Quark distribution inside a pion in many-flavor (2+1)-dimensional QCD using lattice computations: UV listens to IR

We study the changes in the short-distance quark structure of the Nambu-Goldstone boson when the long-distance symmetry-breaking scales are depleted controllably. We achieve this by studying the valence parton distribution function (PDF) of pion in 2 + 1 dimensional two-color QCD, with the number N of massless quarks as the tunable parameter that slides the theory from being strongly broken for N = 0 to the conformal window for N > 4, where the theory is gapped by the fixed finite volume. We perform our study nonperturbatively using lattice simulations with N = 0, 2, 4, 8 flavors of nearly massless two-component Wilson-Dirac sea quarks and employ the leading-twist formalism (LaMET/SDF) to compute the PDF of pion at a fixed valence mass. We find that the relative variations in the first few PDF moments are only mild compared to the changes in decay constant, but the shape of the reconstructed x-dependent PDF itself dramatically changes from being broad in the scale-broken sector to being sharply peaked in the near-conformal region, best reflected in PDF shape observables such as the cumulants.

Automated summary

In this study, changes in the short-distance quark structure of the Nambu-Goldstone boson were investigated in the context of 2+1 dimensional two-color QCD. It was found that the shape of the valence parton distribution function of the pion dramatically changed from being broad in the scale-broken sector to being sharply peaked in the near-conformal region, with relatively mild variations in the first few PDF moments compared to the changes in decay constant.