Zachary Snyder (Penn State)
We demonstrate the mathematical formalism for the construction of the consistent initial conditions for the double parton distribution functions in the collinear approximation. The initial conditions within this framework have an important property that they satisfy exactly simultaneously both the momentum sum rules and the quark sum rules and are at the same time related to the single parton distribution functions. We find that this condition imposes certain relations on the large and small x behavior of both single and double parton distribution functions. We illustrate the double parton correlations for the gluon channel and show how they change with the evolution scale. Possible phenomenological implications are discussed.