# rf708_bphysics¶

Special pdf's: special decay pdf for B physics with mixing and/or CP violation

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 Wednesday, November 30, 2022 at 11:24 AM.

In [1]:
import ROOT

Welcome to JupyROOT 6.27/01


## Construct pdf¶

Observable

In [2]:
dt = ROOT.RooRealVar("dt", "dt", -10, 10)
dt.setBins(40)


Parameters

In [3]:
dm = ROOT.RooRealVar("dm", "delta m(B0)", 0.472)
tau = ROOT.RooRealVar("tau", "tau (B0)", 1.547)
w = ROOT.RooRealVar("w", "flavour mistag rate", 0.1)
dw = ROOT.RooRealVar("dw", "delta mistag rate for B0/B0bar", 0.1)

mixState = ROOT.RooCategory("mixState", "B0/B0bar mixing state", {"mixed": -1, "unmixed": 1})

tagFlav = ROOT.RooCategory("tagFlav", "Flavour of the tagged B0", {"B0": 1, "B0bar": -1})


Use delta function resolution model

In [4]:
tm = ROOT.RooTruthModel("tm", "truth model", dt)


Construct Bdecay with mixing

In [5]:
bmix = ROOT.RooBMixDecay("bmix", "decay", dt, mixState, tagFlav, tau, dm, w, dw, tm, type="DoubleSided")


## Plot pdf in various slices¶

Generate some data

In [6]:
data = bmix.generate({dt, mixState, tagFlav}, 10000)


Plot B0 and B0bar tagged data separately For all plots below B0 and B0 tagged data will look somewhat differently if the flavor tagging mistag rate for B0 and B0 is different (i.e. dw!=0)

In [7]:
frame1 = dt.frame(Title="B decay distribution with mixing (B0/B0bar)")

data.plotOn(frame1, Cut="tagFlav==tagFlav::B0")
bmix.plotOn(frame1, Slice=(tagFlav, "B0"))

data.plotOn(frame1, Cut="tagFlav==tagFlav::B0bar", MarkerColor="c")
bmix.plotOn(frame1, Slice=(tagFlav, "B0bar"), LineColor="c")

Out[7]:
<cppyy.gbl.RooPlot object at 0x8a8ea50>
[#1] INFO:Plotting -- RooTreeData::plotOn: plotting 4542 events out of 10000 total events
[#1] INFO:Plotting -- RooAbsReal::plotOn(bmix) plot on dt represents a slice in (tagFlav)
[#1] INFO:Plotting -- RooAbsReal::plotOn(bmix) plot on dt integrates over variables (mixState)
[#1] INFO:Plotting -- RooTreeData::plotOn: plotting 5458 events out of 10000 total events
[#1] INFO:Plotting -- RooAbsReal::plotOn(bmix) plot on dt represents a slice in (tagFlav)
[#1] INFO:Plotting -- RooAbsReal::plotOn(bmix) plot on dt integrates over variables (mixState)


Plot mixed slice for B0 and B0bar tagged data separately

In [8]:
frame2 = dt.frame(Title="B decay distribution of mixed events (B0/B0bar)")

data.plotOn(frame2, Cut="mixState==mixState::mixed&&tagFlav==tagFlav::B0")
bmix.plotOn(frame2, Slice={tagFlav: "B0", mixState: "mixed"})

data.plotOn(frame2, Cut="mixState==mixState::mixed&&tagFlav==tagFlav::B0bar", MarkerColor="c")
bmix.plotOn(frame2, Slice={tagFlav: "B0bar", mixState: "mixed"}, LineColor="c")

Out[8]:
<cppyy.gbl.RooPlot object at 0x8d62960>
[#1] INFO:Plotting -- RooTreeData::plotOn: plotting 933 events out of 10000 total events
[#1] INFO:Plotting -- RooAbsReal::plotOn(bmix) plot on dt represents a slice in (mixState,tagFlav)
[#1] INFO:Plotting -- RooTreeData::plotOn: plotting 1461 events out of 10000 total events
[#1] INFO:Plotting -- RooAbsReal::plotOn(bmix) plot on dt represents a slice in (mixState,tagFlav)


