Double parton distributions in the pion from lattice QCD

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.

Double parton distributions in the nucleon from lattice QCD

“…The results for the ζ-moments are quite different from those we obtained for the pion [67], where we found a clear linear rise with increasing y. In that case, for y > 1 fm, values of ζ 2 > 0.5 were observed.…”

“…and l.h.s. of (2.8) have been found, while the orders of magnitude are consistent with each other [67]. Similar observations have been made in quark model studies [49].…”

“…This generalizes the well-known relation between single-current matrix elements and the Mellin moments of PDFs, which has been extensively exploited in lattice calculations as reviewed in [64][65][66]. We recently presented a corresponding calculation for DPDs in the pion [67], using n f = 2 ensembles with a pion mass around 300 MeV. The results have rather high statistical precision, and they reveal a number of interesting patterns.…”

“…Further analysis steps require a parameterization of the results obtained for the twist-two functions. In the following, we adapt the approach we developed in [67]. For the description of the y 2 -dependence at py = 0 a sum of two exponentials is found to be suitable in most cases.…”

Two-loop splitting in double parton distributions: the colour non-singlet case

“…To determine DPDs from experimental data is considerably more complicated than the determination of PDFs, and our knowledge of DPDs remains quite fragmentary. There is a large number of calculations of DPDs in quark models [39][40][41][42][43][44][45][46][47][48][49], and information about the Mellin moments of DPDs can be obtained in lattice QCD [50,51]. One may also try to construct an ansatz for DPDs that fulfils non-trivial theory constraints [52][53][54][55].…”