Examination of $k_t$-factorization in a Yukawa theory

Abstract

We discuss the upper limit, $k_{\text{max}}$, of the transverse-momentum integration performed in the $k_t$-factorization formula. Based on explicit calculations in the Yukawa theory and the study of seminal papers, we argue that $k_{\text{max}}$ is equal to the factorization scale ${\mu }_F$ used to factorize the cross section into an off-shell hard coefficient and a universal factor. There is consequently a relation between $k_{\text{max}}$ and the definition of unintegrated parton densities (UPDFs). The use of an inconsistent relation leads potentially to the overestimation of the cross section, which has been observed, e.g., in D-meson production. One of our conclusions is that UPDFs related to collinear PDFs by an integration up to $\mu \sim Q$, where $Q$ is the hard scale and $\mu$ the scale in the collinear PDFs, imply that $k_{\text{max}}^2\sim Q^2$. Integrating the transverse-momentum significantly above may result in the overestimation of the cross section. On the opposite, for UPDFs related to the collinear ones by an integration of the transverse momentum up to infinity, any $k_{\text{max}}^2>Q^2$ is fine.

arXiv comment21 pages

References in corpus (19)

• Unintegrated parton distributions
• Unintegrated parton distributions and inclusive jet production at HERA
• Soft-gluon resolution scale in QCD evolution equations
• Collinear and TMD parton densities from fits to precision DIS measurements in the parton branching method
• Collinear and TMD Quark and Gluon Densities from Parton Branching Solution of QCD Evolution Equations
• Heavy Quark Production at High Energy
• Dynamical resolution scale in transverse momentum distributions at the LHC
• High-Energy Factorization for Drell-Yan process in $pp$ and $p\bar{p}$ collisions with new Unintegrated PDFs
• On the use of the KMR unintegrated parton distribution functions
• Unintegrated parton distributions of pions and nucleons from the CCFM equations in the single-loop approximation
• Soft emissions and the equivalence of BFKL and CCFM final states
• Resummation effects in Higgs boson transverse momentum distribution within the framework of unintegrated parton distributions
• Pathologies of the KMR prescriptions for unintegrated PDFs: Which prescription should be preferred?
• CCFM Evolution with Unitarity Corrections
• Matching next-to-leading-order and high-energy-resummed calculations of heavy-quarkonium-hadroproduction cross sections
• Heavy-quark production with $k_t$-factorization: The importance of the sea-quark distribution
• On the ambiguity between differential and integral forms of the Martin-Ryskin-Watt unintegrated parton distribution function model
• Basics of factorization in a scalar Yukawa field theory
• $J/\psi$ production at NLO with a scale-dependent color-evaporation model

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