Double parton distributions of the pion

Abstract

We present a calculation of valence double parton distributions of the pion in the framework of chiral quark models. The result obtained at the low-energy quark model scale is particularly simple, where in the chiral limit a factorized form follows, D(x(1), x(2), q') = delta(1 - x(1) - x(2))F (q') with x(1,2) standing for the longitudinal momentum fractions of the valence quark and antiquark, and (q) over right arrow denotes the relative transverse momentum. For (q) over right arrow = (0) over right arrow, the result satisfies the Gaunt-Sterling sum rules. The QCD evolution to higher scales is carried out within the dDGLAP framework. We argue that the ratios of the valence Mellin moments < x(1)(n)x(2)(m)> / < x(1)(n)> < x(2)(m)>, which do not depend on the dDGLAP evolution, provide particularly convenient measures of the longitudinal correlations between the partons. Such ratios could be probed in future lattice QCD simulations.