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

摘要

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_z~2 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.