<< ~/SERVER/FYZIKA/MATHEMATICA/PARTIALWAVE/partial_waves.m

(* in p=proj=1 scenario Gama3 is contribution of rho -> bb. Gama3=Gama2 in the limit of negligible top and bottom masses *)
(* in proj=0, b_1 = 0 scenario replace the Gama3 line with Gama3 = 0 *)
Gama1 = 4 Gpi^2/(192 Pi) MRho^3/vev^2;
Gama2 = MRho/(4 Pi) (GVt^2 + GAt^2); 
Gama3 = MRho/(4 Pi) (GVb^2 + GAb^2);
GamaRho = Gama1 + Gama2 + Gama3;

(* pipi -> pipi helicity amplitudes *)
Mschan = (MRho^2/vev^2) Gpi^2 s*Cos[theta]/(s - MRho^2 + I MRho GamaRho);
Mtchan = (MRho^2/vev^2) Gpi^2 (s + s/2 (1 + Cos[theta]))/(-s/2 (1 - Cos[theta]) - MRho^2);
M4vertex = s/(2 vev^2) (1 + Cos[theta]);
Mamp = Mschan + Mtchan + M4vertex;

a0 = Simplify[PWA0[0,0,0,0,0,Mamp]];

a1 = Simplify[PWA0[1,0,0,0,0,Mamp]];
(*a2 = Simplify[PWA0[2,0,0,0,0,Mamp]]*)
(*a3 = Simplify[PWA0[3,0,0,0,0,Mamp]]*)
(*a4 = Simplify[PWA0[4,0,0,0,0,Mamp]]*)

(* plot partial waves as function of ECM and Gpi  *)


GVt = -BR*G''/8. - BL*G''/8.;
GAt = -BR*G''/8. + BL*G''/8.;
GVb = +p^2*BR*G''/8. + BL*G''/8.;
GAb = +p^2*BR*G''/8. - BL*G''/8.;
GVtb = -p*BR*G''/(4.*Sqrt[2]) - BL*G''/(4.*Sqrt[2]); 
GAtb = -p*BR*G''/(4.*Sqrt[2]) + BL*G''/(4.*Sqrt[2]);
Gpi = MRho/(vev*G'');
s = ECM^2;
MRho = 1.0;
mt = 0.175;
vev = 0.246;
(*ECM = 2.5;*)
BL = 0;
p = 0.;

Aa0 = Sqrt[Re[a0]^2 + Im[a0]^2];
Aa1 = Sqrt[Re[a1]^2 + Im[a1]^2];

ECM=2.45;
p1=ContourPlot[Aa0,{BR,-3,3},{G'',0.01,30},PlotRange->{1,100},Contours->{1},PlotPoints->{100,100}]

p2=ContourPlot[Evaluate[Aa1],{BR,-3,3},{G'',0.01,30},PlotRange->{1,100},Contours->{1},PlotPoints->{100,100}]

ECM = 1.0;
p3=ContourPlot[Aa0,{BR,-3,3},{G'',0.01,30}, PlotRange -> {1,100}, Contours -> {1}, PlotPoints -> {100,100}]

p4=ContourPlot[Evaluate[Aa1],{BR,-3,3},{G'',0.01,30}, PlotRange -> {1,100}, Contours -> {1}, PlotPoints -> {100,100}]
p4a=ContourPlot[Evaluate[Aa1],{BR,-0.05,0.05},{G'',0.01,100}, PlotRange -> {1,100}, Contours -> {1}, PlotPoints -> {100,100}]
p4b=ContourPlot[Evaluate[Aa1],{BR,-0.015,0.015},{G'',0.01,15},PlotRange->{1,100},Contours->{1},PlotPoints->{100,100}]

Show[p1,p2,p3,p4]