# Data - Monte Carlo Correction techninques in Particle physics

It is said that the data does not always match with the Monte Carlo simulations in particle physics.(I guess even in the Higgs to gamma gamma channel, the peak in real data was at about 127GeV and thus it was corrected) .Thus,I wished to know what are the different ways in which the differences in Data and MC simulations are corrected, if possible, for the case of jets like bjets.

• $\uparrow$ Read where? – AccidentalFourierTransform May 26 '18 at 21:57
• @AccidentalFourierTransform I was told about that higgs decay example by my prof about 4-5 months ago.. he said that this is generally not shown but exists.. – kbg May 26 '18 at 22:00
• Generally MC generally does a very good job of matching data, at least in pp collisions. If it doesn't, then we generally don't use MC to correct the data, and instead, we study the specific nature of the difference between MC and data to try and determine if it is due to shortcomings in the simulation or real physics (for example, we try multiple MC methods, like using PYTHIA vs. HERWIG vs. Sherpa). – probably_someone May 26 '18 at 23:02
• You figure out why the Monte Carlo is wrong and then fix it ...like any other debugging problem. If you're lucky that means fixing the inputs, if not it means fixing the code. – dmckee May 26 '18 at 23:38
• @probably_someone Many analyses at the LHC use data-driven background estimates because MC frequently does not match the data well. Particularly when jets are involved. And detector issues have come up as well- for instance there can be issues if radiation damage to the detector is better or worse than expected. – Chris May 27 '18 at 10:05

If certain distributions of variables don't agree, then you can reweight the MC sample to match data (typically either using a nice clean control sample or s-weighted signal). There are a variety of reweighting techniques e.g. histograms, kernel-density estimators, boosted decision trees.

If resolution doesn't agree, you can apply 'smearing', whereby a variable is shifted by some random amount on an event-by-event basis according to a Gaussian distribution (or similar).

You have to understand that a Monte Carlo simulation is a way of integrating the predictions of a model.

Theoretical models are often calculable, and can be inserted with "simple" generators. i.e. every event is generated with the probability given by the quantum mechanical calculation.

This is not enough to allow comparison of data with theory. The data itself follows theoretical models, that describe particle interactions through the detector, with errors coming from statistical probability functions and estimates of these functions. All these errors need to be generated with the appropriate statistical probability width. The summation of events is the total integrals giving crossections for generating events in the experiment.

Thus a Monte Carlo program gives one event with the mathematically correctly combined probability of being observed in the detector. A simulation of one real event's probability.

When the Monte Carlo data do not fit the data, then two things are possible:

1) there is a programming error in the numerous generators or the code, which has to be found

2) there is a new discovery and everybody rejoices.

For example, back in the days when quantum chromodynamics was not even well formulated as a theory deep inelastic scattering on protons was thought to be an elementary interaction, and was modeled in monte carlos accordingly, with the appropriate theoretical scattering amplitude in the generator. The data showed deviation in the high momentum transfer region, not reproduced in the monte carlo, which led the way to verifying the complex quark internal structure of the proton.

• Isnt hadronisation a problem, since it is not understood from first principles. Generally there is nothing wrong with empirical models, but they tend to fail faster in new paramete ranges. – lalala May 27 '18 at 9:54
• Hadronization depends on the experiment and the question studied, itneeds models, see here arxiv.org/abs/1712.05213 which depend on previous measurements . Jets have been studied for some time now. If the models fail, it might be due to 2) , in this case different modes of hadronization not thought of previously. – anna v May 27 '18 at 10:37