Pith. sign in

REVIEW 6 minor 188 references

Two low-energy Standard Model tests are limited by the same nuclear current correlator, so methods built for one advance the other.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-30 21:14 UTC pith:ZPUVB5TD

load-bearing objection Solid methods review that cleanly unifies TPE and the γW box under one hadronic tensor; no new numbers, but the synthesis and outlook are useful and the citations track the primary literature.

arxiv 2607.26781 v1 pith:ZPUVB5TD submitted 2026-07-29 nucl-th physics.atom-ph

Recent Progress in Ab-Initio Nuclear Theory for Precision Physics Searches in Muonic Atoms and Superallowed β Decays

Simone Salvatore Li Muli , Michael Gennari This is my paper
classification nucl-th physics.atom-ph
keywords ab initio nuclear theorymuonic atomssuperallowed beta decaynuclear polarizabilityradiative correctionselectroweak interactionsStandard Model testschiral effective field theory
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Precision tests of the Standard Model at low energy are now limited by nuclear-structure theory rather than by experiment. This review argues that the two-photon-exchange correction to the Lamb shift in muonic atoms and the gamma-W box correction to superallowed beta decays are both controlled by one object: the generalized hadronic tensor. Because of that kinship, chiral effective-field-theory Hamiltonians and currents, Lanczos-based response methods, and Bayesian uncertainty quantification developed for either problem carry over directly to the other. Recent ab initio work in light nuclei has sharpened nuclear charge radii, shown that the helium isotope-shift tension is atomic rather than nuclear, and tightened the nuclear correction that dominates the extraction of Vud for the top-row CKM unitarity test.

Core claim

The leading nuclear-structure corrections that limit two flagship low-energy Standard Model programs—the two-photon exchange in the muonic Lamb shift and the nuclear gamma-W box in superallowed beta decay—are two faces of the same generalized hadronic tensor, a forward electroweak current-current correlator. Methods and uncertainty tools built for one therefore transfer to the other, and recent light-nuclei ab initio results already affect charge radii, the helium isotope-shift puzzle, and the extraction of Vud.

What carries the argument

The generalized hadronic tensor: the forward current-current correlator of electroweak operators evaluated with external nuclear states. It carries all the nuclear structure in both the muonic two-photon-exchange amplitude and the gamma-W box radiative correction.

Load-bearing premise

That leftover short-distance and nuclear-shadowing pieces not fully fixed by the low-energy spectral representation can be budgeted as sub-dominant uncertainties without overturning the claimed percent-level control.

What would settle it

An ab initio gamma-W box for a heavier superallowed emitter, or a determination of the short-range EFT constants, that moves the nuclear-structure correction outside the present uncertainty band and shifts the CKM unitarity deficit by more than the claimed improvement.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

Share X Bluesky LinkedIn Reddit HN

If this is right

  • Bayesian-quantified two-photon-exchange corrections yield precise helion and alpha-particle charge radii from muonic helium.
  • Nuclear structure is exonerated as the source of the helium isotope-shift tension; the residual discrepancy is atomic.
  • The first ab initio nuclear gamma-W box for 10C to 10B reduces theory uncertainty on that transition’s contribution to Vud.
  • Updated nuclear polarization on charge radii used in the 26mAl analysis can cut the CKM unitarity deficit by about one standard deviation.
  • The same machinery extends to gamma-Z boxes, muon capture, and neutrino-nucleus scattering.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the shared-tensor claim holds, coordinated work on light muonic atoms and light superallowed emitters is the fastest route to deciding whether the Cabibbo anomaly is real.
  • Bridging exact light-nuclei methods to mean-field treatments for medium-mass muonic X-ray targets is the practical bottleneck for the next round of charge-radius experiments.
  • The still-unfitted short-range constants in the EFT route to the nuclear box are one multi-transition fit away from rivaling the current-algebra uncertainty.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 6 minor

Summary. This review argues that the two-photon-exchange (TPE) correction to the Lamb shift in muonic atoms and the nuclear γW-box correction to superallowed β decays are governed by the same generalized hadronic tensor (forward electroweak current–current correlator). Consequently, χEFT Hamiltonians and currents, Lanczos-based response methods, and Bayesian truncation-error quantification developed for one problem transfer directly to the other. The authors summarize the common formalism (spectral representation and multipole decomposition), modern ab initio methods, recent N3LO Bayesian TPE results for muonic helium and their role in resolving the helium isotope-shift puzzle on the nuclear side, and the first ab initio γW-box calculation for 10C→10B with implications for Vud and top-row CKM unitarity, closing with an outlook toward heavier systems and related electroweak processes.

