/2]-(1+m) Gamma[3+m/2] Gamma[(5+m)/2]) (\[Eta][r,u] \[Eta][s,t]+\[Eta][r,t] \[Eta][s,u]+\[Eta][r,s] \[Eta][t,u]))))/(30 (1+m) Sqrt[\[Pi]] Gamma[3+m/2] Gamma[4+m/2]))]*)


(* ::Input::Closed:: *)
(*	(*Function used for the 5-tensor case, p external, q integrated*)*)


(* ::Input:: *)
(*F65[\[Mu]_,\[Nu]_,\[Rho]_,\[Sigma]_,\[Alpha]_,p_,q2_]:=q2^3/192 (p[\[Sigma]] \[Eta][\[Alpha],\[Rho]] \[Eta][\[Mu],\[Nu]]+p[\[Rho]] \[Eta][\[Alpha],\[Sigma]] \[Eta][\[Mu],\[Nu]]+p[\[Sigma]] \[Eta][\[Alpha],\[Nu]] \[Eta][\[Mu],\[Rho]]+p[\[Nu]] \[Eta][\[Alpha],\[Sigma]] \[Eta][\[Mu],\[Rho]]+p[\[Rho]] \[Eta][\[Alpha],\[Nu]] \[Eta][\[Mu],\[Sigma]]+p[\[Nu]] \[Eta][\[Alpha],\[Rho]] \[Eta][\[Mu],\[Sigma]]+p[\[Sigma]] \[Eta][\[Alpha],\[Mu]] \[Eta][\[Nu],\[Rho]]+p[\[Mu]] \[Eta][\[Alpha],\[Sigma]] \[Eta][\[Nu],\[Rho]]+p[\[Alpha]] \[Eta][\[Mu],\[Sigma]] \[Eta][\[Nu],\[Rho]]+p[\[Rho]] \[Eta][\[Alpha],\[Mu]] \[Eta][\[Nu],\[Sigma]]+p[\[Mu]] \[Eta][\[Alpha],\[Rho]] \[Eta][\[Nu],\[Sigma]]+p[\[Alpha]] \[Eta][\[Mu],\[Rho]] \[Eta][\[Nu],\[Sigma]]+p[\[Nu]] \[Eta][\[Alpha],\[Mu]] \[Eta][\[Rho],\[Sigma]]+p[\[Mu]] \[Eta][\[Alpha],\[Nu]] \[Eta][\[Rho],\[Sigma]]+p[\[Alpha]] \[Eta][\[Mu],\[Nu]] \[Eta][\[Rho],\[Sigma]])*)


(* ::Input::Closed:: *)
(*	(*Rules up to 14 integrated q, p external*)*)


(* ::Input:: *)
(**)
(*rp1410=q[m_]q[n_]q[r_]q[s_]pq^10:>F4[10,m,n,r,s,p,p2,q2];*)
(*rp1411=q[m_]q[n_]q[r_]pq^11:>F3[11,m,n,r,p,p2,q2];*)
(*rp1412=q[m_]q[n_]pq^12:>F2[12,m,n,p,p2,q2];*)
(*rp1413=q[m_]pq^13:>F1[13,m,p,p2,q2];*)
(*rp1414=pq^14:>F0[14,p2,q2];*)
(*rp128=q[m_]q[n_]q[r_]q[s_]pq^8:>F4[8,m,n,r,s,p,p2,q2];*)
(*rp129=q[m_]q[n_]q[r_]pq^9:>F3[9,m,n,r,p,p2,q2];*)
(*rp1210=q[m_]q[n_]pq^10:>F2[10,m,n,p,p2,q2];*)
(*rp1211=q[m_]pq^11:>F1[11,m,p,p2,q2];*)
(*rp1212=pq^12:>F0[12,p2,q2];*)
(*rp106=q[m_]q[n_]q[r_]q[s_]pq^6:>F4[6,m,n,r,s,p,p2,q2];*)
(*rp107=q[m_]q[n_]q[r_]pq^7:>F3[7,m,n,r,p,p2,q2];*)
(*rp108=q[m_]q[n_]pq^8:>F2[8,m,n,p,p2,q2];*)
(*rp109=q[m_]pq^9:>F1[9,m,p,p2,q2];*)
(*rp1010=pq^10:>F0[10,p2,q2];*)
(*rp84=q[m_]q[n_]q[r_]q[s_]pq^4:>F4[4,m,n,r,s,p,p2,q2];*)
(*rp85=q[m_]q[n_]q[r_]pq^5:>F3[5,m,n,r,p,p2,q2];*)
(*rp86=q[m_]q[n_]pq^6:>F2[6,m,n,p,p2,q2];*)
(*rp87=q[m_]pq^7:>F1[7,m,p,p2,q2];*)
(*rp88=pq^8:>F0[8,p2,q2];*)
(*rp61=q[m_]q[n_]q[r_]q[s_]q[a_]pq:>F65[m,n,r,s,a,p,q2];*)
(*rp62=q[m_]q[n_]q[r_]q[s_]pq^2:>F4[2,m,n,r,s,p,p2,q2];*)
(*rp63=q[m_]q[n_]q[r_]pq^3:>F3[3,m,n,r,p,p2,q2];*)
(*rp64=q[m_]q[n_]pq^4:>F2[4,m,n,p,p2,q2];*)
(*rp65=q[m_]pq^5:>F1[5,m,p,p2,q2];*)
(*rp66=pq^6:>F0[6,p2,q2];*)
(*rp40=q[m_]q[n_]q[r_]q[s_]:>F4[0,m,n,r,s,p,p2,q2];*)
(*rp41=q[m_]q[n_]q[r_]pq:>F3[1,m,n,r,p,p2,q2];*)
(*rp42=q[m_]q[n_]pq^2:>F2[2,m,n,p,p2,q2];*)
(*rp43=q[m_]pq^3:>F1[3,m,p,p2,q2];*)
(*rp44=pq^4:>F0[4,p2,q2];*)
(*rp20=q[m_]q[n_]:>(q2/4)\[Eta][m,n];*)
(*rp21=q[m_]pq:>(q2/4)p[m];*)
(*rp22=pq^2:>q2 p2/4;*)


(* ::Input::Closed:: *)
(*	(*Rules up to 14 integrated q, k external*)*)


(* ::Input:: *)
(*rk1410=q[m_]q[n_]q[r_]q[s_]qk^10:>F4[10,m,n,r,s,k,k2,q2];*)
(*rk1411=q[m_]q[n_]q[r_]qk^11:>F3[11,m,n,r,k,k2,q2];*)
(*rk1412=q[m_]q[n_]qk^12:>F2[12,m,n,k,k2,q2];*)
(*rk1413=q[m_]qk^13:>F1[13,m,k,k2,q2];*)
(*rk1414=qk^14:>F0[14,k2,q2];*)
(*rk128=q[m_]q[n_]q[r_]q[s_]qk^8:>F4[8,m,n,r,s,k,k2,q2];*)
(*rk129=q[m_]q[n_]q[r_]qk^9:>F3[9,m,n,r,k,k2,q2];*)
(*rk1210=q[m_]q[n_]qk^10:>F2[10,m,n,k,k2,q2];*)
(*rk1211=q[m_]qk^11:>F1[11,m,k,k2,q2];*)
(*rk1212=qk^12:>F0[12,k2,q2];*)
(*rk106=q[m_]q[n_]q[r_]q[s_]qk^6:>F4[6,m,n,r,s,k,k2,q2];*)
(*rk107=q[m_]q[n_]q[r_]qk^7:>F3[7,m,n,r,k,k2,q2];*)
(*rk108=q[m_]q[n_]qk^8:>F2[8,m,n,k,k2,q2];*)
(*rk109=q[m_]qk^9:>F1[9,m,k,k2,q2];*)
(*rk1010=qk^10:>F0[10,k2,q2];*)
(*rk84=q[m_]q[n_]q[r_]q[s_]qk^4:>Expand[F4[4,m,n,r,s,k,k2,q2]];*)
(*rk85=q[m_]q[n_]q[r_]qk^5:>F3[5,m,n,r,k,k2,q2];*)
(*rk86=q[m_]q[n_]qk^6:>F2[6,m,n,k,k2,q2];*)
(*rk87=q[m_]qk^7:>F1[7,m,k,k2,q2];*)
(*rk88=qk^8:>F0[8,k2,q2];*)
(*rk61=q[m_]q[n_]q[r_]q[s_]q[a_]qk:>F65[m,n,r,s,a,k,q2];*)
(*rk62=q[m_]q[n_]q[r_]q[s_]qk^2:>F4[2,m,n,r,s,k,k2,q2];*)
(*rk63=q[m_]q[n_]q[r_]qk^3:>F3[3,m,n,r,k,k2,q2];*)
(*rk64=q[m_]q[n_]qk^4:>F2[4,m,n,k,k2,q2];*)
(*rk65=q[m_]qk^5:>F1[5,m,k,k2,q2];*)
(*rk66=qk^6:>F0[6,k2,q2];*)
(**)
(*rk41=q[m_]q[n_]q[r_]qk:>F3[1,m,n,r,k,k2,q2];*)
(*rk42=q[m_]q[n_]qk^2:>F2[2,m,n,k,k2,q2];*)
(*rk43=q[m_]qk^3:>F2[3,m,k,k2,q2];*)
(*rk44=qk^4:>F0[4,k2,q2];*)
(**)
(*rk21=q[m_]qk:>(q2/4)k[m];*)
(*rk22=qk^2:>q2 k2/4;*)


