Orbital angular momentum in the pion and kaon: rest-frame and light-front

TL;DR

This paper investigates the observer-dependent nature of orbital angular momentum in hadrons like pions and kaons within quantum chromodynamics, revealing significant intrinsic OAM components that influence their structure and observable properties.

Contribution

It demonstrates the subjective character of in-hadron OAM and quantifies its impact on pion and kaon wave functions using continuum Schwinger methods.

Findings

Pion has ~50/50 mix of OAM zero and one components.

Kaon has ~60/40 OAM component distribution.

Intrinsic OAM is significant in Nambu-Goldstone modes and affects observables.

Abstract

Orbital angular momentum (OAM) is not a Poincar\'e invariant quantity; so, its value is observer dependent. Notwithstanding that, in quantum chromodynamics, a Poincar\'e-invariant theory, OAM is part of every hadron wave function. Using continuum Schwinger function methods, we elucidate both the subjective character of in-hadron OAM and expose some of its impacts on pion and kaon structure and observables. For instance, working with light-front projections of their Bethe-Salpeter wave functions, it is found that the pion is a roughly 50/50 mix of light-front OAM zero and one components and the kaon is a 60/40 system. The overall picture is that (near) Nambu-Goldstone modes are complex bound states, each with significant intrinsic OAM, independent of the observer's reference frame. This feature must be accounted for in the calculation of observables. Inductively, the same is true for all hadrons.