Plot unmixed slice for B0 and B0bar tagged data separately

In [9]:
frame3 = dt.frame(Title="B decay distribution of unmixed events (B0/B0bar)")

data.plotOn(frame3, Cut="mixState==mixState::unmixed&&tagFlav==tagFlav::B0")
bmix.plotOn(frame3, Slice={tagFlav: "B0", mixState: "unmixed"})

data.plotOn(frame3, Cut="mixState==mixState::unmixed&&tagFlav==tagFlav::B0bar", MarkerColor="c")
bmix.plotOn(frame3, Slice={tagFlav: "B0bar", mixState: "unmixed"}, LineColor="c")

Out[9]:
<cppyy.gbl.RooPlot object at 0x7d31070>
[#1] INFO:Plotting -- RooTreeData::plotOn: plotting 3609 events out of 10000 total events
[#1] INFO:Plotting -- RooAbsReal::plotOn(bmix) plot on dt represents a slice in (mixState,tagFlav)
[#1] INFO:Plotting -- RooTreeData::plotOn: plotting 3997 events out of 10000 total events
[#1] INFO:Plotting -- RooAbsReal::plotOn(bmix) plot on dt represents a slice in (mixState,tagFlav)


## Construct pdf¶

Additional parameters needed for B decay with CPV

In [10]:
CPeigen = ROOT.RooRealVar("CPeigen", "CP eigen value", -1)
absLambda = ROOT.RooRealVar("absLambda", "|lambda|", 1, 0, 2)
argLambda = ROOT.RooRealVar("absLambda", "|lambda|", 0.7, -1, 1)
effR = ROOT.RooRealVar("effR", "B0/B0bar reco efficiency ratio", 1)


Construct Bdecay with CP violation

In [11]:
bcp = ROOT.RooBCPEffDecay(
"bcp", "bcp", dt, tagFlav, tau, dm, w, CPeigen, absLambda, argLambda, effR, dw, tm, type="DoubleSided"
)

[#1] INFO:InputArguments -- The formula exp(-abs(@0)/@1)_dt_tau_dm claims to use the variables (dt,tau,dm) but only (dt,tau) seem to be in use.
inputs:         exp(-abs(@0)/@1)


## Plot scenario 1 - sin(2b)=0.7, |l|=1¶

Generate some data

In [12]:
data2 = bcp.generate({dt, tagFlav}, 10000)


Plot B0 and B0bar tagged data separately

In [13]:
frame4 = dt.frame(Title="B decay distribution with CPV(|l|=1,Im(l)=0.7) (B0/B0bar)")

data2.plotOn(frame4, Cut="tagFlav==tagFlav::B0")
bcp.plotOn(frame4, Slice=(tagFlav, "B0"))

data2.plotOn(frame4, Cut="tagFlav==tagFlav::B0bar", MarkerColor="c")
bcp.plotOn(frame4, Slice=(tagFlav, "B0bar"), LineColor="c")

Out[13]:
<cppyy.gbl.RooPlot object at 0x4c2eed0>
[#1] INFO:Plotting -- RooTreeData::plotOn: plotting 4495 events out of 10000 total events
[#1] INFO:Plotting -- RooAbsReal::plotOn(bcp) plot on dt represents a slice in (tagFlav)
[#1] INFO:Plotting -- RooTreeData::plotOn: plotting 5505 events out of 10000 total events
[#1] INFO:Plotting -- RooAbsReal::plotOn(bcp) plot on dt represents a slice in (tagFlav)


# Plot scenario 2 - sin(2b)=0.7, |l|=0.7¶

In [14]:
absLambda.setVal(0.7)


Generate some data

In [15]:
data3 = bcp.generate({dt, tagFlav}, 10000)


Plot B0 and B0bar tagged data separately (sin2b = 0.7 plus direct CPV |l|=0.5)

In [16]:
frame5 = dt.frame(Title="B decay distribution with CPV(|l|=0.7,Im(l)=0.7) (B0/B0bar)")

data3.plotOn(frame5, Cut="tagFlav==tagFlav::B0")
bcp.plotOn(frame5, Slice=(tagFlav, "B0"))

data3.plotOn(frame5, Cut="tagFlav==tagFlav::B0bar", MarkerColor="c")
bcp.plotOn(frame5, Slice=(tagFlav, "B0bar"), LineColor="c")

