Efficient handling of parton distribution functions

by Mr Riccardo Nagar (Deutsches Elektronen-Synchrotron DESY)

Wednesday 9 Oct 2019, 11:00 → 12:00 Europe/Zurich

Edificio U2, Aula 5017 (Dipartimento di Fisica G. Occhialini, U2, Università degli Studi di Milano-Bicocca)

Higher-precision cross-section calculations generally lead to a decrease in the relative size of theoretical uncertainties and, at the same time, to an increase in the complexity of the relevant computations. Both these circumstances call for an adaptation of the numerical treatment of some core elements of the cross section, like parton distributions. We present an efficient method for the interpolation and DGLAP evolution of single and double parton distributions (PDFs and DPDs). The algorithm is based on the Chebyshev interpolation of these functions, and is implemented in a C++ library called ChiliPDF. For PDF evolution, our method reaches higher accuracies using a considerably smaller amount of data points, compared to existing methods. As a consequence of the high interpolation accuracy, operations on PDFs such as differentiation and Mellin convolution with complicated kernels can be done in a fast and precise way. We also introduce the double parton distributions (DPDs), which appear in the double parton scattering (DPS) process cross section. The computational handling of these objects is complicated by their structure, that involves a larger number of independent variables. With ChiliPDF, DPD evolution is realized to a satisfactory degree of accuracy using an affordable number of points, and allows for two independent renormalization scales and flavor-numbers for the two partons. For both PDFs and DPDs we implement the DGLAP and flavor transition kernels up to NNLO.

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