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Abstract
We use the Bessel-inspired behavior of parton densities at small Bjorken x values, obtained in the case of the flat initial conditions for DGLAP evolution equations in the double scaling QCD approximation (DAS), to evaluate the transverse momentum dependent (TMD, or unintegrated) quark and gluon distribution functions in a proton. The calculations are performed analytically using the Kimber-Martin-Ryskin (KMR) prescription with different implementation of kinematical constraint, reflecting the angular and strong ordering conditions. The relations between the differential and integral formulation of the KMR approach is discussed. Several phenomenological applications of the proposed TMD parton densities to the LHC processes are given.
Highlights
Theoretical frameworkSince the KMR approach is based on the standard parton density functions (PDFs), here we present a review of small x behaviour of parton densities
Ratio between the hard scale μ2 and total energy s, and high-energy factorization [4, 5] approach, valid in the limit of a fixed hard scale and high energy
The KMR procedure is believed to take into account effectively the major part of next-to-leading logarithmic (NLL) terms αs(αs ln μ2)n−1 compared to the leading logarithmic approximation (LLA), where terms proportional to αsn lnn μ2 are taken into account
Summary
Since the KMR approach is based on the standard PDFs, here we present a review of small x behaviour of parton densities. The study [52] was extended [40,41,42] to include the finite parts of anomalous dimensions (ADs) of Wilson operators and Wilson coefficients.1 This led to predictions [39,40,41] of the small-x asymptotic form of PDFs in the framework of the DGLAP dynamics, which were obtained starting at some Q20 with the flat function fa(x, Q20) = Aa,. The small-x asymptotic expressions for sea quark and gluon densities fa(x, μ2) can be written as follows (both the LO and NLO results and their derivation can be found [39, 40]): fa(x, μ2) = fa+(x, μ2) + fa−(x, μ2), fg+(x, μ2) = Ag + C Aq I0(σ) e−d+s + O(ρ), fq+(x, μ2).
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