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We compute the second moments of pion and rho parton distribution functions(PDFs) in lattice QCD with $N_f = 2+1$ flavors of improved Wilson fermions. Wedetermine both singlet and non-singlet flavor combinations and, for the firsttime, take disconnected contributions fully into account. In the case of therho, we also calculate the additional contribution arising from the $b_1$structure function. The numerical analysis includes 26 ensembles, mainlygenerated by the CLS effort, with pion masses ranging from 420MeV down to214MeV and with 5 different lattice spacings in the range of 0.1fm to 0.05fm.This enables us to take the continuum limit, as well as to resolve the quarkmass dependencies reliably. Additionally we discuss the contaminations of rhocorrelation functions by two-pion states.

Mellin moments of spin dependent and independent PDFs of the pion and rho meson