I am doing a simulation of heavy ion collision, so I want to know what is the meaning of Monte Carlo tracks, what is a reconstructed track, and also, what is the relation and difference between Monte Carlo and reconstructed tracks? What is the need of MC tracks as we are anyway going to reconstruct that track? Thank you in advance
Particle physics relies a lot on Monte Carlo simulations to compare data to the theoretical model.
The Monte Carlo event generator generates an event from distributions predicted by some theoretical model. The event consists of the fundamental scatter, in this case, two heavy ions colliding and giving a number of four vectors as given by the theoretical model used. These four vectors will be protons, neutrons, gamma, neutrinos etc, leaving the theoretical vertex. The MC propagates these four vectors through a simulation of the detector, to see how their path is distorted by the limitations of the detection.
In the end, an MC event data set is created, that looks like the measured events data set, but is an integration of the hypothesis in the theoretical model to be tested. There is no one to one fit of a measured track to a Monte Carlo generated track or event. There is a comparison of appropriate distributions, angular , momentum transfer, multiplicity etc . The comparison indicates how well the reaction is theoretically modeled, and any deviations are indications that the theoretical model should be expanded, corrected, or rejected.
In a very real sense, you with the MC simulation create a data set assuming you have understood and have in your event generator what Nature uses in its generation of events. The differences in the distributions will highlight where your understanding of the natural processes needs a better mathematical model.
This is seen in the discovery of the Higgs at LHC:
The black dots are the data. The green-red-dots line is what the Monte Carlo gave where the event generator has no signal of a resonance at 125. Once a signal is seen, the event generator is changed and a Monte Carlo data sample is generated to fit the observed signal at 125 GeV.
In one sentence?
The MC track is an expression of what you think you know about how your detector works, the real track is how your detector really works.
Corollary: The (statistical) difference between the two is how little you actually know about your detector and your reconstruction algorithm.
To put it somewhat more seriously/positively: ideally the discrepancy between the MC model and the real measurements can be used to calibrate/refine the detector model to estimate the actual energy/momentum of the particles from the reconstructed energy/momentum with minimal statistical errors and, even more importantly, with minimal bias.