Exit[] Neutral Pion Photoproduction List of data: ANDERSON 1970 http://hepdata.cedar.ac.uk/view/ins67154 BRAUNSCHWEIG 1973 http://hepdata.cedar.ac.uk/view/ins84302 BRAUNSCHWEIG 1973 http://hepdata.cedar.ac.uk/view/ins84301 BOOTH 1972 http://hepdata.cedar.ac.uk/view/ins75858 BELLENGER 1969 http://hepdata.cedar.ac.uk/view/ins55099 OSBORNE 1972 http://hepdata.cedar.ac.uk/view/ins84571 BRAUNSCHWEIG 1968 http://hepdata.cedar.ac.uk/view/red7610 BOLON 1967 http://hepdata.cedar.ac.uk/view/ins51286 BARISH 1974 http://hepdata.cedar.ac.uk/view/ins94529 GOMEZ 1971 http://hepdata.cedar.ac.uk/view/p5186 DEUTSCH 1972 http://hepdata.cedar.ac.uk/view/ins84562 MP=0.938;MPI=0.138; foldername = "/Users/vincent/Dropbox/mes articles/Regge/data"; SetDirectory[foldername]; Needs["PlotLegends`"] Needs["ErrorBarPlots`"] Print["Need to change the variable foldername to the folder where you have the data files"] Print["Need to install the package ErrorBarLogPlots from http://library.wolfram.com/infocenter/MathSource/6747/"] Needs["ErrorBarLogPlots`"] Need to change the variable foldername to the folder where you have the data files Need to install the package ErrorBarLogPlots from http://library.wolfram.com/infocenter/MathSource/6747/ January 2015 Execute the commands in the order Prepare data for fit dat2fit := Block[{sig2,sig3,sig4,sig5,sig58, sig6g,sig18g,sig12g,sig6,sig9,sig12,sig15,dat, datfit1,datfit}, (* create a file with the entries Eγ t dσ/dt Δdσ/dt *) SetDirectory[foldername]; datfit = {}; (* initialization *) (* BRAUNSCHWEIG 1968 http://hepdata.cedar.ac.uk/view/red7610 *) sig2 = Import["Braun68_Sig_PhotPi0_2.txt","Table"]; sig3 = Import["Braun68_Sig_PhotPi0_3.txt","Table"]; sig4 = Import["Braun68_Sig_PhotPi0_4.txt","Table"]; sig5 = Import["Braun68_Sig_PhotPi0_5.txt","Table"]; sig58 = Import["Braun68_Sig_PhotPi0_58.txt","Table"]; dat = sig2; datfit1 = Table[{2,-dat[[i,4]],dat[[i,10]],dat[[i,11]]},{i,Length[dat]}]; datfit = Join[datfit,datfit1]; dat = sig3; datfit1 = Table[{3,-dat[[i,4]],dat[[i,10]],dat[[i,11]]},{i,Length[dat]}]; datfit = Join[datfit,datfit1]; dat = sig4; datfit1 = Table[{4,-dat[[i,4]],dat[[i,10]],dat[[i,11]]},{i,Length[dat]}]; datfit = Join[datfit,datfit1]; dat = sig5; datfit1 = Table[{5,-dat[[i,4]],dat[[i,10]],dat[[i,11]]},{i,Length[dat]}]; datfit = Join[datfit,datfit1]; dat = sig58; datfit1 = Table[{5.8,-dat[[i,4]],dat[[i,10]],dat[[i,11]]},{i,Length[dat]}]; datfit = Join[datfit,datfit1]; (* GOMEZ 1971 http://hepdata.cedar.ac.uk/view/p5186 *) sig6g = Import["Gomez71_Sig_PhotPi0_6.txt","Table"]; sig12g = Import["Gomez71_Sig_PhotPi0_12.txt","Table"]; sig18g = Import["Gomez71_Sig_PhotPi0_18.txt","Table"]; dat = sig6g; datfit1 = Table[{6,-dat[[i,1]],10^3dat[[i,4]],10^3dat[[i,5]]},{i,Length[dat]}]; datfit = Join[datfit,datfit1]; dat = sig12g; datfit1 = Table[{12,-dat[[i,1]],10^3dat[[i,4]],10^3dat[[i,5]]},{i,Length[dat]}]; datfit = Join[datfit,datfit1]; dat = sig18g; datfit1 = Table[{18,-dat[[i,1]],10^3dat[[i,4]],10^3dat[[i,5]]},{i,Length[dat]}]; datfit = Join[datfit,datfit1]; (* ANDERSON 1970 http://hepdata.cedar.ac.uk/view/ins67154 *) sig6 = Import["Anderson_SigPhotPi0_6.txt","Table"]; sig9 = Import["Anderson_SigPhotPi0_9.txt","Table"]; sig12 = Import["Anderson_SigPhotPi0_12.txt","Table"]; sig15 = Import["Anderson_SigPhotPi0_15.txt","Table"]; dat = sig6; datfit1 = Table[{6,dat[[i,1]],dat[[i,4]],dat[[i,5]]},{i,Length[dat]}]; datfit = Join[datfit,datfit1]; dat = sig9; datfit1 = Table[{9,dat[[i,1]],dat[[i,4]],dat[[i,5]]},{i,Length[dat]}]; datfit = Join[datfit,datfit1]; dat = sig12; datfit1 = Table[{12,dat[[i,1]],dat[[i,4]],dat[[i,5]]},{i,Length[dat]}]; datfit = Join[datfit,datfit1]; dat = sig15; datfit1 = Table[{15,dat[[i,1]],dat[[i,4]],dat[[i,5]]},{i,Length[dat]}]; datfit = Join[datfit,datfit1]; datfit (* return the table *) ]; dataBA:=Block[{BeamA4,BeamA6,BeamA10,dat,datfit,datfit1}, SetDirectory[foldername]; datfit = {}; (* initialization *) (* ANDERSON 1970 http://hepdata.cedar.ac.uk/view/ins67154 *) BeamA4 = Import["Anderson_BeamAPhotPi0_4.txt","Table"]; BeamA6 = Import["Anderson_BeamAPhotPi0_6.txt","Table"]; BeamA10 = Import["Anderson_BeamAPhotPi0_10.txt","Table"]; dat = BeamA4; datfit1 = Table[{4,dat[[i,1]],dat[[i,4]],dat[[i,5]]},{i,Length[dat]}]; datfit = Join[datfit,datfit1]; dat = BeamA6; datfit1 = Table[{6,dat[[i,1]],dat[[i,4]],dat[[i,5]]},{i,Length[dat]}]; datfit = Join[datfit,datfit1]; dat = BeamA10; datfit1 = Table[{10,dat[[i,1]],dat[[i,4]],dat[[i,5]]},{i,Length[dat]}]; datfit = Join[datfit,datfit1]; datfit (* return the table *) ]; For the plots SetDirectory[foldername]; Braun68:=Module[{sig2,sig3,sig4,sig5,sig58,dat, ps2,ps3,ps4,ps5,ps6,ps}, (* load