https://doi.org/10.1140/epjc/s10052-018-5634-2
Regular Article - Theoretical Physics
TMD splitting functions in 
factorization: the real contribution to the gluon-to-gluon splitting
1
Departamento de Actuaria, Física y Matemáticas, Universidad de las Americas Puebla, Santa Catarina Martir, 72820, Puebla, Mexico
2
The H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, ul. Radzikowskiego 152, 31-342, Cracow, Poland
3
Department of Physics, Ben Gurion University of the Negev, 8410501, Beer Sheva, Israel
* e-mail: Aleksander.Kusina@ifj.edu.pl
Received:
21
November
2017
Accepted:
10
February
2018
Published online:
2
March
2018
We calculate the transverse momentum dependent gluon-to-gluon splitting function within -factorization, generalizing the framework employed in the calculation of the quark splitting functions in Hautmann et al. (Nucl Phys B 865:54-66, arXiv:1205.1759, 2012), Gituliar et al. (JHEP 01:181, arXiv:1511.08439, 2016), Hentschinski et al. (Phys Rev D 94(11):114013, arXiv:1607.01507, 2016) and demonstrate at the same time the consistency of the extended formalism with previous results. While existing versions of factorized evolution equations contain already a gluon-to-gluon splitting function i.e. the leading order Balitsky–Fadin–Kuraev–Lipatov (BFKL) kernel or the Ciafaloni–Catani–Fiorani–Marchesini (CCFM) kernel, the obtained splitting function has the important property that it reduces both to the leading order BFKL kernel in the high energy limit, to the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) gluon-to-gluon splitting function in the collinear limit as well as to the CCFM kernel in the soft limit. At the same time we demonstrate that this splitting kernel can be obtained from a direct calculation of the QCD Feynman diagrams, based on a combined implementation of the Curci-Furmanski-Petronzio formalism for the calculation of the collinear splitting functions and the framework of high energy factorization.
© The Author(s), 2018
