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 Image may be NSFW.
Clik here to view.
, using the quadrimomenta of two muon tracks which correspond to an estimated mass resolution Image may be NSFW.
Clik here to view.
, when the rapidity of the Z boson is Image may be NSFW.
Clik here to view.
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The above might -and should, if you are not a HEP physicist- sound rather meaningless, but the family of two-dimensional functions Image may be NSFW.
Clik here to view.
is needed for a precise calibration of the CMS tracker. They can be derived by convoluting the production cross-section of Z bosons Image may be NSFW.
Clik here to view. at a given rapidity Image may be NSFW.
Clik here to view.
with the proton’s parton distribution functions using a factorization integral, and then convoluting the resulting functions with a smearing Gaussian distribution of width Image may be NSFW.
Clik here to view..
Still confused ? No worry. Today I will only show one sample result – the probability distribution as a function of Image may be NSFW.
Clik here to view. and Image may be NSFW.
Clik here to view. for Z bosons produced at a rapidity Image may be NSFW.
Clik here to view.
, and tomorrow I will explain in simple terms how I obtained that curve and the other 39 I have extracted today.
Image may be NSFW.
Clik here to view.
In the three-dimensional graph above, one axis has the reconstructed mass of muon pairs Image may be NSFW.
Clik here to view. (from 71 to 111 GeV), the other has the expected mass resolution Image may be NSFW.
Clik here to view. (from 0 to 10 GeV). The height of the function is the probability of observing the mass value Image may be NSFW.
Clik here to view., if the expected resolution is Image may be NSFW.
Clik here to view.. 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…
Image may be NSFW.
Clik here to view.
Image may be NSFW.Clik here to view.
