Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0812.4265

Kl3 and pion form factors using partially twisted boundary conditions

P. A. Boyle·J. M. Flynn·A. Jüttner·C. Kelly·H. Pedroso de Lima·C. M. Maynard·C. T. Sachrajda·J. M. Zanotti
View original source ↗Read source document ↗Export metadata ↓

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 =0.418(31) fm^2 for a physical pion. For the value of the Kl3 form factor, f_{Kπ}^+(q^2), determined directly at q^2=0, we find a value of f_{Kπ}^+(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.

Explore related subjects

hep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

P. A. Boyle, J. M. Flynn, A. Jüttner, C. Kelly, H. Pedroso de Lima, C. M. Maynard, C. T. Sachrajda, J. M. Zanotti. 2008-12-22. Kl3 and pion form factors using partially twisted boundary conditions. https://arxiv.org/abs/0812.4265

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Decomposition of the axial-vector current in a finite box

We consider the matrix element of the axial-vector current between two nucleon states in a finite box. Starting from the chiral Lagrangian density with nucleon and Delta-isobar degrees of freedom, we study the finite-volume effects at the one-loop level. We show that the standard decomposition into the axial-vector and pseudoscalar form factor is incomplete in a finite box. We derive expressions for the complete set of in-box form factors at one loop, and demonstrate how to extract the full set from lattice correlation functions. We verify that the axial Ward identity holds in the chiral limit. We derive the one-loop expressions for the pseudoscalar form factor and verify that the in-box axial Ward identity away from the chiral limit is fulfilled also. Selected numerical results are shown for two flavor-SU(2) lattice ensembles. Sizable finite-volume effects are observed, with an important role for the Delta-isobar. We discuss the implications of our results for lattice studies of the axial-vector current. We conclude that full finite-box results are crucial for a precise determination of the form factors.

hep-lat↗
arXiv2026

A variational framework for variance reduction in lattice field theory

The signal-to-noise problem limits the reach of many lattice calculations. We present a variational framework that recasts it as a transport problem: the loss of signal reflects a mismatch between the distribution one samples and the one needed to measure an observable, and can be reduced by transporting configurations to close that gap. The optimal transport is typically determined either through a stochastic estimator based on Langevin dynamics or by parametrising it as a normalising flow trained with automatic differentiation. We discuss how the framework brings these methods under a common variational principle and present results for scalar theories.

hep-lat↗
arXiv2026

Larger physical volume and bounds on the number of matter fields in noncompact gauge theories on a lattice

The work was motivated by the numerical result that in a pure SU(2) gauge theory the ratio R of the effective non-compact and compact lattice spacing is larger than 1 and increasing with decreasing gauge coupling, as well as the expectation that it should further increase extending the parameter space. This means that with a noncompact regularization, at given number of lattice sites and comparable scaling, one can obtain a larger physical volume, whose importance for the control of size effects has long been known. We confirm qualitatively results and expectation by a perturbative evaluation of the effective lattice spacing in an expansion in the Plank constant of non-compact pure SU(2) and Abelian gauge theories, but we find in addition that R reaches the maximum value of sqrt(2). Including matter fields we find that R increases ( still up to sqrt(2) ) or decreases depending on the difference between the number of scalar and spinor degrees of freedom, and there are bounds on such a difference.

hep-lat↗