Non-perturbative flavor asymmetry in the nucleon and deuteron: The light-front Hamiltonian effective field theory approach

TL;DR

This work develops a non-perturbative light-front Hamiltonian effective field theory to study flavor asymmetry in the nucleon and its extension to the deuteron. By solving the light-front Schrödinger equation with a Fock-sector expansion including multi-pion components in a scalar chiral EFT, the authors compute longitudinal momentum distributions and quark PDFs via a convolution framework, revealing significant deviations from perturbative predictions and strong sensitivity to multi-pion configurations. They tune couplings to reproduce SeaQuest data and obtain an integrated flavor asymmetry in reasonable agreement with experiment, while also showing that the high-$x$ behavior of the ratio $\bar d(x)/\bar u(x)$ is sensitive to non-perturbative dynamics. The deuteron extension, explored through a two-body effective Hamiltonian derived by a Wilson–Bloch transformation, indicates that higher-order pionic contributions are essential for a realistic description of nuclear flavor effects and lays out a path toward a unified treatment of intrinsic nucleon structure and nuclear modifications, with dynamical pions to be incorporated in the near term.

Abstract

We investigate non-perturbative multi-pion contributions to nucleon flavor asymmetry within the framework of Light-Front Hamiltonian Effective Field Theory (LFHEFT). Utilizing a Fock sector expansion, we systematically incorporate pionic degrees of freedom, with the nucleon-pion interactions governed by a scalar variant of chiral effective field theory. Our results demonstrate that the non-perturbatively calculated longitudinal momentum distributions exhibit significant deviations from leading-order perturbative predictions, emphasizing the importance of higher-order Fock components in describing the proton's sea quark structure. Furthermore, we demonstrate the feasibility of extending this framework to investigate nuclear effects in light nuclei, such as the deuteron. This unified approach provides a consistent basis for analyzing the interplay between intrinsic nucleon structure and nuclear modifications, potentially offering new insights into the flavor asymmetry observed in fixed-target and collider experiments.

Figures (3)

• Figure 1: Longitudinal momentum distribution function of the nucleon ($f_{N\pi}$), pion ($f_{\pi N}$), and the $\Delta$ ($f_{\Delta \pi}$) inside the physical nucleon. Results are shown for two-body (baryon $+ \pi$), three-body (baryon $+ 2\pi$), and four-body (baryon $+ 3\pi$) truncations. The two-body truncation is equivalent to the leading-order light-front perturbation theory. For reference, we also include the leading-order perturbation theory results of Alberg et al. obtained using a chiral Lagrangian Alberg:2021nmu.
• Figure 2: The distributions $\bar{d}(x) - \bar{u}(x)$ and $\bar{d}(x)/\bar{u}(x)$, calculated from the perturbative (two-body) and non-perturbative (four-body) solutions of our scalar model, compared with the NuSea NuSea:1998kqi and SeaQuest SeaQuest:2021zxb experimental data at the scale $Q^2 = 25.5~\text{GeV}^2$. The band for the non-perturbative results reflects the difference between the three-body and four-body truncations, illustrating the good convergence of the Fock sector expansion. Results from the leading-order light-front perturbation theory of Alberg et al. Alberg:2021nmu and from the statistical model of Basso et al. Basso:2015lua are also shown for comparison.
• Figure 3: (\ref{['fig:alpha_vs_M']}) Binding energy of the scalar deuteron as a function of the coupling constant $\alpha$. Beyond the critical coupling $\alpha_c \approx 0.33$, the system becomes unstable. (\ref{['fig:deuteron-fn']}) Longitudinal momentum distribution function of the scalar nucleon inside the scalar deuteron for $E_B = 2.2~\text{MeV}$ ($\alpha \approx 0.14$), $E_B = 200~\text{MeV}$ ($\alpha \approx 0.24$) and $E_B = 500~\text{MeV}$ ($\alpha \approx 0.28$). (\ref{['fig:deuteron-LFWF-EB200']}) The deuteron light-front wave function obtained from the Bloch effective Hamiltonian. The binding energy is $E_B \approx 200~\text{MeV}$$(\alpha \approx 0.24)$.