(* ::Input::Closed:: *)
(*(*EXPANSION OF CURVATURE TENSORS UP TO THE 4TH ORDER IN THE GRAVITON FIELD*)*)


(* ::Input:: *)
(**)
(*(*Metric expanded as g[m,n]=\[Eta][m,n]+f[m,n]*)*)
(**)
(*(*Inverse metric*)*)
(**)
(*ginv1[m_,n_,f1_]:=-f1[m,n]*)
(*ginv2[m_,n_,f1_,f2_,a_]:=f1[m,a]f2[a,n]*)
(*ginv3[m_,n_,f1_,f2_,f3_,a_,b_]:=-f1[m,a]f2[a,b]f3[b,n]*)
(**)
(*(*Connection*)*)
(**)
(*\[CapitalGamma]1[m_,n_,r_,f1_,p_]:=Expand[1/2 (I p[m]f1[n,r]+I p[n]f1[m,r]-I p[r]f1[m,n])]*)
(*\[CapitalGamma]2[m_,n_,r_,f1_,p_,f2_,a_]:=Expand[ginv1[r,a,f2]\[CapitalGamma]1[m,n,a,f1,p]]*)
(*\[CapitalGamma]3[m_,n_,r_,f1_,p_,f2_,f3_,a_,b_]:=Expand[ginv2[r,a,f2,f3,b]\[CapitalGamma]1[m,n,a,f1,p]]*)
(*\[CapitalGamma]4[m_,n_,r_,f1_,p_,f2_,f3_,f4_,a_,b_,c_]:=Expand[ginv3[r,a,f2,f3,f4,b,c]\[CapitalGamma]1[m,n,a,f1,p]]*)
(**)
(*(*Ricci tensor*)*)
(**)
(*Ric1[m_,n_,f1_,p_,a_]:=Expand[I p[a]\[CapitalGamma]1[m,n,a,f1,p]-I p[n]\[CapitalGamma]1[m,a,a,f1,p]]*)
(*Ric2[m_,n_,f1_,p_,f2_,k_,a_,b_]:=Expand[I (p[a]+k[a])\[CapitalGamma]2[m,n,a,f1,p,f2,b]-I (p[n]+k[n])\[CapitalGamma]2[m,a,a,f1,p,f2,b]+\[CapitalGamma]1[b,a,a,f1,p]\[CapitalGamma]1[m,n,b,f2,k]-\[CapitalGamma]1[b,n,a,f1,p]\[CapitalGamma]1[m,a,b,f2,k]]*)
(*Ric3[m_,n_,f1_,p_,f2_,k_,f3_,q_,a_,b_,c_]:=Expand[I (p[a]+k[a]+q[a])\[CapitalGamma]3[m,n,a,f1,p,f2,f3,b,c]-I (p[n]+k[n]+q[n])\[CapitalGamma]3[m,a,a,f1,p,f2,f3,b,c]+\[CapitalGamma]2[b,a,a,f1,p,f3,c]\[CapitalGamma]1[m,n,b,f2,k]+\[CapitalGamma]1[b,a,a,f1,p]\[CapitalGamma]2[m,n,b,f2,k,f3,c]-\[CapitalGamma]2[b,n,a,f1,p,f3,c]\[CapitalGamma]1[m,a,b,f2,k]-\[CapitalGamma]1[b,n,a,f1,p]\[CapitalGamma]2[m,a,b,f2,k,f3,c]]*)
(*Ric4[m_,n_,f1_,p_,f2_,k_,f3_,q_,f4_,l_,a_,b_,c_,d_]:=Expand[I (p[a]+k[a]+q[a]+l[a])\[CapitalGamma]4[m,n,a,f1,p,f2,f3,f4,b,c,d]-I (p[n]+k[n]+q[n]+l[n])\[CapitalGamma]4[m,a,a,f1,p,f2,f3,f4,b,c,d]+\[CapitalGamma]3[b,a,a,f1,p,f2,f3,c,d]\[CapitalGamma]1[m,n,b,f4,l]+\[CapitalGamma]2[b,a,a,f1,p,f2,c]\[CapitalGamma]2[m,n,b,f3,q,f4,d]+\[CapitalGamma]1[b,a,a,f1,p]\[CapitalGamma]3[m,n,b,f2,k,f3,f4,c,d]-\[CapitalGamma]3[b,n,a,f1,p,f2,f3,c,d]\[CapitalGamma]1[m,a,b,f4,l]-\[CapitalGamma]2[b,n,a,f1,p,f2,c]\[CapitalGamma]2[m,a,b,f3,q,f4,d]-\[CapitalGamma]1[b,n,a,f1,p]\[CapitalGamma]3[m,a,b,f2,k,f3,f4,c,d]]*)
(**)
(*(*Ricci scalar*)*)
(**)
(*R1[f1_,p_,a_,b_]:=Expand[Ric1[b,b,f1,p,a]]*)
(*R2[f1_,p_,f2_,k_,a_,b_,c_]:=Expand[Expand[Ric2[c,c,f1,p,f2,k,a,b]]+Expand[ginv1[a,b,f1]Ric1[a,b,f2,k,c]]]*)
(*R3[f1_,p_,f2_,k_,f3_,q_,a_,b_,c_,d_]:=Expand[Expand[Ric3[d,d,f1,p,f2,k,f3,q,a,b,c]]+Expand[ginv1[a,b,f3]Ric2[a,b,f1,p,f2,k,c,d]]+Expand[ginv2[a,b,f2,f3,c]Ric1[a,b,f1,p,d]]]*)
(*R4[f1_,p_,f2_,k_,f3_,q_,f4_,l_,a_,b_,c_,d_,e_]:=Expand[Expand[Ric4[a,a,f1,p,f2,k,f3,q,f4,l,b,c,d,e]]+Expand[ginv1[a,b,f4]Ric3[a,b,f1,p,f2,k,f3,q,c,d,e]]+Expand[ginv2[a,b,f1,f2,c]Ric2[a,b,f3,q,f4,l,d,e]]+Expand[ginv3[a,b,f1,f2,f3,c,d]Ric1[a,b,f4,l,e]]]*)
(**)
(*(*Square root of det g*)*)
(**)
(*sqrtg1[f1_,a_]:=1/2 f1[a,a]*)
(*sqrtg2[f1_,f2_,a_,b_]:=1/8 f1[a,a]f2[b,b]-1/4 f1[a,b]f2[b,a]*)
(*sqrtg3[f1_,f2_,f3_,a_,b_,c_]:=1/48 f1[a,a]f2[b,b]f3[c,c]-1/8 f1[a,a]f2[b,c]f3[b,c]+1/6 f1[a,b]f2[b,c]f3[c,a]*)
(*sqrtg4[f1_,f2_,f3_,f4_,a_,b_,c_,d_]:=(f1[a,a]f2[b,b]f3[c,c]f4[d,d])/384-(f1[a,a]f2[b,b] f3[c,d]f4[d,c])/32+(f1[a,b]f2[a,b]f3[c,d]f4[c,d])/32+(f1[a,a] f2[b,c]f3[c,d]f4[d,b])/12-(f1[a,b] f2[b,c]f3[c,d]f4[d,a])/8*)
(**)


