Commit 4151946b authored by Reyesrivera, Jose's avatar Reyesrivera, Jose
Browse files

rep rules for 0,1 jets

parent d3829d52
(* Created with the Wolfram Language for Students - Personal Use Only : www.wolfram.com *)
{PVB[0, 0, MH^2, Sqrt[MT^2], Sqrt[MT^2]], PVC[0, 0, 0, 0, MH^2, 0,
Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]], PVC[0, 1, 1, 0, MH^2, 0, Sqrt[MT^2],
Sqrt[MT^2], Sqrt[MT^2]], PVC[1, 0, 0, 0, MH^2, 0, Sqrt[MT^2], Sqrt[MT^2],
Sqrt[MT^2]]}
(* Created with the Wolfram Language for Students - Personal Use Only : www.wolfram.com *)
{2 + Eps^(-1) + DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]] + Log[Mu^2/MT^2],
Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2/(2*MH^2),
1/(2*MH^2) + (MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/
(2*MT^2)]^2)/(2*MH^4), 3/4 + DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]]/4 +
(MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2)/
(4*MH^2) + (Eps^(-1) + Log[Mu^2/MT^2])/4}
(* Created with the Wolfram Language for Students - Personal Use Only : www.wolfram.com *)
{PVB[0, 0, MH^2, Sqrt[MT^2], Sqrt[MT^2]] ->
2 + Eps^(-1) + DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]] + Log[Mu^2/MT^2],
PVC[0, 0, 0, 0, MH^2, 0, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]] ->
Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2/(2*MH^2),
PVC[0, 1, 1, 0, MH^2, 0, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]] ->
1/(2*MH^2) + (MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/
(2*MT^2)]^2)/(2*MH^4), PVC[1, 0, 0, 0, MH^2, 0, Sqrt[MT^2],
Sqrt[MT^2], Sqrt[MT^2]] -> 3/4 + DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]]/4 +
(MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2)/
(4*MH^2) + (Eps^(-1) + Log[Mu^2/MT^2])/4}
(* Created with the Wolfram Language for Students - Personal Use Only : www.wolfram.com *)
{PVB[0, 0, S, Sqrt[MT^2], Sqrt[MT^2]], PVB[0, 0, T, Sqrt[MT^2], Sqrt[MT^2]],
PVB[0, 0, U, Sqrt[MT^2], Sqrt[MT^2]], PVC[0, 0, 0, 0, U, MH^2, Sqrt[MT^2],
Sqrt[MT^2], Sqrt[MT^2]], PVC[0, 0, 0, MH^2, S, 0, Sqrt[MT^2], Sqrt[MT^2],
Sqrt[MT^2]], PVC[0, 0, 0, MH^2, T, 0, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]],
PVC[0, 0, 1, 0, U, MH^2, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]],
PVC[0, 0, 2, 0, U, MH^2, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]],
PVC[0, 1, 0, MH^2, S, 0, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]],
PVC[0, 1, 0, MH^2, T, 0, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]],
PVC[0, 1, 1, 0, U, MH^2, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]],
PVC[0, 1, 1, MH^2, S, 0, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]],
PVC[0, 1, 1, MH^2, T, 0, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]],
PVC[0, 2, 0, MH^2, S, 0, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]],
