Toward a First-Principles Calculation of Electroweak Box Diagrams.

Area of Science:

• Nuclear Physics
• Quantum Chromodynamics
• Particle Physics

Background:

• The γW and γZ box diagrams are essential for precision physics but suffer from large hadronic uncertainties.
• Accurate theoretical calculations are needed to determine fundamental parameters like CKM matrix elements and the weak mixing angle.

Purpose of the Study:

• To derive a novel Feynman-Hellmann theorem relating nucleon energy shifts to the parity-odd nucleon structure function F_{3}^{N}.
• To provide a method for simplifying the computation of inputs for the γW and γZ box diagrams.

Main Methods:

• Derivation of a Feynman-Hellmann theorem.
• Relating second-order nucleon energy shifts to electromagnetic and isovector axial currents.
• Connecting these shifts to the parity-odd nucleon structure function F_{3}^{N}.

Main Results:

• A new theorem is established, linking energy shifts to the structure function F_{3}^{N}.
• The method demonstrates that only a few energy shifts are needed for a given Q^{2} to obtain box diagram inputs.
• This approach significantly reduces the computational complexity.

Conclusions:

• The derived theorem offers a more efficient way to calculate inputs for the γW and γZ box diagrams.
• Future lattice calculations using this theorem can improve precision in determining fundamental constants.
• This work has implications for refining measurements of CKM matrix elements and the weak mixing angle.