(* ::Input::Closed:: *)
(*(*EUCLIDEAN VERTICES*)*)


(* ::Input:: *)
(*	(*Three graviton vertex, momenta and indices: f1\[Rule](p,\[Mu],\[Nu]), f2\[Rule](k,\[Rho],\[Sigma]), f3\[Rule](q,\[Alpha],\[Beta])*)*)


(* ::Input:: *)
(**)
(*VV3[\[Mu]_,\[Nu]_,p_,\[Rho]_,\[Sigma]_,k_,\[Alpha]_,\[Beta]_,q_,m_,n_,a_,b_,c_]:=Expand[( Aa (Expand[2 Ric2[m,n,f1,p,f2,k,a,b]Ric1[m,n,f3,q,c]]+Expand[sqrtg1[f1,a]Ric1[m,n,f2,k,b]Ric1[m,n,f3,q,c]]+2 Expand[Ric1[m,n,f1,p,a]Ric1[c,n,f2,k,b]ginv1[m,c,f3]])+1/2 (Bb-Aa) (Expand[2Ric2[m,m,f1,p,f2,k,a,b]Ric1[n,n,f3,q,c]]+Expand[sqrtg1[f1,a]Ric1[m,m,f2,k,b]Ric1[n,n,f3,q,c]]+2 Expand[Ric1[m,n,f1,p,a]Ric1[c,c,f2,k,b]ginv1[m,n,f3]])+Cc(ExpandAll[(Expand[Expand[Ric3[c,c,f1,p,f2,k,f3,q,a,b,m]]+Expand[ginv1[a,b,f3]Ric2[a,b,f1,p,f2,k,m,c]]+Expand[ginv2[a,b,f2,f3,m]Ric1[a,b,f1,p,c]]]*)
(*+sqrtg1[f3,n](Expand[Expand[Ric2[m,m,f1,p,f2,k,a,b]]+Expand[ginv1[a,b,f1]Ric1[a,b,f2,k,m]]])+sqrtg2[f3,f2,a,b]Expand[Ric1[c,c,f1,p,m]])])-ExpandAll[2\[CapitalLambda] sqrtg3[f1,f2,f3,a,b,c]])/.{f1[x_,y_]:>1/2 (\[Eta][x,\[Mu]]\[Eta][y,\[Nu]]+\[Eta][x,\[Nu]]\[Eta][y,\[Mu]]),f2[z_,t_]:>1/2 (\[Eta][z,\[Rho]]\[Eta][t,\[Sigma]]+\[Eta][z,\[Sigma]]\[Eta][t,\[Rho]]),f3[u_,w_]:>1/2 (\[Eta][u,\[Alpha]]\[Eta][w,\[Beta]]+\[Eta][u,\[Beta]]\[Eta][w,\[Alpha]])}]*)
(**)
(*V3Sym[\[Mu]_,\[Nu]_,p_,\[Rho]_,\[Sigma]_,k_,\[Alpha]_,\[Beta]_,q_,m_,n_,a_,b_,c_]:=ExpandAll[VV3[\[Mu],\[Nu],p,\[Rho],\[Sigma],k,\[Alpha],\[Beta],q,m,n,a,b,c]+VV3[\[Mu],\[Nu],p,\[Alpha],\[Beta],q,\[Rho],\[Sigma],k,m,n,a,b,c]+VV3[\[Rho],\[Sigma],k,\[Mu],\[Nu],p,\[Alpha],\[Beta],q,m,n,a,b,c]+VV3[\[Rho],\[Sigma],k,\[Alpha],\[Beta],q,\[Mu],\[Nu],p,m,n,a,b,c]+VV3[\[Alpha],\[Beta],q,\[Mu],\[Nu],p,\[Rho],\[Sigma],k,m,n,a,b,c]+VV3[\[Alpha],\[Beta],q,\[Rho],\[Sigma],k,\[Mu],\[Nu],p,m,n,a,b,c]]*)
(**)


(* ::Input::Closed:: *)
(*	(*Four gravitons vertex, momenta and indices f1\[Rule](p,\[Mu],\[Nu]), f2\[Rule](k,\[Rho],\[Sigma]), f3\[Rule](q,\[Alpha],\[Beta]), f4\[Rule](l,\[Gamma],\[Delta])*)*)


