Ab initio calculations of overlap integrals for $μ\to e$ conversion in nuclei

TL;DR

The paper addresses the need for robust, uncertainty- Quantified nuclear-structure inputs in μ→e conversion by computing the leading spin-independent overlap integrals $S^{(N)}$, $V^{(N)}$, and $D$ within an ab initio IMSRG framework across a broad set of chiral EFT Hamiltonians. It leverages strong correlations among charge, proton, and neutron densities to propagate uncertainties and generate full covariance matrices for the overlap integrals in $^{27}$Al, $^{48}$Ca, and $^{48}$Ti, enabling more reliable interpretation of LFV signals. The authors demonstrate that neutron and weak-density predictions are tightly constrained by charge radii and EFT-driven correlations, and they validate their approach against PVES data where possible. Overall, the work provides a principled framework to translate fundamental LFV operators into nuclear observables with quantified uncertainties, with implications for μ→e experiments and related probes in nuclear and particle physics.

Abstract

The rate for $μ\to e$ conversion in nuclei is set to provide the most stringent test of lepton-flavor symmetry and a window into physics beyond the Standard Model. However, to disentangle new lepton-flavor-violating interactions, in combination with information from $μ\to eγ$ and $μ\to 3e$, it is critical that uncertainties at each step of the analysis be controlled and fully quantified. In this regard, nuclear response functions related to the coupling to neutrons are notoriously problematic, since they are not directly constrained by experiment. We address these shortcomings by combining ab initio calculations with a recently improved determination of charge distributions from electron scattering by exploiting strong correlations among charge, point-proton, and point-neutron radii and densities. We present overlap integrals for $^{27}$Al, $^{48}$Ca, and $^{48}$Ti including full covariance matrices, allowing, for the first time, for a comprehensive consideration of nuclear structure uncertainties in the interpretation of $μ\to e$ experiments.

Figures (10)

• Figure 1: Correlations between $\langle r^2\rangle_\text{ch}$ and the overlap integrals from Eq. \ref{['eq:S,V,D_kitano']} using the IMSRG (specifically VS-IMSRG for $^{27}$Al, $^{48}$Ti) based on a representative set of chiral Hamiltonians (see Appendix \ref{['app:Hamiltonians']} for details). The shell-model results, based on Refs. Hoferichter:2022mnaCaurier:1999Caurier:2004gfOtsuka:2018bqqPoves:2000nwBrown:2006gx, are shown for comparison and are not included in the correlation analysis.
• Figure 2: Residual distribution for the $S^{(n)}$ overlap integral of $^{27}$Al. The dark (light) region marks the residual values that are in (outside) 68 % of the closest residuals to zero.
• Figure 3: Correlations of the residuals for $^{27}$Al normalized to the uncertainty based on the distribution as shown in Fig. \ref{['fig:Al27_resid_dist']}, using the same symbols as in Fig. \ref{['fig:Iir2']}. $c_{ij}$ refers to the correlation between the residuals of $I_i$ and $I_j$.
• Figure 4: Correlations between $\rho_\text{ch}$ and $\rho_\text{n}$ illustrated for selected values of $r$ for $^{27}$Al, $^{48}$Ca, and $^{48}$Ti. Symbols are as used in Fig. 1 of the main text.
• Figure 5: Point-proton, point-neutron, and weak distributions for $^{27}$Al, $^{48}$Ca, and $^{48}$Ti based on a correlation analysis at fixed $r$ together with the input charge density; $\rho_\text{ch}=\rho^\text{ref}_\text{ch}$.