Significance. If the synthesis holds—and the manuscript’s Eqs. (2)–(6) and the cited primary calculations support it—the review usefully unifies two precision programs that are often treated separately, and documents concrete impact: Bayesian-quantified TPE corrections for μ3He+ and μ4He+ that helped exonerate nuclear structure in the helium isotope-shift tension, and an ab initio δNS for 10C→10B that reduces theory uncertainty relative to earlier surveys. Strengths include explicit spectral and multipole machinery, clear linkage of Lanczos response methods across both observables, and transparent discussion of residual uncertainties (nuclear shadowing, unfitted short-range EFT LECs). As a methods-and-results review rather than a new primary derivation, its value is organizational and pedagogical for the precision electroweak nuclear-physics community.

minor comments (6)
  1. [Section 2.1] Section 2.1, after Eq. (2): the normalization convention difference between the unit-normalized non-relativistic tensor and the relativistic β-decay Compton tensor is mentioned, but a single explicit cross-reference to the matching relation later given near Eq. (55) would help readers who enter from the muonic-atom side.
  2. [Section 5.4, Table 2] Table 2: the caption and surrounding text correctly note that CA δNS and EFT δ(0)_NS|mag+LS are not directly comparable; a brief footnote listing which pieces of the full δNS each column includes would reduce the chance of misquotation.
  3. [Section 3.3] Section 3.3: the statement that rigorous Bayesian LEC sampling has not yet been applied to polarizabilities or γW-box amplitudes is important; citing the specific emulator/EC references already in the bibliography at that sentence would tighten the outlook.
  4. [Figure 1] Figure 1 caption: “drawn for a β+ transition such as 10C→10B” is clear; ensuring the printed figure labels (a)/(b) match the in-text “two-photon exchange” / “γW box” wording consistently would aid skimming.
  5. A few typographical inconsistencies appear (e.g., “ab initionuclear”, “texorpdfstring” artifacts in the abstract source, occasional missing spaces after commas in author lists). A copy-edit pass would clean these without affecting content.
  6. [Section 5.1] Section 5.1 / Figure 4: the left panel is described as using PDG 2024 values; if any post-2024 updates to Vus or the unitarity plot are intended to be frozen for the review, a one-line date stamp on the figure source would help longevity.

Circularity Check

0 steps flagged

No significant circularity: review summarizes independent ab-initio results linked by standard current-algebra structure, not by construction from fitted inputs.

full rationale

This manuscript is a methods-and-results review. Its load-bearing claim is that the TPE Lamb-shift correction and the nuclear γW-box correction are both instances of the same generalized forward hadronic tensor (Eqs. 2–6), so χEFT Hamiltonians/currents, Lanczos response methods, and Bayesian truncation UQ transfer between the two programs. That kinship is standard multipole/current-algebra formalism stated explicitly in the text, not defined in terms of the numerical conclusions. Reported milestones (Bayesian N3LO TPE in muonic He; ab-initio δNS for 10C→10B) are prior primary calculations summarized against external benchmarks (CREMA Lamb shifts, electronic isotope shifts, Hardy–Towner Ft surveys, CKM unitarity). Self-citations to the authors’ own TPE and γW papers are normal review practice and do not force the structural claim by definition, fit, or uniqueness theorem. Residual pieces (Bμν/shadowing, unfitted EFT LECs) are budgeted as uncertainties in the primary works, not hidden inputs that manufacture the review’s narrative. No self-definitional loop, fitted-input-as-prediction, or ansatz-smuggling reduction is present.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 0 invented entities