(* ::Input:: *)
(*VV4[\[Mu]_,\[Nu]_,p_,\[Rho]_,\[Sigma]_,k_,\[Alpha]_,\[Beta]_,q_,\[Gamma]_,\[Delta]_,l_,m_,n_,a_,b_,c_,d_,e_]:=ExpandAll[(Aa(Expand[Ric1[m,n,f1,p,a]Ric1[c,d,f2,k,b]ginv1[m,c,f3]ginv1[n,d,f4]]+2Expand[Ric1[m,n,f1,p,a]Ric1[c,n,f2,k,b]ginv2[m,c,f3,f4,e]]+4Expand[Ric1[m,n,f1,p,a]Ric2[c,n,f2,k,f3,q,b,e]ginv1[m,c,f4]]+Expand[Ric2[m,n,f1,p,f2,k,a,b]Ric2[m,n,f3,q,f4,l,c,d]]+2Expand[Ric3[m,n,f1,p,f2,k,f3,q,a,b,c]Ric1[m,n,f4,l,d]]+2Expand[sqrtg1[f1,a]Ric1[m,n,f2,k,b]Ric1[c,n,f3,q,d]ginv1[m,c,f4]]+2Expand[sqrtg1[f1,a]Ric1[m,n,f2,k,b]Ric2[m,n,f3,q,f4,l,c,d]]+Expand[sqrtg2[f1,f2,a,b]Ric1[m,n,f3,q,c]Ric1[m,n,f4,l,d]])+1/2 (Bb-Aa)(Expand[Ric1[m,n,f1,p,a]Ric1[c,d,f2,k,b]ginv1[m,n,f3]ginv1[c,d,f4]]+2Expand[Ric1[m,n,f1,p,a]Ric1[c,c,f2,k,b]ginv2[m,n,f3,f4,e]]+2Expand[Ric1[m,n,f1,p,a]Ric2[c,c,f2,k,f3,q,b,e]ginv1[m,n,f4]]+2Expand[Ric1[c,c,f1,p,a]Ric2[m,n,f2,k,f3,q,b,e]ginv1[m,n,f4]]+Expand[Ric2[m,m,f1,p,f2,k,a,b]Ric2[n,n,f3,q,f4,l,c,d]]+2Expand[Ric3[m,m,f1,p,f2,k,f3,q,a,b,c]Ric1[n,n,f4,l,d]]+2Expand[sqrtg1[f1,a]Ric1[m,n,f2,k,b]Ric1[c,c,f3,q,d]ginv1[m,n,f4]]+2Expand[sqrtg1[f1,a]Ric1[m,m,f2,k,b]Ric2[n,n,f3,q,f4,l,c,d]]+Expand[sqrtg2[f1,f2,a,b]Ric1[m,m,f3,q,c]Ric1[n,n,f4,l,d]])*)
(*+Cc(R4[f1,p,f2,k,f3,q,f4,l,a,b,c,d,e]+sqrtg1[f1,a]R3[f2,k,f3,q,f4,l,b,c,d,e]+sqrtg2[f1,f2,a,b]R2[f3,q,f4,l,c,d,e]+sqrtg3[f1,f2,f3,a,b,c]R1[f4,l,d,e])-ExpandAll[2\[CapitalLambda] sqrtg4[f1,f2,f3,f4,a,b,c,d]])/.{f1[x_,y_]->1/2 (\[Eta][x,\[Mu]]\[Eta][y,\[Nu]]+\[Eta][x,\[Nu]]\[Eta][y,\[Mu]]),f2[z_,t_]->1/2 (\[Eta][z,\[Rho]]\[Eta][t,\[Sigma]]+\[Eta][z,\[Sigma]]\[Eta][t,\[Rho]]),f3[u_,w_]->1/2 (\[Eta][u,\[Alpha]]\[Eta][w,\[Beta]]+\[Eta][u,\[Beta]]\[Eta][w,\[Alpha]]),f4[h_,i_]->1/2 (\[Eta][h,\[Gamma]]\[Eta][i,\[Delta]]+\[Eta][h,\[Delta]]\[Eta][i,\[Gamma]])}]*)
(**)
(*V4Sym[\[Mu]_,\[Nu]_,p_,\[Rho]_,\[Sigma]_,k_,\[Alpha]_,\[Beta]_,q_,\[Gamma]_,\[Delta]_,l_,m_,n_,a_,b_,c_,d_,e_]:=ExpandAll[(VV4[\[Mu],\[Nu],p,\[Rho],\[Sigma],k,\[Alpha],\[Beta],q,\[Gamma],\[Delta],l,m,n,a,b,c,d,e]+VV4[\[Mu],\[Nu],p,\[Rho],\[Sigma],k,\[Gamma],\[Delta],l,\[Alpha],\[Beta],q,m,n,a,b,c,d,e]+VV4[\[Mu],\[Nu],p,\[Alpha],\[Beta],q,\[Rho],\[Sigma],k,\[Gamma],\[Delta],l,m,n,a,b,c,d,e]+VV4[\[Mu],\[Nu],p,\[Alpha],\[Beta],q,\[Gamma],\[Delta],l,\[Rho],\[Sigma],k,m,n,a,b,c,d,e]+*)
(*VV4[\[Mu],\[Nu],p,\[Gamma],\[Delta],l,\[Rho],\[Sigma],k,\[Alpha],\[Beta],q,m,n,a,b,c,d,e]+*)
(*VV4[\[Mu],\[Nu],p,\[Gamma],\[Delta],l,\[Alpha],\[Beta],q,\[Rho],\[Sigma],k,m,n,a,b,c,d,e]+*)
(*VV4[\[Rho],\[Sigma],k,\[Mu],\[Nu],p,\[Alpha],\[Beta],q,\[Gamma],\[Delta],l,m,n,a,b,c,d,e]+*)
(*VV4[\[Rho],\[Sigma],k,\[Mu],\[Nu],p,\[Gamma],\[Delta],l,\[Alpha],\[Beta],q,m,n,a,b,c,d,e]+*)
(*VV4[\[Rho],\[Sigma],k,\[Alpha],\[Beta],q,\[Mu],\[Nu],p,\[Gamma],\[Delta],l,m,n,a,b,c,d,e]+*)
(*VV4[\[Rho],\[Sigma],k,\[Alpha],\[Beta],q,\[Gamma],\[Delta],l,\[Mu],\[Nu],p,m,n,a,b,c,d,e]+*)
(*VV4[\[Rho],\[Sigma],k,\[Gamma],\[Delta],l,\[Mu],\[Nu],p,\[Alpha],\[Beta],q,m,n,a,b,c,d,e]+*)
(*VV4[\[Rho],\[Sigma],k,\[Gamma],\[Delta],l,\[Alpha],\[Beta],q,\[Mu],\[Nu],p,m,n,a,b,c,d,e]+*)
(*VV4[\[Alpha],\[Beta],q,\[Mu],\[Nu],p,\[Rho],\[Sigma],k,\[Gamma],\[Delta],l,m,n,a,b,c,d,e]+*)
(*VV4[\[Alpha],\[Beta],q,\[Mu],\[Nu],p,\[Gamma],\[Delta],l,\[Rho],\[Sigma],k,m,n,a,b,c,d,e]+*)
(*VV4[\[Alpha],\[Beta],q,\[Rho],\[Sigma],k,\[Mu],\[Nu],p,\[Gamma],\[Delta],l,m,n,a,b,c,d,e]+*)
(*VV4[\[Alpha],\[Beta],q,\[Rho],\[Sigma],k,\[Gamma],\[Delta],l,\[Mu],\[Nu],p,m,n,a,b,c,d,e]+*)
(*VV4[\[Alpha],\[Beta],q,\[Gamma],\[Delta],l,\[Mu],\[Nu],p,\[Rho],\[Sigma],k,m,n,a,b,c,d,e]+*)
(*VV4[\[Alpha],\[Beta],q,\[Gamma],\[Delta],l,\[Rho],\[Sigma],k,\[Mu],\[Nu],p,m,n,a,b,c,d,e]+*)
(*VV4[\[Gamma],\[Delta],l,\[Mu],\[Nu],p,\[Rho],\[Sigma],k,\[Alpha],\[Beta],q,m,n,a,b,c,d,e]+*)
(*VV4[\[Gamma],\[Delta],l,\[Mu],\[Nu],p,\[Alpha],\[Beta],q,\[Rho],\[Sigma],k,m,n,a,b,c,d,e]+*)
(*VV4[\[Gamma],\[Delta],l,\[Rho],\[Sigma],k,\[Mu],\[Nu],p,\[Alpha],\[Beta],q,m,n,a,b,c,d,e]+*)
(*VV4[\[Gamma],\[Delta],l,\[Rho],\[Sigma],k,\[Alpha],\[Beta],q,\[Mu],\[Nu],p,m,n,a,b,c,d,e]+*)
(*VV4[\[Gamma],\[Delta],l,\[Alpha],\[Beta],q,\[Mu],\[Nu],p,\[Rho],\[Sigma],k,m,n,a,b,c,d,e]+VV4[\[Gamma],\[Delta],l,\[Alpha],\[Beta],q,\[Rho],\[Sigma],k,\[Mu],\[Nu],p,m,n,a,b,c,d,e])]*)
(**)


(* ::Input:: *)
(*	(*Graviton-Ghost-Antighost vertex, momenta and indices: antighost\[Rule](\[Mu],q), ghost\[Rule](\[Nu],p), f1\[Rule](\[Alpha],\[Beta],k)*)*)


(* ::Input:: *)
(**)
(*Vgh[\[Mu]_,\[Nu]_,p_,\[Alpha]_,\[Beta]_,k_,n_]:=Expand[-Expand[I(p[n]+k[n])(f1[\[Mu],\[Nu]]I p[n]+f1[\[Nu],n]I p[\[Mu]]+I k[\[Nu]]f1[\[Mu],n])-\[Omega] I(p[\[Mu]]+k[\[Mu]])(f1[\[Nu],n]I p[n]+1/2 f1[n,n]I k[\[Nu]])]/.{f1[x_,y_]:>1/2 (\[Eta][x,\[Alpha]]\[Eta][y,\[Beta]]+\[Eta][x,\[Beta]]\[Eta][y,\[Alpha]])}]*)


(* ::Input::Closed:: *)
(*	(*Two scalars-one graviton vertex*)*)


(* ::Input:: *)
(*Vs1[p_,k_,\[Mu]_,\[Nu]_,m_,n_]:=Expand[1/2 Expand[sqrtg1[f1,n]p[m]k[m]+p[m]k[n]ginv1[m,n,f1]]/.{f1[x_,y_]:>1/2 (\[Eta][x,\[Mu]]\[Eta][y,\[Nu]]+\[Eta][x,\[Nu]]\[Eta][y,\[Mu]])}]*)
(*Vssym1[p_,k_,\[Mu]_,\[Nu]_,m_,n_]:=Expand[(Vs1[p,k,\[Mu],\[Nu],m,n]+Vs1[k,p,\[Mu],\[Nu],m,n])]*)


(* ::Input::Closed:: *)
(*	(*Two scalars-two graviton vertex*)*)


(* ::Input:: *)
(*Vs2[p_,k_,\[Mu]_,\[Nu]_,\[Rho]_,\[Sigma]_,m_,n_,a_]:=Expand[1/2 Expand[sqrtg2[f1,f2,m,n]p[a]k[a]+p[m]k[n]ginv2[m,n,f1,f2,a]+sqrtg1[f1,a]p[m]k[n]ginv1[m,n,f2]]/.{f1[x_,y_]:>1/2 (\[Eta][x,\[Mu]]\[Eta][y,\[Nu]]+\[Eta][x,\[Nu]]\[Eta][y,\[Mu]]),f2[z_,t_]->1/2 (\[Eta][z,\[Rho]]\[Eta][t,\[Sigma]]+\[Eta][z,\[Sigma]]\[Eta][t,\[Rho]])}]*)
(*Vssym2[p_,k_,\[Mu]_,\[Nu]_,\[Rho]_,\[Sigma]_,m_,n_,a_]:=Expand[(Vs2[p,k,\[Mu],\[Nu],\[Rho],\[Sigma],m,n,a]+Vs2[k,p,\[Mu],\[Nu],\[Rho],\[Sigma],m,n,a]+Vs2[p,k,\[Rho],\[Sigma],\[Mu],\[Nu],m,n,a]+Vs2[k,p,\[Rho],\[Sigma],\[Mu],\[Nu],m,n,a])]*)