PVC[0, 2, 0, MH^2, T, 0, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]],
PVC[1, 0, 0, 0, U, MH^2, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]],
PVC[1, 0, 0, MH^2, S, 0, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]],
PVC[1, 0, 0, MH^2, T, 0, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]]}
(* Created with the Wolfram Language for Students - Personal Use Only : www.wolfram.com *)
{2 + Eps^(-1) + DiscB[S, Sqrt[MT^2], Sqrt[MT^2]] + Log[Mu^2/MT^2],
2 + Eps^(-1) + DiscB[T, Sqrt[MT^2], Sqrt[MT^2]] + Log[Mu^2/MT^2],
2 + Eps^(-1) + DiscB[U, Sqrt[MT^2], Sqrt[MT^2]] + Log[Mu^2/MT^2],
Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2/
(2*(MH^2 - U)) - Log[(2*MT^2 - U + Sqrt[-((4*MT^2 - U)*U)])/(2*MT^2)]^2/
(2*(MH^2 - U)),
Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2/
(2*(MH^2 - S)) - Log[(2*MT^2 - S + Sqrt[-((4*MT^2 - S)*S)])/(2*MT^2)]^2/
(2*(MH^2 - S)),
Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2/
(2*(MH^2 - T)) - Log[(2*MT^2 - T + Sqrt[-((4*MT^2 - T)*T)])/(2*MT^2)]^2/
(2*(MH^2 - T)), DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]]/(MH^2 - U) -
DiscB[U, Sqrt[MT^2], Sqrt[MT^2]]/(MH^2 - U),
-DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]]/(2*(MH^2 - U)) +
DiscB[U, Sqrt[MT^2], Sqrt[MT^2]]/(2*(MH^2 - U)),
DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]]/(MH^2 - S) -
DiscB[S, Sqrt[MT^2], Sqrt[MT^2]]/(MH^2 - S),
DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]]/(MH^2 - T) -
DiscB[T, Sqrt[MT^2], Sqrt[MT^2]]/(MH^2 - T),
-1/(2*(MH^2 - U)) - (MH^2*DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]])/
(2*(MH^2 - U)^2) + (MH^2*DiscB[U, Sqrt[MT^2], Sqrt[MT^2]])/
(2*(MH^2 - U)^2) -
(MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2)/
(2*(MH^2 - U)^2) +
(MT^2*Log[(2*MT^2 - U + Sqrt[-((4*MT^2 - U)*U)])/(2*MT^2)]^2)/
(2*(MH^2 - U)^2), -1/(2*(MH^2 - S)) -
(MH^2*DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]])/(2*(MH^2 - S)^2) +
(MH^2*DiscB[S, Sqrt[MT^2], Sqrt[MT^2]])/(2*(MH^2 - S)^2) -
(MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2)/
(2*(MH^2 - S)^2) +
(MT^2*Log[(2*MT^2 - S + Sqrt[-((4*MT^2 - S)*S)])/(2*MT^2)]^2)/
(2*(MH^2 - S)^2), -1/(2*(MH^2 - T)) -
(MH^2*DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]])/(2*(MH^2 - T)^2) +
(MH^2*DiscB[T, Sqrt[MT^2], Sqrt[MT^2]])/(2*(MH^2 - T)^2) -
(MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2)/
(2*(MH^2 - T)^2) +
(MT^2*Log[(2*MT^2 - T + Sqrt[-((4*MT^2 - T)*T)])/(2*MT^2)]^2)/
(2*(MH^2 - T)^2), -DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]]/(2*(MH^2 - S)) +
DiscB[S, Sqrt[MT^2], Sqrt[MT^2]]/(2*(MH^2 - S)),
-DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]]/(2*(MH^2 - T)) +
DiscB[T, Sqrt[MT^2], Sqrt[MT^2]]/(2*(MH^2 - T)),