As a review, load-bearing content is almost entirely inherited domain machinery: χEFT power counting and currents, non-relativistic spectral representations of forward correlators, multipole decompositions, Lanczos response technology, Bayesian naturalness priors for truncation errors, and Sirlin’s current-algebra organization of radiative corrections. No new particles or forces are postulated. Free parameters appear only as quantities already present in the reviewed primary calculations (χEFT LECs; unknown short-range β-decay LECs in the EFT approach), not as new fits performed here.

free parameters (3)
  • χEFT low-energy constants (LECs) in NN/3N forces and electroweak currents
    Primary calculations reviewed here calibrate LECs to scattering and few-body data; residual LEC uncertainty is not yet fully Bayesian-propagated into polarizabilities or δNS (Section 3.3).
  • Short-range EFT couplings gNN_V1 and gNN_V2 for nucleus-dependent radiative corrections = unknown
    In the tower-of-EFTs approach to δNS these two LECs are presently unknown and dominate the quoted EFT uncertainty until matched to QCD or fit to superallowed data (Section 5.4).
  • EFT breakdown scale Λb and expansion parameter Q in Bayesian truncation model
    Bayesian DOB intervals for δTPE depend on the chosen Q=max(p,mπ)/Λb and naturalness priors for coefficients cn (Section 3.3).
axioms (6)
  • domain assumption Both TPE (muonic atoms) and the nuclear γW box are encoded in the same generalized forward hadronic tensor built from electroweak currents between nuclear states.
    Stated as the theme of the review (Abstract, Section 1, Figure 1, Section 2); standard in the modern reassessment literature but is the organizing premise.
  • domain assumption Weinberg-style χEFT provides a systematically improvable Hamiltonian and consistent electroweak currents for light nuclei at the precision needed.
    Section 3.1; residual cutoff dependence and power-counting debates are acknowledged but not resolved.
  • domain assumption Non-relativistic spectral sums plus multipoles plus Lanczos resolvents suffice for the leading nuclear-structure pieces after matching to relativistic normalizations.
    Sections 2.1–2.2, 3.2, 5.2–5.3; recoil and relativistic corrections are treated as controlled add-ons.
  • domain assumption Bayesian naturalness priors on EFT coefficients yield statistically meaningful truncation errors (DOB intervals).
    Section 3.3, applied to muonic helium in Section 4.4.
  • domain assumption Sirlin current-algebra decomposition isolates the structure-dependent γW box as the dominant nuclear uncertainty in Vud extractions.
    Section 5.1–5.2; standard SM radiative-correction framework.
  • standard math Mathematical completeness relations, multipole orthogonality, and contour deformation of loop integrals are valid as used.
    Sections 2–3 and 5.3 (Wick rotation and residue bookkeeping in Figure 5).

pith-pipeline@v1.2.0-daily-grok45 · 44890 in / 3631 out tokens · 72806 ms · 2026-07-30T21:14:25.216667+00:00 · methodology

0 comments
Cite this review

Pith. "Pith review of Recent Progress in Ab-Initio Nuclear Theory for Precision Physics Searches in Muonic Atoms and Superallowed $\beta$ Decays." pith.science (2026). https://pith.science/paper/ZPUVB5TD

@misc{pith2026260726781,
  author       = {Pith},
  title        = {Pith review of: Recent Progress in Ab-Initio Nuclear Theory for Precision Physics Searches in Muonic Atoms and Superallowed $\beta$ Decays},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZPUVB5TD}},
  note         = {Machine review of arXiv:2607.26781}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Precision tests of the Standard Model at low energy are increasingly limited by nuclear-structure theory rather than by experiment. We review two such cases: the two-photon-exchange correction to the Lamb shift in muonic atoms, and the \texorpdfstring{$\gamma W$}{gamma-W} box radiative correction to superallowed \texorpdfstring{$\beta$}{beta} decays. Although they probe different physics, both are governed by the same generalized hadronic tensor, so that the chiral effective field theory Hamiltonians and currents, Lanczos-based response methods, and Bayesian uncertainty quantification developed for one carry over directly to the other. We summarize recent ab initio progress in light nuclei and its impact on nuclear charge radii, on the helium isotope-shift puzzle, and on the extraction of \texorpdfstring{$V_{ud}$}{Vud} for the top-row CKM unitarity test, and state a future outlook.