(* ::Input::Closed:: *)
(*	(*Two scalar-three graviton vertex*)*)


(* ::Input:: *)
(*Vs3[p_,k_,\[Mu]_,\[Nu]_,\[Rho]_,\[Sigma]_,\[Alpha]_,\[Beta]_,m_,n_,a_,b_]:=Expand[1/2 Expand[sqrtg3[f1,f2,f3,m,n,a]p[b]k[b]+p[m]k[n]ginv3[m,n,f1,f2,f3,a,b]+sqrtg2[f1,f2,a,b]p[m]k[n]ginv1[m,n,f3]+sqrtg1[f1,a]p[m]k[n]ginv2[m,n,f2,f3,b]]/.{f1[x_,y_]:>1/2 (\[Eta][x,\[Mu]]\[Eta][y,\[Nu]]+\[Eta][x,\[Nu]]\[Eta][y,\[Mu]]),f2[z_,t_]->1/2 (\[Eta][z,\[Rho]]\[Eta][t,\[Sigma]]+\[Eta][z,\[Sigma]]\[Eta][t,\[Rho]]),f3[u_,w_]->1/2 (\[Eta][u,\[Alpha]]\[Eta][w,\[Beta]]+\[Eta][u,\[Beta]]\[Eta][w,\[Alpha]])}]*)
(*Vssym3[p_,k_,\[Mu]_,\[Nu]_,\[Rho]_,\[Sigma]_,\[Alpha]_,\[Beta]_,m_,n_,a_,b_]:=Expand[Vs3[p,k,\[Mu],\[Nu],\[Rho],\[Sigma],\[Alpha],\[Beta],m,n,a,b]+Vs3[p,k,\[Mu],\[Nu],\[Alpha],\[Beta],\[Rho],\[Sigma],m,n,a,b]+Vs3[p,k,\[Rho],\[Sigma],\[Mu],\[Nu],\[Alpha],\[Beta],m,n,a,b]+Vs3[p,k,\[Rho],\[Sigma],\[Alpha],\[Beta],\[Mu],\[Nu],m,n,a,b]+Vs3[p,k,\[Alpha],\[Beta],\[Mu],\[Nu],\[Rho],\[Sigma],m,n,a,b]+Vs3[p,k,\[Alpha],\[Beta],\[Rho],\[Sigma],\[Mu],\[Nu],m,n,a,b]+Vs3[k,p,\[Mu],\[Nu],\[Rho],\[Sigma],\[Alpha],\[Beta],m,n,a,b]+Vs3[k,p,\[Mu],\[Nu],\[Alpha],\[Beta],\[Rho],\[Sigma],m,n,a,b]+Vs3[k,p,\[Rho],\[Sigma],\[Mu],\[Nu],\[Alpha],\[Beta],m,n,a,b]+Vs3[k,p,\[Rho],\[Sigma],\[Alpha],\[Beta],\[Mu],\[Nu],m,n,a,b]+Vs3[k,p,\[Alpha],\[Beta],\[Mu],\[Nu],\[Rho],\[Sigma],m,n,a,b]+Vs3[k,p,\[Alpha],\[Beta],\[Rho],\[Sigma],\[Mu],\[Nu],m,n,a,b]]*)


(* ::Input:: *)
(*	(*Kc-C-C vertex, C\[Rule](\[Mu],k),C\[Rule](\[Nu],p), Kc\[Rule]\[Rho]*) *)


(* ::Input:: *)
(*VKC[\[Mu]_,k_,\[Nu]_,p_,\[Rho]_]:=I(p[\[Mu]]\[Eta][\[Nu],\[Rho]]-k[\[Nu]]\[Eta][\[Mu],\[Rho]])*)


(* ::Input:: *)
(*	(*K-ghost-graviton vertex, K\[Rule](\[Mu],\[Nu]), C\[Rule](\[Rho],q), \[Phi]\[Rule](\[Alpha].\[Beta],p)*)*)


(* ::Input:: *)
(*VK[\[Mu]_,\[Nu]_,\[Rho]_,q_,\[Alpha]_,\[Beta]_,p_]:=-I(\[Eta][\[Mu],\[Alpha]]\[Eta][\[Rho],\[Beta]]q[\[Nu]]+\[Eta][\[Nu],\[Alpha]]\[Eta][\[Rho],\[Beta]]q[\[Mu]]+\[Eta][\[Mu],\[Alpha]]\[Eta][\[Nu],\[Beta]]p[\[Rho]])*)
(*VKs[\[Mu]_,\[Nu]_,\[Rho]_,q_,\[Alpha]_,\[Beta]_,p_]:=1/4 (VK[\[Mu],\[Nu],\[Rho],q,\[Alpha],\[Beta],p]+ VK[\[Nu],\[Mu],\[Rho],q,\[Alpha],\[Beta],p]+VK[\[Mu],\[Nu],\[Rho],q,\[Beta],\[Alpha],p]+VK[\[Nu],\[Mu],\[Rho],q,\[Beta],\[Alpha],p])*)


(* ::Input::Closed:: *)
(*(*PROPAGATORS*)*)


(* ::Input:: *)
(*	(*Graviton propagator*)*)


(* ::Input:: *)
(*(*0 momenta in the numerator, Part I*)*)


(* ::Input:: *)
(*(*Numerator*)*)
(*N01[\[Mu]_,\[Nu]_,\[Rho]_,\[Sigma]_,p_]:=  \[Eta][\[Mu],\[Nu]]\[Eta][\[Rho],\[Sigma]]*)
(**)
(*(*Denominator*)*)
(*D01[p2_]:=-(4 \[CapitalLambda] (-Bb p2^2+\[CapitalLambda])+Cc^2 p2^2 \[Lambda] (-2+\[Omega])^2+Aa^2 p2^4 \[Lambda] (-2+\[Omega])^2-2 Cc p2 (\[CapitalLambda]+2 \[Lambda] \[CapitalLambda]+Aa p2^2 \[Lambda] (-2+\[Omega])^2-Bb p2^2 \[Lambda] (-2+\[Omega])^2-\[Lambda] \[CapitalLambda] \[Omega]^2)-2 Aa p2^2 (Bb p2^2 \[Lambda] (-2+\[Omega])^2+\[CapitalLambda] (-1+\[Lambda] (-2+\[Omega]^2))))/((Cc p2-Aa p2^2-2 \[CapitalLambda]) (-6 Bb p2^2 \[CapitalLambda]+4 \[CapitalLambda]^2+Cc^2 p2^2 \[Lambda] (-2+\[Omega])^2+Aa^2 p2^4 \[Lambda] (-2+\[Omega])^2+Aa p2^2 (-3 Bb p2^2 \[Lambda] (-2+\[Omega])^2+2 \[CapitalLambda] (1+\[Lambda]+2 \[Lambda] \[Omega]-2 \[Lambda] \[Omega]^2))-Cc p2 (2 Aa p2^2 \[Lambda] (-2+\[Omega])^2-3 Bb p2^2 \[Lambda] (-2+\[Omega])^2+2 \[CapitalLambda] (1+\[Lambda]+2 \[Lambda] \[Omega]-2 \[Lambda] \[Omega]^2))))*)
(**)
(**)


(* ::Input:: *)
(*(*0 momenta in the numerator Part II*)*)


(* ::Input:: *)
(**)
(*(*Numerator*)*)
(*N02[\[Mu]_,\[Nu]_,\[Rho]_,\[Sigma]_,p_]:=\[Eta][\[Mu],\[Rho]] \[Eta][\[Nu],\[Sigma]]+\[Eta][\[Mu],\[Sigma]] \[Eta][\[Nu],\[Rho]]*)
(**)
(*(*Denominator*)*)
(*D02[p2_]:=1/(Cc p2-Aa p2^2-2 \[CapitalLambda])*)


