Computing tools for data analysis

a practical introduction

First things first:

•  can you launch ROOT? •  Download examples from here (two files) – http://phy.duke.edu/~atarce/Hep101/

– move both files to the directory where you launch ROOT.

What is LHC computing?

pattern recognition

storing events

brokering access to data

simulating events

calculating observables

making pretty pictures

classifying signals

classifying events

analysis  

produc.on    

opera.ons  

Outline

•  Brief overview of production and operations •  The last step: analysis –  introduction to data representation

– Exercise: plotting and fitting data with ROOT

•  The first step: simulation –  introduction to Monte Carlo simulation

– Exercise/homework: writing a toy Monte Carlo

LHC computing is huge!

•  LHC data output estimate: 15 PB/year –  Stored and processed

on shared WLCG

–  and…we need multiple copies!

•  US LHC: nearly 500k CPU-hours daily.

ATLAS computer use

produc.on    

analysis  

ATLAS computing for users

•  Main programming languages: –  FORTRAN (some generators) – C++ (main reconstruction algorithms, analysis) –  python (steering, analysis)

•  Main interactive interfaces: –  athena

•  controls MC and data production

–  root (C++ interface) •  viewing/analyzing reconstructed data •  pyroot (for python fans: python “import root” )

Production: data

ATLAS   trigger   convert  

MERGE&  

derive  

bytestream  

RECO  

esd  

aod  

tag  

D3PD  

aod  

RDO  (raw)  

pattern recognition

fast pattern recognition event sorting

more sorting

Production: Monte Carlo

MERGE  &  

derive  

RECO  

esd  

aod  

tag  

D3PD  

aod  

MONTE  CARLO  PRODUCTION  CHAIN  RDO  (raw)  

Data representation

•  always organized by event •  global quantities:

–  metadata –  missing energy…

•  physics object lists: –  muons –  jets –  tracks –  “truth” particles…

•  object properties: –  hits on tracks –  jet constituents

µ   track  track  track  track  track  track  track  

jet  jet  jet  

track  hit  track  hit  

event  

“n-­‐tuple”    “tree”  

Data representation

Event  number  

nTracks   track  pT   track  eta   track  phi   track  layers…  

0   3   12.4   0.3   2.1   30  

8.1   1.1   1.0   14  

5.0   -­‐0.9   4.0   17  

1   2   24.5   1.1   0.2   22  

20.5   0.9   3.3   17  

2   1   2.0   1.9   1.4   5  

3   5   50.4   0.1   0.8   21  

…   …   …   …  

User’s interface to nature: histograms

: histo = makeHisto(nbins=50, firstbin=0*GeV, lastbin=200*GeV) for thisEvent in allEvents:

if HasZ( thisEvent ): m = recoZMass( thisEvent )

histo.FillWith( m )

•  ``Hello World’’ for HEP computing: making a histogram

TH1F::Fill(value,weight)

TH1F(“name”, “title; x title; y title”, nBins, firstBinValue, LastBinValue)

EXERCISE ONE note: in code examples, your input is given in green

Let’s look at a mini-D3PD:

•  open the ROOT file: –  you% root Hep101MysteryEvents.root

•  Browse it: –  root [1] new TBrowser();

•  Notice the TTree (event data):

•  Look at some histograms – Click to make histograms! – Also try “drawing” more complex

functions…

Interacting with the tree

•  Histograms: TH1F •  Functions: TF1 •  Drawing:

root [2] example->Draw("mc_px"); •  you now have a default histogram called htemp.

root [3] h2 = TH1F(“h2”, “myHist;GeV”, 10, -200, 200); root [4] example->Draw(“mc_px/1000.>>h2”);

– Note: expression can contain most functions: mc_px + mc_py mc_px * cos(1.2 ) sqrt(mc_px*mc_py) Note: ROOT is also a nice command-

line calculator with Lorentz vectors,

special functions, etc…

PART TWO Monte Carlo in HEP

pick  random  x,  random  y  if  y2  <  1-­‐x2:  increment  area  

What is Monte Carlo? •  HEP predictions require a lot

of convolution integrals –  one reason: QM!

Monte Carlo calculation of π

pick  random  x,  random  y  if  y2  <  1-­‐x2:  increment  area  

What is Monte Carlo? •  HEP predictions require a lot

of convolution integrals –  one reason: QM!

•  The Monte Carlo Method: –  use random numbers as

an integration tool

Monte Carlo calculation of π

What is Monte Carlo?

