How are the HEP experiments' invariant mass plots generated?

Question

I am experimenting and playing around with some data, and I'm having trouble seeing how to generate invariant mass plots.

The data I have has a bunch of events, and variables such as $P,P_T,\eta,\phi$ etc.. but no energy. There is a histogram which generates the invariant mass, but no macro provided for this. For example, I know there are tracks for electrons and protons (TPC), and I want to see if there are any pairs as a result of $\gamma\rightarrow e^+ e^-$. Conceptually I need to loop over all positive negative pairs, and plot the histogram. I should get a peak around zero for $\gamma$ pair production. The invariant mass formula is $$m_\gamma^2 = (E_{e^+}+E_{e^-})^2 - (\vec{p}_{e^+}+\vec{p}_{e^-})^2$$

But there is no data for the energy, how do the high energy physicists do it? Do they guess some value for the energy and make plots with that guess?

Answer 1

Without knowing more about your data set I can only offer a few random suggestions:

• If you have some kind of PID reason to believe that the tracks might be electron you just assume that they are and compute the energy from the momentum and $m_e$.
• In you have a calorimeter in the detector stack you measure the energy, and project the maximum likelihood energy loss back to the vertex. Note, however that the measured signal may have error much larger than $m_e$, so it may be better to use the device for PID and fall back on the previous suggestion.

Answer 2

When one has tracks in an ionising chamber, as a bubble chamber or a TPC there may be also information stored on the ionisation measurements across the track. For low enough momenta one can distinguish electrons from protons and pions and assign the appropriate mass, and then the energy is known.

We used to have programs in bubble chamber physics, GRIND, which would calculate probabilities and give the corresponding ionisation values for several hypothesis of masses as well as for the whole event seen, applying energy and momentum balances. The event could be a 4 constraint fit, gold plated, a 1 constrain fit, or a 0 constraint fit, i.e. missing energy with more than one particle.

For the specific exercise you want to do, assign the mass of the electron to the tracks and calculate the energy and the invariant masses. The photons will appear at 0. With a monte carlo you can estimate the background from the wrongly assigned mass.