(* ::Package:: *)

(* S-wave *)
sM=0.85^2;

delta1[0][s_]:=Module[{s0,sM,B0,B1,B2,B3,z0,w,temp,k1},
s0=4mK^2;B0=7.14;B1=-25.3;B2=-33.2;B3=-26.2;z0=mpi;
k1=Sqrt[s/4-mpi^2];
w=(Sqrt[s]-Sqrt[s0-s])/(Sqrt[s]+Sqrt[s0-s]);
temp=Sqrt[s]/(2*k1)mpi^2/(s-z0^2/2)(z0^2/(mpi*Sqrt[s])+B0+B1*w+B2*w^2+B3*w^3);
If[temp>=0,ArcCot[temp],ArcCot[temp]+Pi]];

delta2[0][s_]:=Module[{d0,cc,BB,CC,DD,kM,\[Delta]M,d\[Delta]M,k2,k3,hD},
d0=226.5*Pi/180;cc=-81*Pi/180;BB=93.3*Pi/180;CC=48.7*Pi/180;DD=-88.3*Pi/180;
k2=Sqrt[s/4-mK^2];
k3=Sqrt[s/4-meta^2];
kM=Abs[Sqrt[sM/4-mK^2]];
\[Delta]M=delta1[0][sM];
hD=0.0001;
d\[Delta]M=(delta1[0][sM+hD]-delta1[0][sM-hD])/2/hD;(*D[delta1[0][s2],s2]/.s2->sM*)
If[sM<s<=4mK^2,(d0 (1-Abs[k2]/kM)^2+\[Delta]M*Abs[k2]/kM(2-Abs[k2]/kM)+Abs[k2](kM-Abs[k2])(8*d\[Delta]M+CC*(kM-Abs[k2])/mK^3)),0]+If[4mK^2<s<=1.420^2,(d0+BB*k2^2/mK^2+CC*k2^4/mK^4+DD*UnitStep[s-4meta^2]k3^2/meta^2),0]];

eta[0][s_]:=Module[{\[Epsilon]1,\[Epsilon]2,\[Epsilon]3,\[Epsilon]4,k2,k3},
\[Epsilon]1=4.9;\[Epsilon]2=-15.1;\[Epsilon]3=4.7;\[Epsilon]4=0.32;
k2=Sqrt[s/4-mK^2];
k3=Sqrt[s/4-meta^2];
If[4mpi^2<s<=4mK^2,1,0]+If[4mK^2<s<=1.420^2,1,0](Exp[-k2/Sqrt[s](\[Epsilon]1+\[Epsilon]2 k2/Sqrt[s]+\[Epsilon]3 k2^2/s)^2-\[Epsilon]4 UnitStep[s-4meta^2]k3/Sqrt[s]])];

delta[0][s_]:=If[4mpi^2<s<=sM,delta1[0][s],0]+delta2[0][s];


(* 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];  


(* F-wave *)
delta[3][s_]:=Module[{s0,B0,B1,\[Lambda],w,temp,k1},
s0=1.45^2;B0=1.09*10^5;B1=1.41*10^5;\[Lambda]=0.051*10^5;
k1=Sqrt[s/4-mpi^2];
w=(Sqrt[s]-Sqrt[s0-s])/(Sqrt[s]+Sqrt[s0-s]);
temp=Sqrt[s]/(2k1^7)mpi^6(2\[Lambda] mpi/Sqrt[s]+B0+B1*w);
If[4mpi^2<s<=1.420^2,If[temp>=0,ArcCot[temp],ArcCot[temp]+Pi],0]];
eta[3][s_]:=1;

t[J_][s_]:=Module[{k1}, k1=Sqrt[s/4-mpi^2]; Sqrt[s]/(2k1)(eta[J][s]Exp[2I*delta[J][s]]-1)/(2I)];


(* 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))]
];


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