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Commit 8d6517f2 authored by Bertram Kopf's avatar Bertram Kopf
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added Mathematica script for the K-matrix f0-parametrization

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Scripts/Mathematica/KmatUtils.m
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......@@ -56,7 +56,7 @@ BWBarrier[l_, q_, q0_]:=
];
(* elasticity *)
Sii[s_, m1_, m2_, Tii_] := 1. + 2 I Sqrt[Re[rho[s,m1,m2]]] Tii Sqrt[Re[rho[s,m1,m2]]];
Sii[s_, m1_, m2_, Tii_] := 1. + 2. I Sqrt[Re[rho[s,m1,m2]]] Tii Sqrt[Re[rho[s,m1,m2]]];
(* extract delta phase of an Argand plot *)
......
Scripts/Mathematica/Kmatf0.m 0 → 100644
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(* Copyright 2023
Bertram Kopf (bertram@ep1.rub.de)
Meike Kuessner (mkuessner@ep1.rub.de)
Ruhr-Universität Bochum
This file is part of Pawian.
Pawian is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
Pawian is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with Pawian. If not, see <http://www.gnu.org/licenses/>
***********************************************************************************************
This Mathematica-script calculates some relevant quantities for the scattering process based on the K-matrix parametrization of the f0-wave published in Eur. Phys. J. C81 (2021) no.12, 1056; doi:10.1140/epjc/s10052-021-09821-2; arXiv:2008.11566.
*)
Get[FileNameJoin[{Directory[], "KmatUtils.m"}]]
(* Precision[1.2]; *)
(* Precision[12/10]; *)
(* masses of the decay products *)
mpi := 0.13957;
(* meta := 0.547; *)
meta := 0.547862;
(* m2pi := 2 mpi; *)
m2pi := 0.26996;
mKp := 0.49367;
mK0 := 0.497614;
metaprime := 0.95778;
(* K-matrix parameter *)
mf0500 := 0.5146109988244556;
mf0980 := 0.9062999999986513;
mf01370 := 1.23089000002673;
mf01500 := 1.461043944511787;
mf01710 := 1.696114327468766;
gpipif0500 := 0.749866997688989;
g4pif0500 := -0.01257099832673861;
gKKf0500 := 0.2753599978535977;
getaetaf0500 := -0.1510199937514032;
getaetaprimef0500 := 0.3610299929020451;
gpipif0980 := 0.06400735441028882;
g4pif0980 := 0.002039993700021009;
gKKf0980 := 0.7741299935288173;
getaetaf0980 := 0.5099954460483236;
getaetaprimef0980 := 0.131119996207024;
gpipif01370 := -0.2341669602361275;
g4pif01370 := -0.01031664796738707;
gKKf01370 := 0.7228310629513335;
getaetaf01370 := 0.1193373160160431;
getaetaprimef01370 := 0.3679219171982366;
gpipif01500 := 0.01270001206662291;
g4pif01500 := 0.2670000044701449;
gKKf01500 := 0.09214335545338775;
getaetaf01500 := 0.02742288751616556;
getaetaprimef01500 := -0.04024795048926635;
gpipif01710 := -0.1424226773316178;
g4pif01710 := 0.2277971435654336;
gKKf01710 := 0.1598113086438209;
