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It is anticipated that hard double parton scatterings will occur frequentlyin the collisions of the LHC, producing interesting signals and significantbackgrounds to certain single scattering processes. For double scatteringprocesses in which the same hard scale t = ln(Q^2) is involved in bothcollisions, we require the double parton distributions (dPDFs)D_h^{j_1j_2}(x_1,x_2;t) in order to make theoretical predictions of their ratesand properties. We describe the development of a new set of leading order dPDFsthat represents an improvement on approaches used previously. First, we derivemomentum and number sum rules that the dPDFs must satisfy. The fact that thesemust be obeyed at any scale is used to construct improved dPDFs at the inputscale Q_0, for a particular choice of input scale (Q_0^2 = 1 GeV^2) andcorresponding single PDFs (the MSTW2008LO set). We then describe a novelprogram which uses a direct x-space method to numerically integrate the LODGLAP equation for the dPDFs, and which may be used to evolve the input dPDFsto any other scale. This program has been used along with the improved inputdPDFs to produce a set of publicly available dPDF grids covering the ranges10^{-6}<x_1<1, 10^{-6}<x_2<1, and 1<Q^2<10^9 GeV^2.

Double Parton Distributions Incorporating Perturbative QCD Evolution and Momentum and Quark Number Sum Rules