Wolfram Cloud Document

In[]:=

(*=========================================================================*)(*6.ERRORANALYSIS:PDGGLUEBALLSVSTWISTORSTRINGPREDICTIONS*)(*=========================================================================*)(*ExperimentalMasses(GeV),J,andLevelnfora=1/2*)dataAnti={{1.426,1,0,"f1(1420)"},{1.506,0,1,"f0(1500)"},{1.971,1,1,"f1(1970)"},{2.011,2,0,"f2(2010)"},{2.530,2,1,"f2(2530)"},{2.600,3,0,"X(2600)"}};(*ExperimentalMasses(GeV),J,andLevelmfora=1*)dataPer={{2.101,0,1,"f0(2100)"}};(*TheoreticalMassFunctions(usingsigmaVal=0.18)*)massThAnti[J_,n_]:=Sqrt[4*Pi*sigmaVal*(J+n-1/12)];massThPer[J_,m_]:=Sqrt[8*Pi*sigmaVal*(J+m)];(*---Analysisfora=1/2Sector---*)mExpA=dataAnti[[All,1]];mThA=massThAnti[#[[2]],#[[3]]]&/@dataAnti;errsA=Abs[mExpA-mThA];relErrsA=errsA/mExpA;maeA=Mean[errsA];mreA=Mean[relErrsA];ssTotA=Total[(mExpA-Mean[mExpA])^2];ssResA=Total[errsA^2];r2A=1-ssResA/ssTotA;(*---Analysisfora=1Sector---*)mExpP=dataPer[[All,1]];mThP=massThPer[#[[2]],#[[3]]]&/@dataPer;errsP=Abs[mExpP-mThP];relErrsP=errsP/mExpP;maeP=Mean[errsP];mreP=Mean[relErrsP];(*---CombinedAnalysis---*)mExpAll=Join[mExpA,mExpP];mThAll=Join[mThA,mThP];errsAll=Abs[mExpAll-mThAll];relErrsAll=errsAll/mExpAll;maeAll=Mean[errsAll];mreAll=Mean[relErrsAll];ssTotAll=Total[(mExpAll-Mean[mExpAll])^2];ssResAll=Total[errsAll^2];r2All=1-ssResAll/ssTotAll;(*PrintReport*)Print[""];Print["========================================================================="];Print[" FIT STATISTICS: PDG GLUEBALLS VS ZERO-PARAMETER PREDICTIONS "];Print["========================================================================="];Print["\n[ a=1/2 (Anti-Periodic) Sector ]"];Print[StringForm[" Number of States: ``",Length[dataAnti]]];Print[StringForm[" Mean Absolute Error (MAE): `` MeV",NumberForm[maeA*1000,{4,1}]]];Print[StringForm[" Mean Relative Error (MRE): `` %",NumberForm[mreA*100,{4,2}]]];Print[StringForm[" R^2 Fit Score: ``",NumberForm[r2A,{5,4}]]];Print["\n[ a=1 (Periodic) Sector ]"];Print[StringForm[" Number of States: ``",Length[dataPer]]];Print[StringForm[" Absolute Error: `` MeV",NumberForm[maeP*1000,{4,1}]]];Print[StringForm[" Relative Error: `` %",NumberForm[mreP*100,{4,2}]]];Print[" (R^2 is statistically undefined for a single data point)"];Print["\n[ Combined Sectors ]"];Print[StringForm[" Total States: ``",Length[mExpAll]]];Print[StringForm[" Overall MAE: `` MeV",NumberForm[maeAll*1000,{4,1}]]];Print[StringForm[" Overall MRE: `` %",NumberForm[mreAll*100,{4,2}]]];Print[StringForm[" Overall R^2 Fit Score: ``",NumberForm[r2All,{5,4}]]];Print["\n========================================================================="];Print[" INDIVIDUAL MASS DEVIATIONS (GeV)"];Print["-------------------------------------------------------------------------"];Print[StringPadRight["State",12],StringPadRight["M_exp",10],StringPadRight["M_theory",12],"Difference"];Print["-------------------------------------------------------------------------"];Do[Print[StringPadRight[dataAnti[[i,4]],12],StringPadRight[ToString[NumberForm[mExpA[[i]],{4,3}]],10],StringPadRight[ToString[NumberForm[mThA[[i]],{4,3}]],12],ToString[NumberForm[errsA[[i]],{4,3}]]],{i,1,Length[dataAnti]}];Do[Print[StringPadRight[dataPer[[i,4]],12],StringPadRight[ToString[NumberForm[mExpP[[i]],{4,3}]],10],StringPadRight[ToString[NumberForm[mThP[[i]],{4,3}]],12],ToString[NumberForm[errsP[[i]],{4,3}]]],{i,1,Length[dataPer]}];Print["========================================================================="];