getaetaf01710 := 0.162720778677211;
getaetaprimef01710 := -0.1739657300479793;
c00 := 0.03728069393605827;
c01 := 0.;
c02 := -0.01398000003371962;
c03 := -0.02202999981025169;
c04 := 0.01397000015464572;
c11 := 0.;
c12 := 0.;
c13 := 0.;
c14 := 0.;
c22 := 0.02349000177968514;
c23 := 0.03100999997418123;
c24 := -0.04002991964937379;
c33 := -0.1376928637961125;
c34 := -0.06721849488474475;
c44 := -0.2840099964663654;
s0 := 0.009112500000000001;
s0Adler := 0.1139704455925943;
snormAdler = 1.;
Kmatf0[s_]:=
Module[{resultMatr},
(* Which[Re[s]<0.01, s=0.1 + I 0.0001]; *)
(* Print["s: ", s]; *)
KPiPitoPiPi:=(gpipif0500 gpipif0500/(mf0500 mf0500-s)+c00)
+(gpipif0980 gpipif0980/(mf0980 mf0980-s)+c00)
+(gpipif01370 gpipif01370/(mf01370 mf01370-s)+c00)
+(gpipif01500 gpipif01500/(mf01500 mf01500-s)+c00)
+(gpipif01710 gpipif01710/(mf01710 mf01710-s)+c00);
(* Print["KPiPitoPiPi: " , KPiPitoPiPi]; *)
KPiPito4Pi:=(gpipif0500 g4pif0500/(mf0500 mf0500-s)+c01)
+(gpipif0980 g4pif0980/(mf0980 mf0980-s)+c01)
+(gpipif01370 g4pif01370/(mf01370 mf01370-s)+c01)
+(gpipif01500 g4pif01500/(mf01500 mf01500-s)+c01)
+(gpipif01710 g4pif01710/(mf01710 mf01710-s)+c01);
(* Print["KPiPito4Pi: " , KPiPito4Pi];*)
KPiPitoKK:=(gpipif0500 gKKf0500/(mf0500 mf0500-s)+c02)
+(gpipif0980 gKKf0980/(mf0980 mf0980-s)+c02)
+(gpipif01370 gKKf01370/(mf01370 mf01370-s)+c02)
+(gpipif01500 gKKf01500/(mf01500 mf01500-s)+c02)
+(gpipif01710 gKKf01710/(mf01710 mf01710-s)+c02);
(* Print["KPiPitoKK: " , KPiPitoKK]; *)
KPiPitoEtaEta:=(gpipif0500 getaetaf0500/(mf0500 mf0500-s)+c03)
+(gpipif0980 getaetaf0980/(mf0980 mf0980-s)+c03)
+(gpipif01370 getaetaf01370/(mf01370 mf01370-s)+c03)
+(gpipif01500 getaetaf01500/(mf01500 mf01500-s)+c03)
+(gpipif01710 getaetaf01710/(mf01710 mf01710-s)+c03);
(* Print["KPiPitoEtaEta: " , KPiPitoEtaEta]; *)
KPiPitoEtaEtaprime:=(gpipif0500 getaetaprimef0500/(mf0500 mf0500-s)+c04)
+(gpipif0980 getaetaprimef0980/(mf0980 mf0980-s)+c04)
+(gpipif01370 getaetaprimef01370/(mf01370 mf01370-s)+c04)
+(gpipif01500 getaetaprimef01500/(mf01500 mf01500-s)+c04)
+(gpipif01710 getaetaprimef01710/(mf01710 mf01710-s)+c04);
(* Print["KPiPitoEtaEtaprime: " , KPiPitoEtaEtaprime]; *)
K4Pito4Pi=(g4pif0500 g4pif0500/(mf0500 mf0500-s)+c11)
+(g4pif0980 g4pif0980/(mf0980 mf0980-s)+c11)
+(g4pif01370 g4pif01370/(mf01370 mf01370-s)+c11)
+(g4pif01500 g4pif01500/(mf01500 mf01500-s)+c11)
+(g4pif01710 g4pif01710/(mf01710 mf01710-s)+c11);
K4PitoKK=(g4pif0500 gKKf0500/(mf0500 mf0500-s)+c12)
+(g4pif0980 gKKf0980/(mf0980 mf0980-s)+c12)
+(g4pif01370 gKKf01370/(mf01370 mf01370-s)+c12)
+(g4pif01500 gKKf01500/(mf01500 mf01500-s)+c12)
+(g4pif01710 gKKf01710/(mf01710 mf01710-s)+c12);
K4PitoEtaEta=(g4pif0500 getaetaf0500/(mf0500 mf0500-s)+c13)