Figures

Figures reproduced from arXiv: 2607.26781 by Michael Gennari, Simone Salvatore Li Muli.

Figure 1
Figure 1. Figure 1: Diagrammatic kinship of the two corrections reviewed here: (a) two-photon exchange in muonic atoms and (b) the γW box in superallowed β decay, drawn for a β + transition such as 10C → 10B. Thin and double lines denote the leptons and the nucleus, respectively. The hatched blob is the same object in both diagrams, the generalized hadronic tensor, carrying two electromagnetic currents in (a) and one electrom… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Self-energy correction to the bound-muon spectrum due to nuclear polarization, given by the sum of the (b) ladder, (c) crossed, and (d) seagull two-photon-exchange diagrams. its heavy-baryon [101–103] or manifestly covariant [104] formulation, or a data-driven approach, in which the two-photon-exchange correction is evaluated through dispersion relations using measured proton form factors and structure… view at source ↗
Figure 3
Figure 3. Figure 3: Pictured is the contribution from a higher-order, virtual electroweak box diagram to the beta decay process of Ψi → Ψf + νe + e +, known as the γW box. We will assume isospin symmetry in the following relativistic derivations, however, it should be noted that isospin-breaking effects are included in all nuclear-structure-dependent pieces of the calculation. This is well-enough justified as superallowed tra… view at source ↗
Figure 4
Figure 4. Figure 4: (Left) The modern CKM unitarity landscape with values for Vud, Vus and the ratio Vud/Vus annotated with their corresponding experimental extractions [7]. The dashdot lines and bands respectively represent the central value and uncertainty in the extraction of a given top-row element of the CKM matrix. The black line indicates the exact unitarity constraint. Note that the contribution of Vub is O(10−5 ) and… view at source ↗
Figure 5
Figure 5. Figure 5: Example trajectories of the ν-integral poles in Eq. (53) arising from the dynamics of: (i) the nuclear propagators in T3, plotted in red for ∆n > 0 and green for ∆n < 0; (ii) the photon propagator, plotted in purple; and (iii) the electron propagator, plotted in orange. The corresponding sets are labelled by N , γ and e, respectively. The chosen contour deformation Γ is the oriented contour defined by Γ = … view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

188 extracted references · 77 canonical work pages

  1. [1]

    Precision Beta Decay as a Probe of New Physics, 2019, [arXiv:nucl-ex/1907.02164]

    Cirgiliano, V .; Garcia, A.; Gazit, D.; Naviliat-Cuncic, O.; Savard, G.; Young, A. Precision Beta Decay as a Probe of New Physics, 2019, [arXiv:nucl-ex/1907.02164]

    Pith/arXiv arXiv 2019

  2. [2]

    Nuclearβ decay as a probe for physics beyond the Standard Model2023

    Brodeur, M.; Buzinsky, N.; Caprio, M.A.; Cirigliano, V .; Clark, J.A.; Fasano, P .J.; et al. Nuclearβ decay as a probe for physics beyond the Standard Model2023. [arXiv:nucl-ex/2301.03975]

    Pith/arXiv arXiv

  3. [3]

    Search for new physics with atoms and molecules.Rev

    Safronova, M.S.; Budker, D.; DeMille, D.; Kimball, D.F.J.; Derevianko, A.; Clark, C.W. Search for new physics with atoms and molecules.Rev. Mod. Phys.2018,90, 025008. https://doi.org/10.1103/RevModPhys.90.025 008

    work page doi:10.1103/revmodphys.90.025 2018

  4. [4]

    Superallowed 0+ → 0+ nuclear β decays: 2020 critical survey, with implications for Vud and CKM unitarity.Physical Review C2020,102, 045501

