rf209_anaconv.py

## \ingroup tutorial_roofit_main

## \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")