During the colissions of high energy electrons and positrons, new particles are created from the available energy. The particles fly in different directions. Most of them decay very fast in the lighter particles. Only several particles can be detected directly in the detector (photons, electrons, muons, pions, kaons and protons), while the others have to be reconstructed from their decay products. Each particle is described by its energy, momentum vector, charge and its identity. These quantities are calculated from the measured electrical signals, that particle leaves in the particle detector. These examples consists of three parts: First download the latest version of the ROOT software from here and follow the installation instructions. Then download the scripts and unpack them in your local folder. The sample program consists of several files: First open the terminal and navigate to the folder with the scripts. Then start the ROOT by typing root + Enter. You will get the output that will be similar to

   ************************************************ 
   * * 
   * WELCOME to ROOT *          
   * * 
   * Version 5.10 / 00 29 1 March 2006 * 
   * * 
   * You are welcome to visit our Web site * 
   * Http://root.cern.ch * 
   * * 
   ************************************************ 
Compiled on 2 March 2006 for win32. 

CINT / ROOT C / C ++ Interpreter version 5.16.8, February 9, 2006 
Type? For help. Commands must be C ++ statements. 
Enclose multiple statements between {}. 
root [0] 
At the beginning the library with the definitions of the particles and the event, needed to read the data by loading the fie rootalias.C have been loaded in the framework. In the command prompt you can now type-in different commands: Bellow is the description of the exercises with the instructions for their implementation. In the following exercises you will have to find the particles, which have not been detected directly in the detector by combining the tracks in the data.

Exercise 1

Different particles have different masses. The mass of the particle can be calculated from particle energy and particle momentum, which are recorded in the data file: mass = sqrt( energy**2 - momentumvec**2) In this exercise we will plot the frequency distribution (histogram) of the mass of the particles. From the distribution one can see what kinds of particles and have been created in the collisions. In addition you will see how often each particle species are created. First start the ROOT. Then run the analysis from the script mlist.cc with two arguments: number of events - 5000 and filename - hadron-1. If you don't specify the number of events, all events will be processed, which is quite time consuming.

root [0] .x mlist.cc( 5000, "hadron-1.root" )
Only one histogram is displayed, although more are created during the analysis. You can display them by opening a ROOT Object Browser: If you bring the mouse cursor to the bottom of the coordinate axes, the mouse pointer will change to the shape of the human hand. In this state, it is possible to zoom the histogram by selecting the range. The range is selected by clicking the left mouse button and dragging it over the coordinate axis, it can be arbitrarily expanded display a histogram. By selecting the right mouse button, you get an access to a variety of functions with the histogram. Try several of them.

Exercise 2

In the first exercise, only energy and momentum of the particle were used and the distributions we made were for all of the particles. In this exercise we will in addition plot the mass distributions for pions. We will separately plot them for neutral pions and charged pions. Run the analysis from the script pion.cc with two arguments: filename - hadron-1.root and number of events - 5000.

root [0] .x pion.cc( 5000,  "hadron-1.root")
Open the File Browser to display different histograms

Exercise 3

In Exercise 1 and 2, we calculate the mass of particles from the magnitude of the energy and momentum. In the experiment the momentum is measured and the energy of the particles is calculated from the mass. This exercise demonstrates the search for the particles break into two particles. The neutral pion π0 is unstable and it decays instantly to two photons (gamma, γ). To find the neutral pion we plot the mass distribution of combination of two photons. In the distribution we find a peak at 0.135GeV, which is the mass of the neutral pion. Run the analysis script pi0.cc with two arguments: filename - hadron-1.root and number of events - 20000.

root [0] .x pi0.cc(  20000, "hadron-1.root")
Several histograms are created during the analysis. You will notice that the mass of the neutral pion in the first two exercises is constant, whereas in this exercise it has a finite width due to the measurements uncertainty of the photon momentum. Because we know the mass of the neutral pion is constant and amounts to 0.135 GeV, we can after we identify the neutral pion, calculate its energy. Note that the neutral pion peak is superimposed on the distribution of the smooth background. Photons that have been identified as children of neutral pions, are not removed from the data, but remains in it. This means that such photons, have been registered in the the photon data and the neutral pion data.

Exercise 4

Neutral K meson short (Ks) has a mass of 0.498 GeV and decays to teo charged pion (π+ and π -). In the same way as in the Exercise 3, we plot the mass distribution of a combination of a positive and negative charged pions and find a peak at 0.498 GeV. Run the analysis script ks.cc with two arguments: filename - hadron-1.root and number of events - 20000.

root [0] .x ks.cc( 20000, "hadron-1.root")
Several histograms are created during the analysis. You'll see that there is a peak in the vicinity of 0.5 GeV. Ks in the data file that you are using has been identified from such a peak. In the real exercise other conditions for the identification reduce the background even more. Charged pions that have been identified as children of Ks, are not removed from the data of the charged pion, but remain in the data. That is such a charged pion has been registered twice.

Exercise 5

Some of the meson have larger masses than the K meson. One is a φ meson with mass of 1.02 GeV. The particle is made of the s quark and anti-quark s and decay into two charged Ks mesons (K+ and K-). Follow the previous exercise Exercise 4 and write an analysis program in which you plot a mass distribution of a combination of K+ and K- and look for a φ meson.

Exercise 6

A particle called Jpsi J/ψ is a particle consisting of a c quark and anti-c quark with the mass of 3.10 GeV. J/ψ decays to positron and electron or positive μ meson and negative μ meson (J/ψ → e+ e- or J/ψ → μ+ μ- ). Find the J/ψ particles from the data. Since the J/ψ particle is a rare particle, you will have to analyze at least 100,000 events.

Exercise 7

Charm quark and light quarks (u, d quarks) form D mesons with mass of 1.86 GeV. These neutral D mesons decay in the charged K mesons and the charged π mesons. Find the neutral D mesons from the data. Due to the charge conservation, the amount of charge before and after the interaction is the same. Since the original D meson was neutral, the combination of charge after the decay is K+π- or K-π+.

Exercise 8

One of the important objectives of the Belle experiment is a study of various decays of B mesons. B meson can decay in hudreds of different ways. As an exercise, charged B meson decays to a J/ψ and a charged K (B+ → J/ψ K+ ). In this exercise your task is to study this decay. As in the exercise 6, J/ψ particle decays to e+ and e- or μ + and μ. You will combine the particle with the K+ to get search for a B meson. Not all combinations of particles create a real J/ψ. We can select the the J/ψ particles by checking their mass and selecting the combinations within a mass range between jpsimass1 and jpsimass2. This particles we combine further with K+. This means that we must add another loop to our program.

if (mass > jpsimass1 && mass < jpsimass2) { 
    for(TIter next3(event-> GetParticleList()); BParticle * p3 =(BParticle *) next3();) {
      int pid3 = p3-> pid () ; 
	  ....
	}  
} 
We search for the peak around the mass of the B mesons. Note that although in the above description we only described decays with K+, also an anti-particle K- is supposed to be formed during decays (B- decays to J/ψ and K- ). Study both decays by looking in the mass distributions.

Exercise 9

In the exercise 7 we were looking for a D*(2010) particle. The particles consists of charm quark and a lighter quark (u, d quarks), the charge is 1 or -1. They is heavier than D mesons (they have mass of 2.01GeV), and they decay instantly to neutral D mesons (D0) and the charged π mesons.

D*+ → D0 π+  
D*- → D0 π- 
D0 → K+ π- / K- π+
Study this decay. The analysis is similar to the one in exercise 8.