<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>-odd gluonic operators in QCD spin physics
Yoshitaka Hatta
Abstract
We explore connections between high energy QCD spin physics and $CP$-odd scalar gluonic operators ${\stackrel{\texttildelow{}}{F}}^{\ensuremath{\mu}\ensuremath{\nu}}{F}_{\ensuremath{\mu}\ensuremath{\nu}}$ and ${\stackrel{\texttildelow{}}{F}}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\alpha}}{F}_{\ensuremath{\alpha}}^{\ensuremath{\nu}}$, the latter being called the Weinberg operator in the context of the nucleons' electric dipole moment. We first introduce the twist-four generalized parton distribution associated with the topological operator ${F}_{\ensuremath{\mu}\ensuremath{\nu}}{\stackrel{\texttildelow{}}{F}}^{\ensuremath{\mu}\ensuremath{\nu}}$. This has interesting applications in spin physics which go beyond the standard framework in terms of twist-two and twist-three distributions. In the second part, we show that the off-forward matrix element of the Weinberg operator is proportional to a certain twist-four correction to the ${g}_{1}$ structure function in polarized deep inelastic scattering.