    Hardy, J.C.; Towner, I.S. Superallowed 0+ → 0+ nuclear β decays: 2020 critical survey, with implications for Vud and CKM unitarity.Physical Review C2020,102, 045501. https://doi.org/10.1103/PhysRevC.102.045501

    doi:10.1103/physrevc.102.045501 2020

  5. [5]

    Superallowed Nuclear Beta Decays and Precision Tests of the Standard Model

    Gorchtein, M.; Seng, C.Y. Superallowed Nuclear Beta Decays and Precision Tests of the Standard Model. Annual Review of Nuclear and Particle Science2024,74, 23–47. https://doi.org/https://doi.org/10.1146/ annurev-nucl-102622-020726

  6. [6]

    Reduced Hadronic Uncertainty in the Determi- nation ofV ud.Physical Review Letters2018,121, 241804

    Seng, C.Y.; Gorchtein, M.; Patel, H.H.; Ramsey-Musolf, M.J. Reduced Hadronic Uncertainty in the Determi- nation ofV ud.Physical Review Letters2018,121, 241804. https://doi.org/10.1103/PhysRevLett.121.241804

    work page doi:10.1103/physrevlett.121.241804

  7. [7]

    Review of Particle Physics.Physical Review D2024,110, 030001

    Navas, S.; et al. Review of Particle Physics.Physical Review D2024,110, 030001. https://doi.org/10.1103/ PhysRevD.110.030001

  8. [8]

    Nuclear ab initio calculations of 6Heβ -decay for beyond the Standard Model studies.Physics Letters B2022,832, 137259

    Glick-Magid, A.; Forssén, C.; Gazda, D.; Gazit, D.; Gysbers, P .; Navrátil, P . Nuclear ab initio calculations of 6Heβ -decay for beyond the Standard Model studies.Physics Letters B2022,832, 137259. https://doi.org/ https://doi.org/10.1016/j.physletb.2022.137259

    arXiv 2022

  9. [9]

    Ab initio calculation of the β-decay spectrum of 6He.Phys

    King, G.B.; Baroni, A.; Cirigliano, V .; Gandolfi, S.; Hayen, L.; Mereghetti, E.; Pastore, S.; Piarulli, M. Ab initio calculation of the β-decay spectrum of 6He.Phys. Rev. C2023,107, 015503. https://doi.org/10.1103/ PhysRevC.107.015503

  10. [10]

    Comprehensive theory of the Lamb shift in light muonic atoms.Rev

    Pachucki, K.; Lensky, V .; Hagelstein, F.; Li Muli, S.S.; Bacca, S.; Pohl, R. Comprehensive theory of the Lamb shift in light muonic atoms.Rev. Mod. Phys.2024,96, 015001. https://doi.org/10.1103/RevModPhys.96.015 001

    work page doi:10.1103/revmodphys.96.015 2024

  11. [11]

    Muonic-Atom Spectroscopy and Impact on Nuclear Structure and Precision QED Theory2022

    Antognini, A.; et al. Muonic-Atom Spectroscopy and Impact on Nuclear Structure and Precision QED Theory2022. [arXiv:nucl-th/2210.16929]

    Pith/arXiv arXiv

  12. [12]

    The size of the proton.Nature2010,466, 213–216

    Pohl, R.; et al. The size of the proton.Nature2010,466, 213–216. https://doi.org/10.1038/nature09250

    doi:10.1038/nature09250

  13. [13]

    Proton Structure from the Measurement of 2S-2P Transition Frequencies of Muonic Hydrogen.Science2013,339, 417–420, [https://science.sciencemag.org/content/339/6118/417.full.pdf]

    Antognini, A.; et al. Proton Structure from the Measurement of 2S-2P Transition Frequencies of Muonic Hydrogen.Science2013,339, 417–420, [https://science.sciencemag.org/content/339/6118/417.full.pdf]. https://doi.org/10.1126/science.1230016

    doi:10.1126/science.1230016

  14. [14]

