Multi-boson block factorization of fermions

TL;DR

This paper reviews a novel fermion determinant factorization method in lattice QCD that enables multi-level Monte Carlo integration, potentially reducing statistical errors in complex calculations like baryon masses and muon g-2 contributions.

Contribution

It introduces a new fermion determinant factorization approach that creates a local action, facilitating multi-level Monte Carlo methods for fermionic systems in lattice QCD.

Findings

Preliminary results show improved statistical error reduction.

Method enables multi-level Monte Carlo with fermions.

Potential to enhance precision in key QCD observables.

Abstract

The numerical computations of many quantities of theoretical and phenomenological interest are plagued by statistical errors which increase exponentially with the distance of the sources in the relevant correlators. Notable examples are baryon masses and matrix elements, the hadronic vacuum polarization and the light-by-light scattering contributions to the muon g-2, and the form factors of semileptonic B decays. Reliable and precise determinations of these quantities are very difficult if not impractical with state-of-the-art standard Monte Carlo integration schemes. I will review a recent proposal for factorizing the fermion determinant in lattice QCD that leads to a local action in the gauge field and in the auxiliary boson fields. Once combined with the corresponding factorization of the quark propagator, it paves the way for multi-level Monte Carlo integration in the presence of fermions opening new perspectives in lattice QCD. Exploratory results on the impact on the above mentioned observables will be presented.