Convergence in charmonium structure: light-front wave functions from basis light-front quantization and Dyson-Schwinger equations

TL;DR

This work benchmarks two non-perturbative QCD approaches—Basis Light-Front Quantization (BLFQ) and Dyson-Schwinger Equations (DSE)—by comparing their charmonium light-front wave functions across multiple observables: charge and gravitational form factors, light-cone distribution amplitudes, decay constants, and two-photon transition form factors. Despite their different foundations and parameters, BLFQ and DSE show remarkable agreement, validating both methods for heavy quarkonia and highlighting the universality of charmonium structure. The results reinforce the reliability of the BSA projection method and establish a solid baseline for extending these Hamiltonian- and Lagrangian-based techniques to more complex hadronic systems. The cross-method convergence strengthens confidence for interpreting experimental data at facilities like Jefferson Lab and future electron-ion colliders.

Abstract

We present a systematic comparison of charmonium light-front wave functions obtained through two complementary non-perturbative approaches: Basis Light-Front Quantization (BLFQ) and Dyson-Schwinger Equations (DSE). Key observables include the charge form factor, gravitational form factors, light-cone distribution amplitudes, decay constants, and two-photon transition form factors. Despite their distinct theoretical foundations and model parameters, the predictions from BLFQ and DSE exhibit remarkable agreement across all observables. This convergence validates both frameworks for studying charmonium structure and highlights the complementary strengths of Hamiltonian-based -- BLFQ -- and Lagrangian-based -- DSE -- methods in addressing non-perturbative QCD.

Figures (5)

• Figure 1: Comparison of the light-front wave functions for the ground-state charmonium $\eta_c$ computed from basis light-front quantization (BLFQ) and from Dyson-Schwinger equations (DSE). The negative $k_\perp$ region shows the DSE results. The positive $k_\perp$ region shows the BLFQ results with $N_\text{max} = 8$. The spin singlet component of the LFWF is defined as $\psi_{\uparrow\downarrow-\downarrow\uparrow} = (\psi_{\uparrow\downarrow} - \psi_{\downarrow\uparrow})/\sqrt{2}$.
• Figure 2: (Colors online) Comparison of the (fictitious) charge form factor $F(Q^2)$ for the ground-state charmonium $\eta_c$ computed using LFWFs from BLFQ and from DSE. The dashed line is the DSE result. The solid line is the BLFQ result with $N_\mathrm{max} = 8$. And the band represents the uncertainty associated with the basis sensitivity in BLFQ as computed from the difference between $N_\mathrm{max} = 8$ and $N_\mathrm{max} = 16$ results. See texts for more details.
• Figure 3: (Colors online) Comparison of the gravitational form factors $A(Q^2)$ and $D(Q^2)$ for the ground-state charmonium $\eta_c$ computed using LFWFs from BLFQ ($N_\text{max} = 8$, solid lines) and from DSE (dashed lines). The uncertainty bands are computed from the difference between $N_\mathrm{max} = 8$ and $N_\mathrm{max} = 16$ results in BLFQ. See texts for more details.
• Figure 4: (Colors online) Comparison of the leading-twist LCDA of $\eta_c$ as obtained from BLFQ ($N_\text{max} = 8$, solid lines) and from DSE (dashed lines). The uncertainty bands are computed from the difference between $N_\text{max} = 8$ and $N_\text{max} = 16$ results in BLFQ. The dot-dashed lines correspond to the pQCD asymptotic form $6x(1-x)$Lepage:1980fj. The DSE results are evolved from $\mu_0 = 2.6\,\mathrm{GeV}$ to $\mu = 2.8\,\mathrm{GeV}$ to match the BLFQ energy scale.
• Figure 5: (Colors online) Comparison of the transition form factor of $\eta_c$ as obtained from BLFQ ($N_\text{max} = 8$, solid lines) and from DSE (dashed lines). The uncertainty bands are computed from the difference between $N_\text{max} = 8$ and $N_\text{max} = 16$ results in BLFQ.