Lattice QCD constraints on pion electroproduction off a nucleon

Abstract

Very recently, a lattice QCD collaboration has explored threshold pion electroproduction near the physical pion mass and has simulated the relevant multipole amplitudes. Different multipole amplitudes are usually entangled in experimental data, and thus extracting each of them independently from first principles provides additional essential constraints on phenomenological theories. We use nonperturbative Hamiltonian theory to investigate the electroproduction process, providing an advanced approach with additional two-particle coupled channels to acquire the physical electric dipole amplitudes from the original lattice QCD data. We note that future lattice QCD simulations of the electric dipole amplitudes at higher energies will be much closer to their physical counterparts than the current ones near threshold. In addition, we obtain a new expression which, like that of Lellouch-Lüscher, depends only on the final-state interactions but provides both the real and imaginary parts of the transition amplitudes.

Figures (2)

• Figure 1: The multipole amplitude $E_{0+}$ (in units of $10^{-3}/m_{\pi}$) at the $\pi N$ threshold, with isospin $I_{\pi N}=1/2$. Our results are shown as the red solid lines. Other line styles represent different partial-wave analysis groups: SAID (blue dash-dotted) GWUBriscoe:2023gmb, EBAC (green dashed) site:SL, and MAID 2007 (black dotted) maidDrechsel:2007if. The data points are from lattice QCD simulations with the spatial extent $L=4.6$ fm and 24D or 32Df ensembles Gao:2025loz, after application of the Lellouch-Lüscher factor.
• Figure 2: The dependence of the multipole amplitude $E_{0+}$ on the center-of-mass energy $E_{\rm cm}$ for $q^2 = 0$. The red dashed line represents the infinite volume $E_{0+}$, and the hollow and filled data points refer to the finite-volume $E^L_{0+}$ corresponding to the two lowest finite-volume eigenstates $|G(0)\rangle$ and $|G(1)\rangle$, respectively. The gray vertical line marks the $|\pi N(k_0)\rangle$ threshold. The green, blue, and purple vertical lines indicate the noninteracting $|\pi N(k_1)\rangle$ levels with different box sizes $L$.