Eur. Phys. J. C (2014) 74: 3039
https://doi.org/10.1140/epjc/s10052-014-3039-4

Regular Article - Theoretical Physics

Parton distribution functions at LO, NLO and NNLO with correlated uncertainties between orders

¹ DESY, Hamburg, Germany
² Department of Physics, University of Oxford, Oxford, UK
³ CPPM, IN2P3-CNRS, Univ. Mediterranee, Marseille, France
⁴ Joint Institute for Nuclear Research (JINR), Joliot-Curie 6, 141980 , Dubna, Moscow Region, Russia
⁵ T. Kosciuszko Cracow University of Technology, Kraków, Poland
⁶ Institut für Experimentelle Kernphysik, Karlsruhe, Germany
⁷ Institute of Physics,  Jagiellonian University, Ul. Reymonta 4, 30-059 , Kraków, Poland
⁸ Department of Physics and Astronomy, Sussex House, University of Sussex, Brighton, BN1 9RH, UK
⁹ Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 , Warsaw, Poland
¹⁰ Physikalisches Institut, Universität Heidelberg, Heidelberg, Germany
¹¹ Institute for Particle Physics Phenomenology, Durham University, Durham, DH1 3LE, UK
¹² Department of Physics, St. Petersburg State University, Ulyanovskaya 1, 198504 , St. Petersburg, Russia
¹³ CEA, DSM/Irfu, CE-Saclay, Gif-sur-Yvette, France
¹⁴ DESY, Platanenallee 6, 15738 , Zeuthen, Germany

^* e-mail: alexandre.glazov@desy.de
^** e-mail: pirumov@mail.desy.de
^*** e-mail: ringaile@mail.desy.de
^**** e-mail: voica@mail.desy.de
^***** e-mail: mlisovyi@mail.desy.de

Received: 5 May 2014
Accepted: 22 August 2014
Published online: 30 September 2014

Abstract

Sets of parton distribution functions (PDFs) of the proton are reported for the leading (LO), next-to-leading (NLO) and next-to-next-to-leading-order (NNLO) QCD calculations. The parton distribution functions are determined with the HERAFitter program using the data from the HERA experiments and preserving correlations between uncertainties for the LO, NLO and NNLO PDF sets. The sets are used to study cross-section ratios and their uncertainties when calculated at different orders in QCD. A reduction of the overall theoretical uncertainty is observed if correlations between the PDF sets are taken into account for the ratio of di-boson to boson production cross sections at the LHC.