3/4 + (MH^2*DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]])/(4*(MH^2 - U)) -
(U*DiscB[U, Sqrt[MT^2], Sqrt[MT^2]])/(4*(MH^2 - U)) +
(MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2)/
(4*(MH^2 - U)) + (Eps^(-1) + Log[Mu^2/MT^2])/4 -
(MT^2*Log[(2*MT^2 - U + Sqrt[-((4*MT^2 - U)*U)])/(2*MT^2)]^2)/
(4*(MH^2 - U)), 3/4 + (MH^2*DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]])/
(4*(MH^2 - S)) - (S*DiscB[S, Sqrt[MT^2], Sqrt[MT^2]])/(4*(MH^2 - S)) +
(MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2)/
(4*(MH^2 - S)) + (Eps^(-1) + Log[Mu^2/MT^2])/4 -
(MT^2*Log[(2*MT^2 - S + Sqrt[-((4*MT^2 - S)*S)])/(2*MT^2)]^2)/
(4*(MH^2 - S)), 3/4 + (MH^2*DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]])/
(4*(MH^2 - T)) - (T*DiscB[T, Sqrt[MT^2], Sqrt[MT^2]])/(4*(MH^2 - T)) +
(MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2)/
(4*(MH^2 - T)) + (Eps^(-1) + Log[Mu^2/MT^2])/4 -
(MT^2*Log[(2*MT^2 - T + Sqrt[-((4*MT^2 - T)*T)])/(2*MT^2)]^2)/
(4*(MH^2 - T))}
(* Created with the Wolfram Language for Students - Personal Use Only : www.wolfram.com *)
{PVB[0, 0, S, Sqrt[MT^2], Sqrt[MT^2]] ->
2 + Eps^(-1) + DiscB[S, Sqrt[MT^2], Sqrt[MT^2]] + Log[Mu^2/MT^2],
PVB[0, 0, T, Sqrt[MT^2], Sqrt[MT^2]] ->
2 + Eps^(-1) + DiscB[T, Sqrt[MT^2], Sqrt[MT^2]] + Log[Mu^2/MT^2],
PVB[0, 0, U, Sqrt[MT^2], Sqrt[MT^2]] ->
2 + Eps^(-1) + DiscB[U, Sqrt[MT^2], Sqrt[MT^2]] + Log[Mu^2/MT^2],
PVC[0, 0, 0, 0, U, MH^2, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]] ->
Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2/
(2*(MH^2 - U)) - Log[(2*MT^2 - U + Sqrt[-((4*MT^2 - U)*U)])/(2*MT^2)]^2/
(2*(MH^2 - U)), PVC[0, 0, 0, MH^2, S, 0, Sqrt[MT^2], Sqrt[MT^2],
Sqrt[MT^2]] ->
Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2/
(2*(MH^2 - S)) - Log[(2*MT^2 - S + Sqrt[-((4*MT^2 - S)*S)])/(2*MT^2)]^2/
(2*(MH^2 - S)), PVC[0, 0, 0, MH^2, T, 0, Sqrt[MT^2], Sqrt[MT^2],
Sqrt[MT^2]] ->
Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2/
(2*(MH^2 - T)) - Log[(2*MT^2 - T + Sqrt[-((4*MT^2 - T)*T)])/(2*MT^2)]^2/
(2*(MH^2 - T)), PVC[0, 0, 1, 0, U, MH^2, Sqrt[MT^2], Sqrt[MT^2],
Sqrt[MT^2]] -> DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]]/(MH^2 - U) -
DiscB[U, Sqrt[MT^2], Sqrt[MT^2]]/(MH^2 - U),
PVC[0, 0, 2, 0, U, MH^2, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]] ->
-DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]]/(2*(MH^2 - U)) +
DiscB[U, Sqrt[MT^2], Sqrt[MT^2]]/(2*(MH^2 - U)),
PVC[0, 1, 0, MH^2, S, 0, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]] ->
DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]]/(MH^2 - S) -
DiscB[S, Sqrt[MT^2], Sqrt[MT^2]]/(MH^2 - S),
PVC[0, 1, 0, MH^2, T, 0, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]] ->
DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]]/(MH^2 - T) -
DiscB[T, Sqrt[MT^2], Sqrt[MT^2]]/(MH^2 - T),
