Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0709.2889

The complete lowest order chiral Lagrangian from a little box

Thomas DeGrand·Stefan Schaefer
View original source ↗Read source document ↗Export metadata ↓

Abstract

We recently performed a pilot study determining the parameters of the leading order chiral Lagrangian from distributions of the eigenvalues of a quenched Dirac operator coupled to an imaginary isospin chemical potential. We complement a quick survey of our recent preprint arXiv:0708.1731 [hep-lat] by addressing some points raised during discussions at the conference.

Explore related subjects

hep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Thomas DeGrand, Stefan Schaefer. 2007-09-18. The complete lowest order chiral Lagrangian from a little box. https://arxiv.org/abs/0709.2889

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

KEEP EXPLORING

Related papers

arXiv2026

Mellin Moments of Proton Unpolarized GPDs at Nonzero Skewness from Lattice QCD with a Neural-Network Parametrization

We use lattice QCD to determine the generalized form factors (GFFs) entering the first four Mellin moments of the unpolarized isovector $u-d$ proton GPDs at nonzero skewness. The framework combines the polynomiality of the moments in the skewness $ξ$, with the short-distance expansion formalism, allowing the lattice-extracted reduced Ioffe-time distributions (ITDs) to be expressed in terms of GFFs. In order to extract the GFFs by fitting these relations to the lattice data, we parameterize each GFF with an artificial neural network (ANN) as a continuous function of the invariant momentum transfer squared $t$, which accommodates the kinematic coverage of the data in a flexible way. With this fit, we determine the fourteen GFFs that enter the first four Mellin moments, including the skewness-dependent GFFs. From the extracted GFFs, we obtain the quark total angular momentum of the isovector combination, $J^{u-d}=0.296(11)(7)$ in the $\overline{\mathrm{MS}}$ scheme at $μ=2~\mathrm{GeV}$, in agreement with previous lattice determinations based on nonlocal operators and with a smaller total uncertainty. We also determine the impact-parameter distributions of the first three Mellin moments in an unpolarized and in a transversely polarized proton. We finally identify and discuss the principal systematic uncertainties which enter this extraction, and the challenges specific to the nonzero-skewness regime.

hep-lat↗
arXiv2026

Progress on meson-glueball mixing in lattice gauge theories coupled to fermions in multiple representations

We present preliminary results from our numerical lattice investigation of the low-lying flavour-singlet bound states in the ${\rm Sp}(4)$ gauge theory coupled to fermions transforming in the fundamental and two-index antisymmetric representations. We use the Wilson gauge action and Wilson fermions. We employ the generalized eigenvalue problem (GEVP) method with a basis of smeared glueball and meson interpolating operators. We analyse two high-statistics ensembles with the same lattice coupling and different fermion mass. We study both the scalar and pseudoscalar states. We observe the first evidence for meson-glueball mixing in this theory. We improve upon previous determinations of the energy eigenstates and mixing angles in the flavour-singlet pseudoscalar sector.

hep-lat↗
arXiv2026

Complex-momentum form factors from lattice QCD

We demonstrate that form factors evaluated with momenta analytically continued into the complex plane can be accessed directly from position-space Euclidean correlators such as those computed numerically in lattice quantum field theory, without continuing the correlators themselves or solving an inverse problem. The method applies a bilateral Laplace transform to lattice data, yielding the form factor throughout the transform's domain of convergence. For the pion form factor in Quantum Chromodynamics (QCD), this domain contains all complex values of the invariant $Q^2$ satisfying $\mathrm{Re} \, Q^2>-4m_π^2$, where $m_π$ denotes the pion mass. This extended kinematic reach could improve charge-radius determinations and provide more complete input for fits based on conformal mappings. After developing the method for infinite-volume correlators, we discuss several finite-volume estimators suitable for realistic calculations, including position-space fits and the use of a spatial chemical potential implemented through boundary conditions with an imaginary twist angle. Finally, we test the method in the two-dimensional $O(3)$ nonlinear sigma model using Monte Carlo data.

hep-lat↗