Mass Spectra for the (Subscript[m, q])=0 Limit

mρs={0.7039858705155417`,0.6504802534247337`,0.5940655616572006`,0.5347161782476973`,0.47246192623562`,0.4066567357860551`,0.33949309851221887`,0.27098643290615665`,0.20262895564767572`,0.1359718503953471`,0.07499228281999042`,0.026790694166293514`,0.001957730366324809`(*,5.257501425045325`*^-6*)};
fρs={0.3073514324269752`,0.2839041512739803`,0.2591852834448883`,0.23318709644337324`,0.205926599714195`,0.17713071368549196`,0.14776074217728527`,0.11782990345724267`,0.08800389931878824`,0.058973770091178865`,0.03247139236088075`,0.011576141864221508`,0.0008438991852451367`(*,2.2622487265945206`*^-6*)};
fπs={0.05776809503534308`,0.054062021831054956`,0.050074814023980375`,0.04578525435648057`,0.041172948945435044`,0.03614763353558889`,0.03086813638517084`,0.025290480046418044`,0.019488373592135098`,0.013550671487986079`,0.007804019492331792`,0.002946927154113874`,0.00023240698088424543`(*,6.620065555291642`*^-7*)};

nf={1,2,3,4,5,6,7,8,9,10,11,12,13(*,13.5*)};

AppendTo[mρs,Vmass1];
AppendTo[fρs,(Sqrt[fvsq1])];
AppendTo[fπs,(Sqrt[fpisq1])];
mρs
fρs
fπs

mρf={0.5560805438242872`,0.4968958269097069`,0.4355659780664688`,0.37283718002242944`,0.30988438692881404`,0.24717826068427576`,0.18820993619299117`,0.13348856956763033`,0.08591043854513683`,0.04752133387396175`,0.02031045943640634`,0.005089009604481677`,0.00023042281320098952`(*,4.322512658338105`*^-7*)};
fρf={0.2095977430725626`,0.22274718186873071`,0.21608653748134202`,0.19874131340647117`,0.17463065544279416`,0.1457477477714957`,0.11529033728653448`,0.0845071648986368`,0.05596932887005831`,0.03175979029262518`,0.013885482107262951`,0.0035516872147173437`,0.00016381048002456843`(*,3.099053926765056`*^-7*)};
fπf={0.03226857744041908`,0.03691060581204389`,0.036506863074074004`,0.03367521347766093`,0.029507210754506737`,0.024518929497119493`,0.01930617261820836`,0.014100454982630515`,0.0093183982046137`,0.005283710619154371`,0.0023159781563122533`,0.0005943506007067837`,0.00002774116612794617`(*,5.29110423186711`*^-8*)};

AppendTo[mρf,Vmass];
AppendTo[fρf,(Sqrt[fvsq])];
AppendTo[fπf,(Sqrt[fpisq])];
mρf
fρf
fπf

mσs={0.37186917059045127`,0.31305556982074967`,0.25800046654828995`,0.20766636069268887`,0.16234442959252626`,0.12153045179770174`,0.08784910886012856`,0.0589314931454635`,0.035964359561223604`,0.018977180757740974`,0.0077783749835512945`,0.0018222906462112014`,0.00006235388298982674`(*,7.458246665031554`*^-8*)};
mas={0.9396846597451998`,0.8711902172239474`,0.798476687051468`,0.7214289691668422`,0.6400083855337144`,0.5532249644848009`,0.4639453348950434`,0.372143974996082`,0.27971692137310966`,0.18874733634868787`,0.10472630804477441`,0.03766368901135473`,0.002773731574508729`(*,7.486364469849137`*^-6*)};
fσs={0.9901731787419323`,1.0245421240464383`,1.0677374063738778`,1.1198705517068144`,1.1822807874034595`,1.2593836749557141`,1.3409640730893835`,1.3086855185248913`,1.1416405368403069`,0.8145020132063554`,0.4278752022861359`,0.13638928182936408`,0.008788348663663485`(*,0.00002225426814029254`*)};
fas={0.3108569622955491`,0.28678281470168376`,0.2613987389118957`,0.2347095829879382`,0.20674883319576934`,0.17728184305359962`,0.14729487027335403`,0.11687222673177923`,0.08673943198883965`,0.05765794854173895`,0.03141951847815241`,0.011049110586718227`,0.0007899707105788862`(*,2.0869570095642636`*^-6*)};