Z  picks  mass  

and  decay  angles  

electron  ET  

•  The Monte Carlo Method:

–  use random numbers as an integration tool

–  Useful because predictions in HEP require a lot of convolution integrals!

•  Much simpler picture:

–  a series of random choices

What is Monte Carlo?

Z  picks  mass  

and  decay  angles  

electron  ET  

calorimeter  mismeasurement  

ovserved  electron  ET  

•  The Monte Carlo Method:

–  use random numbers as an integration tool

–  Useful because predictions in HEP require a lot of convolution integrals!

•  Much simpler picture:

–  a series of random choices

Meet your Monte Carlo

Slides: Sjöstrand

Meet your MC: #PYTHIA, HERWIG, MadGraph, MCFM, MC@NLO, BaurMC, POWHEG, &c.…

Meet your MC: #PYTHIA, HERWIG, MadGraph, MCFM, MC@NLO, BaurMC, POWHEG, &c.…

Meet your MC: #PYTHIA, HERWIG/JIMMY, …

Meet your MC: #PYTHIA, HERWIG/JIMMY, …

EXERCISE TWO note: in code examples, your input is given in green

Let’s write a Monte Carlo!#B± meson decays in top events

•  The B± is unstable but has a long lifetime (picoseconds) because it decays weakly.

•  We often measure the lifetime from the flight distance (picoseconds are hard to measure, micrometers are not).

•  The flight distance for a B± produced at the origin of the ATLAS detector is L. Lxy is the projection of this distance on to the plane perpendicular to the beam.

z

x

y

Generating the Lxy distribution

path of B±

tracks from decay products  

z

Lxy

xy-plane we use Lxy because distances perpendicular to beam

are most precisely measured

Writing the Monte Carlo

The “proper decay length”

•  proper decay length = –  c * (lifetime in B± rest frame)

•  Tables often list c * mean lifetime (cτ)

•  Useful particle data for B± –  reference: pdg.lbl.gov

Calculate and plot Lxy choose  decay  .me  in  rest  frame  

choose  B  velocity  vector  

calculate  decay  .me  in  lab  frame  

calculate  decay  distance  in  lab  frame  

project  onto  x-­‐y  plane  

e  

A program outline

choose  decay  .me  in  rest  frame  

choose  B  velocity  vector  

calculate  decay  .me  in  lab  frame  

calculate  decay  distance  in  lab  frame  

project  onto  x-­‐y  plane  

fill  your  histogram  

create  an  empty  histogram  

plot  and  save  your  histogram!  

calculate  Lxy  

“event”  loop  

these  3  steps  can  be  com

bined!  

Random Numbers

•  Any MC generator needs random numbers! Use the ROOT class TRandom3.

•  Example – root [1] TRandom3 r; – root [2] float random1 = r.Gaus(0,35);

•  //generate a gaussian-distributed random number with mean 0 and width 35;

– root [3] float random2 = r.Exp(492.0); •  //generate a B± decay length (cτ) in microns

Hints

Note: This assignment requires a little modest programming (loops and conditionals).

•  You might want to break this problem into two steps: –  write an Lxy generator for B decays with fixed E = 25 GeV, pT = 16 GeV –  modify this generator to use any (E, pT) distribution

•  The relativistic calculation is simple (and good practice). –  try it by hand! How simple can you make the expression for Lxy ? –  Give up? Try Google – but be sure you understand the steps in the calculation. –  Compare the result you get using ROOT classes TLorentzVector and TLorentzRotation!

•  Now add a more realistic B (E, pT) distribution. –  Look in the file Hep101AdvancedDecay.root. It should have the information you need to

finish your generator (i.e., choose the B decay vector).

•  Run your final Monte Carlo, and fill a histogram with the observable decay length Lxy ! •  Good statistical practices:

–  how many decays did you generate? Why? •  Print your histogram!

More homework help: •  About TRandom:

–  http://root.cern.ch/root/html/TRandom3 •  About TLorentzVector

–  http://root.cern.ch/root/html/TLorentzVector.html •  Getting correlated random numbers from a histogram:

–  http://root.cern.ch/root/html/TH2.html •  see TH2::GetRandom2()

•  You can write your program out on the command line, or in a separate file “myprog.C” (this is easier)

•  to run it in root, type –  root [1]

•  You can print your histogram to a PDF file by clicking the menu in the canvas, or typing –  root [1]