(* ::Input:: *)
(*(*2 momenta in the numerator*)*)


(* ::Input:: *)
(*(*Numerator*)*)
(*N2[\[Mu]_,\[Nu]_,\[Rho]_,\[Sigma]_,p_]:=(p[\[Rho]] p[\[Sigma]] \[Eta][\[Mu],\[Nu]]+p[\[Mu]] p[\[Nu]] \[Eta][\[Rho],\[Sigma]])*)
(**)
(*(*Denominator*)*)
(*D2[p2_]:=(2 (Cc^2 p2 \[Lambda] (2-3 \[Omega]+\[Omega]^2)+Cc \[Lambda] (Bb p2^2 (-2+\[Omega])^2+2 \[CapitalLambda] (-1+\[Omega])-2 Aa p2^2 (2-3 \[Omega]+\[Omega]^2))+p2 (-2 Bb \[CapitalLambda]-Aa \[Lambda] (Bb p2^2 (-2+\[Omega])^2+2 \[CapitalLambda] (-1+\[Omega]))+Aa^2 p2^2 \[Lambda] (2-3 \[Omega]+\[Omega]^2))))/((Cc p2-Aa p2^2-2 \[CapitalLambda]) (-6 Bb p2^2 \[CapitalLambda]+4 \[CapitalLambda]^2+Cc^2 p2^2 \[Lambda] (-2+\[Omega])^2+Aa^2 p2^4 \[Lambda] (-2+\[Omega])^2+Aa p2^2 (-3 Bb p2^2 \[Lambda] (-2+\[Omega])^2+2 \[CapitalLambda] (1+\[Lambda]+2 \[Lambda] \[Omega]-2 \[Lambda] \[Omega]^2))-Cc p2 (2 Aa p2^2 \[Lambda] (-2+\[Omega])^2-3 Bb p2^2 \[Lambda] (-2+\[Omega])^2+2 \[CapitalLambda] (1+\[Lambda]+2 \[Lambda] \[Omega]-2 \[Lambda] \[Omega]^2))))*)


(* ::Input:: *)
(*(*4 momenta in the numerator*)*)


(* ::Input:: *)
(*(*Numerator*)*)
(*N4[\[Mu]_,\[Nu]_,\[Rho]_,\[Sigma]_,p_]:=(p[\[Mu]] p[\[Nu]] p[\[Rho]]p[\[Sigma]])*)
(**)
(*(*Denominator*)*)
(*D4[p2_]:=(4 (4 Bb \[CapitalLambda]^2-Cc^3 p2 \[Lambda] (-1+\[Omega]) (-3+\[Lambda]+\[Omega]+\[Lambda] \[Omega])+Aa^3 p2^4 \[Lambda] (-1+\[Omega]) (-3+\[Lambda]+\[Omega]+\[Lambda] \[Omega])-4 Aa Bb p2^2 \[Lambda] \[CapitalLambda] (2-4 \[Omega]+\[Omega]^2)+Aa^2 p2^2 \[Lambda] (4 \[CapitalLambda] (-1+\[Omega]) (-1+\[Lambda] \[Omega])+Bb p2^2 (\[Lambda] (-2+\[Omega])^2-3 (3-4 \[Omega]+\[Omega]^2)))+Cc^2 \[Lambda] (4 \[CapitalLambda] (-1+\[Omega]) (-1+\[Lambda] \[Omega])+3 Aa p2^2 (-1+\[Omega]) (-3+\[Lambda]+\[Omega]+\[Lambda] \[Omega])+Bb p2^2 (\[Lambda] (-2+\[Omega])^2-3 (3-4 \[Omega]+\[Omega]^2)))+Cc p2 \[Lambda] (-3 Aa^2 p2^2 (-1+\[Omega]) (-3+\[Lambda]+\[Omega]+\[Lambda] \[Omega])+4 Bb \[CapitalLambda] (2-4 \[Omega]+\[Omega]^2)-2 Aa (4 \[CapitalLambda] (-1+\[Omega]) (-1+\[Lambda] \[Omega])+Bb p2^2 (\[Lambda] (-2+\[Omega])^2-3 (3-4 \[Omega]+\[Omega]^2))))))/((Cc p2-Aa p2^2-2 \[CapitalLambda]) (Cc p2 \[Lambda]-Aa p2^2 \[Lambda]-2 \[CapitalLambda]) (-6 Bb p2^2 \[CapitalLambda]+4 \[CapitalLambda]^2+Cc^2 p2^2 \[Lambda] (-2+\[Omega])^2+Aa^2 p2^4 \[Lambda] (-2+\[Omega])^2+Aa p2^2 (-3 Bb p2^2 \[Lambda] (-2+\[Omega])^2+2 \[CapitalLambda] (1+\[Lambda]+2 \[Lambda] \[Omega]-2 \[Lambda] \[Omega]^2))-Cc p2 (2 Aa p2^2 \[Lambda] (-2+\[Omega])^2-3 Bb p2^2 \[Lambda] (-2+\[Omega])^2+2 \[CapitalLambda] (1+\[Lambda]+2 \[Lambda] \[Omega]-2 \[Lambda] \[Omega]^2))))*)


(* ::Input:: *)
(*(*Part which vanishes at \[Lambda]=1*)*)


(* ::Input:: *)
(*(*Numerator*)*)
(*NL[\[Mu]_,\[Nu]_,\[Rho]_,\[Sigma]_,p_]:=(p[\[Mu]] p[\[Rho]] \[Eta][\[Nu],\[Sigma]]+p[\[Mu]] p[\[Sigma]] \[Eta][\[Nu],\[Rho]]+p[\[Nu]] p[\[Rho]] \[Eta][\[Mu],\[Sigma]]+p[\[Nu]] p[\[Sigma]] \[Eta][\[Mu],\[Rho]])*)
(**)
(*(*Denominator*)*)
(*DL[p2_]:=-(((Cc-Aa p2) (-1+\[Lambda]))/((Cc p2-Aa p2^2-2 \[CapitalLambda]) (Cc p2 \[Lambda]-Aa p2^2 \[Lambda]-2 \[CapitalLambda])))*)


(* ::Input:: *)
(*	(*Ghost propagator*)*)


(* ::Input:: *)
(*(*Numerator*)*)
(*Ngh[\[Mu]_,\[Nu]_,p_,a_]:=(\[Omega]-1)/(\[Omega]-2) p[\[Mu]]p[\[Nu]]-p[a]p[a]\[Eta][\[Mu],\[Nu]]*)
(*(*Denominator 1/p2^2*)*)
(**)


(* ::Input::Closed:: *)
(*(*DIAGRAMS AND COEFFICIENTS*)*)


(* ::Input::Closed:: *)
(*	(*Kc-C-C Diagram*)*)


(* ::Input:: *)
(*		(*Diagram evaluation and extract the divergent part*)*)


(* ::Input:: *)
(*p2=0;*)
(*k2=0; (*Additional simplifications*)*)
(*KCC=Expand[VKC[\[Mu]1,k-q,\[Nu]1,q+p,\[Rho]]Ngh[\[Nu]1,\[Nu]2,p+q,a2] 1/(p2+q2+2pq)^2 Vgh[\[Nu]2,\[Nu],p,\[Alpha]1,\[Beta]1,q,n3](N01[\[Alpha]1,\[Beta]1,\[Alpha]2,\[Beta]2,q]D01[q2]+N02[\[Alpha]1,\[Beta]1,\[Alpha]2,\[Beta]2,q]D02[q2]+N2[\[Alpha]1,\[Beta]1,\[Alpha]2,\[Beta]2,q]D2[q2]+N4[\[Alpha]1,\[Beta]1,\[Alpha]2,\[Beta]2,q]D4[q2]+NL[\[Alpha]1,\[Beta]1,\[Alpha]2,\[Beta]2,q]DL[q2])Vgh[\[Mu]2,\[Mu],k,\[Alpha]2,\[Beta]2,-q,n4]Ngh[\[Mu]1,\[Mu]2,q-k,a5] 1/(k2+q2-2qk)^2];*)
(*Clear[p2,k2];*)
(*Expand[KCC]/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(*Expand[Simplify[%]];*)
(*Expand[%/.{rp106,rp107,rp108,rp109,rp1010,rk106,rk107,rk108,rk109,rk1010}];*)
(*Expand[%/.{rp84,rp85,rp86,rp87,rp88,rk84,rk85,rk86,rk87,rk88}];*)
(*Expand[%/.{rp62,rp63,rp64,rp65,rp66,rk62,rk63,rk64,rk65,rk66}];*)
(*Expand[%/.{rp40,rp41,rp42,rp43,rp44,rk41,rk42,rk43,rk44}];*)
(*Expand[%/.{rp20,rp21,rp22,rk21,rk22}];*)
(*DivVKC=Simplify[Expand[%/.{1/q2^2->2/((4 Pi)^2 \[Epsilon])}]];*)
(**)


