Critique of the angular momentum sum rules and a new angular momentum sum rule

A critique of the angular momentum sum rules and a new angular momentum sum rule

We present a study of the tensorial structure of the hadronic matrix elements of the angular momentum operators J . Well known results in the literature are shown to be incorrect, and we have taken pains to derive the correct expressions in three different ways, two involving explicit physical wave packets and the third, totally independent, based upon the rotational properties of the state vec...

The Gauge-Invariant Angular Momentum Sum-Rule for the Proton

We give a gauge-invariant treatment of the angular momentum sum-rule for the proton in terms of matrix elements of three gauge-invariant, local composite operators. These matrix elements are decomposed into three independent form factors, one of which is the flavour singlet axial charge. We further show that the axial charge cancels out of the sum-rule, so that it is unaffacted by the axial ano...

Cluster sum rules for three - body systems with angular - momentum dependent interactions

We derive general expressions for non-energy-weighted and energy-weighted cluster sum rules for systems of three charged particles. The interferences between pairs of particles are found to play a substantial role. The energy-weighted sum rule is usually determined by the kinetic energy operator, but we demonstrate that it has similar additional contributions from the angular momentum and parit...

Angular Momentum

Asymptotic Sum Rules at Infinite Momentum

By combining the qO-im method for asymptotic sum rules with the P-CQ method of Fubini and Furlan, we relate the structure functions W2 and WI in inelastic lepton-nucleon scattering to matrix elements of commutators of currents at almost-equal times at infinite momentum. We argue that the infinite momentum limit for these commutators does not diverge but may vanish. If the limit is nonvanishing ...