First Two-Hadron Form Factor from QCD
Abstract
We present the first QCD determination of an energy-dependent form factor for a two-hadron scattering state. In particular, we calculate the QCD contribution to the forward electromagnetic π+π+ + γ→π+π+ amplitude at mπ≈ 400~MeV using lattice QCD. Because lattice calculations are performed in a finite Euclidean spacetime, where asymptotic scattering states are absent, this amplitude cannot be accessed directly from correlation functions. Instead, we can constrain this and related amplitudes nonperturbatively using a finite-volume formalism that requires two ingredients: the discrete finite-volume spectrum and finite-volume matrix elements of the electromagnetic current. We calculate three-point correlation functions coupling π+π+ finite-volume states and extract the corresponding electromagnetic matrix elements. Combining these results with the previously determined spectrum, we constrain the infinite-volume π+π+ + γ→π+π+ amplitude in the forward limit. Using constraints from Lorentz symmetry, unitarity, and analyticity, we describe this amplitude in terms of a single real-valued energy-dependent two-hadron form factor. The resulting amplitude and form factor agree with the Ward-Takahashi identity across all energies and moving frames considered, providing the first QCD validation of this finite-volume approach and a pathway toward first-principles studies of the electromagnetic structure and electroweak responses of resonances and multi-hadron bound states.
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BibTeX
@misc{ortegagama2026first,
title = {{First Two-Hadron Form Factor from QCD}},
author = {Felipe G. Ortega-Gama and Raúl A. Briceño and Ivan M. Burbano and Robert G. Edwards},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04142},
eprint = {2609.04142},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04142},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - First Two-Hadron Form Factor from QCD
AU - Felipe G. Ortega-Gama
AU - Raúl A. Briceño
AU - Ivan M. Burbano
AU - Robert G. Edwards
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04142
UR - https://arxiv.org/abs/2609.04142
AB - We present the first QCD determination of an energy-dependent form factor for a two-hadron scattering state. In particular, we calculate the QCD contribution to the forward electromagnetic π^+π^+ + γ→π^+π^+ amplitude at m_π≈ 400~MeV using lattice QCD. Because lattice calculations are performed in a finite Euclidean spacetime, where asymptotic scattering states are absent, this amplitude cannot be accessed directly from correlation functions. Instead, we can constrain this and related amplitudes nonperturbatively using a finite-volume formalism that requires two ingredients: the discrete finite-volume spectrum and finite-volume matrix elements of the electromagnetic current. We calculate three-point correlation functions coupling π^+π^+ finite-volume states and extract the corresponding electromagnetic matrix elements. Combining these results with the previously determined spectrum, we constrain the infinite-volume π^+π^+ + γ→π^+π^+ amplitude in the forward limit. Using constraints from Lorentz symmetry, unitarity, and analyticity, we describe this amplitude in terms of a single real-valued energy-dependent two-hadron form factor. The resulting amplitude and form factor agree with the Ward-Takahashi identity across all energies and moving frames considered, providing the first QCD validation of this finite-volume approach and a pathway toward first-principles studies of the electromagnetic structure and electroweak responses of resonances and multi-hadron bound states.
ER -