Small-$x$ Helicity Evolution: an Operator Treatment

Understand

We rederive the small-$x$ evolution equations governing quark helicity distribution in a proton using solely an operator-based approach.

• In our previous works on the subject, the evolution equations were derived using a mix of diagrammatic and operator-based methods.
• In this work, we re-derive the double-logarithmic small-$x$ evolution equations for quark helicity in terms of the "polarized Wilson lines", the operators consisting of light-cone Wilson lines with one or two non-eikonal local operator insertions which bring in helicity dependence.
• For the first time we give explicit and complete expressions for the quark and gluon polarized Wilson line operators, including insertions of both the gluon and quark sub-eikonal operators.