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

TL;DR

This study calculates the second moments of pion and rho meson PDFs using lattice QCD, including disconnected contributions and continuum extrapolation, providing new insights into meson structure.

Contribution

First comprehensive lattice QCD calculation of second moments of pion and rho PDFs including disconnected diagrams and rho's $b_1$ structure function.

Findings

Computed second moments for pion and rho PDFs.

Included disconnected contributions for the first time.

Analyzed quark mass dependence and continuum limit.

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 non-singlet 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 $b_1$ structure function. The numerical analysis includes 26 ensembles, mainly generated by the CLS effort, with pion masses ranging from 420MeV down to 214MeV 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 quark mass dependencies reliably. Additionally we discuss the contaminations of rho correlation functions by two-pion states.