Spin-1 quarkonia in a rotating frame and their spin contents

TL;DR

This paper introduces a novel approach to analyze the spin structure of spin-1 quarkonia by examining their response in a rotating frame, revealing nuanced spin contributions beyond the naive quark model.

Contribution

It presents a relativistic formalism linking spin-rotation coupling with total spin, providing new insights into the spin content of vector and axial vector quarkonia.

Findings

The spin contents of $J/\psi$, $\chi_{c1}$, $\Upsilon(1S)$, and $\chi_{b1}$ differ from naive expectations.

Both perturbative and non-perturbative contributions follow a universal spin-rotation coupling formula.

Quarks do not carry all of the total spin in these quarkonia.

Abstract

We propose a new way of studying the spin content of a hadron by looking at its response in a rotating frame. By collecting all responses of quarks and gluons in a rotating frame, we describe the spin-rotation coupling of spin-1 quarkonia and thereby reveal their spin contents in a relativistic formalism. We demonstrate that both the perturbative and non-perturbative contributions in the operator product expansion follow a universal formula that identifies the spin-rotation coupling with unit strength. This allows us to recognize the total spin-1 of the vector and axial vector quarkonia in terms of the total angular momentum of quarks and gluons. Specifically, we find the spin contents of $J/\psi$, $\chi_{c1}$, $\Upsilon(1S)$, and $\chi_{b1}$ are slightly different from the naive quark model picture. For example, the $J/\psi$ is traditionally considered as an S-wave particle, but we find quarks do not carry all of the total spin.