(* ::Input::Closed:: *)
(*	(*Extract coefficient s1, s2, s3*)*)


(* ::Input:: *)
(*s2=Simplify[Coefficient[-I DivVKC,p[\[Rho]]\[Eta][\[Mu],\[Nu]]]]*)
(*s3=Simplify[Coefficient[-I/2 DivVKC,p[\[Nu]]\[Eta][\[Mu],\[Rho]]]]*)
(*s1=Simplify[Coefficient[-I DivVKC,p[\[Mu]]\[Eta][\[Nu],\[Rho]]]-s2]*)
(**)


(* ::Input::Closed:: *)
(*	(*Kg-C Diagram*)*)


(* ::Input::Closed:: *)
(*		(*Diagram evaluation and extract the divergent part*)*)


(* ::Input:: *)
(*p2=0;*)
(*k2=0; (*Additional simplifications*)*)
(*KC=Expand[VKs[\[Mu],\[Nu],\[Rho]1,-p-q,\[Alpha]1,\[Beta]1,q](N01[\[Alpha]1,\[Beta]1,\[Alpha]2,\[Beta]2,q]D01[q2]+N02[\[Alpha]1,\[Beta]1,\[Alpha]2,\[Beta]2,q]D02[q2]+N2[\[Alpha]1,\[Beta]1,\[Alpha]2,\[Beta]2,q]D2[q2]+N4[\[Alpha]1,\[Beta]1,\[Alpha]2,\[Beta]2,q]D4[q2]+NL[\[Alpha]1,\[Beta]1,\[Alpha]2,\[Beta]2,q]DL[q2])Vgh[\[Rho]2,\[Rho],-p,\[Alpha]2,\[Beta]2,-q,n1]Ngh[\[Rho]1,\[Rho]2,p+q,a2] 1/(p2+q2+2pq)^2];*)
(*Clear[p2,k2];*)
(*Expand[KC]/.{q2->q2/y1^2,pq->pq/y1,q[m_]->q[m]/y1};*)
(*Expand[Simplify[Coefficient[Normal[Series[%,{y1,0,4}]],y1,4]]];*)
(*Expand[Simplify[ExpandAll[%]]];*)
(*Expand[%/.{rp106,rp107,rp108,rp109,rp1010}];*)
(*Expand[%/.{rp84,rp85,rp86,rp87,rp88}];*)
(*Expand[%/.{rp62,rp63,rp64,rp65,rp66}];*)
(*Expand[%/.{rp40,rp41,rp42,rp43,rp44}];*)
(*Expand[%/.{rp20,rp21,rp22}];*)
(*DivKC=Simplify[Expand[%/.{1/q2^2->2/((4 Pi)^2 \[Epsilon])}]];*)
(**)


(* ::Input::Closed:: *)
(*	(*Extract coefficient t1, t2*)*)


(* ::Input:: *)
(*t1=Simplify[s1-Coefficient[-I DivKC,p[\[Mu]]\[Eta][\[Rho],\[Nu]]+p[\[Nu]]\[Eta][\[Rho],\[Mu]]]]*)
(*t2=Simplify[-1/2 Coefficient[1/I DivKC,p[\[Rho]]\[Eta][\[Mu],\[Nu]]]]*)


(* ::Input::Closed:: *)
(*	(*Kg-C-h diagram*)*)


(* ::Input::Closed:: *)
(*		(*Diagram 1*)*)


(* ::Input:: *)
(*			(*Diagram evaluation and divergent parts*)*)


(* ::Input:: *)
(*(*Additional simplifications*)*)
(*p2=0;*)
(*k2=0; *)
(*ExpandAll[Vgh[\[Mu]1,\[Nu]2,q,\[Alpha],\[Beta],p,n1]Ngh[\[Rho]1,\[Mu]1,p+q,a2]ExpandAll[VKs[\[Mu],\[Nu],\[Rho]1,p+q,\[Alpha]1,\[Beta]1,k-q](N01[\[Alpha]1,\[Beta]1,\[Alpha]2,\[Beta]2,k-q])]Vgh[\[Rho]2,\[Rho],k,\[Alpha]2,\[Beta]2,q-k,n3]Ngh[\[Rho]2,\[Nu]2,q,a4]];*)
(*Expand[% D01[k2+q2-2qk] 1/(q2)^2 1/(q2+p2+2pq)^2];*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK01=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*ExpandAll[Vgh[\[Mu]1,\[Nu]2,q,\[Alpha],\[Beta],p,n1]Ngh[\[Rho]1,\[Mu]1,p+q,a2]ExpandAll[VKs[\[Mu],\[Nu],\[Rho]1,p+q,\[Alpha]1,\[Beta]1,k-q](N02[\[Alpha]1,\[Beta]1,\[Alpha]2,\[Beta]2,k-q])]Vgh[\[Rho]2,\[Rho],k,\[Alpha]2,\[Beta]2,q-k,n3]Ngh[\[Rho]2,\[Nu]2,q,a4]];*)
(*Expand[% D02[k2+q2-2qk] 1/(q2)^2 1/(q2+p2+2pq)^2];*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK02=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*ExpandAll[Vgh[\[Mu]1,\[Nu]2,q,\[Alpha],\[Beta],p,n1]Ngh[\[Rho]1,\[Mu]1,p+q,a2]ExpandAll[VKs[\[Mu],\[Nu],\[Rho]1,p+q,\[Alpha]1,\[Beta]1,k-q](N2[\[Alpha]1,\[Beta]1,\[Alpha]2,\[Beta]2,k-q])]Vgh[\[Rho]2,\[Rho],k,\[Alpha]2,\[Beta]2,q-k,n3]Ngh[\[Rho]2,\[Nu]2,q,a4]];*)
(*Expand[% D2[k2+q2-2qk] 1/(q2)^2 1/(q2+p2+2pq)^2];*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK2=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*ExpandAll[Vgh[\[Mu]1,\[Nu]2,q,\[Alpha],\[Beta],p,n1]Ngh[\[Rho]1,\[Mu]1,p+q,a2]ExpandAll[VKs[\[Mu],\[Nu],\[Rho]1,p+q,\[Alpha]1,\[Beta]1,k-q](N4[\[Alpha]1,\[Beta]1,\[Alpha]2,\[Beta]2,k-q])]Vgh[\[Rho]2,\[Rho],k,\[Alpha]2,\[Beta]2,q-k,n3]Ngh[\[Rho]2,\[Nu]2,q,a4]];*)
(*Expand[% D4[k2+q2-2qk] 1/(q2)^2 1/(q2+p2+2pq)^2];*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK4=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*ExpandAll[Vgh[\[Mu]1,\[Nu]2,q,\[Alpha],\[Beta],p,n1]Ngh[\[Rho]1,\[Mu]1,p+q,a2]ExpandAll[VKs[\[Mu],\[Nu],\[Rho]1,p+q,\[Alpha]1,\[Beta]1,k-q](NL[\[Alpha]1,\[Beta]1,\[Alpha]2,\[Beta]2,k-q])]Vgh[\[Rho]2,\[Rho],k,\[Alpha]2,\[Beta]2,q-k,n3]Ngh[\[Rho]2,\[Nu]2,q,a4]];*)
(*Expand[% DL[k2+q2-2qk] 1/(q2)^2 1/(q2+p2+2pq)^2];*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VKL=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(**)
(*Clear[p2,k2];*)
(*Expand[Simplify[VK01+VK02+VK2+VK4+VKL]];*)
(*Expand[Simplify[%]];*)
(*Expand[%/.{rp106,rk106}];*)
(*Expand[%/.{rp84,rp85,rp86,rp87,rp88,rk84,rk85,rk86,rk87,rk88}];*)
(*Expand[%/.{rp61,rp62,rp63,rp64,rp65,rp66,rk61,rk62,rk63,rk64,rk65,rk66}];*)
(*Expand[%/.{rp40,rp41,rp42,rp43,rp44,rk41,rk42,rk43,rk44}];*)
(*Expand[%/.{rp20,rp21,rp22,rk21,rk22}];*)
(*DivVK1=Simplify[Expand[%/.{1/q2^2->2/((4 Pi)^2 \[Epsilon])}]];*)


