Eur. Phys. J. C (2014) 74:3039
DOI 10.1140/epjc/s10052-014-3039-4
Regular Article - Theoretical Physics
Parton distribution functions at LO, NLO and NNLO
with correlated uncertainties between orders
HERAFitter developers’ team
a
:P.Belov
1,12
, D. Britzger
1
, S. Camarda
1
, A. M. Cooper-Sarkar
2
, C. Diaconu
3
,
J.Feltesse
13
,A.Gizhko
1
,A.Glazov
1,b
, V. Kolesnikov
4
, K. Lohwasser
14
, A. Luszczak
5
, V. Myronenko
1
,H.Pirumov
1,c
,
R. Plaˇcakyt˙e
1,d
, K. Rabbertz
6
, V. Radescu
1,e
, A. Sapronov
4
, A. Schöning
10
, S. Shushkevich
1
, W. Slominski
7
,
P. Starovoitov
1
, M. Sutton
8
, J. Tomaszewska
9
, O. Turkot
1
,G.Watt
11
, K. Wichmann
1
, and M. Lisovyi
1,f
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
Present address: 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
Received: 5 May 2014 / Accepted: 22 August 2014 / Published online: 30 September 2014
© The Author(s) 2014. This article is published with open access at Springerlink.com
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 cal-
culations. The parton distribution functions are determined
with the HERAFitter program using the data from the HERA
experiments and preserving correlations between uncertain-
ties for the LO, NLO and NNLO PDF sets. The sets are used
to study cross-section ratios and their uncertainties when cal-
culated 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 WW di-boson
to Z boson production cross sections at the LHC.
1 Introduction
Accurate knowledge of the parton distribution functions
(PDFs) of the proton is required for precision physics at the
a
e-mail: herafitter-help@desy.de
b
e-mail: alexandre.glazov@desy.de
c
e-mail: pirumov@mail.desy.de
d
e-mail: ringaile@mail.desy.de
e
e-mail: voica@mail.desy.de
f
e-mail: mlisovyi@mail.desy.de
LHC. PDF sets are now available as determined by several
groups [1–6] at leading-order (LO), next-to-leading-order
(NLO) and next-to-next-to-leading-order (NNLO) accuracy
in QCD. To obtain the cross-section predictions, the PDF sets
should be paired with calculations of the coefficient functions
at the matching order of the accuracy. Theoretical uncer-
tainties for the predictions arise from both the PDF and the
coefficient-function uncertainties.
Most of the Standard Model processes at the LHC are cal-
culated to NLO accuracy. The uncertainties due to missing
higher orders for the coefficient functions are typically deter-
mined by varying factorisation and renormalisation scales.
This leads to large uncertainties often as large as 10 % of
predicted cross sections, which usually exceed uncertainties
due to the PDFs determination. For a handful of processes
known at NNLO, the PDF uncertainties often exceed uncer-
tainties due to missing higher orders in coefficient-function
calculations.
The experimental precision achieved by the LHC experi-
ments often exceeds the precision of theoretical calculations.
Ultimately a more complete set of NNLO calculations should
remedy the situation in future. At present, special meth-
ods are employed to reduce theoretical uncertainties. One
such method is to measure ratios of observables which are
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