
Eur. Phys. J. C (2014) 74:3082
DOI 10.1140/epjc/s10052-014-3082-1
Special Article - Tools for Experiment and Theory
The CCFM uPDF evolution uPDFevolv Version 1.0.00
F. Hautmann
1,2,3
, H. Jung
4,5,a
, S. Taheri Monfared
6
1
Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK
2
Rutherford Appleton Laboratory, Chilton OX11 0QX, UK
3
Department of Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK
4
DESY,Hamburg,Germany
5
University of Antwerp, Antwerp, Belgium
6
School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran
Received: 23 July 2014 / Accepted: 15 September 2014 / Published online: 1 October 2014
© The Author(s) 2014. This article is published with open access at Springerlink.com
Abstract uPDFevolvis an evolution code for TMD parton
densities using the CCFM evolution equation. A description
of the underlying theoretical model and technical realisation
is given together with a detailed program description, with
emphasis on parameters the user may want to change.
1 Theoretical input
1.1 CCFM evolution equation and transverse momentum
dependent PDFs
QCD calculations of multiple-scale processes and complex
final-states require in general transverse-momentum depen-
dent (TMD), or unintegrated, parton density and parton
decay functions [1–10]. TMD factorization has been proven
recently [1] for inclusive and semi-inclusive deep-inelastic
scattering (DIS). Forspecial processes in hadron-hadron scat-
PROGRAM SUMMARY Title of Program: uPDFevolv
1.0.00. Computer for which the program is designed and others on
which it is operable: any with standard Fortran 77 (gfortran) and C++,
tested on Linux, MAC. Programming Language used: FORTRAN
77, C++. High-speed storage required: No. Separate documentation
available: No. Keywords: QCD, small x, high-energy factorization, k
t
-
factorization, CCFM, unintegrated PDF (uPDF), transverse momentum
dependent PDF (TMD). Nature of physical problem: At high energies
collisions of hadrons are described by parton densities dependent
on the longitudinal momentum fraction x, the transverse momentum
k
t
and t he evolution scale p (transverse momentum dependent (TMD)
or unintegrated parton density functions (uPDF)). The evolution
of the parton density with the scale p valid at both small and moderate
x is given by the CCFM evolution equation. Method of solution:
Since the CCFM evolution equation cannot be solved analytically,
a Monte Carlo approach is applied, simulating at each step of the
evolution the full four-momenta of the initial state partonic cascade.
Restrictions on the complexity of the problem: None. Other Program
used: Root for plotting the result. Download of the program: https://
updfevolv.hepforge.org. Unusual features of the program: None.
a
e-mail: hannes.jung@desy.de
tering, like heavy flavor or heavy boson (including Higgs)
production, TMD factorization holds in the high-energy limit
(small x)[11–13].
In the framework of high-energy factorization [11,14]the
deep-inelastic scattering cross section can be written as a
convolution in both longitudinal and transverse momenta of
the TMD parton density function A(x, k
t
,μ) with off-shell
partonic matrix elements, as follows
σ
j
(x, Q
2
) =
1
x
dz
d
2
k
t
ˆσ
j
(x, Q
2
, z, k
t
) A(z, k
t
, p),
(1)
with the DIS cross sections σ
j
( j = 2, L) related to the
structure functions F
2
and F
L
by σ
j
= 4π
2
F
j
/Q
2
.The
hard-scattering kernels ˆσ
j
of Eq. (1)arek
t
-dependent and the
evolution of the transverse momentum dependent gluon den-
sity A is obtained by combining the resummation of small-x
logarithmic contributions [15–17] with medium-x and large-
x contributions to parton splitting [18–20] according to the
CCFM evolution equation [21–23].
The factorization formula (1) allows one to resum loga-
rithmically enhanced x → 0 contributions to all orders in
perturbation theory, both in the hard scattering coefficients
and in the parton evolution, taking fully into account the
dependence on the factorization scale p and on the factoriza-
tion scheme [24,25].
The CCFM evolution equation [21–23] is an exclusive
equation for final state partons and includes finite-x contribu-
tions to parton s plitting. It incorporates soft gluon coherence
for any value of x.
1.1.1 Gluon distribution
The evolution equation for the TMD gluon density
A(x, k
t
, p), depending on x, k
t
and the evolution variable
p,is
123