data *) sig2 = Import["Braun68_Sig_PhotPi0_2.txt","Table"]; sig3 = Import["Braun68_Sig_PhotPi0_3.txt","Table"]; sig4 = Import["Braun68_Sig_PhotPi0_4.txt","Table"]; sig5 = Import["Braun68_Sig_PhotPi0_5.txt","Table"]; sig58 = Import["Braun68_Sig_PhotPi0_58.txt","Table"]; ScaleFacB68 = {10^4,10^3,10^2,10^1,10^0}; dat = sig2; ps2 = ErrorListLogPlot[ Table[{{dat[[i,4]],dat[[i,10]]ScaleFacB68[[1]]}, ErrorBar[ ScaleFacB68[[1]]dat[[i,11]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Blue]; dat = sig3; ps3 = ErrorListLogPlot[ Table[{{dat[[i,4]],dat[[i,10]]ScaleFacB68[[2]]}, ErrorBar[ScaleFacB68[[2]] dat[[i,11]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Darker[Green]]; dat = sig4; ps4 = ErrorListLogPlot[ Table[{{dat[[i,4]],dat[[i,10]]ScaleFacB68[[3]]}, ErrorBar[ScaleFacB68[[3]]dat[[i,11]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Red]; dat = sig5; ps5 = ErrorListLogPlot[ Table[{{dat[[i,4]],dat[[i,10]]ScaleFacB68[[4]]},ErrorBar[ScaleFacB68[[4]] dat[[i,11]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Black]; dat = sig58; ps6 = ErrorListLogPlot[ Table[{{dat[[i,4]],dat[[i,10]]ScaleFacB68[[5]]}, ErrorBar[ScaleFacB68[[5]] dat[[i,11]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Orange]; ps = {ps2,ps3,ps4,ps5,ps6}; {ps} ]; Bolon67:=Module[{sig2,sig25,sig3,sig35,sig4,sig5,sig45,dat, ps2,ps25,ps3,ps35,ps4,ps45,ps5,ps}, (* load data *) sig2 = Import["Bolon67_Sig_PhotPi0_2.txt","Table"]; sig25 = Import["Bolon67_Sig_PhotPi0_2.5.txt","Table"]; sig3 = Import["Bolon67_Sig_PhotPi0_3.txt","Table"]; sig35 = Import["Bolon67_Sig_PhotPi0_3.5.txt","Table"]; sig4 = Import["Bolon67_Sig_PhotPi0_4.txt","Table"]; sig45 = Import["Bolon67_Sig_PhotPi0_4.5.txt","Table"]; sig5 = Import["Bolon67_Sig_PhotPi0_5.txt","Table"]; ScaleFacB67 =(1/10) {10^7,10^6,10^5,10^4,10^3,10^2,10^1}; dat = sig2; ps2 = ErrorListLogPlot[ Table[{{dat[[i,1]],dat[[i,4]]10^3ScaleFacB67[[1]]}, ErrorBar[dat[[i,1]]-dat[[i,2]], 10^3ScaleFacB67[[1]]dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Blue]; dat = sig25; ps25 = ErrorListLogPlot[ Table[{{dat[[i,1]],dat[[i,4]]10^3ScaleFacB67[[2]]}, ErrorBar[dat[[i,1]]-dat[[i,2]],10^3 ScaleFacB67[[2]]dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Darker[Green]]; dat = sig3; ps3 = ErrorListLogPlot[ Table[{{dat[[i,1]],dat[[i,4]]10^3ScaleFacB67[[3]]}, ErrorBar[dat[[i,1]]-dat[[i,2]],10^3ScaleFacB67[[3]] dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Red]; dat = sig35; ps35 = ErrorListLogPlot[ Table[{{dat[[i,1]],dat[[i,4]]10^3ScaleFacB67[[4]]}, ErrorBar[dat[[i,1]]-dat[[i,2]],10^3 ScaleFacB67[[4]]dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Black]; dat = sig4; ps4 = ErrorListLogPlot[ Table[{{dat[[i,1]],dat[[i,4]]10^3ScaleFacB67[[5]]}, ErrorBar[dat[[i,1]]-dat[[i,2]],10^3ScaleFacB67[[5]]dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Orange]; dat = sig45; ps45 = ErrorListLogPlot[ Table[{{dat[[i,1]],dat[[i,4]]10^3ScaleFacB67[[6]]}, ErrorBar[dat[[i,1]]-dat[[i,2]],10^3ScaleFacB67[[6]]dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Cyan]; dat = sig5; ps5 = ErrorListLogPlot[ Table[{{dat[[i,1]],dat[[i,4]]10^3ScaleFacB67[[7]]},ErrorBar[dat[[i,1]]-dat[[i,2]],10^3ScaleFacB67[[7]] dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle-> Magenta]; ps = {ps2,ps25,ps3,ps35,ps4,ps45,ps5}; {ps} ]; (* Gomez 71 and Barish 74 *) (* Barish 74 is included in Gomez 71*) Gomez71:=Module[{sig6g,sig12g,sig18g,dat,ps6g,ps12g,ps18g,ps}, (* load data *) sig6g = Import["Gomez71_Sig_PhotPi0_6.txt","Table"]; sig12g = Import["Gomez71_Sig_PhotPi0_12.txt","Table"]; sig18g = Import["Gomez71_Sig_PhotPi0_18.txt","Table"]; ScaleFacG71 ={10^0,10^0,10^0}; dat = sig6g; ps6g = ErrorListLogPlot[ Table[{{dat[[i,1]],dat[[i,4]]10^3ScaleFacG71[[1]]}, ErrorBar[ 10^3ScaleFacG71[[1]]dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Blue]; dat = sig12g; ps12g = ErrorListLogPlot[ Table[{{dat[[i,1]],dat[[i,4]]10^3ScaleFacG71[[2]]}, ErrorBar[ 10^3ScaleFacG71[[2]]dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Darker[Green]]; dat = sig18g; ps18g = ErrorListLogPlot[ Table[{{dat[[i,1]],dat[[i,4]]10^3ScaleFacG71[[3]]}, ErrorBar[10^3 ScaleFacG71[[3]]dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Red]; ps = {ps6g,ps12g,ps18g}; {ps} ]; Anderson:= Module[{ Sig6,Sig9,Sig12, Sig15,BeamA4,BeamA6, BeamA10, ps6,ps9,ps12,ps15,pb4,pb6,pb10,ps,pb, dat,datasig, errsig,databa,errba}, (* load data *) Sig6 = Import["Anderson_SigPhotPi0_6.txt","Table"]; Sig9 = Import["Anderson_SigPhotPi0_9.txt","Table"]; Sig12 = Import["Anderson_SigPhotPi0_12.txt","Table"]; Sig15 = Import["Anderson_SigPhotPi0_15.txt","Table"]; ScaleFac = {10^6,10^4,10^2,10^0}; ScaleFac = {1,1,1,1}; BeamA4 = Import["Anderson_BeamAPhotPi0_4.txt","Table"]; BeamA6 = Import["Anderson_BeamAPhotPi0_6.txt","Table"]; BeamA10 = Import["Anderson_BeamAPhotPi0_10.txt","Table"]; (* Differential cross section *) (* Create Plots and the data object for the fit*) (* There is no error on x *) dat = Sig6; ps6 = ErrorListLogPlot[ Table[{{-dat[[i,1]],dat[[i,4]]ScaleFac[[1]]}, ErrorBar[ScaleFac[[1]]dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Blue]; dat = Sig9; ps9 = ErrorListLogPlot[ Table[{{-dat[[i,1]],dat[[i,4]]ScaleFac[[2]]},ErrorBar[ ScaleFac[[2]]dat[[i,5]] ]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Darker[Green]]; dat = Sig12; ps12 = ErrorListLogPlot[ Table[{{-dat[[i,1]],dat[[i,4]]ScaleFac[[3]]}, ErrorBar[ScaleFac[[3]]dat[[i,5]] ]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Red]; dat = Sig15; ps15 = ErrorListLogPlot[ Table[{{-dat[[i,1]],dat[[i,4]]ScaleFac[[4]]}, ErrorBar[ScaleFac[[4]]dat[[i,5]] ]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Black]; ps = {ps6,ps9,ps12,ps15}; (* Beam Asymmetry *) (* Create Plots and the data object for the fit *) dat = BeamA4; pb4 = ErrorListPlot[ Table[{{-dat[[i,1]],dat[[i,4]]}, ErrorBar[dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Blue]; dat = BeamA6; pb6 = ErrorListPlot[ Table[{{-dat[[i,1]],dat[[i,4]]}, ErrorBar[dat[[i,5]] ]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Darker[Green]]; dat = BeamA10; pb10 = ErrorListPlot[ Table[{{-dat[[i,1]],dat[[i,4]]}, ErrorBar[dat[[i,5]] ]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Red]; pb = {pb4,pb6,pb10}; {ps,pb} ]; Ratio := Module[{Rat4,Rat47,Rat82,pr4,pr47,pr82,dat,plotrat}, Rat4 = Import["Braun_RatioNP_PhotPi0_4.txt","Table"]; Rat47 = Import["Osborn2_RatioNP_PhotPi0_47.txt","Table"]; Rat82 = Import["Osborn2_RatioNP_PhotPi0_82.txt","Table"]; dat = Rat4; pr4 = ErrorListPlot[ Table[{{-dat[[i,1]],dat[[i,4]]}, ErrorBar[dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Blue]; dat = Rat47; pr47 = ErrorListPlot[ Table[{{-dat[[i,1]],dat[[i,4]]}, ErrorBar[dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Darker[Green]]; dat = Rat82; pr82 = ErrorListPlot[ Table[{{-dat[[i,1]],dat[[i,4]]}, ErrorBar[dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->Automatic,PlotStyle->Red]; plotrat ={pr4,pr47,pr82}; {Rat4,Rat47,Rat82,plotrat}] (* Plot for Anderson data *) pAfitS[name_] := LogPlot[{name[6,-t],name[9,-t],name[12,-t],name[15,-t]},{t,0.05,1.5}, PlotStyle-> {{Blue,Thick},{Thick,Darker[Green]},{Thick,Red},{Thick,Black}}, PlotPoints->2]; pAfitD[name_] := LogPlot[{name[6,-t],name[9,-t],name[12,-t],name[15,-t]},{t,0.05,1.5}, PlotStyle-> {{Blue,Thick,Dashed},{Thick,Darker[Green],Dashed},{Thick,Red,Dashed},{Thick,Black,Dashed}}, PlotPoints->2]; (* Plot for Braun68 data *) pBfitS[name_]:= LogPlot[{ ScaleFacB68[[1]]name[2,-t], ScaleFacB68[[2]]name[3,-t], ScaleFacB68[[3]]name[4,-t], ScaleFacB68[[4]]name[5,-t], ScaleFacB68[[5]]name[5.8,-t]},{t,0.01,2}, PlotStyle-> {{Blue,Thick},{Thick,Darker[Green]},{Thick,Red},{Thick,Black},{Thick, Orange}}, PlotPoints->5]; SetDirectory[foldername]; ander = Anderson; rat = Ratio; gomez = Gomez71; braun = Braun68; bolon = Bolon67; Amplitudes (* Compute the differential cross section in μ barn/Gev^2 for pseudoscalar-photoproduction processes*) DiffCrossSectPhot[plab_,t_,flag1_,flag2_,flag3_,a1ω_,a4ω_,a2B_,a1ρ_,a4ρ_,a1c_,a4c_,α0ω_,αpω_,α0c_,αpc_,α0B_,αpB_]:= Module[{DCSp,DCSn,BA,res1,res2, res3,Fi,S,kt,pt,Σ,cost,sint,ϕ,u,αρ,αω,αB,αωc,ξω,ξB,ξρ,ξωc,f01p,f11p,f01m,f11m,F1,F2,F3,F4}, Σ = 2 MP^2+MPI^2; S = MP^2+2MP Sqrt[plab^2]; kt = (t-MPI^2)/2/Sqrt[t]; pt = Sqrt[t-4MP^2]/2; cost = (2S+t-Σ)/(4 kt pt); sint = Sqrt[1-cost^2]; αρ = α0ω+αpω t;αω =α0ω+αpω t; αB =α0B+αpB t; αωc =α0c+αpc t; ξρ =Gamma[1-αρ](1-Exp[-I π αρ])/2 S^(αρ-1); ξω =Gamma[1-αω](1-Exp[-I π αω])/2 S^(αω-1); ξB =Gamma[1-αB] (1-Exp[-I π αB])/2 S^(αB-1); ξωc =Gamma[1-αωc](1-Exp[-I π αωc])/2 S^(αωc-1)/Log[S]; F1 =-(t a1ω - 2MP a4ω)ξω -(t a1c- 2MP a4c )ξωc - (t a1ρ - 2MP a4ρ )ξρ ; F2 = t a2B ξB; F3 =t(2MP a1ω - a4ω )ξω + t(2MP a1c - a4c )ξωc + t(2MP a1ρ - a4ρ )ξρ; F4 = 0; f01p = kt Sqrt[t]/2. F1; f11p = kt/2 F3; f01m = pt kt F2; f11m = -pt kt Sqrt[t]F4; res1 = 2(Abs[f01p]^2 + Abs[f01m]^2) Abs[sint]^2; res1 = res1 + Abs[f11p-f11m]^2 (1-cost)^2 + Abs[f11p+f11m]^2 (1+cost)^2; res2 = 2(Abs[f01p]^2 - Abs[f01m]^2) Abs[sint]^2; res2 = res2 + Abs[f11p]^2 (1-cost)^2 + Abs[f11p]^2 (1+cost)^2; res2 = res2 - Abs[f11m]^2 (1-cost)^2 - Abs[f11m]^2 (1+cost)^2; DCSp=Re[res1]/(64π MP^2plab^2)389.3; (* for neutron target ; I=1 changes sign *) F1 =-(t a1ω - 2MP a4ω )ξω -(t a1c - 2MP a4c )ξωc + (t a1ρ - 2MP a4ρ )ξρ ; F2 =- t a2B ξB; F3 =t(2MP