##### Mission 1: number of reconstructed particles

In the data you fill find a list of reconstructed particles with their properties stored for each event. Each particle is desribed by its:

• momentum $p=(p_x,p_y,p_z)$,
• energy $E$,
• electric charge and
• identity.

List the particles in the data for several events and plot a frequency histogram of the number of reconstructed particles per event. This is done by using the "Main" (blue) block and by pressing the "Run Analysis" button.

Try to change the number of events and the data source file and observe how the distribution changes.

• ##### Mission 2: invariant mass

The mass of a particle is defined in terms of particle energy $E$ and its momentum $p$. The mass is invariant in any reference system an we call it invariant mass:

$mc^2=\sqrt{E^2-p^2 c^2}$

In this application, the mass is always calculated automatically.

Plot the distribution of particles according to their mass.

Change particle identity and see how the distribution changes in the following ranges:

• From $0$ to $3$ $\text{GeV}/c^2$;
• From $0$ to $0.0005$ $\text{GeV}/c^2$.
• ##### Mission 3: decay of a neutral pion to photons

From the measured momentum and energy of two particles ($p_1$, $E_1$) and ($p_2$, $E_2$) the mass of the mother particle can be calculated as $mc^2=\sqrt{(E_1+E_2)^2-(p_1+p_2)^2 c^2 )}$

"Combine two particles" (green) block calculates the mass of the combined particle for each combination of particles.

Plot the mass distribution of a neutral pion $\pi^0$ which decays to two photons: $\pi^0 \longrightarrow \gamma\gamma$ You will find a peak at $0.135$ $\text{GeV}/c^2$, which is exactly the mass of a neutral pion $\pi^0$.

##### Mission 4: decay of a neutral kaon to charged pions

Plot the mass distribution of a neutral kaon $K_s^0$ which decays to two charged pions: $K_s^0 \longrightarrow \pi^+ \pi^-$

You will find a peak at $0.498$ $\text{GeV}/c^2$ , which is exactly the mass of a $K_s^0$.

##### Mission 5: decay of a $\phi$ to charged kaons

Plot the mass distribution of a $\phi$ meson which decays to two charged kaons: $\phi \longrightarrow K^+ K^-$

You will find a peak at 1.02 $\text{GeV}/c^2$, which is exactly the mass of the $\phi$.

##### Mission 6: decay of a $J/\psi$ to charged leptons

Plot the mass distribution of a $J/\psi$ meson which decays to two leptons:

$J/\psi \longrightarrow e^+ e^-\quad\text{or}\quad J/\psi \longrightarrow \mu^+ \mu^-$

You will find a peak at $3.10$ $\text{GeV}/c^2$, which is exactly the mass of the $J/\psi$.

The probability for the production of a $J/\psi$ is very small, so you will have to process at least $100000$ events.

##### Mission 7: decay of a $D^0$ to charged kaons and pions

Plot the mass distribution of a neutral $D^0$ meson which decays to a combination of $K^+\pi^-$ or $K^-\pi^+$: $D^0 \longrightarrow K^+\pi^- \quad\text{or}\quad D^0 → K^-\pi^+$

You will find a peak at $1.86$ $\text{GeV}/c^2$, which is exactly the mass of the $D^0$.

The probability for a production of a $D^0$ is very small, so you will have to process at least $100000$ events.

##### Mission 8: decay of a $B^+$ to a $J/\psi$ and a charged kaon

Plot the mass distribution of a charged $B$ meson which decays to a combination of $J/\psi$ and $K^+$ $B^+ \longrightarrow J/\psi K^+\quad\text{or}\quad B^- \longrightarrow J/\psi K^-$

You will find a peak at $5.28$ $\text{GeV}/c^2$, which is exactly the mass of the $B^+$.

Use the green block "Combine two particles" and describe the process in two stages.

Be sure to select only the particles with an invariant mass very close to the $J/\psi$ mass for further analysis.

##### Mission 9: decay of a $D^{*+}$ to a $D^0$ and a charged pion

Plot the mass distribution of a charged $D^*$ which decays to a combination of $D^0\pi^-$ or $D^0 \pi^+$: $D^0 \longrightarrow K^+π^- \quad\text{or}\quad D^0 \longrightarrow K^-\pi^+$

You will find a peak in the $D^{*+}$ mass distribution at at $2.01$ $\text{GeV}/c^2$.

Use the green block "Combine two particles" and describe the process in two stages.

Be sure to select only the particles with an invariant mass very close to the $D^0$ mass for further analysis.

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