Abstract
The transversely-polarized state of a proton with arbitrary momentum is not an eigenstate of transverse angular momentum operator. The latter does not commute with the QCD Hamiltonian. However, the expectation value of the transverse angular momentum in the state is well-defined and grows proportionally to the energy of the particle. The transverse spin content of the proton is analyzed in terms of the QCD angular momentum structure. In particular, we reconfirm that the generalized parton distributions H+E provide the leading-twist transverse angular momentum densities of quarks and gluons in the infinite momentum frame.
Highlights
The spin structure of the proton has been an important subject in hadronic physics for more than 30 years
Much of the discussion so far has been focused on the proton helicity, the projection of spin or total angular momentum (AM) along the direction of motion, in a longitudinallypolarized state
We show that canonical AM decomposition in the light-cone gauge A+ = 0 and infinite momentum frame (IMF) gives the same result
Summary
Xiangdong Ji1, 2, ∗ and Feng Yuan3, † 1Center for Nuclear Femtography, SURA, 1201 New York Ave. NW, Washington, DC 20005, USA. The transversely-polarized state of a proton with arbitrary momentum is not an eigenstate of transverse angular momentum operator. The latter does not commute with the QCD Hamiltonian. The expectation value of the transverse angular momentum in the state is well-defined and grows proportionally to the energy of the particle. The transverse spin content of the proton is analyzed in terms of the QCD angular momentum structure. We reconfirm that the generalized parton distributions H + E provide the leading-twist transverse angular momentum densities of quarks and gluons in the infinite momentum frame
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