Kl3 and pion form factors using partially twisted boundary conditions

TL;DR

This paper calculates Kl3 and pion form factors directly at zero momentum transfer using partially twisted boundary conditions, enabling precise determination of these quantities without interpolation, on a lattice with Domain Wall Fermions.

Contribution

It introduces a method to compute form factors directly at q^2=0 using partially twisted boundary conditions, improving accuracy and efficiency over traditional interpolation methods.

Findings

Pion charge radius at 330 MeV pion mass: 0.354(31) fm^2.

Kl3 form factor at q^2=0: 0.9742(41), consistent with previous results.

Method reduces systematic errors associated with q^2 interpolation.

Abstract

We compute the Kl3 and pion form factors using partially twisted boundary conditions. The twists are chosen so that the Kl3 form factors are calculated directly at zero momentum transfer (q^2=0), removing the need for a q^2 interpolation, while the pion form factor is determined at values of q^2 close to q^2=0. The simulations are performed on an ensemble of the RBC/UKQCD collaboration's gauge configurations with Domain Wall Fermions and the Iwaski gauge action with an inverse lattice spacing of 1.73(3) GeV. Simulating at a single pion mass of 330 MeV, we find the pion charge radius to be < r^2>_{330 MeV}=0.354(31) fm^2 which, using NLO SU(2) chiral perturbation theory, translates to a value of <r_\pi^2>=0.418(31) fm^2 for a physical pion. For the value of the Kl3 form factor, f_{K\pi}^+(q^2), determined directly at q^2=0, we find a value of f_{K\pi}^+(0)=0.9742(41) at this particular quark mass, which agrees well with our earlier result (0.9774(35)) obtained using the standard, indirect method.