Quark structure of hadrons from lattice QCD

W. Detmold, W. Melnitchouk (JLab) and A.W. Thomas (Adelaide)

Information about the quark substructure of a given hadron, $h$, is contained in its so-called quark distribution functions, $q^h(x)$ (where $q=u,\bar{u},d,\bar{d},s,\ldots$ and Bjorken $x$ is the longitudinal momentum fraction of the struck quark). Forward matrix elements of certain local operators, ${\cal O}^{(n)}$, correspond to the Mellin moments of these distributions and their spin dependent analogues.

Lattice QCD provides a first principles approach to the calculation of such matrix elements. However current lattice simulations involve various approximations, one of which is that the quark masses that are used are at least a factor of 5-10 too large. This approximation is made because the computational resources required by lattice calculations increase very rapidly as the quark masses used in them decrease. Consequently, an extrapolation must be made in the quark mass to connect lattice results to experimental determinations of the moments. This is complicated by the fact that as the masses decrease, pion (pseudo-Goldstone boson) loops give rise to variation of the moments that is non-analytic in the quark mass. This rapidly varying behavior can be studied in chiral perturbation theory [16] and when it is incorporated taking in to account the finite size of the hadron leads to good agreement with experimental data [17].

Our previous calculations for the various isovector valence quark distributions of the nucleon have recently been extended to the case of the pion [18]. Additionally, the reconstruction of the $x$-dependence of the underlying quark distributions from their moments was examined. Our analysis indicates that the next generation of lattice simulations may provide insight into the puzzling discrepancy of the large $x$ behavior of experimental (Drell-Yan) data on the pion quark distribution with the expectations of hadron helicity conservation.