Abstract
The knowledge of parton distribution functions is a fundamental input to theoretical predictions in hadronic collisions. The uncertainty on the PDFs feeds into the theoretical uncertainty on the inclusive jet cross section, as shown in the previous chapter. It also impacts new physics measurements in terms of e.g. the QCD background model used and expected production cross sections
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- 1.
This is generally done exploiting external programs.
- 2.
This assumption does not necessarily hold in the inclusive jet cross section, where jets in different bins come from the same event. Even though correlations can be relevant in bins with low statistics (as in the case of high \(p_T\)/high rapidity bins) and have been estimated after the unfolding procedure, the treatment of correlated statistical uncertainties in PDF fits is left for future studies.
- 3.
The Hessian matrix represents the error on a measurement \(X\) due to the different parameters \(i\) and \(j\) (\(\sigma ^2_X=(\partial _i \partial _j \chi ^2_{min}) (\partial _i \partial _j X)\), where \(\partial _k\) represents the partial derivative of a quantity with respect to the \(k\)-th PDF parameter. The underlying assumption that linear error propagation holds is made).
- 4.
This is not necessarily worrisome because the gluon density is not an observable quantity and it has to be convoluted with coefficient functions. On the other hand if the structure function related to the gluon PDF were predicted to have the same negative behaviour, it would indicate a breakdown of the DGLAP formalism at these scales. This is also hinted at by the values of the \(B\) coefficients for gluon and sea: at low \(Q^2\), \(B_g > B_{sea}\), contradicting the common idea that sea quarks are produced mainly from gluon splitting.
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Doglioni, C. (2012). Impact of ATLAS Jet Data on PDF Fits. In: Measurement of the Inclusive Jet Cross Section with the ATLAS Detector at the Large Hadron Collider. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30538-2_8
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