Towards a Real-Time Computation of Timelike Hadronic Vacuum Polarization and Light-by-Light Scattering: Schwinger Model Tests

TL;DR

This paper explores a novel approach using the Schwinger Model and tensor network techniques to compute hadronic vacuum polarization and light-by-light scattering, aiming to improve Standard Model predictions for the muon's magnetic moment.

Contribution

It introduces a new methodology employing 1+1D QED, tensor networks, and quantum emulators to study HVP and HLBL, facilitating future quantum computing applications.

Findings

Feasibility demonstrated in a simplified 1+1D model.

Tensor network methods successfully used for calculations.

Lays groundwork for future quantum computing implementations.

Abstract

Hadronic vacuum polarization (HVP) and light-by-light scattering (HLBL) are crucial for evaluating the Standard Model predictions concerning the muon's anomalous magnetic moment. However, direct first-principle lattice gauge theory-based calculations of these observables in the timelike region remain challenging. Discrepancies persist between lattice quantum chromodynamics (QCD) calculations in the spacelike region and dispersive approaches relying on experimental data parametrization from the timelike region. Here, we introduce a methodology employing 1+1-dimensional quantum electrodynamics (QED), i.e. the Schwinger Model, to investigate the HVP and HLBL. To that end, we use both tensor network techniques, specifically matrix product states, and classical emulators of digital quantum computers. Demonstrating feasibility in a simplified model, our approach sets the stage for future endeavors leveraging digital quantum computers.