Addition and convolution: decay function p.d.fs 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))
```

**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, July 05, 2020 at 08:20 AM.*

In [ ]:

```
import ROOT
```

Variables of decay p.d.f.

In [ ]:

```
dt = ROOT.RooRealVar("dt", "dt", -10, 10)
tau = ROOT.RooRealVar("tau", "tau", 1.548)
```

Build a truth resolution model (delta function)

In [ ]:

```
tm = ROOT.RooTruthModel("tm", "truth model", dt)
```

Construct decay(t) (x) delta(t)

In [ ]:

```
decay_tm = ROOT.RooDecay("decay_tm", "decay", dt,
tau, tm, ROOT.RooDecay.DoubleSided)
```

Plot p.d.f. (dashed)

In [ ]:

```
frame = dt.frame(ROOT.RooFit.Title("Bdecay (x) resolution"))
decay_tm.plotOn(frame, ROOT.RooFit.LineStyle(ROOT.kDashed))
```

Build a gaussian resolution model

In [ ]:

```
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)

In [ ]:

```
decay_gm1 = ROOT.RooDecay("decay_gm1", "decay",
dt, tau, gm1, ROOT.RooDecay.DoubleSided)
```

Plot p.d.f.

In [ ]:

```
decay_gm1.plotOn(frame)
```

Build another gaussian resolution model

In [ ]:

```
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

In [ ]:

```
gm1frac = ROOT.RooRealVar("gm1frac", "fraction of gm1", 0.5)
gmsum = ROOT.RooAddModel(
"gmsum",
"sum of gm1 and gm2",
ROOT.RooArgList(
gm1,
gm2),
ROOT.RooArgList(gm1frac))
```

Construct decay(t) (x) (f*gm1 + (1-f)*gm2)

In [ ]:

```
decay_gmsum = ROOT.RooDecay(
"decay_gmsum", "decay", dt, tau, gmsum, ROOT.RooDecay.DoubleSided)
```

Plot p.d.f. (red)

In [ ]:

```
decay_gmsum.plotOn(frame, ROOT.RooFit.LineColor(ROOT.kRed))
```

Draw all frames on canvas

In [ ]:

```
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")
```

Draw all canvases

In [ ]:

```
from ROOT import gROOT
gROOT.GetListOfCanvases().Draw()
```