{
"cells": [
{
"cell_type": "markdown",
"id": "f359dc40",
"metadata": {},
"source": [
"# rf209_anaconv\n",
"Addition and convolution: decay function pdfs with optional B physics effects (mixing\n",
"and CP violation) that can be analytically convolved with e.g. Gaussian resolution functions\n",
"\n",
"```\n",
"pdf1 = decay(t,tau) (x) delta(t)\n",
"pdf2 = decay(t,tau) (x) gauss(t,m,s)\n",
"pdf3 = decay(t,tau) (x) (f*gauss1(t,m1,s1) + (1-f)*gauss2(t,m1,s1))\n",
"```\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Clemens Lange, Wouter Verkerke (C++ version) \n",
"This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, May 19, 2026 at 08:30 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "ced25eca",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:10.614454Z",
"iopub.status.busy": "2026-05-19T20:30:10.614333Z",
"iopub.status.idle": "2026-05-19T20:30:11.591126Z",
"shell.execute_reply": "2026-05-19T20:30:11.590387Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "4e2a06a2",
"metadata": {},
"source": [
"B-physics pdf with truth resolution\n",
"---------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "1e00e692",
"metadata": {},
"source": [
"Variables of decay pdf"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "90f40561",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:11.593331Z",
"iopub.status.busy": "2026-05-19T20:30:11.593182Z",
"iopub.status.idle": "2026-05-19T20:30:11.755876Z",
"shell.execute_reply": "2026-05-19T20:30:11.755172Z"
}
},
"outputs": [],
"source": [
"dt = ROOT.RooRealVar(\"dt\", \"dt\", -10, 10)\n",
"tau = ROOT.RooRealVar(\"tau\", \"tau\", 1.548)"
]
},
{
"cell_type": "markdown",
"id": "0fc23fb0",
"metadata": {},
"source": [
"Build a truth resolution model (delta function)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "1917957a",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:11.757934Z",
"iopub.status.busy": "2026-05-19T20:30:11.757802Z",
"iopub.status.idle": "2026-05-19T20:30:11.873807Z",
"shell.execute_reply": "2026-05-19T20:30:11.873186Z"
}
},
"outputs": [],
"source": [
"tm = ROOT.RooTruthModel(\"tm\", \"truth model\", dt)"
]
},
{
"cell_type": "markdown",
"id": "e81e108b",
"metadata": {},
"source": [
"Construct decay(t) (x) delta(t)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "0b2d9eda",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:11.875828Z",
"iopub.status.busy": "2026-05-19T20:30:11.875694Z",
"iopub.status.idle": "2026-05-19T20:30:12.004650Z",
"shell.execute_reply": "2026-05-19T20:30:12.003381Z"
}
},
"outputs": [],
"source": [
"decay_tm = ROOT.RooDecay(\"decay_tm\", \"decay\", dt, tau, tm, type=\"DoubleSided\")"
]
},
{
"cell_type": "markdown",
"id": "644611b4",
"metadata": {},
"source": [
"Plot pdf (dashed)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "06f79930",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:12.006284Z",
"iopub.status.busy": "2026-05-19T20:30:12.006142Z",
"iopub.status.idle": "2026-05-19T20:30:12.188698Z",
"shell.execute_reply": "2026-05-19T20:30:12.188009Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"frame = dt.frame(Title=\"Bdecay (x) resolution\")\n",
"decay_tm.plotOn(frame, LineStyle=\"--\")"
]
},
{
"cell_type": "markdown",
"id": "2e5444c6",
"metadata": {},
"source": [
"B-physics pdf with Gaussian resolution\n",
"----------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "bfb336a7",
"metadata": {},
"source": [
"Build a gaussian resolution model"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "772e0013",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:12.191185Z",
"iopub.status.busy": "2026-05-19T20:30:12.191049Z",
"iopub.status.idle": "2026-05-19T20:30:12.302336Z",
"shell.execute_reply": "2026-05-19T20:30:12.301566Z"
}
},
"outputs": [],
"source": [
"bias1 = ROOT.RooRealVar(\"bias1\", \"bias1\", 0)\n",
"sigma1 = ROOT.RooRealVar(\"sigma1\", \"sigma1\", 1)\n",
"gm1 = ROOT.RooGaussModel(\"gm1\", \"gauss model 1\", dt, bias1, sigma1)"
]
},
{
"cell_type": "markdown",
"id": "fdf0aaf5",
"metadata": {},
"source": [
"Construct decay(t) (x) gauss1(t)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "347039d3",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:12.304181Z",
"iopub.status.busy": "2026-05-19T20:30:12.304046Z",
"iopub.status.idle": "2026-05-19T20:30:12.407906Z",
