rf513_wsfactory_tools

Organization and simultaneous fits: illustration use of ROOT.RooCustomizer and ROOT.RooSimWSTool interface in factory workspace tool in a complex standalone B physics example

Author: Clemens Lange, Wouter Verkerke (C++ version)
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Sunday, November 27, 2022 at 11:07 AM.

In [1]:
import ROOT


w = ROOT.RooWorkspace("w")
Welcome to JupyROOT 6.27/01

Build a complex example pdf

Make signal model for CPV: A bmixing decay function in t (convoluted with a triple Gaussian resolution model) times a Gaussian function the reconstructed mass

In [2]:
w.factory(
    "PROD::sig(  BMixDecay::sig_t( dt[-20,20], mixState[mixed=1,unmix=-1], tagFlav[B0=1,B0bar=-1], "
    "tau[1.54], dm[0.472], w[0.05], dw[0], "
    "AddModel::gm({GaussModel(dt,biasC[-10,10],sigmaC[0.1,3],dterr[0.01,0.2]), "
    "GaussModel(dt,0,sigmaT[3,10]), "
    "GaussModel(dt,0,20)},{fracC[0,1],fracT[0,1]}), "
    "DoubleSided ), "
    "Gaussian::sig_m( mes[5.20,5.30], mB0[5.20,5.30], sigmB0[0.01,0.05] ))"
)
Out[2]:
<cppyy.gbl.RooProdPdf object at 0x8559b80>

Make background component: A plain decay function in t times an Argus function in the reconstructed mass

In [3]:
w.factory("PROD::bkg(  Decay::bkg_t( dt, tau, gm, DoubleSided), " "ArgusBG::bkg_m( mes, 5.291, k[-100,-10]))")
Out[3]:
<cppyy.gbl.RooProdPdf object at 0x89e4b30>

Make composite model from the signal and background component

In [4]:
w.factory("SUM::model( Nsig[5000,0,10000]*sig, NBkg[500,0,10000]*bkg )")
Out[4]:
<cppyy.gbl.RooAddPdf object at 0x8a0d730>

Example of RooSimWSTool interface

Introduce a flavour tagging category tagCat as observable with 4 states corresponding to 4 flavour tagging techniques with different performance that require different parameterizations of the fit model

ROOT.RooSimWSTool operation:

- Make 4 clones of model (for each tagCat) state, will gain an individual
  copy of parameters w, and biasC. The other parameters remain common
- Make a simultaneous pdf of the 4 clones assigning each to the appropriate
  state of the tagCat index category

ROOT.RooSimWSTool is interfaced as meta-type SIMCLONE in the factory. The $SplitParam() argument maps to the SplitParam() named argument in the ROOT.RooSimWSTool constructor

In [5]:
w.factory("SIMCLONE::model_sim( model, $SplitParam({w,dw,biasC},tagCat[Lep,Kao,NT1,NT2]))")
Out[5]:
<cppyy.gbl.RooSimultaneous object at 0x8be03f0>

Example of RooCustomizer interface

Class ROOT.RooCustomizer makes clones of existing pdfs with certain prescribed modifications (branch of leaf node replacements)

Here we take our model (the original before ROOT.RooSimWSTool modifications) and request that the parameter w (the mistag rate) is replaced with an expression-based function that calculates w in terms of the Dilution parameter D that is defined D = 1-2*w

Make a clone model_D of original 'model' replacing 'w' with 'expr('0.5-D/2',D[0,1])'

In [6]:
w.factory("EDIT::model_D(model, w=expr('0.5-D/2',D[0,1]) )")
Out[6]:
<cppyy.gbl.RooAddPdf object at 0x8b85970>

Print workspace contents

In [7]:
w.Print()
RooWorkspace(w) w contents

variables
---------
(D,NBkg,Nsig,biasC,biasC_Kao,biasC_Lep,biasC_NT1,biasC_NT2,dm,dt,dterr,dw,dw_Kao,dw_Lep,dw_NT1,dw_NT2,fracC,fracT,k,mB0,mes,mixState,sigmB0,sigmaC,sigmaT,tagCat,tagFlav,tau,w,w_Kao,w_Lep,w_NT1,w_NT2)

