Quantifying finite-momentum effects in the quark quasidistribution functions of mesons

Abstract

The recently proposed large momentum effective theory (LaMET) of Ji [1] has led to a burst of activity among lattice practitioners to perform and control the first pioneering calculations of the quasi-PDFs of the nucleon. These calculations represent approximations to the standard, exact PDFs defined as correlation functions of fields with lightlike separation, being instead correlations along a longitudinal direction of the operator γ z ; as such, they differ from standard PDFs by a perturbative matching condition with powersuppressed 1=p 2 z corrections, becoming exact in the limit p z → ∞. Investigating the systematics of this behavior thus becomes crucial to understanding the validity of LaMET calculations. While this has been done using models for the nucleon, an analogous dedicated study has not been carried out for the π and ρ valence quark distribution functions. Using a constituent quark model, a systematic calculation is performed to estimate the size and x dependence of the finite-p z effects in these quasi-PDFs, finding them to be potentially tamer for lighter mesons than for the collinear quasi-PDFs of the nucleon.

Exploring twist-2 GPDs through quasidistributions in a diquark spectator model

“…In particular, the first lattice QCD results for quasi-PDFs and related quantities can be considered milestones in this field [15,24,25,28,. Additionally, the convergence of quasi-PDFs to the corresponding standard PDFs has been explored in several models [83][84][85][86][87][88][89][90]. The progress in this field was recently reviewed in Refs.…”

Generalized quasi parton distributions in a diquark spectator model

“…In particular, the first encouraging lattice results for quasi-PDFs and similar quantities became available [15,23,24,27,[52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67]. Moreover, several model calculations of quasi-PDFs have been carried out [68][69][70][71][72][73][74]. These studies have largely focused on how well, for a given model, the quasi-PDFs describe the corresponding standard GPDs as functions of P 3 .In the first paper on quasi-PDFs it has already been suggested that generalized parton distributions (GPDs) could also be studied by means of spatial correlation functions (quasi-GPDs) [3].…”

Charting the coming synergy between lattice QCD and high-energy phenomenology

“…A consequence specific to lattice QCD is the fact that contributions from disconnected insertions vanish in the difference (assuming parton-level charge symmetry), and a much less computationally costly calculation based purely on connected insertions is generally adequate. For this main reason, the isovector combinations have been a focus of lattice calculations for both the PDF Mellin moments-and, more recently, the quasidistributions in both the nucleon [48][49][50][51][52][53] and the pion [54][55][56][57].…”