a1ω- a4ω )ξω + t(2MP a1c - a4c )ξωc - t(2MP a1ρ - a4ρ )ξρ; f01p = kt Sqrt[t]/2. F1; f11p = kt/2 F3; f01m = pt kt F2; f11m = -pt kt Sqrt[t]F4; res3 = 2(Abs[f01p]^2 + Abs[f01m]^2) Abs[sint]^2; res3 = res3 + Abs[f11p-f11m]^2 (1-cost)^2 + Abs[f11p+f11m]^2 (1+cost)^2; BA=Re[res2/res1]; DCSn=Re[res3/res1]; flag1 DCSp + flag2 BA + DCSn flag3]; (* Compute the differential cross section in μ barn/Gev^2 for pseudoscalar-photoproduction processes IN THE LEADING S APPROXIMATION *) HELObserv[plab_,t_,flag1_,flag2_,flag3_,a1ω_,a4ω_,a2B_,a1ρ_,a4ρ_,a1c_,a4c_,α0ω_,αpω_,α0c_,αpc_,α0B_,αpB_]:= Module[{DCSp,DCSn,BA,res1,res2, res3,S, αρ,αω,αB,αωc, ξω,ξB,ξρ,ξωc, F1,F2,F3,F4}, S = MP^2+2MP Sqrt[plab^2]; αρ = α0ω+αpω t;αω =α0ω+αpω t; αB =α0B+αpB t; αωc =α0c+αpc t; ξρ =Gamma[1-αρ](1-Exp[-I π αρ])/2.0 S^(αρ-1); ξω =Gamma[1-αω](1-Exp[-I π αω])/2.0 S^(αω-1); ξB =Gamma[1-αB] (1-Exp[-I π αB])/2.0 S^(αB-1); ξωc =Gamma[1-αωc](1-Exp[-I π αωc])/2.0 S^(αωc-1)/Log[S]; F1 =-(t a1ω - 2MP a4ω)ξω -(t a1c- 2MP a4c )ξωc - (t a1ρ - 2MP a4ρ )ξρ ; F2 = t a2B ξB; F3 =t(2MP a1ω - a4ω )ξω + t(2MP a1c - a4c )ξωc + t(2MP a1ρ - a4ρ )ξρ; F4 = 0; res1 = (Abs[F3]^2 -t Abs[F1]^2)/(4MP^2-t) + (Abs[F2]^2 -t Abs[F4]^2); res2 = (Abs[F3]^2 -t Abs[F1]^2)/(4MP^2-t) - (Abs[F2]^2 -t Abs[F4]^2); (* for neutron target ; I=1 changes sign *) F1 =-(t a1ω - 2MP a4ω )ξω -(t a1c - 2MP a4c )ξωc + (t a1ρ - 2MP a4ρ )ξρ ; F2 =- t a2B ξB; F3 =t(2MP a1ω- a4ω )ξω + t(2MP a1c - a4c )ξωc - t(2MP a1ρ - a4ρ )ξρ; res3 = (Abs[F3]^2 -t Abs[F1]^2)/(4MP^2-t) + (Abs[F2]^2 -t Abs[F4]^2); DCSp=Re[res1]/(32π)389.3; BA=Re[res2/res1]; DCSn=Re[res3/res1]; flag1 DCSp + flag2 BA + DCSn flag3]; Mass = {0.,MP,MPI,MP}; Cos2T[plab_,cos_,mass_]:=Block[ {ma,mb,mc,md,qi,qf,s,t,coef,tmin,tmax,som}, ma = mass[[1]];mb = mass[[2]]; mc = mass[[3]]; md = mass[[4]]; s=ma^2+mb^2+2mb Sqrt[plab^2+ma^2]; qi = Sqrt[(s-(ma+mb)^2)(s-(ma-mb)^2)/(4.s)]; qf = Sqrt[(s-(mc+md)^2)(s-(mc-md)^2)/(4.s)]; som = ma^2+mb^2+mc^2+md^2; t = 2 qi qf cos+ som/2 - s/2. - (ma^2-mb^2)(mc^2-md^2)/(2. s); coef = π/(qi qf); tmin = (ma^2-mb^2-mc^2+md^2)^2/4./s-(qi-qf)^2; tmax = (ma^2-mb^2-mc^2+md^2)^2/4./s-(qi+qf)^2; {t,coef, tmin, tmax} ] T2Cos[plab_,t_,mass_]:=Block[ {ma,mb,mc,md,qi,qf,s,cos,coef,som}, ma = mass[[1]];mb = mass[[2]]; mc = mass[[3]]; md = mass[[4]]; s=ma^2+mb^2+2mb Sqrt[plab^2+ma^2]; qi = Sqrt[(s-(ma+mb)^2)(s-(ma-mb)^2)/(4.s)]; qf = Sqrt[(s-(mc+md)^2)(s-(mc-md)^2)/(4.s)]; som = ma^2+mb^2+mc^2+md^2; cos = (t + (ma^2-mb^2)(mc^2-md^2)/(2. s)-som/2 + s/2 ) /(2 qi qf ); coef = π/(qi qf); {cos,coef} ] Fit with Eγ >= 4 GeV and t <= 3.0 (* select data *) dat1 = dat2fit ; pdat05 = Select[dat1,0.011/errsig^2,VarianceEstimatorFunction->(1&),AccuracyGoal->5]; (* consider Eγ >= 4 and t <= 3.0 *) xpdat = pdat30; pdat = Select[xpdat,Part[#,1]>=4.0&]; datsig = pdat[[All,1;;3]]; errsig = pdat[[All,4]]; (* with Full expression *) nlmγπ=FitFullCutα[datsig,errsig]; χ2 =nlmγπ["EstimatedVariance",VarianceEstimatorFunction->Automatic]; Print["Eγ >= 4 GeV ; χ^2 = ",χ2] plotSigA = Show[{ander[[1]],pAfitS[nlmγπ]},PlotRange-> {{0,1.5},{-5,0.7}}, AxesOrigin-> {0,-5}]; 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ContentSelectable->True, ImageSize->{1062., Automatic}, PlotRangePadding->{6, 5}] Plot differential cross section with data (* Anderson *) leg = Graphics[Text[Column[{ Row[{Style["•",Blue,20],Style[" 6 GeV",20]},Spacer[10]] , Row[{Style["•",Darker[Green],20],Style[" 9 GeV",20]},Spacer[10]], Row[{Style["•",Red,20],Style["12 GeV",20]},Spacer[10]], Row[{Style["•",Black,20],Style["15 GeV",20]},Spacer[10]] }],{1,-0.6}]]; psig1 = Show[{ander[[1]],plotSigA,leg},PlotRange-> {{0,1.5},{-5,0.7}}, AxesOrigin-> {0,-5},FrameLabel->{Style["-t (GeV^2)",20],Style[ "dσ/dt (μb.GeV^-2)",20]},Frame->True,FrameStyle->FontSize->15]; (* Braun *) SetDirectory[foldername]; braun = Braun68; leg = Graphics[Text[Column[{ Row[{Style["•",Blue,15],Style[" 2 GeV x 10^4",15]},Spacer[10]] , Row[{Style["•",Darker[Green],15],Style[" 3 GeV x 10^3",15]},Spacer[10]] , Row[{Style["•",Red,15],Style[" 4 GeV x 10^2",15]},Spacer[10]], Row[{Style["•",Black,15],Style[" 5 GeV x 10^1",15]},Spacer[10]], Row[{Style["•",Orange,15],Style["5.8 GeV x 10^0",15]},Spacer[10]] }],{1.5,12.5}]]; psig2 = Show[{plotSigB ,leg}, PlotRange-> {{0,2},{-4,15}}, AxesOrigin-> {0,-4}, FrameLabel->{Style["-t (GeV^2)",20],Style[ "dσ/dt (μb.GeV^-2)",20]},Frame->True,FrameStyle->FontSize->15]; (* Bolon67 *) SetDirectory[foldername]; bolon = Bolon67; pfit6 = LogPlot[{ ScaleFacB67[[1]]nlmγπ[2.0,-t], ScaleFacB67[[2]]nlmγπ[2.5,-t], ScaleFacB67[[3]]nlmγπ[3.0,-t], ScaleFacB67[[4]]nlmγπ[3.5,-t], ScaleFacB67[[5]]nlmγπ[4.0,-t], ScaleFacB67[[6]]nlmγπ[4.5,-t], ScaleFacB67[[7]]nlmγπ[5.0,-t]},{t,0.01,5}, PlotStyle-> {{Blue,Thick},{Thick,Darker[Green]},{Thick,Red},{Thick,Black},{Thick, Orange},{Thick, Cyan},{Thick, Magenta}}, PlotPoints->10]; leg = Graphics[Text[Column[{ Row[{Style["•",Blue,15],Style["2.0 GeV x 10^6",15]},Spacer[10]] , Row[{Style["•",Darker[Green],15],Style["2.5 GeV x 10^5",15]},Spacer[10]] , Row[{Style["•",Red,15],Style["3.0 GeV x 10^4",15]},Spacer[10]], Row[{Style["•",Black,15],Style["3.5 GeV x 10^3",15]},Spacer[10]], Row[{Style["•",Orange,15],Style["4.0 GeV x 10^02",15]},Spacer[10]], Row[{Style["•",Cyan,15],Style["4.5 GeV x 10^1",15]},Spacer[10]], Row[{Style["•",Magenta,15],Style["5.0 GeV x 10^0",15]},Spacer[10]] }],{0.5,-9}]]; psig3 = Show[{pfit6,bolon[[1]],leg}, PlotRange-> {{0,4.5},{-15,18}},AxesOrigin-> {0,-15}, FrameLabel->{Style["-t (GeV^2)",20],Style[ "dσ/dt (μb.GeV^-2)",20]},Frame->True,FrameStyle->FontSize->15]; (* Gomez 71 *) SetDirectory[foldername]; gom71 = Gomez71; pfit7 = LogPlot[{ ScaleFacG71[[1]]nlmγπ[6,-t], ScaleFacG71[[2]]nlmγπ[12,-t], ScaleFacG71[[3]]nlmγπ[18,-t]},{t,0.01,3.1}, PlotStyle-> {{Blue,Thick},{Thick,Darker[Green]},{Thick,Red}}]; leg = Graphics[Text[Column[{ Row[{Style["•",Blue,20],Style[" 6 GeV",20]},Spacer[10]] , Row[{Style["•",Darker[Green],20],Style["12 GeV",20]},Spacer[10]] , Row[{Style["•",Red,20],Style["18 GeV",20]},Spacer[10]] }],{.4,-6}]]; psig4=Show[pfit7,gom71[[1]],leg, FrameLabel->{Style["-t (GeV^2)",20],Style[ "dσ/dt 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{Thickness[0.001]}}, {-2.419118909249997, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}}}], {576., -355.98757751993935`}, ImageScaled[{0.5, 0.5}], {360., 222.4922359499621}]}}, {}}, ContentSelectable->True, ImageSize->{1118., Automatic}, PlotRangePadding->{6, 5}] Beam Asymmetry fit fitModelBA[plab_,t_,a2B_,α0B_,αpB_]:=DiffCrossSectPhot[plab,t,0,1,0,0,a4ω,a2B,a1ρ,0,a1ρc,a4ωc,α0v,αpv,α0c,αpc,α0B,αpB]/.nlmγπ["BestFitParameters"] datBA = dataBA[[All,1;;3]]; errBA = dataBA[[All,4]]; (* axial pole and trajectories : 3 parameters *) nlmBA:=NonlinearModelFit[datBA,{fitModelBA[pl,t,a2B,α0B,αpB]}, {{a2B,-1 },{α0B,0},{αpB,0.7}}, {pl,t}, Weights->1/errBA^2,VarianceEstimatorFunction->(1&),AccuracyGoal->5]; χ2 =nlmBA["EstimatedVariance",VarianceEstimatorFunction->Automatic]; Print["χ^2 = ",χ2] nlmBA["ParameterTable"] (* The dimensions of the parameters are a4 GeV-3 a2 GeV-4 a1 GeV-2 αp GeV-2 *) χ^2 = 1.72781 Estimate Standard Error t-Statistic P-Value a2B -8.887 2.30404 -3.85713 0.000564596 α0B -0.193332 0.29573 -0.653745 0.518256 αpB 1.0213 0.184277 5.54222 5.04154*10^-6 plot modelBA[plab_,t_]:=DiffCrossSectPhot[plab,t,0,1,0,0,a4ω,-8.887,a1ρ,0,a1ρc,a4ωc,α0v,αpv,α0c,αpc,-0.193,1.021]/.nlmγπ["BestFitParameters"] modelRat[plab_,t_]:=DiffCrossSectPhot[plab,t,0,0,1,0,a4ω,-8.887,a1ρ,0,a1ρc,a4ωc,α0v,αpv,α0c,αpc,-0.193,1.021]/.nlmγπ["BestFitParameters"] pfit2 = Plot[{modelBA[4.,-t],modelBA[6.,-t],modelBA[10.,-t]},{t,0.1,1.5}, PlotStyle-> {{Blue,Thick},{Thick,Darker[Green]},{Thick,Red}}, PlotPoints->2]; leg = Graphics[Text[Column[{ Row[{Style["•",Blue,20],Style[" 4 GeV",20]},Spacer[10]] , Row[{Style["•",Darker[Green],20],Style[" 6 GeV",20]},Spacer[10]] , Row[{Style["•",Red,20],Style["10 GeV",20]},Spacer[10]] }],{1.,0.5}]]; plotBA = Show[{ander[[2]],pfit2,leg},PlotRange-> {{0,1.5},{0,1.2}}, AxesOrigin-> {0,0},FrameLabel->{Style["-t (GeV^2)",20],Style[ "Σ",20]},Frame->True,FrameStyle->FontSize->15]; (* Ratio neutron/proton *) leg = Graphics[Text[Column[{ 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PlotRangePadding->{Scaled[0.02], Scaled[0.02]}], {576., -116.80842387373012`}, ImageScaled[{0.5, 0.5}], {360., 222.49223594996212`}]}, {}}, ContentSelectable->True, ImageSize->{838., Automatic}, PlotRangePadding->{6, 5}] Target and Recoil Asymmetries SetDirectory[foldername]; tarA1 = Import["Beinlein_TargetA_PhotPi0_4.txt","Table"]; tarA2 = Import["Booth_TargetA_PhotPi0_4.txt","Table"]; recA = Import["Deutsch72_RecoilA4-6.txt","Table"]; dat = tarA1; ps1 = ErrorListPlot[ Table[{{-dat[[i,1]],dat[[i,4]]}, ErrorBar[dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->{●,15},PlotStyle->Blue]; dat = tarA2; ps2 = ErrorListPlot[ Table[{{-dat[[i,1]],dat[[i,4]]}, ErrorBar[dat[[i,5]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->{■,15},PlotStyle->Red]; dat = recA; ps3 = ErrorListPlot[ Table[{{-dat[[i,5]],dat[[i,7]]}, ErrorBar[dat[[i,8]]]},{i,1,Dimensions[dat][[1]]}],PlotMarkers->{●,15},PlotStyle->Black]; (* Target and recoil Asymmetries are the same since F4=0 *) targetA[plab_,t_,a1ω_,a4ω_,a2B_,a1ρ_,a4ρ_,a1c_,a4c_,α0ω_,αpω_,α0c_,αpc_,α0B_,αpB_]:= Module[{res1,S, αρ,αω,αB,αωc, ξω,ξB,ξρ,ξωc, F1,F2,F3,F4}, S = MP^2+2MP Sqrt[plab^2]; (*αρ = 0.5+0.8t;αω = 0.5 +0.8t; αB = 0 + 0.7t; αωc = 0.5+0.15t;*) αρ = α0ω+αpω t;αω =α0ω+αpω t; αB =α0B+αpB t; αωc =α0c+αpc t; ξρ =-Gamma[1-αρ](1-Exp[-I π αρ])/2 S^(αρ-1); ξω =-Gamma[1-αω](1-Exp[-I π αω])/2 S^(αω-1); ξB =-Gamma[1-αB] (1-Exp[-I π αB])/2 S^(αB-1); ξωc =Gamma[1-αωc](1-Exp[-I π αωc])/2 S^(αωc-1)/Log[S]; F1 =-(t a1ω - 2MP a4ω)ξω -(t a1c- 2MP a4c )ξωc - (t a1ρ - 2MP a4ρ )ξρ ; F2 = t a2B ξB; F3 =t(2MP a1ω - a4ω )ξω + t(2MP a1c - a4c )ξωc + t(2MP a1ρ - a4ρ )ξρ; F4 = 0; res1 = F1 Conjugate[F3]/(4MP^2-t) - F4 Conjugate[F2]; Im[res1]Sqrt[-t]/(16π)389.3]; tarA[pl_,t_]:=targetA[pl,t,0,a4ω,-8.887,a1ρ,0,a1ρc,a4ωc,α0v,αpv,α0c,αpc,-0.193,1.021]/.nlmγπ["BestFitParameters"]; pth1 =Plot[{tarA[4.,-t],tarA[5.,-t],tarA[6.,-t]},{t,0,2},PlotStyle->{{Thick, Blue},{Thick, Darker[Green]},{Thick, Red}}, 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FullExp[5,-1,1,0,0]/Approx[5,-1,1,0,0] 0.888002 papprox = Plot[{Approx[2,-t,1,0,0]/FullExp[2,-t,1,0,0], Approx[3,-t,1,0,0]/FullExp[3,-t,1,0,0], Approx[4,-t,1,0,0]/FullExp[4,-t,1,0,0], Approx[5,-t,1,0,0]/FullExp[5,-t,1,0,0], Approx[6,-t,1,0,0]/FullExp[6,-t,1,0,0], Approx[9,-t,1,0,0]/FullExp[9,-t,1,0,0]},{t,0.05,1.5}, PlotStyle->{{Blue,Thick},{Thick,Darker[Green]},{Thick,Red},{Thick,Black},{Thick, Orange},{Thick, Magenta}}, PlotPoints->2,FrameLabel->{Style["-t (GeV^2)",20],Style[ "dσ/dt (μb.GeV^-2)",20]}]; leg = Graphics[Text[Column[{ Row[{Style["-",Blue,20],Style["2 GeV",20]},Spacer[10]] , Row[{Style["-",Darker[Green],20],Style["3 GeV",20]},Spacer[10]], Row[{Style["-",Red,20],Style["4 GeV",20]},Spacer[10]], Row[{Style["-",Black,20],Style["5 GeV",20]},Spacer[10]], Row[{Style["-",Orange,20],Style["6 GeV",20]},Spacer[10]], Row[{Style["-",Magenta,20],Style["9 GeV",20]},Spacer[10]] }],{.2,1.5}]]; psig7 = Show[leg,papprox,Frame->True,FrameStyle->FontSize->15, PlotRange->{{0,1.5},All}, AxesOrigin->{0,1},FrameLabel->{Style["-t (GeV^2)",20]},Frame->True,FrameStyle->FontSize->15]  GraphicsBox[{InsetBox[ TagBox[GridBox[{ { TemplateBox[{StyleBox["\"-\"", StripOnInput -> False, LineColor -> RGBColor[0, 0, 1], FrontFaceColor -> RGBColor[0, 0, 1], BackFaceColor -> RGBColor[0, 0, 1], GraphicsColor -> RGBColor[0, 0, 1], FontSize -> 20, FontColor -> RGBColor[0, 0, 1]],StyleBox["\"2 GeV\"", StripOnInput -> False, FontSize -> 20]}, "Row", DisplayFunction->(RowBox[{#, InterpretationBox[StyleBox[GraphicsBox[{}, ImageSize -> {10, 0}, BaselinePosition -> Baseline], "CacheGraphics" -> False], Spacer[10]], #2}]& ), InterpretationFunction->(RowBox[{"Row", "[", RowBox[{RowBox[{"{", RowBox[{#, ",", #2}], "}"}], ",", InterpretationBox[StyleBox[GraphicsBox[{}, ImageSize -> {10, 0}, BaselinePosition -> Baseline], "CacheGraphics" -> False], Spacer[10]]}], "]"}]& )]}, { TemplateBox[{StyleBox["\"-\"", StripOnInput -> False, LineColor -> RGBColor[0, Rational[2, 3], 0], FrontFaceColor -> 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(2S+t-Σ)/(4 kt pt); sint = Sqrt[1-cost^2]; αv = α0v+αpv t; αc =α0c+αpc t;αd =α0d+αpd t; ξv =Gamma[1-αv](1-Exp[-I π αv])/2 S^(αv-1); ξd =Gamma[1-αd](1-Exp[-I π αd])/2 S^(αd-1); ξc =Gamma[1-αc](1-Exp[-I π αc])/2 S^(αc-1)/Log[S]; F1 =-( 0- 2MP gv )ξv -(0- 2MP gc )ξc - ( 0 - 2MP gd )ξd ; F2 = 0; F3 =t( 0- gv )ξv + t(0 - gc )ξc + t(0 - gd )ξd; F4 = 0; f01p = kt Sqrt[t]/2. F1; f11p = kt/2 F3; f01m = pt kt F2; f11m = -pt kt Sqrt[t]F4; res1 = 2(Abs[f01p]^2 + Abs[f01m]^2) Abs[sint]^2; res1 = res1 + Abs[f11p-f11m]^2 (1-cost)^2 + Abs[f11p+f11m]^2 (1+cost)^2; DCSp=Re[res1]/(64π MP^2plab^2)389.3; DCSp ]; Clear[fig] pole[plab_,t_] := SimpleModel[plab,t,1,0,0,α0v,αpv,0,0,0,0]/.nlmγπ["BestFitParameters"]; polecut[plab_,t_] := SimpleModel[plab,t,1,.1,0,α0v,αpv,α0c,αpc,0,0]/.nlmγπ["BestFitParameters"]; poledau[plab_,t_] := SimpleModel[plab,t,1,0,0.5,α0v,αpv,0,0,α0v-1,αpv]/.nlmγπ["BestFitParameters"]; polecutdau[plab_,t_] := SimpleModel[plab,t,1,0.1,0.5,α0v,αpv,α0c,αpc,α0v-1,αpv]/.nlmγπ["BestFitParameters"]; leg = Graphics[Text[Column[{ Row[{Style["-",Blue,30],Style["Pole",20]},Spacer[10]] , Row[{Style["-",Darker[Green],30],Style["Pole+Cut",20]},Spacer[10]], Row[{Style["-",Orange,30],Style["Pole+Daugther",20]},Spacer[10]], Row[{Style["-",Red,30],Style["Pole+Cut+Daugther",20]},Spacer[10]] }],{-1,-17}]]; En1 = 9; En2 = 3; fig[1]=LogPlot[{pole[En1,t],polecut[En1,t],poledau[En1,t],polecutdau[En1,t]},{t,-3,-.01}, PlotPoints->3, PlotStyle->{{Thick,Blue},{Thick,Darker[Green]},{Thick,Orange},{Thick,Red}}]; fig[2]=LogPlot[{100pole[En2,t],100polecut[En2,t],100poledau[En2,t],100polecutdau[En2,t]},{t,-3,-.01}, PlotPoints->3,PlotStyle->{{Thick,Blue},{Thick,Darker[Green]},{Thick,Orange},{Thick,Red}}]; Show[fig[1],fig[2],leg,PlotRange->All,Frame->True,FrameStyle->FontSize->15] leg = Graphics[Text[Column[{ Row[{Style["-",Blue,40],Style["Pole+Cut",20]},Spacer[10]], Row[{Style["--",Darker[Green],20],Style["Pole+Daugther",20]},Spacer[10]] }],{1,-17}]]; fig[3]=LogPlot[{polecut[En1,-t],poledau[En1,-t]},{t,.01,3}, PlotPoints->3, PlotStyle->{{Thick,Blue},{Thick,Darker[Green],Dashed},{Thick,Orange},{Thick,Red}}]; fig[4]=LogPlot[{polecut[En2,-t],poledau[En2,-t]},{t,.01,3}, PlotPoints->3,PlotStyle->{{Thick,Blue},{Thick,Darker[Green],Dashed},{Thick,Orange},{Thick,Red}}]; 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{0.00375, 0.