(* ::Package:: *)

(* P-wave *)
delta1[1][s_]:=Module[{s0,B0,B1,w,temp,k1},
s0=1.05^2;B0=1.043;B1=0.19;
k1=Sqrt[s/4-mpi^2];
w=(Sqrt[s]-Sqrt[s0-s])/(Sqrt[s]+Sqrt[s0-s]);

Which[4mpi^2<s<=4mK^2,
temp=Sqrt[s]/(2k1^3)(Mrho^2-s)(2mpi^3/(Mrho^2Sqrt[s])+B0+B1*w);
If[temp>=0,ArcCot[temp],ArcCot[temp]+Pi],s==4mpi^2,1.8133289890064535`*(s-4mpi^2)^(3/2),s>4mK^2,0]];

delta2[1][s_]:=Module[{\[Lambda]0,\[Lambda]1,\[Lambda]2},
\[Lambda]1=1.39;\[Lambda]2=-1.70;
\[Lambda]0=delta1[1][4mK^2];
If[4mK^2<s<=1.420^2,(\[Lambda]0+\[Lambda]1(Sqrt[s/(4mK^2)]-1)+\[Lambda]2 (Sqrt[s/(4mK^2)]-1)^2),0]];

eta[1][s_]:=Module[{\[Epsilon]1,\[Epsilon]2},
\[Epsilon]1=0.00;\[Epsilon]2=0.07;
If[4mpi^2<s<=4mK^2,1,0]+If[4mK^2<s<=1.420^2,(1-\[Epsilon]1 Sqrt[1-4mK^2/s]-\[Epsilon]2(1-4mK^2/s)),0]]

delta[1][s_]:=delta1[1][s]+delta2[1][s];  


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(* Smoothly extrapolated phase shifts for s>\[CapitalLambda]\[CapitalOmega] *)
deltaFinal[J_][s_]:=Module[{hD,Der,a,b,nJ},hD=0.0001;

nJ=Which[J==0,2,J==1,1];
Der=(delta[J][LamPhShift^2+hD]-delta[J][LamPhShift^2-hD])/2/hD;
a=3(nJ Pi-delta[J][LamPhShift^2])^2/(2LamPhShift^2 Der);
b=-1+3(nJ Pi-delta[J][LamPhShift^2])/(2LamPhShift^2 Der);

Which[s<=LamPhShift^2,delta[J][s],s>LamPhShift^2,nJ Pi-a/(b+(s/LamPhShift^2)^(3/2))]
];
