Variance-Reduction Techniques for Disconnected Isospin-Breaking QED Corrections

Sub-percent calculations of an increasing number of physical observables are within the reach of modern Lattice QCD. In order to achieve such precision, we must include the (typically) O(1%) corrections from isospin-breaking contributions in our calculations. These corrections include disconnected diagrams, which can be prohibitively expensive to resolve using standard techniques.

In this talk, I will discuss ongoing efforts to calculate several disconnected topologies relevant at O(alpha) to e.g. Kl2 decays, on RBC-UKQCD physical-point domain-wall ensembles, following on from exploratory calculations [1]. We make use of the ‘split-even’ estimator [1, 2], which can improve statistical errors by an order of magnitude or more, and explore the use of a distance-splitting technique [1] to take advantage of the dominant short-distance behaviour of some topologies. These techniques are applicable beyond disconnected diagrams, and might improve statistical errors in many contractions involving noisy loop estimators. I will explore the potential to make great improvements on the statistical error of our previous result for rare K+->Pi+l+l- decays [3] using these techniques.