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

By studying the spin-1 system composed of a heavy quark and its anti-quark in a rotating frame, we investigate its spin-rotation coupling and thereby reveal the spin contents of the spin-1 quarkonia. We demonstrate that both the perturbative and non-perturbative contributions in the operator product expansion follow a universal relation that identifies the spin-rotation coupling with unit strength. This allows us to recognize the total spin-1 of the vector quarkonia in terms of the total angular momentum of quarks and gluons. We also find that a similar behavior follows for the axial vector case but identify the different composition of the spin due to the P-wave nature of the state.