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 $Q^2$ satisfying $\mathrm{Re}{Q}^2>-4m_{\pi }^2$, where $m_{\pi }$ 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.

40 pages, 11 figures; v2: revised abstract and text for clarity, updated Figure 1, added references