Forward Compton Scattering with weak neutral current: constraints from sum rules

TL;DR

This paper extends the theory of forward Compton scattering to include weak neutral currents, deriving new sum rules and applying them to constrain the dispersive gamma-Z box correction to the proton's weak charge.

Contribution

It introduces a generalized forward Compton amplitude with weak interactions, formulates related sum rules, and applies them to improve constraints on the proton's weak charge correction.

Findings

Derived new sum rules relating weak and electromagnetic structure functions.

Proposed a sum rule linking nucleon axial charge and magnetic moment to structure functions.

Provided constraints on the gamma-Z box correction to the proton's weak charge.

Abstract

We generalize forward real Compton amplitude to the case of the interference of the electromagnetic and weak neutral current, formulate a low-energy theorem, relate the new amplitudes to the interference structure functions and obtain a new set of sum rules. We address a possible new sum rule that relates the product of the axial charge and magnetic moment of the nucleon to the 0th moment of the structure function $g_5(\nu,0)$. We apply the GDH and the finite energy sum rule for constraining the dispersive $\gamma Z$-box correction to the proton's weak charge.