Abstract
We perform a lattice study of double parton distributions in the pion, using the relationship between their Mellin moments and pion matrix elements of two local currents. A good statistical signal is obtained for almost all relevant Wick contractions. We investigate correlations in the spatial distribution of two partons in the pion, as well as correlations involving the parton polarisation. The patterns we observe depend significantly on the quark mass. We investigate the assumption that double parton distributions approximately factorise into a convolution of single parton distributions.
Highlights
We perform a lattice study of double parton distributions in the pion, using the relationship between their Mellin moments and pion matrix elements of two local currents
When interpreting the results of the present section, we will assume that these configurations are not dominant, and that the qualitative features of invariant functions at py = 0 are the same as for Mellin moments of double parton distributions (DPDs) at ζ = 0
We recall from (2.19) that the regime with a quark and an antiquark in the pion contributes with a negative sign to the lowest Mellin moment of a DPD
Summary
We recall some basics about double parton distributions. An extended introduction to the subject can be found in [67]. Lattice studies can give information about this dependence, whose knowledge is crucial for computing double parton scattering cross sections Both unpolarised and polarised DPDs can exhibit correlations in their dependence on x1, x2 and y. We cannot address this aspect in our present study, because the matrix elements we compute are related to the lowest Mellin moments of DPDs, i.e. their integrals over both x1 and x2. Where fa(x) denotes a standard PDF and G(y) is a factor describing the dependence on the transverse parton distance This assumption leads to the so-called “pocket formula”, which expresses double parton scattering cross sections in terms of the cross sections for each single scattering and a universal factor σe−ff1 = d2y [G(y)]2.
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