"shell.execute_reply": "2026-05-19T20:30:12.407166Z"
}
},
"outputs": [],
"source": [
"decay_gm1 = ROOT.RooDecay(\"decay_gm1\", \"decay\", dt, tau, gm1, type=\"DoubleSided\")"
]
},
{
"cell_type": "markdown",
"id": "527206fe",
"metadata": {},
"source": [
"Plot pdf"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "e8d722aa",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:12.409773Z",
"iopub.status.busy": "2026-05-19T20:30:12.409639Z",
"iopub.status.idle": "2026-05-19T20:30:12.514757Z",
"shell.execute_reply": "2026-05-19T20:30:12.514070Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"decay_gm1.plotOn(frame)"
]
},
{
"cell_type": "markdown",
"id": "9852ded4",
"metadata": {},
"source": [
"B-physics pdf with double Gaussian resolution\n",
"------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "759252d8",
"metadata": {},
"source": [
"Build another gaussian resolution model"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "8fc1b32d",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:12.516882Z",
"iopub.status.busy": "2026-05-19T20:30:12.516749Z",
"iopub.status.idle": "2026-05-19T20:30:12.620376Z",
"shell.execute_reply": "2026-05-19T20:30:12.619712Z"
}
},
"outputs": [],
"source": [
"bias2 = ROOT.RooRealVar(\"bias2\", \"bias2\", 0)\n",
"sigma2 = ROOT.RooRealVar(\"sigma2\", \"sigma2\", 5)\n",
"gm2 = ROOT.RooGaussModel(\"gm2\", \"gauss model 2\", dt, bias2, sigma2)"
]
},
{
"cell_type": "markdown",
"id": "f3015417",
"metadata": {},
"source": [
"Build a composite resolution model f*gm1+(1-f)*gm2"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "ba0d4291",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:12.622506Z",
"iopub.status.busy": "2026-05-19T20:30:12.622373Z",
"iopub.status.idle": "2026-05-19T20:30:12.809645Z",
"shell.execute_reply": "2026-05-19T20:30:12.800084Z"
}
},
"outputs": [],
"source": [
"gm1frac = ROOT.RooRealVar(\"gm1frac\", \"fraction of gm1\", 0.5)\n",
"gmsum = ROOT.RooAddModel(\"gmsum\", \"sum of gm1 and gm2\", [gm1, gm2], [gm1frac])"
]
},
{
"cell_type": "markdown",
"id": "8f66b95f",
"metadata": {},
"source": [
"Construct decay(t) (x) (f*gm1 + (1-f)*gm2)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "f1e9d2fb",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:12.821306Z",
"iopub.status.busy": "2026-05-19T20:30:12.821166Z",
"iopub.status.idle": "2026-05-19T20:30:12.924998Z",
"shell.execute_reply": "2026-05-19T20:30:12.924257Z"
}
},
"outputs": [],
"source": [
"decay_gmsum = ROOT.RooDecay(\"decay_gmsum\", \"decay\", dt, tau, gmsum, ROOT.RooDecay.DoubleSided)"
]
},
{
"cell_type": "markdown",
"id": "b7358000",
"metadata": {},
"source": [
"Plot pdf (red)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "a09cd27b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:12.926936Z",
"iopub.status.busy": "2026-05-19T20:30:12.926803Z",
"iopub.status.idle": "2026-05-19T20:30:13.041024Z",
"shell.execute_reply": "2026-05-19T20:30:13.040437Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"decay_gmsum.plotOn(frame, LineColor=\"r\")"
]
},
{
"cell_type": "markdown",
"id": "c26e7ee4",
"metadata": {},
"source": [
"Draw all frames on canvas"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "76fce254",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:13.043118Z",
"iopub.status.busy": "2026-05-19T20:30:13.042983Z",
"iopub.status.idle": "2026-05-19T20:30:13.260187Z",
"shell.execute_reply": "2026-05-19T20:30:13.259415Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf209_anaconv.png has been created\n"
]
}
],
"source": [
"c = ROOT.TCanvas(\"rf209_anaconv\", \"rf209_anaconv\", 600, 600)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame.GetYaxis().SetTitleOffset(1.6)\n",
"frame.Draw()\n",
"\n",
"c.SaveAs(\"rf209_anaconv.png\")"
]
},
{
"cell_type": "markdown",
"id": "bd049d47",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "093516a6",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:13.281479Z",
"iopub.status.busy": "2026-05-19T20:30:13.281329Z",
"iopub.status.idle": "2026-05-19T20:30:13.461407Z",
"shell.execute_reply": "2026-05-19T20:30:13.460385Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ROOT import gROOT \n",
"gROOT.GetListOfCanvases().Draw()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.12.12"
}
},
"nbformat": 4,
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}