Lattice study of semileptonic form factors with twisted boundary conditions

Abstract

We apply twisted boundary conditions to lattice QCD simulations of three-point correlation functions in order to access spatial components of hadronic momenta different from the integer multiples of $2\ensuremath{\pi}/L$. We calculate the vector and scalar form factors relevant to the $K\ensuremath{\rightarrow}\ensuremath{\pi}$ semileptonic decay and consider all the possible ways of twisting one of the quark lines in the three-point functions. We show that the momentum shift produced by the twisted boundary conditions does not introduce any additional noise and easily allows us to determine within a few percent of statistical accuracy the form factors at quite small values of the four-momentum transfer, which are not accessible when periodic boundary conditions are considered. The use of twisted boundary conditions turns out to be crucial for a precise determination of the form factor at zero-momentum transfer, when a precise lattice point sufficiently close to zero-momentum transfer is not accessible with periodic boundary conditions.