Lattice study of semileptonic form factors with twisted boundary conditions

TL;DR

This paper demonstrates that twisted boundary conditions in lattice QCD enable precise calculation of semileptonic form factors at small momentum transfers, improving accuracy near zero momentum transfer compared to periodic boundary conditions.

Contribution

It introduces the application of twisted boundary conditions to lattice QCD for better access to small-momentum form factors in semileptonic decays, reducing noise and increasing precision.

Findings

Twisted boundary conditions do not add noise to lattice calculations.

Form factors at small momentum transfer can be determined with a few percent accuracy.

Precise determination of form factors at zero momentum transfer is achieved.

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 pi / L. We calculate the vector and scalar form factors relevant to the K -> 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 to determine within a few percent 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.