Momentum sum rule and factorization of double parton distributions

Abstract

We show that the momentum sum rule is a necessary condition for factorization of double parton distributions into a product of two single parton distributions for small values of the parton momentum fractions x and large enough values of the evolution scale Q. This is a somewhat surprising result since the momentum sum rule involves integration over all values of the momentum fraction. In essence, the momentum sum rule provides a proper relation between the double and single parton distributions, which is necessary for the small x factorization at large $Q$.

11 pages, 4 figures, version published in Phys. Rev. D

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• Two-loop evolution kernels for colour dependent double parton distributions
• Double parton distributions of the proton from basis light-front quantization
• Nonlinear Corrections to the Momentum Sum Rule
• Numerical Study of MRW-Type Unintegrated Double Parton Distribution Functions from Non-Factorized DPDFs