Extracting Resonance Width from Lattice Quantum Monte Carlo Simulations Using Analytical Continuation Method

Abstract

Nuclear lattice effective field theory (NLEFT) provides an efficient ab initio framework for computing low-lying states via imaginary-time projection. However, the extraction of unstable resonances, especially those with broad widths, remains a significant challenge. Traditional techniques such as the complex scaling method are often limited by sign problems or inherent statistical uncertainties. In this work, we present the first direct extraction of a nuclear resonance width within NLEFT by combining a high-precision, sign-problem-free nuclear interaction with the analytical continuation in the coupling constant (ACCC) approach. To address numerical instabilities in the ACCC framework, we implement a robust Pade solver based on singular value decomposition (SVD), incorporating ridge regularization and pole-safety criteria to ensure reliable extrapolation to the resonance pole. We detail the methodology and apply it to the unbound ground state of $^5$He ($J^π=3/2^-$). Our calculation yields a resonance energy $E=0.80(10)$ MeV and a width $Γ=1.05(9)$ MeV, in agreement with recent experimental results ($E_{\rm exp}=0.798$ MeV, $Γ_{\rm exp}=0.648$ MeV). This work establishes a practical and precise strategy for studying resonances within the ab initio lattice framework, paving the way for investigations of many-body resonances in exotic nuclei near the drip lines.

Figures (3)

• Figure 1: Analytic continuation of the complex momentum $k(z)=i\kappa(z)$ in the complex momentum plane. As $\mathrm{Im}(z)$ varies, $k(z)$ traces the colored trajectory (color bar: $\mathrm{Im}(z)$), starting from the bound-state input points $k(z_i)$ on the positive imaginary axis (red crosses), passing through the threshold point $k=0$, and ending at the resonance pole $k(z_\star)$ (open blue circle) in the fourth quadrant.
• Figure 2: Comparison of Padé $(5,5)$ approximants obtained with two different ridge regularization strengths. The blue curves show the fit function values $P(z)/Q(z)$, while red crosses denote the input data points $\kappa(z)$. Left panel: for $\lambda_T = 10^{-2}$, the Padé approximant remains smooth and free of real-axis poles within the fitting interval. Right panel: for a much smaller regularization, $\lambda_T = 10^{-5}$, several spurious poles (marked by blue crosses) enter the interpolation domain, producing sharp unphysical spikes in $P(z)/Q(z)$ .
• Figure 3: Dependence of LOOCV (left panel) and RMS (right panel) on the ridge regularization parameter $\lambda_T$ for PAII approximants of different orders. Squares, diamonds, upward triangles, and downward triangles correspond to the PAII $(3/3)$, $(4/4)$, $(5/5)$, and $(6/6)$ approximants, respectively. The light yellow shaded region marks the small-regularization regime in which spurious poles emerge.