p.d.f.s
-------
RooProdPdf::bkg[ bkg_t * bkg_m ] = 0.307193
RooProdPdf::bkg_Kao[ bkg_t_Kao * bkg_m ] = 0.307193
RooProdPdf::bkg_Lep[ bkg_t_Lep * bkg_m ] = 0.307193
RooProdPdf::bkg_NT1[ bkg_t_NT1 * bkg_m ] = 0.307193
RooProdPdf::bkg_NT2[ bkg_t_NT2 * bkg_m ] = 0.307193
RooArgusBG::bkg_m[ m=mes m0=5.291 c=k p=0.5 ] = 0.279062
RooDecay::bkg_t[ t=dt tau=tau ] = 1.10081
RooDecay::bkg_t_Kao[ t=dt tau=tau ] = 1.10081
RooDecay::bkg_t_Lep[ t=dt tau=tau ] = 1.10081
RooDecay::bkg_t_NT1[ t=dt tau=tau ] = 1.10081
RooDecay::bkg_t_NT2[ t=dt tau=tau ] = 1.10081
RooAddPdf::model[ Nsig * sig + NBkg * bkg ] = 1.88229/1
RooAddPdf::model_D[ Nsig * sig_model_D + NBkg * bkg ] = 1.5029/1
RooAddPdf::model_Kao[ Nsig * sig_Kao + NBkg * bkg_Kao ] = 1.88229/1
RooAddPdf::model_Lep[ Nsig * sig_Lep + NBkg * bkg_Lep ] = 1.88229/1
RooAddPdf::model_NT1[ Nsig * sig_NT1 + NBkg * bkg_NT1 ] = 1.88229/1
RooAddPdf::model_NT2[ Nsig * sig_NT2 + NBkg * bkg_NT2 ] = 1.88229/1
RooSimultaneous::model_sim[ indexCat=tagCat Lep=model_Lep Kao=model_Kao NT1=model_NT1 NT2=model_NT2 ] = 0.470573
RooProdPdf::sig[ sig_t * sig_m ] = 2.0398
RooProdPdf::sig_Kao[ sig_t_Kao * sig_m ] = 2.0398
RooProdPdf::sig_Lep[ sig_t_Lep * sig_m ] = 2.0398
RooProdPdf::sig_NT1[ sig_t_NT1 * sig_m ] = 2.0398
RooProdPdf::sig_NT2[ sig_t_NT2 * sig_m ] = 2.0398
RooGaussian::sig_m[ x=mes mean=mB0 sigma=sigmB0 ] = 1
RooProdPdf::sig_model_D[ sig_t_model_D * sig_m ] = 1.62247
RooBMixDecay::sig_t[ mistag=w delMistag=dw mixState=mixState tagFlav=tagFlav tau=tau dm=dm t=dt ] = 2.0398
RooBMixDecay::sig_t_Kao[ mistag=w_Kao delMistag=dw_Kao mixState=mixState tagFlav=tagFlav tau=tau dm=dm t=dt ] = 2.0398
RooBMixDecay::sig_t_Lep[ mistag=w_Lep delMistag=dw_Lep mixState=mixState tagFlav=tagFlav tau=tau dm=dm t=dt ] = 2.0398
RooBMixDecay::sig_t_NT1[ mistag=w_NT1 delMistag=dw_NT1 mixState=mixState tagFlav=tagFlav tau=tau dm=dm t=dt ] = 2.0398
RooBMixDecay::sig_t_NT2[ mistag=w_NT2 delMistag=dw_NT2 mixState=mixState tagFlav=tagFlav tau=tau dm=dm t=dt ] = 2.0398
RooBMixDecay::sig_t_model_D[ mistag=model_D_2 delMistag=dw mixState=mixState tagFlav=tagFlav tau=tau dm=dm t=dt ] = 1.62247

analytical resolution models
----------------------------
RooAddModel::gm[ x=dt (fracC * gm_11 + fracT * gm_12 + [%] * gm_13) ] = 1.25632
RooGaussModel::gm_11[ x=dt mean=biasC sigma=sigmaC msf=dterr ssf=dterr ] = 2.45126
RooGaussModel::gm_11_Kao[ x=dt mean=biasC_Kao sigma=sigmaC msf=dterr ssf=dterr ] = 2.45126
RooGaussModel::gm_11_Lep[ x=dt mean=biasC_Lep sigma=sigmaC msf=dterr ssf=dterr ] = 2.45126
RooGaussModel::gm_11_NT1[ x=dt mean=biasC_NT1 sigma=sigmaC msf=dterr ssf=dterr ] = 2.45126
RooGaussModel::gm_11_NT2[ x=dt mean=biasC_NT2 sigma=sigmaC msf=dterr ssf=dterr ] = 2.45126
RooGaussModel::gm_12[ x=dt mean=0 sigma=sigmaT msf=1 ssf=1 ] = 0.0613757
RooGaussModel::gm_13[ x=dt mean=0 sigma=20 msf=1 ssf=1 ] = 0.0199471
RooAddModel::gm_Kao[ x=dt (fracC * gm_11_Kao + fracT * gm_12 + [%] * gm_13) ] = 1.25632
RooAddModel::gm_Lep[ x=dt (fracC * gm_11_Lep + fracT * gm_12 + [%] * gm_13) ] = 1.25632
RooAddModel::gm_NT1[ x=dt (fracC * gm_11_NT1 + fracT * gm_12 + [%] * gm_13) ] = 1.25632
RooAddModel::gm_NT2[ x=dt (fracC * gm_11_NT2 + fracT * gm_12 + [%] * gm_13) ] = 1.25632

functions
--------
RooFormulaVar::model_D_2[ actualVars=(D) formula="0.5-D/2" ] = 0.25

Make workspace visible on command line

In [8]:
ROOT.gDirectory.Add(w)