}, {Thickness[0.001]}}, {-9.433483923290392, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-9.315700887634009, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-8.517193191416238, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-8.111728083308073, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-7.824046010856292, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-7.600902459542082, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-7.418580902748127, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-7.264430222920869, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-7.1308988302963465`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-7.013115794639964, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-6.214608098422191, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-5.809142990314028, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-5.521460917862246, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-5.298317366548036, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-5.115995809754082, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-4.961845129926823, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-4.8283137373023015`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-4.710530701645918, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}}}, {Automatic, Automatic}}, GridLines->{None, None}, ImageSize->{535., Automatic}, Method->{}, PlotRange->All, PlotRangeClipping->True, PlotRangePadding->{Scaled[0.02], Scaled[0.02]}, Ticks->{Automatic, {{-18.420680743952367`, FormBox[TemplateBox[{"10", RowBox[{"-", "8"}]}, "Superscript", SyntaxForm -> SuperscriptBox], TraditionalForm]}, {-16.11809565095832, FormBox[TemplateBox[{"10", RowBox[{"-", "7"}]}, "Superscript", SyntaxForm -> SuperscriptBox], TraditionalForm]}, {-13.815510557964274`, FormBox[TemplateBox[{"10", RowBox[{"-", "6"}]}, "Superscript", SyntaxForm -> SuperscriptBox], TraditionalForm]}, {-11.512925464970229`, FormBox[TemplateBox[{"10", RowBox[{"-", "5"}]}, "Superscript", SyntaxForm -> SuperscriptBox], TraditionalForm]}, {-9.210340371976182, FormBox[TemplateBox[{"10", RowBox[{"-", "4"}]}, "Superscript", SyntaxForm -> SuperscriptBox], TraditionalForm]}, {-6.907755278982137, FormBox["0.001`", TraditionalForm]}, {-4.605170185988091, FormBox["0.01`", TraditionalForm]}, {-17.72753356339242, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-17.322068455284256`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-17.034386382832476`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-16.811242831518264`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-16.62892127472431, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-16.474770594897052`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-16.34123920227253, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-16.223456166616145`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-15.424948470398375`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-15.01948336229021, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-14.73180128983843, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-14.508657738524219`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-14.326336181730264`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-14.172185501903007`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-14.038654109278484`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-13.9208710736221, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-13.122363377404328`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-12.716898269296165`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-12.429216196844383`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-12.206072645530174`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-12.02375108873622, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-11.86960040890896, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-11.736069016284437`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