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

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.

Towards studying the structural differences between the pion and its radial excitation

“…A better determination of the quark structure of pion is also part of the goals of upcoming experimental facilities [21,22]. In addition to experimental determinations, due to the recent breakthroughs in computing parton structure using the Euclidean lattice QCD simulations via leading-twist perturbative factorization approaches (Large Momentum Effective Theory [23,24], shortdistance factorization of the pseudo distribution [25,26], current-current correlators [27][28][29], which has also been dubbed as good lattice cross sections [29], and Refs [30][31][32][33][34] for extensive reviews on the methodology), the valence quark structure of pion has also been investigated from first-principle QCD computations [35][36][37][38][39][40][41][42]. The large-x behavior of the valence pion PDF has been an unresolved issue that has been approached using all the above lines of attack, with the promise of being settled in the near future by lattice computations with finer lattices, realistic physical pion masses and with the usage of highly boosted pion states to reduce higher-twist effects that might be amplified [43][44][45] near x = 1.…”

Insights into the Emergence of Mass from Studies of Pion and Kaon Structure

“…the ability to vary the underlying theory and its parameters as a means of revealing the emergence of the important physics. A recent example is a study of the pion's valence quark DF in 2 + 1-dimensional two-colour QCD, where varying the number of quark flavours, N , allows an investigation of how meson structure evolves as the theory changes from being one with strongly broken scale invariance at N = 0 to a conformal theory as N is increased [417].…”

Gluon Parton Distribution of the Pion from Lattice QCD

“…Many lattice works have been done on nucleon and meson PDFs, and generalized parton distributions (GPDs) based on the quasi-PDF approach . Alternative approaches to lightcone PDFs in lattice QCD are "good lattice cross sections" [37,[72][73][74][75] and the pseudo-PDF approach [76][77][78][79][80][81][82][83][84][85][86][87][88][89]. However, LQCD calculations of the x dependence of the pion PDFs have only been done for the valence-quark distribution [49,64,74,75,81,90,91].…”