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We study the changes in the short-distance quark structure of theNambu-Goldstone boson when the long-distance symmetry-breaking scales aredepleted controllably. We achieve this by studying the valence PartonDistribution Function (PDF) of pion in 2+1 dimensional two-color QCD, with thenumber $N$ of massless quarks as the tunable parameter that slides the theoryfrom being strongly broken for $N=0$ to the conformal window for $N>4$, wherethe theory is gapped by the fixed finite volume. We perform our studynon-perturbatively using lattice simulations with $N=0,2,4,8$ flavors of nearlymassless two-component Wilson-Dirac sea quarks and employ the leading-twistformalism (LaMET/SDF) to compute the PDF of pion at a fixed valence mass. Wefind that the relative variations in the first few PDF moments are only mildcompared to the changes in decay constant, but the shape of the reconstructed$x$-dependent PDF itself dramatically changes from being broad in thescale-broken sector to being sharply peaked in the near-conformal region, bestreflected in PDF shape observables such as the cumulants.

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