HEP data analysis using ROOT

Transcription

1 HEP data analysis using ROOT week 3 ROOT Maths and Physics Libraries ROOT Geometries Mark Hodgkinson 1

2 Week 3 ROOT maths and physics libraries vectors and their operations data modelling with RooFit ROOT geometries internal TGeo classes interfaces to other platforms 2

3 ROOT vectors TLorentzVector probably the most useful for HEP data analysis root [1] TLorentzVector v root [2] v.print() (x,y,z,t)=( , , , ) (P,eta,phi,E)=( , , , ) root [3] initialised to (0,0,0,0) Other 2D and 3D vectors available root [3] TVector TVectorT<double> TVectorT<float> TVector2 TVector3 3

4 TLorentzVector Assumes beam along z-axis transverse variables derived accordingly e.g. DeltaPhi: angle between two 4 momenta in transverse plane E t : transverse energy 4

5 Extended ROOT vectors Extended vector libs now available root [1] gsystem->load("libgenvector.so"); many useful operations e.g. vector projections 5

6 GenVector example Find mathcorevectorcollection.c in $ROOTSYS copy to your working directory and run (compiled) $ root mathcorevectorcollection.c+ Time for new Vector ****************************************************************************** *Tree :t1 : Tree with new LorentzVector * *Entries : : Total = bytes File Size = * * : : Tree compression factor = 1.11 * ****************************************************************************** *Br 0 :tracks : Int_t tracks_ * *Entries : : Total Size= bytes File Size = * *Baskets : 4 : Basket Size= bytes Compression= 3.34 * *...* *Br 1 :tracks.fcoordinates.fx : Double_t fx[tracks_] * *Entries : : Total Size= bytes File Size = * *Baskets : 16 : Basket Size= bytes Compression= 1.07 * *...* *Br 2 :tracks.fcoordinates.fy : Double_t fy[tracks_] * *Entries : : Total Size= bytes File Size = * *Baskets : 16 : Basket Size= bytes Compression= 1.07 * 6 *...*

7 300 h1 E n t r i e s Mean RMS h2 E n t r i e s Mean RMS GenVector example h3 E n t r i e s Mean RMS h5 E n t r i e s Mean RMS h4 E n t r i e s Mean RMS h6 E n t r i e s Mean RMS

8 GenVector example Look at the macro writes an STL vector of LorentzVectors to a TTree Don t use magic numbers to define fundamental constants! root [1] TDatabasePDG db root [2] db.getparticle(211).mass() (const Double_t) e-01 8

9 Task Here you will practice using a TTree to fill some histograms - in this case we need to make a plot of the visible tau mass. ROOT files with trees from MC simulation of Z->tautau are available. Run the example and look at the printed visible tau pt - it is always zero! In TauTruthClassifiers_MC12.cxx you need to fill in the setvisiblevectors function - use the getnprong function as an example of what to do. Then create and fill a histogram of the true visible mass (i.e. don t include invisible particles - remember each tau always decays into a W boson and a neutrino, followed by the W decay to leptons or hadrons), and write it out to a file. Need Monte Carlo particle numbering scheme here. Will use your knowledge of TLorentzVector, c++ vectors, ROOT histograms and file I/ O. Also notice it uses a std::map, but this is setup for you. Map is c++ way of storing data with a key - it maps a key to a variable. In this case the key is an integer and the data retrieved is a TLorentzVector. Can find many webpages explaining maps and other c++ data structures (pair, set etc) you might find useful with google search. Copy the folder from /home/hodgkinson/roottutorial_week3 to your own area. 9

10 Task You can build an executable by typing make. Next week we will discuss more details about compilation. Then run the ROOTTutorial executable and specify the range of events to process - in the above we process all events between 0 and Input files have events in total. What is actually being run starts from the code inside main.cxx, which in turn calls functions in the other source code files. We have instructions to submit jobs to our linux box cluster here - so you might also think about running jobs in parallel to speed up things, and then hadding the output files. If you get errors when you add your code in, typical things to do are: use google - often lots of hits from stackoverflow website about the exact errors you get ask someone more experienced for help (people in your office etc) 10

11 RooFit Introduction from main author W. Wekerke (Nikhef) here. As with all software tools, you need to judge if you need this or if native ROOT fitting is enough - it is if all you want to do is fit a simple Gaussian for example. e.g. for one of my projects, we are just using TH1F->Fit() functionality 11

12 Taken from link on previous slide Short answer - sufficiently complex fit might be better done in Roofit. Rootfit is an extension of ROOT, and nowadays comes by default when you install (default ROOT version, now on HEP0 has it - other versions may not, but can ask M. Robinson to install if needed). 12