(* ::Input::Closed:: *)
(*		(*Diagram 2*)*)


(* ::Input::Closed:: *)
(*			(*Diagram evaluation and divergent parts*)*)


(* ::Input:: *)
(*(*Additional simplifications*)*)
(*p2=0;*)
(*k2=0; *)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N01[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N01[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*%  D01[q2] D01[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK0101=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]*)
(*Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N02[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N01[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D02[q2] D01[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK0201=Expand[Coefficient[Normal[Series[%,{z,0,4}]],z,4]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]*)
(*Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N01[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N02[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D01[q2] D02[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK0102=Expand[Coefficient[Normal[Series[%,{z,0,4}]],z,4]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N2[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N01[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D2[q2] D01[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK201=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N01[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N2[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D01[q2] D2[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK012=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N4[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N01[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D4[q2] D01[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK401=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N01[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N4[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D01[q2] D4[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK014=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N02[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N02[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D02[q2] D02[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK0202=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N2[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N02[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D2[q2] D02[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK202=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N02[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N2[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D02[q2] D2[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK022=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N4[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N02[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D4[q2] D02[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK402=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N02[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N4[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D02[q2] D4[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK024=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N2[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N2[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D2[q2] D2[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK22=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N4[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N2[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D4[q2] D2[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK42=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N2[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N4[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D2[q2] D4[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK24=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N4[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N4[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D4[q2] D4[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK44=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]NL[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N01[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% DL[q2] D01[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VKL01=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N01[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]NL[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D01[q2] DL[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK01L=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]NL[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N02[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% DL[q2] D02[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VKL02=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N02[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]NL[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D02[q2] DL[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK02L=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]NL[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N2[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% DL[q2] D2[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VKL2=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N2[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]NL[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D2[q2] DL[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK2L=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]NL[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]N4[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% DL[q2] D4[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VKL4=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]N4[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]NL[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% D4[q2] DL[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VK4L=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(**)
(**)
(*Expand[Expand[Vgh[\[Rho]3,\[Rho],k,\[Alpha]2,\[Beta]2,-q,n4]]Expand[Ngh[\[Rho]2,\[Rho]3,k-q,a3]]Expand[ExpandAll[V3Sym[\[Alpha],\[Beta],p,\[Mu]1,\[Nu]1,-p-q,\[Rho]1,\[Sigma]1,q,m1,n1,a1,b1,c1]]Expand[ExpandAll[VKs[\[Mu],\[Nu],\[Rho]2,k-q,\[Alpha]1,\[Beta]1,p+q]NL[\[Rho]1,\[Sigma]1,\[Alpha]2,\[Beta]2,q]NL[\[Mu]1,\[Nu]1,\[Alpha]1,\[Beta]1,p+q]]]]];*)
(*% DL[q2] DL[q2+p2+2pq] 1/(q2+k2-2qk)^2;*)
(*(%)/.{q2->q2/z^2,qk->qk/z,pq->pq/z,q[m_]->q[m]/z};*)
(*VKLL=Expand[Simplify[Coefficient[Normal[Series[%,{z,0,4}]],z,4]]];*)
(*Clear[p2,k2];*)
(*Expand[Simplify[VK0101+VK0201+VK0102+VK201+VK012+VK401+VK014+VK0202+VK202+VK022+VK402+VK024+VK22+VK42+VK24+VK44+VK01L+VKL01+VK02L+VKL02+VK2L+VKL2+VK4L+VKL4+VKLL]];*)
(*Expand[%/.{rp106,rk106}];*)
(*Expand[%/.{rp84,rp85,rp86,rp87,rp88,rk84,rk85,rk86,rk87,rk88}];*)
(*Expand[%/.{rp61,rp62,rp63,rp64,rp65,rp66,rk61,rk62,rk63,rk64,rk65,rk66}];*)
(*Expand[%/.{rp40,rp41,rp42,rp43,rp44,rk41,rk42,rk43,rk44}];*)
(*Expand[%/.{rp20,rp21,rp22,rk21,rk22}];*)
(**)
(*DivVK2=Simplify[Expand[%/.{1/q2^2->2/((4 Pi)^2 \[Epsilon])}]];*)


(* ::Input::Closed:: *)
(*		(*Diagram 1 + Diagram 2*)*)


(* ::Input:: *)
(*DivVKT=Expand[-Simplify[DivVK1+DivVK2]];*)


(* ::Input::Closed:: *)
(*	(*Extract coefficients t3, t4, t5, t6*)*)


(* ::Input:: *)
(*t3=Simplify[-2Coefficient[-I DivVKT,k[\[Beta]]\[Eta][\[Mu],\[Alpha]]\[Eta][\[Nu],\[Rho]]]];*)
(*t4=Simplify[-Coefficient[-I DivVKT,k[\[Rho]]\[Eta][\[Mu],\[Alpha]]\[Eta][\[Nu],\[Beta]]]];*)
(*t5=Simplify[1/4 (-2Coefficient[-I DivVKT,k[\[Alpha]]\[Eta][\[Rho],\[Beta]]\[Eta][\[Nu],\[Mu]]]-2t2)];*)
(*t6=Simplify[-1/4 Coefficient[-I DivVKT,k[\[Rho]]\[Eta][\[Mu],\[Nu]]\[Eta][\[Alpha],\[Beta]]]];*)


(* ::Input::Closed:: *)
(*(*COEFFICIENTS, PAPER NOTATION*)*)


(* ::Input:: *)
(*ss1=Expand[Simplify[2s1/.{Aa->\[Alpha],Bb->-\[Eta],\[Omega]->2\[Omega]+2}/.\[Eta]->(\[Xi]-\[Alpha])/3]]*)
(*ss2=Expand[Simplify[4 s2/.{Aa->\[Alpha],Bb->-\[Eta],\[Omega]->2\[Omega]+2}/.\[Eta]->(\[Xi]-\[Alpha])/3]]*)
(*ss3=Expand[Simplify[4 s3/.{Aa->\[Alpha],Bb->-\[Eta],\[Omega]->2\[Omega]+2}/.\[Eta]->(\[Xi]-\[Alpha])/3]]*)
(*tt1=Expand[Simplify[4 t1/.{Aa->\[Alpha],Bb->-\[Eta],\[Omega]->2\[Omega]+2}/.\[Eta]->(\[Xi]-\[Alpha])/3]]*)
(*tt2=Expand[Simplify[4 t2/.{Aa->\[Alpha],Bb->-\[Eta],\[Omega]->2\[Omega]+2}/.\[Eta]->(\[Xi]-\[Alpha])/3]]*)
(*tt3=Expand[Simplify[8 t3/.{Aa->\[Alpha],Bb->-\[Eta],\[Omega]->2\[Omega]+2}/.\[Eta]->(\[Xi]-\[Alpha])/3]]*)
(*tt4=Expand[Simplify[8 t4/.{Aa->\[Alpha],Bb->-\[Eta],\[Omega]->2\[Omega]+2}/.\[Eta]->(\[Xi]-\[Alpha])/3]]*)
(*tt5=Expand[Simplify[8 t5/.{Aa->\[Alpha],Bb->-\[Eta],\[Omega]->2\[Omega]+2}/.\[Eta]->(\[Xi]-\[Alpha])/3]]*)
(*tt6=Expand[Simplify[8 t6/.{Aa->\[Alpha],Bb->-\[Eta],\[Omega]->2\[Omega]+2}/.\[Eta]->(\[Xi]-\[Alpha])/3]]*)