Perturbative EFT calculation of the deuteron longitudinal response function

TL;DR

The paper develops a perturbatively renormalized chiral EFT framework to compute the deuteron longitudinal response in deuteron electrodisintegration up to NNLO, while enforcing exact RG invariance order by order. It extends the Lorentz Integral Transform method to this perturbative RG-invariant setting and formulates a momentum-space, partial-wave LIT equation with a common kernel for all orders, enabling a bound-state–like treatment of the continuum. The authors implement chiral NN interactions with cutoff regularization, including LO nonperturbative dynamics and NLO/N2LO corrections to both the potential and current operators, along with relativistic boost considerations. Through convergence tests and inversion of the LIT, they achieve good agreement with available data and demonstrate proper renormalization as Λ is varied, providing a foundation for applying perturbatively renormalized EFT to inelastic processes in light nuclei.

Abstract

In this work, we study the longitudinal response function of the deuteron up to next-to-next-to-leading order in chiral effective field theory (Chiral EFT). We use an approach that maintains exact renormalization group (RG) invariance at each order of the EFT expansion by treating all subleading corrections in perturbation theory. To that end, we extent the Lorentz Integral Transform (LIT) method to allow for such a perturbative treatment. In doing so, we further develop the existing work on strictly RG invariant Chiral EFT, which has so far focused primarily on binding energies and static properties, to inelastic processes. We carefully analyze the convergence properties of the theory and find good agreement with available experimental data. Our findings provide the foundation for similar studies of inelastic processes in a range of nuclei, based on perturbatively renormalized EFT schemes.

Figures (8)

• Figure 1: LIT of the deuteron longitudinal response for $\mathbf{q}^2 = 0.6~\text{fm}^{-2}$, $\sigma_I = 3.0~\text{MeV}$ at (a) LO (b) NLO and (c) N2LO. Each panel shows the LIT for three different values of the momentum cutoff $\Lambda$.
• Figure 2: LIT of the deuteron longitudinal response at different orders for $\sigma_I = 3.0~\text{MeV}$, $\mathbf{q}^2 = 0.5~\text{fm}^{-2}$.
• Figure 3: N2LO LIT of the deuteron response for $\Lambda = 1600$ MeV, $\sigma_I = 3.0$ MeV for momentum transfer (a) $\mathbf{q}^2 = 0.1$ fm$^{-2}$, (b) $\mathbf{q}^2 = 0.5$ fm$^{-2}$ and (c) $\mathbf{q}^2 = 1.0$ fm$^{-2}$.
• Figure 4: N2LO LIT of the deuteron response for $\Lambda = 800$ MeV, $\sigma_I = 3.0$ MeV for momentum transfer $\mathbf{q}^2 = 0.6$ fm$^{-2}, 1.0$ fm$^{-2}, 1.5$ fm$^{-2}$.
• Figure 5: Deuteron response from the inverted LIT for $\Lambda = 800$ MeV, $\sigma_I = 3.0$ MeV for momentum transfer $\mathbf{q}^2 \approx 0.6$ fm$^{-2}$ for orders LO, NLO, N2LO. The experimental data presented are from Ref. Simon:1979bu.