FDC软件包在分波分析中的应用

1、 FDC软件包在分波分析中的应用 1.简单介绍FDC系统2.强相互作用的有效拉氏量的构造规则3.FDC-PWA 分波分析版本的简介4.简单演示5.总结 BESIII物理分析讲习班, 2008年6月25日北京 王建雄中国科学院高能物理研究所, 理论室1. 简单介绍Feynman Diagram Calculation(FDC), 1993年开始. PROGRESS IN FDC PROJECT.Nucl.Instrum.Meth.A534:241-245,2004 FDC的主页：所内版：8/fdc/index.html(可以看到最新的结果)所外版：http:/

2、 (更新不定期) FDC-SM-and-Many-Extensions FDC-NRQCD FDC-MSSM FDC-EMT FDC-PWA FDC-LOOP FDC-PWA 1998开始, 邹冰松,祝玉灿,.There is a common kernel. The Source is written in REDUCE,RLISP. 分波分析在分波分析在BES物理分析中的重要性物理分析中的重要性.确定各种量子数确定各种量子数,质量质量,宽度宽度-复杂结构的谱、共振态、奇特态、胶球复杂结构的谱、共振态、奇特态、胶球,. 以前应用分波分析做理论计算，物理分析，编写以前应用分波分析做理论计算，物

3、理分析，编写Fortran程序都是手做的，就算程序都是手做的，就算不包括不包括3/2、2、 5/2, 7/2 自旋态，也得花几个月的时间，如果包括了自旋态，也得花几个月的时间，如果包括了3/2、2、5/2,7/2 自旋态，计算量和表达式会大几十倍。另外人工做这些工作怎样检查错误也自旋态，计算量和表达式会大几十倍。另外人工做这些工作怎样检查错误也很困难。而很困难。而FDC系统，其中各个部份，各种核心算法在这么多年的发展和应用中，系统，其中各个部份，各种核心算法在这么多年的发展和应用中，已经进行了很多次的检验。（例如手算与已经进行了很多次的检验。（例如手算与FDC算对比，算对比，FDC与与KEK的

4、的Grace对比等）。对比等）。2. FDC-PWA: FDC在在BEPC-II物理分析中的应用物理分析中的应用 在在FDC系统中实现了自动化构造分波分析有效拉氏量模型的部分（与邹冰松，系统中实现了自动化构造分波分析有效拉氏量模型的部分（与邹冰松，祝玉灿合作），以及产生包括祝玉灿合作），以及产生包括3/5, 5/2,7/2及整数自旋态的物理过程的费曼图，产及整数自旋态的物理过程的费曼图，产生所有生所有Fortran源程序以及最大似然法的拟合程序的部分，在其中结合最大似然法源程序以及最大似然法的拟合程序的部分，在其中结合最大似然法拟合程序的算法，对于矩阵元平方的算法在结构上进行了两次大的优化拟合

5、程序的算法，对于矩阵元平方的算法在结构上进行了两次大的优化, 使得产使得产生的程序在实验分析拟合中计算速度两次都有生的程序在实验分析拟合中计算速度两次都有10倍的提高倍的提高2.1 强相互作用的有效拉氏量的构造规则 Lorentz Invariance C-parity conservation P-parity conservation CP conservation H=H SvOutPlaceObjectABCDecayDecayABCDThe coefficients of all the indepent terms are constantThe coefficients of a

6、ll the indepent terms depend on two varibales每个系数都有独立的复数相因子.每个传播子都有off-shell贡献的压低因子对于一个粒子列表,给出所有可能的有效相互作用顶角.ABC (off mass shell)For NN scatting, T-channel vertices must be considered:The Coefficients of independent terms depend on the: 2 t=(PA PB) The propagator for resonance:1p2m2im Suppersion Fact

7、or for interaction vertices when the resonance is off mass shell: Barrier, ep2m2a2There is an option to choose the suppersion factorOption to apply Isopin symmetry:pn 101 Globel Options in Model Generation (in file: addvertices)%just_v_type:=ok; It will generate all the type of the interaction verti

8、ces as reqired and without the real vertices if the line was uncommented. %direct_model:=ok; The line is used to chose the two different kinds of effective lagrangian. The default is choosed to use the pure-orbital-angular-momentum covariant tensors and the covariant spin wave function for contructi

9、on of the effective lagrangian. To uncomment it means to choose a naive independent lorentz set of the combination of momentum, spin wave function. The difference of these two models is from the off-shell part of theresonace particles. %final_particle_list:=(p pi K eta pi0 K0); This line is used to

10、put the particles into the list of external particles. Thelist is used in the Feynman diagram generation procedure by FDC and allthe particles in the list will not appeared in the resonace place. %keep_sm_part_in_tex:=ok; The option is used to chose if the interaction vertices in the Standard model

11、are kept in the model.tex file or not. The default iskeep_sm_part_in_tex:=nil; and it means the vertices in the SM are droped. http:=ok; This option is used to chose the type of model.tex file which is generatedby FDC. http:=ok; means the model.tex is for http version.The default is http:=nil; and i

12、t means the model.tex is for PS version. n_particles:=3; The is the limit to the number of particles in each vertex. The smallest number is 3 and the default is 3. It can be changed into 4 or bigger and it means that all possible the one particles decays into three particles vertices will begenerate

13、d if the number is set to 4. n_total_spin:=6; This number is the limit to the sum of the spin of each particles in aneffective interaction vertex. The default is 6. it means that the FDC will use 6 for the n_totla_spin if it is not given. 2.2 FDC-PWA 分波分析版本的简介有效拉氏量模型的自动化产生费曼图的产生 diag矩阵元及平方的Fortran程序

14、的产生 amp相空间程序及Likelihood fitting 的Fortran程序的产生 kine 进入Fortran 目录和编译 cd fort make 开始进行Likelihood 拟合 fit FDC3.1, 1999, 开始在BES的分波分析中应用, 模型不是完全 自动化产生的, 并且没有包括末态是纯波色子过程FDC3.3 2003 开始应用, 模型产生完全的自动化, 包括末态是 纯波色子过程1. FDC-PWA Application: gmodel doall cd fort make fit Numerical results &Required plots in H

15、book formatPhysical model evaluationFull Feynman RulesPhysical parametersLatex version of then modelInput for physical modelNumerical integration,fittingTreatment of kinematicsAmplitude manipulationFeynman diagram generationInput for physical processChoose physical modeland processesList of all the

16、non-elementaryparticles and their quantum numbersThe generated physical model for FDC system.Latex version of the geneartedphysical modelList of all the particlesList of all the propagatorsList of all the interaction verticesConstruct all the possible interaction vertices from allthe particles by ap

17、plying the following conditions:H=H,Lorentz invariance, CP invariance, P invariance,C invariance, Isospin invariance,Baryon number conservation, .Standard Modelinput without QCDUsers should prepare two files:pdata1.dat experiment events data filepdata1.mc -phase space monte carlo event fileControl f

18、lag and parameters files generated by FDC which can be changed later by users: flag.inp, amptable.inp,fpara.inp, reson.inpOutput: , pep.res, mplot.hbook, dplot.hbookInput for a physical process: physical model can be chosenMany options, histograms, scatter plots can be demanded.Generate Fe

19、ynman DiagramManipulate amplitudes for each diagram and generate FORTRAN77 source for calculation of amplitudes and their squareFORTRAN77 source to do likelihood fitting for all the free parametersthat were introduced in physical modelFind and properly treat all the resonnance, t-channel singularities, .and generate FORTRAN77 source for phase space integralCompile FORTRAN77 programs and run fit for likelihood fitting系统的检验: 1) FDC系统内部的检