FDC軟件包在分波分析中的應用

FDC軟件包在分波分析中的應用

簡單介紹FDC系統(tǒng)強相互作用的有效拉氏量的構(gòu)造規(guī)則FDC-PWA分波分析版本的簡介簡單演示總結(jié)BESIII物理分析講習班,2008年6月25日北京王建雄中國科學院高能物理研究所,理論室

簡單介紹FeynmanDiagramCalculation(FDC),1993年開始.PROGRESSINFDCPROJECT.Nucl.Instrum.Meth.A534:241-245,2004

FDC的主頁：所內(nèi)版：8/fdc/index.html(可以看到最新的結(jié)果)所外版：/lunwen/wjx/public_html/index.html

(更新不定期)

FDC-SM-and-Many-ExtensionsFDC-NRQCDFDC-MSSMFDC-EMTFDC-PWAFDC-LOOP

FDC-PWA1998開始,鄒冰松,祝玉燦,..Thereisacommonkernel.TheSourceiswritteninREDUCE,RLISP.分波分析在BES物理分析中的重要性確定各種量子數(shù),質(zhì)量,寬度復雜結(jié)構(gòu)的譜、共振態(tài)、奇特態(tài)、膠球,以前應用分波分析做理論計算，物理分析，編寫Fortran程序都是手做的，就算不包括3/2、2、5/2,7/2自旋態(tài)，也得花幾個月的時間，如果包括了3/2、2、5/2,7/2自旋態(tài)，計算量和表達式會大幾十倍。另外人工做這些工作怎樣檢查錯誤也很困難。而FDC系統(tǒng)，其中各個部份，各種核心算法在這么多年的發(fā)展和應用中，已經(jīng)進行了很多次的檢驗。（例如手算與FDC算對比，F(xiàn)DC與KEK的Grace對比等）。2.FDC-PWA:FDC在BEPC-II物理分析中的應用在FDC系統(tǒng)中實現(xiàn)了自動化構(gòu)造分波分析有效拉氏量模型的部分（與鄒冰松，祝玉燦合作），以及產(chǎn)生包括3/5,5/2,7/2及整數(shù)自旋態(tài)的物理過程的費曼圖，產(chǎn)生所有Fortran源程序以及最大似然法的擬合程序的部分，在其中結(jié)合最大似然法擬合程序的算法，對于矩陣元平方的算法在結(jié)構(gòu)上進行了兩次大的優(yōu)化,使得產(chǎn)生的程序在實驗分析擬合中計算速度兩次都有10倍的提高2.1強相互作用的有效拉氏量的構(gòu)造規(guī)則LorentzInvarianceC-parityconservationP-parityconservationCPconservationH=HABCDecayDecayABCDThecoefficientsofalltheindepenttermsareconstantThecoefficientsofalltheindepenttermsdependontwovaribales每個系數(shù)都有獨立的復數(shù)相因子.每個傳播子都有off-shell貢獻的壓低因子對于一個粒子列表,給出所有可能的有效相互作用頂角.ABC(offmassshell)ForNNscatting,T-channelverticesmustbeconsidered:TheCoefficientsofindependenttermsdependonthe:2

t=(PA

–

PB)

Thepropagatorforresonance:SuppersionFactorforinteractionverticeswhentheresonanceisoffmassshell:

Barrier,

ThereisanoptiontochoosethesuppersionfactorOptiontoapplyIsopinsymmetry:

GlobelOptionsinModelGeneration(infile:addvertices)%just_v_type:='ok;

Itwillgenerateallthetypeoftheinteractionverticesasreqiredandwithouttherealverticesifthelinewasuncommented.

%direct_model:='ok;

Thelineisusedtochosethetwodifferentkindsofeffectivelagrangian.Thedefaultischoosedtousethepure-orbital-angular-momentumcovarianttensorsandthecovariantspinwavefunctionforcontructionoftheeffectivelagrangian.Touncommentitmeanstochooseanaiveindependentlorentzsetofthecombinationofmomentum,spinwavefunction.

