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.
Highlights
Over the last three decades we have had an extraordinary conceptual, algorithmic and technical progress in numerical lattice gauge theory which have led to the simulation of Quantum Chromodynamics (QCD) with quark masses at the physical point, see Ref. [1] for a recent review
The thickness ∆ of the overlapping region regulates the rate of convergence of the associated Neumann series, making Schwarz alternating procedure (SAP) with overlapping domains a valid alternative for computing the quark propagator in lattice QCD with respect to the case of non-overlapping domains4 [21]
No attempt was made to reach the value of n1 at which the reduction of the variance starts to slow down. These results suggest that, when applied to full QCD with light quark masses, the two-level integration can solve the problem of large statistical errors in the lattice determination of the hadron contributions to the muon g − 2
Summary
Over the last three decades we have had an extraordinary conceptual, algorithmic and technical progress in numerical lattice gauge theory which have led to the simulation of Quantum Chromodynamics (QCD) with quark masses at the physical point, see Ref. [1] for a recent review. This problem afflicts many computations at the forefront of research in lattice QCD: the hadronic vacuum polarization and light-by-light scattering contributions to the muon g − 2, the amplitudes of leptonic and semileptonic B decays, masses and matrix elements of (multi) baryons states, etc. The multi-level Monte Carlo integration takes advantage of the fact that, when the action and the observables depend locally on the integration variables, the degradation of the signal-to-noise ratio with the distance of the sources can be avoided by measuring independently the local building blocks of the observables This leads to an impressive acceleration of the simulations [4,5,6,7,8,9], and fully solves the problem in some cases. In the remaining part of this section we list some examples which at present are the object of an intense theoretical and experimental research activity
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