Sea-quark loop contributions to the $\bar d$-$\bar u$ asymmetry in the proton

TL;DR

This paper examines how sea-quark loop contributions, including unphysical ones, influence the observed asymmetry between anti-down and anti-up quarks in the proton, highlighting a 12% enhancement from physical sea-quark loops.

Contribution

It clarifies the role of unphysical sea-quark loop contributions and demonstrates their cancellation, emphasizing the significance of physical sea-quark loops in the $ar d - ar u$ asymmetry.

Findings

Unphysical contributions cancel out when considering physical baryons.

Physical sea-quark loops contribute significantly to the asymmetry.

Sea-quark loop contributions enhance the asymmetry by 12%.

Abstract

QCD interactions for equal-mass fermion flavors are flavor blind. This fact is often used to state that disconnected sea-quark loop contributions are equal for $u$ and $d$ quarks in the mass symmetric case and therefore these disconnected sea-quark loop contributions cannot contribute to the well-known $\bar d - \bar u$ asymmetry in the proton. Instead, it is argued that one must look to the connected sector of lattice QCD correlation functions to find this difference. In this presentation, we note that these statements are true provided unphysical contributions in the sea-quark loop sector are included, contributions from baryons that do not appear in the physical spectrum. To respect the Pauli principle, these unphysical contributions from the disconnected sea-quark loop sector must cancel equally unphysical contributions in the connected sector. The remaining disconnected sea-quark loop contributions no longer have a balance between $\bar d$ and $\bar u$. Upon considering only physically observed baryons in the loop contributions, we illustrate an important contribution from the sea-quark loop sector to $\bar d - \bar u$ that enhances the leading connected contribution by 12\%.