Controlling unwanted exponentials in lattice calculations of radiative leptonic decays

Abstract

Two important sources of systematic errors in lattice QCD calculations of radiative leptonic decays are unwanted exponentials in the sum over intermediate states and unwanted excited states created by the meson interpolating field. Performing the calculation using a 3d sequential propagator allows for better control over the systematic uncertainties from intermediate states, while using a 4d sequential propagator allows for better control over the systematic uncertainties from excited states. We calculate form factors using both methods and compare how reliably each controls these systematic errors. We also employ a hybrid approach involving global fits to data from both methods.

Isospin-breaking corrections to weak decays: the current status and a new infrared improvement

“…This contribution has been studied in refs. [39][40][41][42][43][44][45] and it is relevant for decays of pions and kaons into electrons or decays of heavy mesons, while it can be neglected in the calculations of 𝜋 𝜇2 and 𝐾 𝜇2 . This method has been applied to two different numerical calculations, first by the RM123S group to the rates of 𝜋 𝜇2 and 𝐾 𝜇2 [30,31], and more recently by the RBC/UKQCD collaboration to the ratio Γ(𝐾 𝜇2 )/Γ(𝜋 𝜇2 ) [32].…”