Although equivalent in the infinite-momentum limit,large-momentum effective theory(LaMET)and short-distance operator product expansion(SDE)are 2 very different approaches to obtain parton distribution functions(PDFs)f...Although equivalent in the infinite-momentum limit,large-momentum effective theory(LaMET)and short-distance operator product expansion(SDE)are 2 very different approaches to obtain parton distribution functions(PDFs)from coordinate-space correlation functions computed in a large-momentum proton through lattice quantum chromodynamics(QCD).LaMET implements a momentum-space expansion inΛ_(QCD)[/x(1-x)P^(z)]to directly calculate PDFs f(x)in a middle region of Bjorken x∈[x_(min)~Λ_(QCD)/xP^(z)x_(max)~1-x_(min)].SDE applies perturbative QCD at small Euclidean distances z to extract a range[0,λ_(max)]of leading-twist correlations,h(λ=zP^(z)),corresponding to the Fourier transformation of PDFs.An incomplete leading-twist correlation from SDE cannot be readily converted to a momentum-space distribution,and solving its constraints on the PDFs(or the so-called"inverse problem")involves phenomenological modeling of the missing information beyondλ_(max)and has no systematic control of errors.I argue that the best use of short-distance correlations is to constrain the PDFs in the LaMET-complementary regions:x∈[0,x_(min)]and[x_(max),1]through expected end-point asymptotics,and use the results of the pion valence quark distribution from the ANL/BNL collaboration to demonstrate how this can be done.展开更多
基金supported by the Maryland Center for Fundamental Physics,University of Maryland.
文摘Although equivalent in the infinite-momentum limit,large-momentum effective theory(LaMET)and short-distance operator product expansion(SDE)are 2 very different approaches to obtain parton distribution functions(PDFs)from coordinate-space correlation functions computed in a large-momentum proton through lattice quantum chromodynamics(QCD).LaMET implements a momentum-space expansion inΛ_(QCD)[/x(1-x)P^(z)]to directly calculate PDFs f(x)in a middle region of Bjorken x∈[x_(min)~Λ_(QCD)/xP^(z)x_(max)~1-x_(min)].SDE applies perturbative QCD at small Euclidean distances z to extract a range[0,λ_(max)]of leading-twist correlations,h(λ=zP^(z)),corresponding to the Fourier transformation of PDFs.An incomplete leading-twist correlation from SDE cannot be readily converted to a momentum-space distribution,and solving its constraints on the PDFs(or the so-called"inverse problem")involves phenomenological modeling of the missing information beyondλ_(max)and has no systematic control of errors.I argue that the best use of short-distance correlations is to constrain the PDFs in the LaMET-complementary regions:x∈[0,x_(min)]and[x_(max),1]through expected end-point asymptotics,and use the results of the pion valence quark distribution from the ANL/BNL collaboration to demonstrate how this can be done.