Out[16]:
<cppyy.gbl.RooPlot object at 0x91e18c0>
[#1] INFO:Plotting -- RooTreeData::plotOn: plotting 3617 events out of 10000 total events
[#1] INFO:Plotting -- RooAbsReal::plotOn(bcp) plot on dt represents a slice in (tagFlav)
[#1] INFO:Plotting -- RooTreeData::plotOn: plotting 6383 events out of 10000 total events
[#1] INFO:Plotting -- RooAbsReal::plotOn(bcp) plot on dt represents a slice in (tagFlav)


## Construct pdf¶

Model parameters

In [17]:
DGbG = ROOT.RooRealVar("DGbG", "DGamma/GammaAvg", 0.5, -1, 1)
Amix = ROOT.RooRealVar("Amix", "2Im(l)/[1+abs(l)**2]", 0.7)


Derived input parameters for pdf

In [18]:
DG = ROOT.RooFormulaVar("DG", "Delta Gamma", "@1/@0", [tau, DGbG])


Construct coefficient functions for sin,cos, modulations of decay distribution

In [19]:
fsin = ROOT.RooFormulaVar("fsin", "fsin", "@0*@1*(1-2*@2)", [Amix, tagFlav, w])
fcos = ROOT.RooFormulaVar("fcos", "fcos", "@0*@1*(1-2*@2)", [Adir, tagFlav, w])
fsinh = ROOT.RooFormulaVar("fsinh", "fsinh", "@0", [Adel])


Construct generic B decay pdf using above user coefficients

In [20]:
bcpg = ROOT.RooBDecay(
"bcpg", "bcpg", dt, tau, DG, ROOT.RooFit.RooConst(1), fsinh, fcos, fsin, dm, tm, type="DoubleSided"
)


## Plot - Im(l)=0.7, e(l)=0.7 |l|=1, G/G=0.5¶

Generate some data

In [21]:
data4 = bcpg.generate({dt, tagFlav}, 10000)


Plot B0 and B0bar tagged data separately

In [22]:
frame6 = dt.frame(Title="B decay distribution with CPV(Im(l)=0.7,Re(l)=0.7,|l|=1,dG/G=0.5) (B0/B0bar)")

data4.plotOn(frame6, Cut="tagFlav==tagFlav::B0")
bcpg.plotOn(frame6, Slice=(tagFlav, "B0"))

data4.plotOn(frame6, Cut="tagFlav==tagFlav::B0bar", MarkerColor="c")
bcpg.plotOn(frame6, Slice=(tagFlav, "B0bar"), LineColor="c")

c = ROOT.TCanvas("rf708_bphysics", "rf708_bphysics", 1200, 800)
c.Divide(3, 2)
c.cd(1)
frame1.GetYaxis().SetTitleOffset(1.6)
frame1.Draw()
c.cd(2)
frame2.GetYaxis().SetTitleOffset(1.6)
frame2.Draw()
c.cd(3)
frame3.GetYaxis().SetTitleOffset(1.6)
frame3.Draw()
c.cd(4)
frame4.GetYaxis().SetTitleOffset(1.6)
frame4.Draw()
c.cd(5)
frame5.GetYaxis().SetTitleOffset(1.6)
frame5.Draw()
c.cd(6)
frame6.GetYaxis().SetTitleOffset(1.6)
frame6.Draw()

c.SaveAs("rf708_bphysics.png")

[#1] INFO:Plotting -- RooTreeData::plotOn: plotting 4991 events out of 10000 total events
[#1] INFO:Plotting -- RooAbsReal::plotOn(bcpg) plot on dt represents a slice in (tagFlav)
[#1] INFO:Plotting -- RooTreeData::plotOn: plotting 5009 events out of 10000 total events
[#1] INFO:Plotting -- RooAbsReal::plotOn(bcpg) plot on dt represents a slice in (tagFlav)

Info in <TCanvas::Print>: png file rf708_bphysics.png has been created


Draw all canvases

In [23]:
from ROOT import gROOT
gROOT.GetListOfCanvases().Draw()