+(g4pif0980 getaetaf0980/(mf0980 mf0980-s)+c13)
+(g4pif01370 getaetaf01370/(mf01370 mf01370-s)+c13)
+(g4pif01500 getaetaf01500/(mf01500 mf01500-s)+c13)
+(g4pif01710 getaetaf01710/(mf01710 mf01710-s)+c13);
K4PitoEtaEtaprime=(g4pif0500 getaetaprimef0500/(mf0500 mf0500-s)+c14)
+(g4pif0980 getaetaprimef0980/(mf0980 mf0980-s)+c14)
+(g4pif01370 getaetaprimef01370/(mf01370 mf01370-s)+c14)
+(g4pif01500 getaetaprimef01500/(mf01500 mf01500-s)+c14)
+(g4pif01710 getaetaprimef01710/(mf01710 mf01710-s)+c14);
KKKtoKK=(gKKf0500 gKKf0500/(mf0500 mf0500-s)+c22)
+(gKKf0980 gKKf0980/(mf0980 mf0980-s)+c22)
+(gKKf01370 gKKf01370/(mf01370 mf01370-s)+c22)
+(gKKf01500 gKKf01500/(mf01500 mf01500-s)+c22)
+(gKKf01710 gKKf01710/(mf01710 mf01710-s)+c22);
KKKtoEtaEta=(gKKf0500 getaetaf0500/(mf0500 mf0500-s)+c23)
+(gKKf0980 getaetaf0980/(mf0980 mf0980-s)+c23)
+(gKKf01370 getaetaf01370/(mf01370 mf01370-s)+c23)
+(gKKf01500 getaetaf01500/(mf01500 mf01500-s)+c23)
+(gKKf01710 getaetaf01710/(mf01710 mf01710-s)+c23);
KKKtoEtaEtaprime=(gKKf0500 getaetaprimef0500/(mf0500 mf0500-s)+c24)
+(gKKf0980 getaetaprimef0980/(mf0980 mf0980-s)+c24)
+(gKKf01370 getaetaprimef01370/(mf01370 mf01370-s)+c24)
+(gKKf01500 getaetaprimef01500/(mf01500 mf01500-s)+c24)
+(gKKf01710 getaetaprimef01710/(mf01710 mf01710-s)+c24);
KEtaEtatoEtaEta=(getaetaf0500 getaetaf0500/(mf0500 mf0500-s)+c33)
+(getaetaf0980 getaetaf0980/(mf0980 mf0980-s)+c33)
+(getaetaf01370 getaetaf01370/(mf01370 mf01370-s)+c33)
+(getaetaf01500 getaetaf01500/(mf01500 mf01500-s)+c33)
+(getaetaf01710 getaetaf01710/(mf01710 mf01710-s)+c33);
KEtaEtatoEtaEtaprime=(getaetaf0500 getaetaprimef0500/(mf0500 mf0500-s)+c34)
+(getaetaf0980 getaetaprimef0980/(mf0980 mf0980-s)+c34)
+(getaetaf01370 getaetaprimef01370/(mf01370 mf01370-s)+c34)
+(getaetaf01500 getaetaprimef01500/(mf01500 mf01500-s)+c34)
+(getaetaf01710 getaetaprimef01710/(mf01710 mf01710-s)+c34);
KEtaEtaprimetoEtaEtaprime=(getaetaprimef0500 getaetaprimef0500/(mf0500 mf0500-s)+c44)
+(getaetaprimef0980 getaetaprimef0980/(mf0980 mf0980-s)+c44)
+(getaetaprimef01370 getaetaprimef01370/(mf01370 mf01370-s)+c44)
+(getaetaprimef01500 getaetaprimef01500/(mf01500 mf01500-s)+c44)
+(getaetaprimef01710 getaetaprimef01710/(mf01710 mf01710-s)+c44);
adlerTerm=(s - s0)/snormAdler;
resultMatr = {
{KPiPitoPiPi, KPiPito4Pi, KPiPitoKK, KPiPitoEtaEta, KPiPitoEtaEtaprime},
{KPiPito4Pi, K4Pito4Pi, K4PitoKK, K4PitoEtaEta, K4PitoEtaEtaprime},
{KPiPitoKK, K4PitoKK, KKKtoKK, KKKtoEtaEta, KKKtoEtaEtaprime},
{KPiPitoEtaEta, K4PitoEtaEta, KKKtoEtaEta, KEtaEtatoEtaEta, KEtaEtatoEtaEtaprime},
{KPiPitoEtaEtaprime, K4PitoEtaEtaprime, KKKtoEtaEtaprime, KEtaEtatoEtaEtaprime, KEtaEtaprimetoEtaEtaprime}
};
resultMatr = adlerTerm resultMatr;
resultMatr
];