PVC[0, 1, 1, 0, U, MH^2, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]] ->
-1/(2*(MH^2 - U)) - (MH^2*DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]])/
(2*(MH^2 - U)^2) + (MH^2*DiscB[U, Sqrt[MT^2], Sqrt[MT^2]])/
(2*(MH^2 - U)^2) -
(MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2)/
(2*(MH^2 - U)^2) +
(MT^2*Log[(2*MT^2 - U + Sqrt[-((4*MT^2 - U)*U)])/(2*MT^2)]^2)/
(2*(MH^2 - U)^2), PVC[0, 1, 1, MH^2, S, 0, Sqrt[MT^2], Sqrt[MT^2],
Sqrt[MT^2]] -> -1/(2*(MH^2 - S)) -
(MH^2*DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]])/(2*(MH^2 - S)^2) +
(MH^2*DiscB[S, Sqrt[MT^2], Sqrt[MT^2]])/(2*(MH^2 - S)^2) -
(MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2)/
(2*(MH^2 - S)^2) +
(MT^2*Log[(2*MT^2 - S + Sqrt[-((4*MT^2 - S)*S)])/(2*MT^2)]^2)/
(2*(MH^2 - S)^2), PVC[0, 1, 1, MH^2, T, 0, Sqrt[MT^2], Sqrt[MT^2],
Sqrt[MT^2]] -> -1/(2*(MH^2 - T)) -
(MH^2*DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]])/(2*(MH^2 - T)^2) +
(MH^2*DiscB[T, Sqrt[MT^2], Sqrt[MT^2]])/(2*(MH^2 - T)^2) -
(MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2)/
(2*(MH^2 - T)^2) +
(MT^2*Log[(2*MT^2 - T + Sqrt[-((4*MT^2 - T)*T)])/(2*MT^2)]^2)/
(2*(MH^2 - T)^2), PVC[0, 2, 0, MH^2, S, 0, Sqrt[MT^2], Sqrt[MT^2],
Sqrt[MT^2]] -> -DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]]/(2*(MH^2 - S)) +
DiscB[S, Sqrt[MT^2], Sqrt[MT^2]]/(2*(MH^2 - S)),
PVC[0, 2, 0, MH^2, T, 0, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]] ->
-DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]]/(2*(MH^2 - T)) +
DiscB[T, Sqrt[MT^2], Sqrt[MT^2]]/(2*(MH^2 - T)),
PVC[1, 0, 0, 0, U, MH^2, Sqrt[MT^2], Sqrt[MT^2], Sqrt[MT^2]] ->
3/4 + (MH^2*DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]])/(4*(MH^2 - U)) -
(U*DiscB[U, Sqrt[MT^2], Sqrt[MT^2]])/(4*(MH^2 - U)) +
(MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2)/
(4*(MH^2 - U)) + (Eps^(-1) + Log[Mu^2/MT^2])/4 -
(MT^2*Log[(2*MT^2 - U + Sqrt[-((4*MT^2 - U)*U)])/(2*MT^2)]^2)/
(4*(MH^2 - U)), PVC[1, 0, 0, MH^2, S, 0, Sqrt[MT^2], Sqrt[MT^2],
Sqrt[MT^2]] -> 3/4 + (MH^2*DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]])/
(4*(MH^2 - S)) - (S*DiscB[S, Sqrt[MT^2], Sqrt[MT^2]])/(4*(MH^2 - S)) +
(MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2)/
(4*(MH^2 - S)) + (Eps^(-1) + Log[Mu^2/MT^2])/4 -
(MT^2*Log[(2*MT^2 - S + Sqrt[-((4*MT^2 - S)*S)])/(2*MT^2)]^2)/
(4*(MH^2 - S)), PVC[1, 0, 0, MH^2, T, 0, Sqrt[MT^2], Sqrt[MT^2],
Sqrt[MT^2]] -> 3/4 + (MH^2*DiscB[MH^2, Sqrt[MT^2], Sqrt[MT^2]])/
(4*(MH^2 - T)) - (T*DiscB[T, Sqrt[MT^2], Sqrt[MT^2]])/(4*(MH^2 - T)) +
(MT^2*Log[(-MH^2 + 2*MT^2 + Sqrt[-(MH^2*(-MH^2 + 4*MT^2))])/(2*MT^2)]^2)/
(4*(MH^2 - T)) + (Eps^(-1) + Log[Mu^2/MT^2])/4 -
(MT^2*Log[(2*MT^2 - T + Sqrt[-((4*MT^2 - T)*T)])/(2*MT^2)]^2)/
(4*(MH^2 - T))}
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