rf209_anaconv.py

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## \file
## \ingroup tutorial_roofit
## \notebook
## Addition and convolution: decay function pdfs with optional B physics effects (mixing
## and CP violation) that can be analytically convolved with e.g. Gaussian resolution functions
##
## ```
## pdf1 = decay(t,tau) (x) delta(t)
## pdf2 = decay(t,tau) (x) gauss(t,m,s)
## pdf3 = decay(t,tau) (x) (f*gauss1(t,m1,s1) + (1-f)*gauss2(t,m1,s1))
## ```
##
## \macro_image
## \macro_code
## \macro_output
##
## \date February 2018
## \authors Clemens Lange, Wouter Verkerke (C++ version)
 
import ROOT
 
# B-physics pdf with truth resolution
# ---------------------------------------------------------------------
 
# Variables of decay pdf
dt = ROOT.RooRealVar("dt", "dt", -10, 10)
tau = ROOT.RooRealVar("tau", "tau", 1.548)
 
# Build a truth resolution model (delta function)
tm = ROOT.RooTruthModel("tm", "truth model", dt)
 
# Construct decay(t) (x) delta(t)
decay_tm = ROOT.RooDecay("decay_tm", "decay", dt, tau, tm, type="DoubleSided")
 
# Plot pdf (dashed)
frame = dt.frame(Title="Bdecay (x) resolution")
decay_tm.plotOn(frame, LineStyle="--")
 
# B-physics pdf with Gaussian resolution
# ----------------------------------------------------------------------------
 
# Build a gaussian resolution model
bias1 = ROOT.RooRealVar("bias1", "bias1", 0)
sigma1 = ROOT.RooRealVar("sigma1", "sigma1", 1)
gm1 = ROOT.RooGaussModel("gm1", "gauss model 1", dt, bias1, sigma1)
 
# Construct decay(t) (x) gauss1(t)
decay_gm1 = ROOT.RooDecay("decay_gm1", "decay", dt, tau, gm1, type="DoubleSided")
 
# Plot pdf
decay_gm1.plotOn(frame)
 
# B-physics pdf with double Gaussian resolution
# ------------------------------------------------------------------------------------------
 
# Build another gaussian resolution model
bias2 = ROOT.RooRealVar("bias2", "bias2", 0)
sigma2 = ROOT.RooRealVar("sigma2", "sigma2", 5)
gm2 = ROOT.RooGaussModel("gm2", "gauss model 2", dt, bias2, sigma2)
 
# Build a composite resolution model f*gm1+(1-f)*gm2
gm1frac = ROOT.RooRealVar("gm1frac", "fraction of gm1", 0.5)
gmsum = ROOT.RooAddModel("gmsum", "sum of gm1 and gm2", [gm1, gm2], [gm1frac])
 
# Construct decay(t) (x) (f*gm1 + (1-f)*gm2)
decay_gmsum = ROOT.RooDecay("decay_gmsum", "decay", dt, tau, gmsum, ROOT.RooDecay.DoubleSided)
 
# Plot pdf (red)
decay_gmsum.plotOn(frame, LineColor="r")
 
# Draw all frames on canvas
c = ROOT.TCanvas("rf209_anaconv", "rf209_anaconv", 600, 600)
ROOT.gPad.SetLeftMargin(0.15)
frame.GetYaxis().SetTitleOffset(1.6)
frame.Draw()
 
c.SaveAs("rf209_anaconv.png")