Correction and Unfolding
Our goal is to provide distributions of data which can be compared to predictions of various Monte Carlo generators without reference to any detector.
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Correction and Unfolding
Our goal is to provide distributions of data which can be compared to predictions of various Monte Carlo generators without reference to any detector. The relationship between the desired true distributions, which is represented as f true (xtrue ), and the measured distribution at detector-reconstruction level, which is represented as f reco (xreco ), can be expressed as: reco reco f (x ) = R(xtrue , xreco )f true (xtrue )dxtrue (7.1) where R(xtrue , xreco ) is the response matrix. The response matrix encapsulates the detector response for the measurement. Response matrices are obtained from MadGraph interfaced with pythia 6 tune Z2 full simulation sample here. The steps to unfolding involves building a response matrix that maps the true distribution at generator-truth level to the measured distribution at detector-reconstruction level. For a given number of events in a bin of the true distribution, the response matrix element R(xtrue , xreco ) gives the fraction of events that end up in the measured bin. The response matrices are constructed for each measured observables, as follows. • Events are accepted if they can satisfy the generator-truth level selection and detector-reconstruction level selection with the same kinematic acceptance. • If the event satisfies the generator-truth level acceptance criteria, but has no counterpart inside the detector acceptance, such event is tagged as ”missing” and is recorded as lost due to detector inefficiency. • If the event accepted at detector-reconstruction level, but has no counterpart at generator-truth level, such event is tagged as “fake” and is also recorded in the response matrices.
© Springer Nature Singapore Pte Ltd. 2017 Y.-H. Chang, Study of Double Parton Scattering in Photon + 3 Jets Final State, Springer Theses, DOI 10.1007/978-981-10-3824-2_7
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7 Correction and Unfolding
7.1 Acceptance, Background, Purity and Stability In order to further investigate the reliability of response matrices of the measured observables, the migration effects inside and outside the defined phase space have to be deeply studied. Due to the detection inefficiencies or resolution, event selected at detector-reconstruction level may not have its corresponding event at generator-truth level, or event selected at generator-truth level may not be measured at detectorreconstruction level. Such phenomena are defined as the migration effect outside the phase space. Furthermore, the quantities of measured observables of events selected at both two level may correspond to different values or even belong to different bins. This is labeled as the migration effect inside the phase space. Some quantities used to study the migration effects are introduced in the following paragraphs. It should be noted that the events selected at both generator-truth and detector-reconstruction level are labeled as “matched events”. For the migration effects outside the phase space, we study the corresponding quantities, acceptance and background, respectively. The acceptance i
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