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Register a new userInitial conditions for evolution of double parton distributions
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Double parton distribution functions (DPDFs) are used in the QCD description of double parton scattering. The DPDFs evolve with hard scales through relatively new QCD evolution equations which obey nontrivial momentum and valence quark number sum rules. Based on the constructed numerical program, we present results on the QCD evolution of the DPDFs. In particular, we discuss the problem how to specify initial conditions for the evolution equations which exactly fulfill the sum rules.
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We present the construction of unintegrated double parton distribution functions which include dependence on transverse momenta of partons. We extend the formulation which was used to obtain the single unintegrated parton distributions from the standard, integrated parton distribution functions. Starting from the homogeneous part of the evolution equations for the integrated double parton distributions, we construct the unintegrated double parton distributions as the convolutions of the integrated double distributions and the splitting functions, multiplied by the Sudakov form factors. We show that there exist three domains of external hard scales which require three distinct forms of the unintegrated double distributions. The additional transverse momentum dependence which arises through the Sudakov form factors leads to non-trivial correlations in the parton momenta. We also discuss the non-homogeneous contribution to the unintegrated double parton distributions, which arises due to the splitting of a single parton into daughter partons with high transverse momenta. We analyze two cases, the unfolding of the transverse momenta dependence from the last step of the evolution of two partons, and the case where the transverse momenta are generated directly from the single parton splitting.
We show how the double parton distributions may be obtained consistently from the many-body light-cone wave functions. We illustrate the method on the example of the pion with two Fock components. The procedure, by construction, satisfies the Gaunt-Stirling sum rules. The resulting single parton distributions of valence quarks and gluons are consistent with a phenomenological parametrization at a low scale.
We study the Q^2 evolution of parton distributions at small x values, obtained in the case of flat initial conditions. The contributions of twist-two and (renormalon-type) higher-twist operators of the Wilson operator product expansion are taken into account. The results are in good agreement with deep inelastic scattering experimental data from HERA.
We present main elements of the construction of unintegrated double parton distribution functions which depend on transverse momenta of partons. We follow the method proposed by Kimber, Martin and Ryskin for a construction of unintegrated single parton distributions from the standard parton distribution functions.
We present two equivalent consistency checks of the momentum sum rule for double parton distributions and show the importance of the inclusion of the so-called inhomogeneous term in order to preserve correct longitudinal momentum correlations. We further discuss in some detail the kinematics of the splitting at the basis of the inhomogeneous term and update the double parton distributions evolution equations at different virtualities.
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