Constraining the double gluon distribution by the single gluon distribution

Understand

We show how to consistently construct initial conditions for the QCD evolution equations for double parton distribution functions in the pure gluon case.

• We use to momentum sum rule for this purpose and a specific form of the known single gluon distribution function in the MSTW parameterization.
• The resulting double gluon distribution satisfies exactly the momentum sum rule and is parameter free.
• We also study numerically its evolution with a hard scale and show the approximate factorization into product of two single gluon distributions at small values of x, whereas at large values of x the factorization is always violated in agreement with the sum rule.