Nucleon generalized form factors from two-flavor lattice QCD

Abstract

We determine the generalized form factors, which correspond to the second Mellin moment (i.e., the first x-moment) of the generalized parton distributions of the nucleon at leading twist. The results are obtained using lattice QCD with N f = 2 nonperturbatively improved Wilson fermions, employing a range of quark masses down to an almost physical value with a pion mass of about 150 MeV. We also present results for the isovector quark angular momentum and for the first xmoment of the transverse quark spin density. We compare two different fit strategies and find that directly fitting the ground state matrix elements to the functional form expected from Lorentz invariance and parametrized in terms of form factors yields comparable, and usually more stable results than the traditional approach where the form factors are determined from an overdetermined linear system based on the fitted matrix elements.

Strong QCD from Hadron Structure Experiments

“…GPDs are encoded in the off-forward matrix elements of two currents separated along the light cone. The formulation of lattice QCD in Euclidean space precludes their direct calculation, and therefore the approach of exploiting the operator product expansion to express the moments with respect to Bjorken x as the matrix elements of local operators that are accessible to calcula-tion on a Euclidean lattice, yielding Generalized Form Factors [182][183][184][185]. These computations have provided important information on the three-dimensional imaging of the nucleon, notably in the decomposition of angular momentum within the nucleon [182,183].…”

Moments of nucleon isovector structure functions in 2+1+1 -flavor QCD

“…The central value from χQCD [34], using partially quenched analysis, is smaller but consistent within 1σ. Results for the momentum fraction and the helicity moment from RQCD 18 [35] are taken from their Set A with the difference between Set A and B values quoted as a second systematic uncertainty. Their result for the transversity moment is from a single 150 MeV ensemble.…”

Distillation at High-Momentum

“…mentum ranges were chosen to emphasize that, although one would naively expect eigenvectors modified according to (5) to have optimal overlap with momenta ap z = 3 (2π/L) and ( 6) with ap z = 6 (2π/L), a broad coverage in momentum is possible within each modified space, thereby obviating the need to use many distillation bases each with its own computational cost.…”

“…This robust momentum-smearing technique is now ubiquitous in lattice studies that demand a wide range of momenta, such as the mapping of nucleon electromagnetic form factors (FFs) [4], generalized FFs [5], and semi-leptonic decay FFs needed to quantify elements of the Cabibbo-Kobayashi-Maskawa matrix [6,7]. Perhaps the greatest usage has been seen in LQCD calculations of matrix elements of certain non-local space-likeseparated operators, which when computed over a range of momenta can be related to various light-cone distributions fundamental to hadron structure.…”