[Paper Review] On calculating disconnected-type hadronic light-by-light scattering diagrams from lattice QCD

Masashi Hayakawa, Thomas Blum+4 more|arXiv (Cornell University)|Nov 4, 2015

Particle physics theoretical and experimental studies2 references3 citations

TL;DR

This paper presents a nonperturbative QED method to compute disconnected-type hadronic light-by-light scattering (HLbL) diagrams in lattice QCD, addressing the critical challenge of double-counting O(α³) hadronic vacuum polarization (HVP) contributions. By explicitly subtracting unwanted HVP terms through a newly defined kernel operator (−K_D), the method enables first-principles, controlled calculations of HLbL contributions essential for precision tests of the muon g−2 within the Standard Model.

ABSTRACT

For reliable comparison of the standard model prediction to the muon g-2 with its experimental value, the hadronic light-by-light scattering (HLbL) contribution must be calculated by lattice QCD simulation. HLbL contribution has many types of disconnected-type diagrams. Here, we start with recalling the point that must be taken care of in every method to calculate them by lattice QCD, and present one concrete method called nonperturbative QED method.

Motivation & Objective

• To address the critical theoretical uncertainty in the Standard Model prediction of the muon g−2, particularly from the hadronic light-by-light (HLbL) scattering contribution.
• To develop a reliable lattice QCD method for computing disconnected-type HLbL diagrams, which are challenging due to noise and double-counting issues.
• To ensure that O(α³) hadronic vacuum polarization (HVP) contributions are explicitly subtracted to avoid double counting in the final HLbL amplitude.
• To present a concrete, nonperturbative QED-based method that corrects for spurious HVP contributions arising from disconnected quark contractions.

Proposed method

• The method employs a dynamical QCD+QED simulation framework, where quarks and photons are treated as quantum degrees of freedom on the lattice.
• It introduces a kernel operator (−K_D) to subtract unwanted O(α³) HVP contributions that arise from disconnected contractions in the HLbL amplitude.
• The subtraction is achieved by identifying and canceling HVP contributions that originate from fully red (QED-averaged) quark loops, which are not part of the true HLbL amplitude.
• The method ensures that only the genuine, disconnected HLbL contributions remain by verifying that the unwanted diagrams (Fig. 12) are canceled exactly via the kernel operator.
• It builds on and improves a prior proposal [5] by explicitly accounting for the degeneracy and topology of unwanted diagrams, ensuring consistency across all disconnected-type diagrams.

Experimental results

Research questions

• RQ1 How can disconnected-type hadronic light-by-light scattering diagrams be computed in lattice QCD without double-counting O(α³) hadronic vacuum polarization contributions?
• RQ2 What is the correct way to subtract spurious HVP terms that arise from disconnected contractions in the HLbL amplitude?
• RQ3 Can a nonperturbative QED method be constructed that systematically removes unwanted contributions while preserving the full nonperturbative QCD dynamics?
• RQ4 How can the kernel operator (−K_D) be defined such that it exactly cancels the unwanted O(α³) HVP contributions across all disconnected diagram topologies?

Key findings

• The nonperturbative QED method successfully isolates genuine disconnected HLbL contributions by explicitly subtracting O(α³) HVP terms that would otherwise lead to double counting.
• The method verifies that the unwanted HVP contributions (Fig. 12) appear with identical degeneracy and topology, ensuring exact cancellation when combined with the kernel operator (−K_D).
• The subtraction mechanism is robust across all disconnected-type diagrams, including (2_E, 2)-type and other topologies, by ensuring that only HVP contributions from fully red quark loops are removed.
• The approach provides a systematic, first-principles framework for computing HLbL contributions in lattice QCD, essential for reducing theoretical uncertainty in the muon g−2 prediction.
• The method is validated by showing that the kernel (−K_D) reproduces the exact set of unwanted diagrams, confirming that the subtraction is both necessary and sufficient.