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rf209_anaconv.py
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1## \file
2## \ingroup tutorial_roofit
3## \notebook
4## Addition and convolution: decay function pdfs with optional B physics effects (mixing
5## and CP violation) that can be analytically convolved with e.g. Gaussian resolution functions
6##
7## ```
8## pdf1 = decay(t,tau) (x) delta(t)
9## pdf2 = decay(t,tau) (x) gauss(t,m,s)
10## pdf3 = decay(t,tau) (x) (f*gauss1(t,m1,s1) + (1-f)*gauss2(t,m1,s1))
11## ```
12##
13## \macro_code
14##
15## \date February 2018
16## \authors Clemens Lange, Wouter Verkerke (C++ version)
17
18import ROOT
19
20# B-physics pdf with truth resolution
21# ---------------------------------------------------------------------
22
23# Variables of decay pdf
24dt = ROOT.RooRealVar("dt", "dt", -10, 10)
25tau = ROOT.RooRealVar("tau", "tau", 1.548)
26
27# Build a truth resolution model (delta function)
28tm = ROOT.RooTruthModel("tm", "truth model", dt)
29
30# Construct decay(t) (x) delta(t)
31decay_tm = ROOT.RooDecay("decay_tm", "decay", dt,
32 tau, tm, ROOT.RooDecay.DoubleSided)
33
34# Plot pdf (dashed)
35frame = dt.frame(ROOT.RooFit.Title("Bdecay (x) resolution"))
36decay_tm.plotOn(frame, ROOT.RooFit.LineStyle(ROOT.kDashed))
37
38# B-physics pdf with Gaussian resolution
39# ----------------------------------------------------------------------------
40
41# Build a gaussian resolution model
42bias1 = ROOT.RooRealVar("bias1", "bias1", 0)
43sigma1 = ROOT.RooRealVar("sigma1", "sigma1", 1)
44gm1 = ROOT.RooGaussModel("gm1", "gauss model 1", dt, bias1, sigma1)
45
46# Construct decay(t) (x) gauss1(t)
47decay_gm1 = ROOT.RooDecay("decay_gm1", "decay",
48 dt, tau, gm1, ROOT.RooDecay.DoubleSided)
49
50# Plot pdf
51decay_gm1.plotOn(frame)
52
53# B-physics pdf with double Gaussian resolution
54# ------------------------------------------------------------------------------------------
55
56# Build another gaussian resolution model
57bias2 = ROOT.RooRealVar("bias2", "bias2", 0)
58sigma2 = ROOT.RooRealVar("sigma2", "sigma2", 5)
59gm2 = ROOT.RooGaussModel("gm2", "gauss model 2", dt, bias2, sigma2)
60
61# Build a composite resolution model f*gm1+(1-f)*gm2
62gm1frac = ROOT.RooRealVar("gm1frac", "fraction of gm1", 0.5)
63gmsum = ROOT.RooAddModel(
64 "gmsum",
65 "sum of gm1 and gm2",
66 ROOT.RooArgList(
67 gm1,
68 gm2),
69 ROOT.RooArgList(gm1frac))
70
71# Construct decay(t) (x) (f*gm1 + (1-f)*gm2)
72decay_gmsum = ROOT.RooDecay(
73 "decay_gmsum", "decay", dt, tau, gmsum, ROOT.RooDecay.DoubleSided)
74
75# Plot pdf (red)
76decay_gmsum.plotOn(frame, ROOT.RooFit.LineColor(ROOT.kRed))
77
78# Draw all frames on canvas
79c = ROOT.TCanvas("rf209_anaconv", "rf209_anaconv", 600, 600)
80ROOT.gPad.SetLeftMargin(0.15)
81frame.GetYaxis().SetTitleOffset(1.6)
82frame.Draw()
83
84c.SaveAs("rf209_anaconv.png")