Toward a First-Principles Calculation of Electroweak Box Diagrams

Abstract

We derive a Feynman-Hellmann theorem relating the second-order nucleon energy shift resulting from the introduction of periodic source terms of electromagnetic and isovector axial currents to the parity-odd nucleon structure function $F_3^N$. It is a crucial ingredient in the theoretical study of the $\gamma W$ and $\gamma Z$ box diagrams that are known to suffer from large hadronic uncertainties. We demonstrate that for a given $Q^2$, one only needs to compute a small number of energy shifts in order to obtain the required inputs for the box diagrams. Future lattice calculations based on this approach may shed new light on various topics in precision physics including the refined determination of the Cabibbo-Kobayashi-Maskawa matrix elements and the weak mixing angle.

arXiv commentVersion to appear in PRL

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• First-principles calculation of electroweak box diagrams from lattice QCD
• Dispersion relation analysis of the radiative corrections to $g_A$ in the neutron $\beta$-decay
• Lattice QCD evaluation of the Compton amplitude employing the Feynman-Hellmann theorem
• Lattice QCD calculation of the electroweak box diagrams for the kaon semileptonic decays
• Vector-like Quark Interpretation for the CKM Unitarity Violation, Excess in Higgs Signal Strength, and Bottom Quark Forward-Backward Asymmetry
• New method for calculating electromagnetic effects in semileptonic beta-decays of mesons
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• Gross-Llewellyn Smith sum rule from lattice QCD