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

TL;DR

This study investigates how the internal quark structure of a pion changes as the underlying QCD theory transitions from strong symmetry breaking to near-conformal behavior, using lattice simulations in 2+1 dimensions with varying quark flavors.

Contribution

It provides the first non-perturbative lattice analysis of pion PDFs across different flavor numbers in 2+1D QCD, revealing significant shape changes in the PDFs.

Findings

PDF shape becomes sharply peaked near the conformal window

First few PDF moments vary mildly with flavor number

Decay constant shows more variation than PDF moments

Abstract

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 non-perturbatively 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.