Thedifferenceofthesetwomodelsisfromtheoff-shellpartoftheresonaceparticles.%final_particle_list:='("p""\pi""K""eta""\pi^0""K^0");

Thislineisusedtoputtheparticlesintothelistofexternalparticles.ThelistisusedintheFeynmandiagramgenerationprocedurebyFDCandalltheparticlesinthelistwillnotappearedintheresonaceplace.

%keep_sm_part_in_tex:='ok;

TheoptionisusedtochoseiftheinteractionverticesintheStandardmodelarekeptinthe"model.tex"fileornot.Thedefaultiskeep_sm_part_in_tex:='nil;anditmeanstheverticesintheSMaredroped.

http:='ok;

Thisoptionisusedtochosethetypeof"model.tex"filewhichisgeneratedbyFDC.http:='ok;meansthe"model.tex"isforhttpversion.Thedefaultishttp:='nil;anditmeansthe"model.tex"isforPSversion.n_particles:='3;

Theisthelimittothenumberofparticlesineachvertex.Thesmallestnumberis3andthedefaultis3.Itcanbechangedinto4orbiggeranditmeansthatallpossibletheoneparticlesdecaysintothreeparticlesverticeswillbegeneratedifthenumberissetto4.

n_total_spin:='6;

Thisnumberisthelimittothesumofthespinofeachparticlesinaneffectiveinteractionvertex.Thedefaultis6.itmeansthattheFDCwilluse6forthe"n_totla_spin"ifitisnotgiven.

2.2FDC-PWA分波分析版本的簡介有效拉氏量模型的自動化產(chǎn)生費曼圖的產(chǎn)生>diag矩陣元及平方的Fortran程序的產(chǎn)生>amp相空間程序及Likelihoodfitting的Fortran程序的產(chǎn)生>kine進入Fortran目錄和編譯>cdfort>make開始進行Likelihood擬合>fit

FDC3.1,1999,開始在BES的分波分析中應用,模型不是完全自動化產(chǎn)生的,并且沒有包括末態(tài)是純波色子過程FDC3.32003開始應用,模型產(chǎn)生完全的自動化,包括末態(tài)是純波色子過程FDC-PWAApplication:

>gmodel>doall>cdfort>make>fit

FDCSystemNumericalresults&RequiredplotsinHbookformatPhysicalmodelevaluationFullFeynmanRulesPhysicalparametersLatexversionofthenmodelInputforphysicalmodelNumericalintegration,fittingTreatmentofkinematicsAmplitudemanipulationFeynmandiagramgenerationInputforphysicalprocessChoosephysicalmodelandprocessesFIG.1:FDCsystemflowchartTopreparephenomenologicalmodelListofallthenon-elementaryparticlesandtheirquantumnumbersThegeneratedphysicalmodelforFDCsystemLatexversionofthegeneartedphysicalmodelListofalltheparticlesListofallthepropagatorsListofalltheinteractionverticesConstructallthepossibleinteractionverticesfromalltheparticlesbyapplyingthefollowingconditions:H?=H,Lorentzinvariance,CPinvariance,Pinvariance,Cinvariance,Isospininvariance,Baryonnumberconservation,...StandardModelinputwithoutQCDFIG.3:SystemflowchartforphysicalprocessPhysicalProcessUsersshouldpreparetwofiles:pdata1.dat–experimenteventsdatafilepdata1.mc-phasespacemontecarloeventfileControlflagandparametersfilesgeneratedbyFDCwhichcanbechangedlaterbyusers:flag.inp,amptable.inp,fpara.inp,reson.inpOutput:,pep.res,mplot.hbook,dplot.hbookInputforaphysicalprocess:physicalmodelcanbechosenManyoptions,histograms,scatterplotscanbedemanded.GenerateFeynmanDiagramManipulateamplitudesforeachdiagramandgenerateFORTRAN77sourceforcalculationofamplitudesandtheirsquareFORTRAN77sourcetodolikelihoodfittingforallthefreeparametersthatwereintroducedinphysicalmodelFindandproperlytreatalltheresonnance,t-channelsingularities,...andgenerateFORTRAN77sourceforphasespaceintegralCompileFORTRAN77programsandrun'fit'forlikelihoodfitting系統(tǒng)的檢驗:1)FDC系統(tǒng)內(nèi)部的檢驗,各種核心程序:三種矩陣元,矩陣元平方算法的相互檢驗,