-11.618285980628055`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-10.819778284410283`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-10.414313176302118`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-10.126631103850338`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-9.903487552536127, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-9.721165995742174, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-9.567015315914915, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-9.433483923290392, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-9.315700887634009, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-8.517193191416238, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-8.111728083308073, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-7.824046010856292, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-7.600902459542082, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-7.418580902748127, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-7.264430222920869, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-7.1308988302963465`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-7.013115794639964, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-6.214608098422191, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-5.809142990314028, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-5.521460917862246, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-5.298317366548036, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-5.115995809754082, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-4.961845129926823, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-4.8283137373023015`, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}, {-4.710530701645918, FormBox["\"\"", TraditionalForm], {0.00375, 0.}, {Thickness[0.001]}}}}] Prediction for CLAS tvec = Range[-3.0,-0.01,0.02]; Elab1 = 3; (* Beam energy in GeV *) Elab2 = 4; (* Beam energy in GeV *) Elab3 = 5; (* Beam energy in GeV *) Elab4 = 6; (* Beam energy in GeV *) Elab5 = 9; (* Beam energy in GeV *) fullmodel[plab_,t_]:=DiffCrossSectPhot[plab,t,1,0,0,0,a4ω,-8.887,a1ρ,0,a1ρc,a4ωc,α0v,αpv,α0c,αpc,-0.193,1.021]/.nlmγπ["BestFitParameters"]; ord1 = Table[fullmodel[Elab1,tvec[[it]]]/T2Cos[Elab1,tvec,Mass][[2]],{it,Length[tvec]}]; ord2 = Table[fullmodel[Elab2,tvec[[it]]]/T2Cos[Elab2,tvec,Mass][[2]],{it,Length[tvec]}]; ord3 = Table[fullmodel[Elab3,tvec[[it]]]/T2Cos[Elab3,tvec,Mass][[2]],{it,Length[tvec]}]; ord4 = Table[fullmodel[Elab4,tvec[[it]]]/T2Cos[Elab4,tvec,Mass][[2]],{it,Length[tvec]}]; ord5 = Table[fullmodel[Elab5,tvec[[it]]]/T2Cos[Elab4,tvec,Mass][[2]],{it,Length[tvec]}]; pcos1 = ListLogPlot[Transpose[{T2Cos[Elab1,tvec,Mass][[1]],ord1}], PlotRange->{{-1,1},{10^-4,1}}, AxesOrigin->{-1,0}, Joined->True, PlotStyle->{Blue, Thick}, Frame->True]; pcos2 = ListLogPlot[Transpose[{T2Cos[Elab2,tvec,Mass][[1]],ord2}], PlotRange->{{-1,1},{10^-4,1}}, AxesOrigin->{-1,0}, Joined->True, PlotStyle->{Darker[Green], Thick}, Frame->True]; pcos3 = ListLogPlot[Transpose[{T2Cos[Elab3,tvec,Mass][[1]],ord3}], PlotRange->{{-1,1},{10^-4,1}}, AxesOrigin->{-1,0}, Joined->True, PlotStyle->{Red, Thick}, Frame->True]; pcos4 = ListLogPlot[Transpose[{T2Cos[Elab4,tvec,Mass][[1]],ord4}], PlotRange->{{-1,1},{10^-4,1}}, AxesOrigin->{-1,0}, Joined->True, PlotStyle->{Black, Thick}, Frame->True]; pcos5 = ListLogPlot[Transpose[{T2Cos[Elab5,tvec,Mass][[1]],ord4}], PlotRange->{{-1,1},{10^-4,1}}, AxesOrigin->{-1,0}, Joined->True, PlotStyle->{Orange, Thick}, Frame->True]; leg = Graphics[Text[Column[{ Row[{Style["-",Blue,40],Style["3 GeV",20]},Spacer[10]] , Row[{Style["-",Darker[Green],40],Style["4 GeV",20]},Spacer[10]], Row[{Style["-",Red,40],Style["5 GeV",20]},Spacer[10]], Row[{Style["-",Black,40],Style["6 GeV",20]},Spacer[10]], Row[{Style["-",Orange,40],Style["9 GeV",20]},Spacer[10]] }],{-0.7,-3}]]; pclas1=Show[pcos1,pcos2,pcos3,pcos4,pcos5,leg,FrameLabel->{Style["Cos θ",20],Style[ "dσ/dt (μb.GeV^-2)",20]},FrameStyle->FontSize->15]; pfull = LogPlot[{fullmodel[Elab1,t],fullmodel[Elab2,t],fullmodel[Elab3,t],fullmodel[Elab4,t],fullmodel[Elab5,t]},{t,-3,-0.03}, PlotStyle->{{Blue,Thick},{Thick,Darker[Green]},{Thick,Red},{Thick,Black},{Thick, Orange}}, PlotPoints->5]; leg = Graphics[Text[Column[{ Row[{Style["-",Blue,40],Style["3 GeV",20]},Spacer[10]] , Row[{Style["-",Darker[Green],40],Style["4 GeV",20]},Spacer[10]], Row[{Style["-",Red,40],Style["5 GeV",20]},Spacer[10]], Row[{Style["-",Black,40],Style["6 GeV",20]},Spacer[10]], Row[{Style["-",Orange,40],Style["9 GeV",20]},Spacer[10]] }],{-3.5,-3}]]; pclas2 = 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