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TMD splitting functions in [Formula: see text] factorization: the real contribution to the gluon-to-gluon splitting
M Hentschinski1, A Kusina2, K Kutak2
1Departamento de Actuaria, Física y Matemáticas, Universidad de las Americas Puebla, Santa Catarina Martir, 72820 Puebla, Mexico.
The European Physical Journal. C, Particles and Fields
|March 13, 2018
Summary
We introduce a new transverse momentum dependent gluon-to-gluon splitting function within k-factorization. This function unifies leading-order BFKL, DGLAP, and CCFM kernels in different limits.
Area of Science:
- High Energy Physics
- Quantum Chromodynamics (QCD)
- Parton Physics
Background:
- Existing k-factorization formalisms utilize gluon-to-gluon splitting functions like the Balitsky-Fadin-Kuraev-Lipatov (BFKL) or Ciafaloni-Catani-Fiorani-Marchesini (CCFM) kernels.
- A unified description of these kernels within a single framework is needed for comprehensive theoretical calculations.
Purpose of the Study:
- To calculate the transverse momentum dependent gluon-to-gluon splitting function within the k-factorization framework.
- To generalize existing methods used for quark splitting functions to include gluon splitting.
- To demonstrate the consistency of the extended formalism with previous results.
Main Methods:
- Generalization of the framework used for quark splitting functions in previous studies.
- Combined implementation of the Curci-Furmanski-Petronzio formalism for collinear splitting functions.
- Application of the high energy factorization framework for direct QCD Feynman diagram calculations.
Main Results:
- A novel transverse momentum dependent gluon-to-gluon splitting function is derived.
- The derived function reduces to the leading-order BFKL kernel in the high energy limit.
- It also reproduces the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) splitting function in the collinear limit and the CCFM kernel in the soft limit.
Conclusions:
- The developed splitting function provides a consistent and unified description within k-factorization.
- This advancement reconciles different theoretical limits (high energy, collinear, soft) of gluon-to-gluon splitting.
- The results validate the extended formalism and its applicability in high energy QCD.
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