5 research outputs found
Studying Spin-Orbit Dynamics using Measurements of the Proton's Polarized Gluon Asymmetry
Measurements involving the gluon spin density, Delta G=G++ - G+-, can play an
important role in the quantitative understanding of proton structure. To
demonstrate this, we show that the shape of the gluon asymmetry, A(x,t)=Delta
G(x,t)/G(x,t), contains significant dynamical information about
non-perturbative spin-orbit effects. It is instructive to use a separation
A(x,t)=A_0^epsilon(x)+epsilon(x,t), where A_0^epsilon(x) is an approximately
scale-invariant form that can be calculated within a given factorization
prescription from the measured distributions Delta q(x,t), q(x,t) and G(x,t).
Applying this separation with the J_z=1/2 sum rule provides a convenient way to
determine the total amount of orbital angular momentum generated by mechanisms
associated with confinement and chiral dynamics. The results are consistent
with alternate non-perturbative approaches to the determination of orbital
angular momentum in the proton. Our studies help to specify the accuracy that
future measurements should achieve to constrain theoretical models for nucleon
structure.Comment: 24 pages, 3 figure
Shape invariance and the exactness of quantum Hamilton-Jacobi formalism
Quantum Hamilton-Jacobi Theory and supersymmetric quantum mechanics (SUSYQM)
are two parallel methods to determine the spectra of a quantum mechanical
systems without solving the Schr\"odinger equation. It was recently shown that
the shape invariance, which is an integrability condition in SUSYQM formalism,
can be utilized to develop an iterative algorithm to determine the quantum
momentum functions. In this paper, we show that shape invariance also suffices
to determine the eigenvalues in Quantum Hamilton-Jacobi Theory.Comment: Accepted for publication in Phys. Lett.