Abstract
Models for double parton distributions that are realistic and consistent with theoretical constraints are crucial for a reliable description of double parton scattering. We show how an ansatz that has the correct behaviour in the limit of small transverse distance between the partons can be improved step by step, such as to fulfil the sum rules for double parton distributions with an accuracy around 10%.
Highlights
Particular on the spatial separation y of the two partons in the plane transverse to the proton momentum
We show how an ansatz that has the correct behaviour in the limit of small transverse distance between the partons can be improved step by step, such as to fulfil the sum rules for double parton distributions with an accuracy around 10%
We have shown that one can construct physically plausible models for double parton distributions (DPDs) in position space that approximately fulfil these constraints
Summary
Given the complexity of measuring and computing DPS cross sections, a largely model-independent fit of DPDs to experimental data, akin to what is done for single parton distributions (PDFs), will not be possible for a considerable time. There are sum rules [77,78], which involve DPDs integrated over y (or evaluated at Δ = 0) and express the conservation of momentum and quark number. Only a small number of studies [2,77,79,80,81] have used these sum rule to constrain DPDs, and it is the goal of the present paper to continue this line of work. Whereas the DPD models in [2,77,79,80] are formulated for DPDs at Δ = 0, we work with DPDs in y space, because these are the quantities required for computing DPS cross sections in the formalism of [45].
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