Nucleon Generalized Parton Distributions from Full Lattice QCD (0705.4295v2)

Abstract: We present a comprehensive study of the lowest moments of nucleon generalized parton distributions in N_f=2+1 lattice QCD using domain wall valence quarks and improved staggered sea quarks. Our investigation includes helicity dependent and independent generalized parton distributions for pion masses as low as 350 MeV and volumes as large as (3.5 fm)^3, for a lattice spacing of 0.124 fm. We use perturbative renormalization at one-loop level with an improvement based on the non-perturbative renormalization factor for the axial vector current, and only connected diagrams are included in the isosinglet channel.

Analysis of Nucleon Generalized Parton Distributions from Full Lattice QCD

The paper, "Nucleon Generalized Parton Distributions from Full Lattice QCD," conducted by the LHPC Collaboration, presents a detailed investigation of nucleon generalized parton distributions (GPDs) using lattice quantum chromodynamics (QCD). This research is notably significant as GPDs offer a critical framework to enhance our understanding of the hadronic structure, encapsulating both position and momentum information of partons inside the nucleon.

The authors employ a sophisticated lattice QCD setup with domain wall valence quarks and improved staggered sea quarks to calculate the lowest moments of nucleon GPDs. The calculation spans a range of pion masses as low as 350 MeV and explores lattice volumes up to (3.5 fm)$^3$, providing a robust and reliable dataset for analysis. The paper uses one-loop level perturbative renormalization techniques with non-perturbative improvement factors to ensure the accuracy and reliability of their results, focusing solely on connected diagrams in the isosinglet channel.

A significant aspect of this work is its focus on both helicity-dependent and independent GPDs, offering a comprehensive view of the nucleon's internal structure. The researchers present lattice data for the unpolarized and polarized GPDs, characterized by moments $n=1, 2, 3$. These moments are systematically explored to paper their dependence on the pion mass and momentum transfer squared ($t$), thereby providing insights into the transverse structure of the nucleon and quark orbital angular momentum.

Key findings in the results include the nuanced behavior of the generalized form factors (GFFs) $A_{20}$, $B_{20}$, and $C_{20}$ as functions of $t$. Notably, the analysis of the transverse size of the nucleon reveals a dependence on the quark's momentum fraction, $x$, with higher moments showing reduced transverse size—consistent with the expected behavior from theory. Further, the GFFs exhibit a trend whereby their slopes become increasingly flatter with larger momentum fractions, suggesting a more localized transverse structure for higher $x$ values.

The paper also engages in chiral extrapolations of the GFFs to the physical pion mass using both heavy baryon and covariant baryon chiral perturbation theory (ChPT), providing a bridge between lattice QCD results and phenomenological data. The extrapolations notably reveal a significant proportion of the nucleon spin being attributed to the orbital angular momentum of the quarks, particularly highlighting the sizable, albeit opposite, contributions from up and down quark orbital angular momentum that nearly cancel each other.

The implications of these results are multifold, reaffirming the non-trivial structure of the nucleon inclusive of substantial orbital angular momentum contributions. The findings align well with phenomenological PDF data, such as those from CTEQ and MRST, reinforcing the validity of the lattice QCD methodology in unraveling the intricate features of nucleonic structure.

Future directions of the research are expected to focus on refinement of the computational models, inclusion of disconnected diagrams, and running simulations at even lower pion masses to further close the gap with experimental observations. This paper represents a significant step in connecting theoretical lattice QCD calculations with empirical data, enhancing our fundamental understanding of the nucleon's partonic composition in realms unexplored by conventional means.