Result now, explanation later December 18, 2008Posted by dorigo in personal, physics, science.
Tags: CMS, momentum scale, PDF, Z boson
Tonight I feel accomplished, since I have completed a crucial update of the cornerstone of the algorithm which provides the calibration of the CMS momentum scale. I have no time to discuss the details tonight, but I will share with you the final result of a complicated multi-part calculation (at least, for my mediocre standards): the probability distribution function of measuring the Z boson mass at a certain value , using the quadrimomenta of two muon tracks which correspond to an estimated mass resolution , when the rapidity of the Z boson is .
The above might -and should, if you are not a HEP physicist- sound rather meaningless, but the family of two-dimensional functions is needed for a precise calibration of the CMS tracker. They can be derived by convoluting the production cross-section of Z bosons at a given rapidity with the proton’s parton distribution functions using a factorization integral, and then convoluting the resulting functions with a smearing Gaussian distribution of width .
Still confused ? No worry. Today I will only show one sample result – the probability distribution as a function of and for Z bosons produced at a rapidity , and tomorrow I will explain in simple terms how I obtained that curve and the other 39 I have extracted today.
In the three-dimensional graph above, one axis has the reconstructed mass of muon pairs (from 71 to 111 GeV), the other has the expected mass resolution (from 0 to 10 GeV). The height of the function is the probability of observing the mass value , if the expected resolution is . On top of the graph one also sees in colors the curves of equal probability displayed on a projected plane. It will not escape to the keen eye that the function is asymmetric in mass around its peak: that is entirely the effect of the parton distribution functions…