Complex-momentum form factors from lattice QCD
Abstract
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 Q2 satisfying Re Q2>−4mπ2, where mπ 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.
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BibTeX
@misc{hansen2026complexmomentum,
title = {{Complex-momentum form factors from lattice QCD}},
author = {Maxwell T. Hansen and Gurtej Kanwar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03553},
eprint = {2610.03553},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03553},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Complex-momentum form factors from lattice QCD
AU - Maxwell T. Hansen
AU - Gurtej Kanwar
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.03553
UR - https://arxiv.org/abs/2610.03553
AB - 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 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.
ER -