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On the Importance of Confident Error Bands for Extrapolations of σ(pp)^tot to High Energies

AutorPérez-Peraza, J.; Velasco, Jorge; Gallegos-Cruz, A.; Faus, Ángeles ; Rodríguez-Frías, M. D.; Peral-Gochicoa, L. del
Palabras claveElastic proton-proton scattering
Total proton cross section
Extensive Air Shower
Extrapolation to high energies
Confident statistical error interval
Fecha de publicaciónjul-2002
EditorInternational Institute of Informatics and Systemics
Citación6th World Multiconference on Systemics, Cybernetics and Informatics and 8th International Conference on Information System Analysis and Synthesis (SCI/ISAS 2002) ; 002704
ResumenElastic proton-proton scattering is the most simple process in high-energy hadronic interactions. One of the main tasks in this field is to detemine the total proton cross section σ(pp)^tot in order to reproduce experimental data. Total cross sections are known long ago from accelerator experiments in the energy range sqrt{s} <= 1:8 TeV and in the range sqrt{s} = 6 - 40 TeV from Extensive Air Shower. In order to know the σ(pp)^tot energy behavior within the accelerator data range and beyond, it is generally proceeded to fit the available set data and also to predict data by extrapolation to high energies. However, if we analize the diverse works existing in the literature about the extrapolation problem, we find in some of them that the uncertainty associated to the σ(pp)^tot prediction points is relatively large or even in other cases the corresponding uncertainties associated to their predictions are not reported. Besides, the disagreement existing between the extrapolated data to high energies from accelerator data and cosmic data, widely discussed in the literature, can be better studied, if prediction methods would offer a confident error interval. The main goal of different methods is to minimize the involved errors to obtain highly precise predictions. In this work we present an alternative prediction method that allows to determine a confident statistical error interval around each of the σ(pp)^tot predicted points. Predictions are developed on the basis of the multiple-diffraction model to estimate σ(pp)^tot in the center of mass range 10 - 40 TeV (10^17 - 10^18 eV in lab) which covers both LHC and the highest cosmic ray energies. We conclude that at least in this case the proposed method is not only more precise that the conventionnal Χ2 technique but also more economic from the point of view of calculation time, because the process is based in a unique calculation instead of multiple iterations.
Descripción6 pages, 6 figures.-- Communication presented at the 6th World Multiconference on Systemics, Cybernetics and Informatics and 8th International Conference on Information System Analysis and Synthesis (SCI/ISAS 2002, Orlando, Florida, Jul 14-18, 2002).
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