13 Simulating data with RooFit Very often hear people talking about Toy MC use parameterisations of input PDFs for speed often useful to reweight PDFs to study propagation of errors RooFit provides such functionality worked example from 13

14 RooFit example PDF functions in RooFit Landau: parameterisation of de/dx Argus: empirical function describing n-body decay Breit-Wigner: ( Gaussian) describes a resonance Crystal-Ball: radiative energy loss Decay: can be symmetric and convoluted This e.g. uses the Argus function 14

15 RooFit Example RooRealVar has a name, a title and a range. Optionally can specify a unit as well. RooRealVar by default initialises the value at mid-range. But can also specify both initial value and range. Finally can create Gaussian PDF of the mass with a mean and width. 15

16 RooFit Example We can put the gaussian pdf in a RooPlot, and then draw the RooPlot. Task: Setup a Landau PDF and draw that. 16

17 RooFit example Argus background component // --- Build Argus background PDF --- RooRealVar argpar("argpar","argus shape parameter",-20.0,-100.,-1.) ; RooConstVar argconst("argconst","argus constant",5.291); RooArgusBG argus("argus","argus PDF",mes,argconst,argpar) ; Signal + Background PDF // --- Construct signal+background PDF --- RooRealVar nsig("nsig","#signal events",200,0.,10000) ; RooRealVar nbkg("nbkg","#background events",800,0.,10000) ; RooAddPdf sum("sum","g+a",rooarglist(gauss,argus),rooarglist(nsig,nbkg)) ; 17

18 RooFit example Generate unbinned toy data and perform Max Likelihood fit // --- Generate a toymc sample from composite PDF --- RooDataSet *data = sum.generate(mes,2000); // --- Perform extended ML fit of composite PDF to toy data --- sum.fitto(*data); // --- Plot toy data and composite PDF overlaid --- RooPlot* mesframe = mes.frame(); data->ploton(mesframe); sum.ploton(mesframe); sum.ploton(mesframe,roofit::components(argus),roofit::linestyle(kdashed)); mesframe->draw(); 18

19 RooFit example 19

20 Task Lets re-use tree2.root, that we generated in previous lecture tasks. We can import the destep variable into a RootDataSet and then use a RootPlot to draw it. Task: Set up an appropriate PDF and use it to fit this data. Compare this to using native ROOT fit functionality with appropriate shape. 20

21 Fitting Have only scratched the surface - enough to get you going, but much more you can learn. Other tools exist, e.g. HistFitter developed by ATLAS extends Roofit to make it fits of multiple data regions more convenient (e.g. typical ATLAS search for supersymmetry has histograms from 10 signal regions, each of which may have say 6 control and validation regions to constrain the PDFs) Task: Remake the tau visible mass histogram, only for 3-prong taus (Hint: you need only change 1-2 lines of code for this) Then read in the tau visible mass histogram, choose a shape and do a fit to the mass (use either RooFit or standard Fitting, as you prefer) Hint: You will need to run on all 45k events eventually, most of these 3 prong taus decay via the a1 resonance - a Breit-Wigner shape might be a good bet according to the PDG book. ROOT tutorials (in tutorials folder underneath $ROOTSYS) there are many Rootfit examples. 21

22 ROOT Geometries Many HEP experiments use ROOT compatible geometry definitions Some cross-platform interfaces VMC, GEANT, XML, GDML 22

23 T2K Near Detector (ND280) 23

24 T2K Near Detector (ND280) 24

25 ACoRNE 25

26 examples in tutorials/geom e.g. rootgeom.c run it invoke the OpenGL viewer try some of the others ROOT TGeo 26

27 Interfaces to other platforms 27

28 geant4 Virtual MC Extension to ROOT built against Geant4 (or Geant3) Permits use of different transport codes without changing user code and geometry a little beyond the scope of this course 28

29 Tasks Recap Run the mathcorevectorcollection.c example and read it. Plot the visible tau mass using ROOTTutorial_Week3 Plot a Landau shape using Roofit Import data from tree2.root into Rootfit and perform a fit of the destep variable. Fit the tau mass from 3-prong decays using ROOTTutorial_Week3 Have a look at the ROOT geometry tutorials. If you don t have time for this all the geometry are probably the least important, as this is a rather specialised use case most people won t ever use. 29

30 Closing remarks Many physics objects and mathematical operations supported only skimmed surface today Don t rewrite/reinvent unnecessarily shouldn t be coding e.g. coordinate transformations and vector products Magic numbers are bad saw some today 30

31 Closing remarks Introduced macro compilation lots more on this next week Next time: compiling binaries and libs ROOT as a dependency bindings to other languages Any questions? 31

32 end

33 backups