ChewMmat[s_]:={{c[s,mpi,mpi], 0., 0., 0., 0.},
{0., c[s,m2pi,m2pi], 0. ,0., 0.},
{0., 0., c[s,mKp,mK0], 0., 0.},
{0., 0., 0., c[s,meta,meta], 0.},
{0., 0., 0., 0., c[s,meta,metaprime]}
};
KChewMmat[s_]:=Kmatf0[s].ChewMmat[s];
(* Print["CM[1.8]: ", ChewMmat[1.8] // MatrixForm]; *)
Idmat:=IdentityMatrix[5];
IKChewMmat[s_]:= Idmat + KChewMmat[s];
invIKChewMmat[s_]:= Inverse[IKChewMmat[s]];
Tmat[s_]:=invIKChewMmat[s].Kmatf0[s];
(* Print["Tmat[1.8]: ", Tmat[1.8 + I 0.00001] // MatrixForm]; *)
f0PiPitoPiPiTreal=Plot[Re[Tmat[b*b + I 0.000001][[1,1]]],{b, mpi+mpi, 1.9}, AxesLabel->{M [GeV/(c c)], Re[T(\[Pi]\[Pi] -> \[Pi]\[Pi])]}];
Export["f0PiPitoPiPiTreal.pdf", f0PiPitoPiPiTreal];
f0PiPitoPiPiTimag=Plot[Im[Tmat[b*b + I 0.000001][[1,1]]],{b, mpi+mpi, 1.9}, AxesLabel->{M [GeV/(c c)], Im[T(\[Pi]\[Pi] -> \[Pi]\[Pi])]}];
Export["f0PiPitoPiPiTimag.pdf", f0PiPitoPiPiTimag];
f0PiPiElasticity=Plot[Abs[Sii[b*b + I 0.000001, mpi, mpi, Tmat[b*b + I 0.000001][[1,1]]]],{b, mpi+mpi, 1.9}, AxesLabel->{M [GeV/(c c)], \[Eta](\[Pi]\[Pi] -> \[Pi]\[Pi])}];
Export["f0PiPiElasticity.pdf", f0PiPiElasticity];
f0PiPitoPiPiPhase=Plot[deltaArgand[m, mpi, mpi, Tmat[m*m + I 0.000001][[1,1]]],{m, mpi+mpi, 1.9}, AxesLabel->{M [GeV/(c c)], \[Delta](\[Pi]\[Pi] -> \[Pi]\[Pi])}];
Export["f0PiPitoPiPiPhase.pdf", f0PiPitoPiPiPhase];
f0PiPitoPiPiArgand=ParametricPlot[{rho[m*m,mpi,mpi] Re[Tmat[m*m + I 0.000001][[1,1]]], rho[m*m,mpi,mpi] Im[Tmat[m*m + I 0.000001][[1,1]]]},{m, mpi+mpi, 1.9}, AxesLabel->{Re[T(\[Pi]\[Pi] -> \[Pi]\[Pi])], Im[T(\[Pi]\[Pi] -> \[Pi]\[Pi])]}];
Export["f0PiPitoPiArgand.pdf", f0PiPitoPiPiArgand];
f0PiPitoKKTsqr=Plot[ { rho[m*m,mpi,mpi] rho[m*m,mKp,mK0] Norm[Tmat[m*m + I 0.0000001][[1,3]]] Norm[Tmat[m*m + I 0.0000001][[1,3]]]}, {m, mKp+mK0, 1.9}, AxesLabel->{M [GeV/(c c)], "\[Rho](\[Pi]\[Pi])" "\[Rho](KK)" Abs[T(\[Pi]\[Pi] -> KK)] Abs[T(\[Pi]\[Pi] -> KK)]}];
Export["f0PiPitoKKArgandUnits.pdf", f0PiPitoKKTsqr];
f0PiPitoEtaEtaTsqr=Plot[ { rho[m*m,mpi,mpi] rho[m*m,meta,meta] Norm[Tmat[m*m + I 0.0000001][[1,4]]] Norm[Tmat[m*m + I 0.0000001][[1,4]]] }, {m, meta+meta, 1.9}, AxesLabel->{M [GeV/(c c)], "\[Rho](\[Pi]\[Pi])" "\[Rho](\[Eta]\[Eta])" Abs[T(\[Pi]\[Pi] -> \[Eta]\[Eta])] Abs[T(\[Pi]\[Pi] -> \[Eta]\[Eta])]}];
Export["f0PiPitoEtaEtaArgandUnits.pdf", f0PiPitoEtaEtaTsqr];
f0PiPitoEtaEtaprimeTsqr=Plot[ { rho[m*m,mpi,mpi] rho[m*m,meta,metaprime] Norm[Tmat[m*m + I 0.0000001][[1,5]]] Norm[Tmat[m*m + I 0.0000001][[1,5]]] }, {m, meta+metaprime, 1.9}, AxesLabel->{M [GeV/(c c)], "\[Rho](\[Pi]\[Pi])" "\[Rho](\[Eta]\[Eta]')" Abs[T(\[Pi]\[Pi] -> \[Eta]\[Eta]')] Abs[T(\[Pi]\[Pi] -> \[Eta]\[Eta]')]}];
Export["f0PiPitoEtaEtaprimeArgandUnits.pdf", f0PiPitoEtaEtaprimeTsqr];
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