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

Abstract

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. We determine both singlet and nonsinglet flavor combinations and, for the first time, take disconnected contributions fully into account. In the case of the rho, we also calculate the additional contribution arising from the b1 structure function. The numerical analysis includes 26 ensembles, mainly generated by the CLS effort, with pion masses ranging from 420 MeV down to 214 MeV and with 5 different lattice spacings in the range of 0.1 fm to 0.05 fm. This enables us to take the continuum limit, as well as to resolve the quark mass dependencies reliably. Additionally we discuss the contaminations of rho correlation functions by two-pion states.

Quark and gluon momentum fractions in the pion from $N_f=2+1+1$ lattice QCD

“…[44,45] we find reasonable agreement within relatively large uncertainties. Comparing to the only other lattice QCD computation [20] including quark disconnected contributions, but not the mixing and the gluon contribution, we observe a deviation well ouside uncertainties. Future plans include determining x in the pion for two more lattice spacing values directly at the physical point.…”

“…Most of the computations available so far [12][13][14][15][16][17][18][19] neglect potentially important contributions, the so-called quark disconnected contributions. While we were finalising the present work a first com-putation including disconnected contributions was put forward [20]. Also for the gluon contributions there exists only a single computation and only in the quenched approximation [21].…”

“…The only other lattice result was presented in Ref. [20], where N f = 2 + 1 flavour QCD was used and results have been extrapolated to the continuum and the physical point. However, the gluon contribution has not been computed and, thus, the mixing could not be taken into account.…”