AppendTo[mσs,Smass1];
AppendTo[mas,Amass1];
AppendTo[fσs,(Sqrt[fssq1])];
AppendTo[fas,(Sqrt[fasq1])];
mσs
mas
fσs
fas

mσf={0.672059725281842`,0.593211638828637`,0.5136407956801109`,0.43046388301363453`,0.3481788826031583`,0.2681198243854614`,0.1948653755551033`,0.12976745329671924`,0.07675149004048026`,0.03795357241190369`,0.01413294185059542`,0.003052838982569719`,0.0001064078516307861`(*,1.9047486073136637`*^-7*)};
maf={0.8012250825430401`,0.6264395858168875`,0.5169705170323929`,0.42759992542176556`,0.3476152765303424`,0.27302674849542574`,0.20554342522830707`,0.1445275005150266`,0.0923878143937803`,0.05083025929991616`,0.021630752727656386`,0.005399727829797182`,0.00024385691137977165`(*,4.569396554363852`*^-7*)};
fσf={0.42358276457194827`,0.46799717653969714`,0.4754794722909424`,0.4591162238874516`,0.4282846438393874`,0.3692955017374409`,0.3039730137364655`,0.2317353828209699`,0.15951717635692245`,0.0943865089774375`,0.043513579524594906`,0.01186580584872826`,0.0006269610704839763`(*,1.2813031198942183`*^-6*)};
faf={0.2301092325736832`,0.22556352508407587`,0.21468409402091457`,0.1962952968136314`,0.1721457793315823`,0.14359398323837985`,0.11358557818993281`,0.0832647218624427`,0.05516213786351182`,0.03130517931742755`,0.013688696235423813`,0.0035014592286653186`,0.00016141393668467935`(*,3.0528760767192377`*^-7*)};

AppendTo[mσf,Smass];
AppendTo[maf,Amass];
AppendTo[fσf,(Sqrt[fssq])];
AppendTo[faf,(Sqrt[fasq])];
mσf
maf
fσf
faf

Show[ListPlot[{Table[{nf[[i]],((mρs[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((mρf[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((mσs[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((mσf[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((mas[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((maf[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}]}],ListPlot[{Table[{nf[[i]],((mρs[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((mρf[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((mσs[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((mσf[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((mas[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((maf[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}]},Joined->True],AxesOrigin->{1,0},AxesLabel->{(Subscript[N, f]),M},PlotRange->All,ImageSize->Large]
(*blue is the ρ symmetric, ochre is the ρ fundamental, green is the σ symmetric, orange is the σ fundamental, purple is the axial symmetric, brown is the axial fundamental*)

Show[ListLogPlot[{Table[{nf[[i]],((fρs[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((fρf[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((fσs[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((fσf[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((fas[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((faf[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((fπs[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((fπf[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}]}],ListLogPlot[{Table[{nf[[i]],((fρs[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((fρf[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((fσs[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((fσf[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((fas[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((faf[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((fπs[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],((fπf[[i]])/(mρs[[i]]))},{i,1,Dimensions[nf][[1]],1}]},Joined->True],AxesOrigin->{1,-5},AxesLabel->{(Subscript[N, f]),F},PlotRange->All,ImageSize->Large]
(*blue is the ρ symmetric, ochre is the ρ fundamental, green is the σ symmetric, orange is the σ fundamental, purple is the axial symmetric, brown is the axial fundamental, cyan is the π symmetric, yellow is the π fundamental*)

(*1*)(*nf*)
0.3
0.2
0.2

(*2*)
0.2
0.14
0.17

(*3*)
0.19
0.12
0.14

(*4*)
0.17
0.1
0.12

(*5*)
0.15
0.07
0.1

(*6*)
0.13
0.05
0.08

(*7*)
0.11
0.03
0.06

(*Nf=8*)
0.09
0.02
0.05

(*Nf=9*)
0.07
0.005
0.03

(*Nf=10*)
0.05
0.0005
0.02

(*Nf=11*)
0.03
6.*(10^(-7))
0.007

(*Nf=12*)
0.008
9.7*(10^(-13))
0.002

(*Nf=13*)
0.0006
2.1*(10^(-13))
0.00008

(*Nf=13.5*)
2.*(10^(-6))
1.2*(10^(-13))
2.*(10^(-7))

Show[ListLogPlot[{Table[{nf[[i]],mρs[[i]]},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],mρf[[i]]},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],mσs[[i]]},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],mσf[[i]]},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],mas[[i]]},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],maf[[i]]},{i,1,Dimensions[nf][[1]],1}]}],ListLogPlot[{Table[{nf[[i]],mρs[[i]]},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],mρf[[i]]},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],mσs[[i]]},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],mσf[[i]]},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],mas[[i]]},{i,1,Dimensions[nf][[1]],1}],Table[{nf[[i]],maf[[i]]},{i,1,Dimensions[nf][[1]],1}]},Joined->True],AxesOrigin->{1,0},AxesLabel->{(Subscript[N, f]),M},PlotRange->All,ImageSize->Large]
(*blue is the ρ symmetric, ochre is the ρ fundamental, green is the σ symmetric, orange is the σ fundamental, purple is the axial symmetric, brown is the axial fundamental*)