    CODATA recommended values of the fundamental physical constants: 2018.Rev

    Tiesinga, E.; Mohr, P .J.; Newell, D.B.; Taylor, B.N. CODATA recommended values of the fundamental physical constants: 2018.Rev. Mod. Phys.2021,93, 025010. https://doi.org/10.1103/RevModPhys.93.025010

    doi:10.1103/revmodphys.93.025010 2018

  15. [15]

    Measuring the α-particle charge radius with muonic helium-4 ions.Nature2021,589, 527–531

    Krauth, J.; et al. Measuring the α-particle charge radius with muonic helium-4 ions.Nature2021,589, 527–531. https://doi.org/10.1038/s41586-021-03183-1

    doi:10.1038/s41586-021-03183-1

  16. [16]

    The helion charge radius from laser spectroscopy of muonic helium-3 ions

    Schuhmann, K.; Fernandes, L.M.P .; Nez, F.; Ahmed, M.A.; Amaro, F.D.; Amaro, P .; Biraben, F.; Chen, T.L.; Covita, D.S.; Dax, A.J.; et al. The helion charge radius from laser spectroscopy of muonic helium-3 ions. Science2025,388, 854–858. https://doi.org/10.1126/science.adj2610

    work page doi:10.1126/science.adj2610

  17. [17]

    The alpha and helion particle charge radius difference from spectroscopy of quantum-degenerate helium2023

    van der Werf, Y.; Steinebach, K.; Jannin, R.; Bethlem, H.L.; Eikema, K.S.E. The alpha and helion particle charge radius difference from spectroscopy of quantum-degenerate helium2023. [arXiv:physics.atom- ph/2306.02333]

    Pith/arXiv arXiv

  18. [18]

    Revisiting the Helium Isotope-Shift Puzzle with Improved Uncer- tainties from Nuclear Structure Corrections.Phys

    Li Muli, S.S.; Richardson, T.R.; Bacca, S. Revisiting the Helium Isotope-Shift Puzzle with Improved Uncer- tainties from Nuclear Structure Corrections.Phys. Rev. Lett.2025,134, 032502. https://doi.org/10.1103/ PhysRevLett.134.032502

    2025

  19. [19]

    Toward resolving the discrepancy in helium-3 and helium-4 nuclear charge radii.Phys

    Qi, X.Q.; Zhang, P .P .; Yan, Z.C.; Tang, L.Y.; Chen, A.X.; Shi, T.Y.; Zhong, Z.X. Toward resolving the discrepancy in helium-3 and helium-4 nuclear charge radii.Phys. Rev. Res.2025,7, L022020. https: //doi.org/10.1103/PhysRevResearch.7.L022020

    work page doi:10.1103/physrevresearch.7.l022020 2025

  20. [20]

    Second-order hyperfine correction to H, D, and3He energy levels

    Pachucki, K.; Patkóš, V .c.v.; Yerokhin, V .A. Second-order hyperfine correction to H, D, and3He energy levels. Phys. Rev. A2024,110, 062806. https://doi.org/10.1103/PhysRevA.110.062806. 29 of 36

    work page doi:10.1103/physreva.110.062806

  21. [21]

    Binding energy of muonic beryllium: perturbative versus all-order calculations.Journal of Physics B: Atomic, Molecular and Optical Physics2026,59, 125002

    Rathi, S.; Jentschura, U.D.; Indelicato, P .; Ohayon, B. Binding energy of muonic beryllium: perturbative versus all-order calculations.Journal of Physics B: Atomic, Molecular and Optical Physics2026,59, 125002. https://doi.org/10.1088/1361-6455/ae7b9a

    work page doi:10.1088/1361-6455/ae7b9a

  22. [22]

    Ab initio calculation of nuclear-structure corrections in muonic atoms.Journal of Physics G: Nuclear and Particle Physics2018,45, 093002

    Ji, C.; Bacca, S.; Barnea, N.; Hernandez, O.J.; Dinur, N.N. Ab initio calculation of nuclear-structure corrections in muonic atoms.Journal of Physics G: Nuclear and Particle Physics2018,45, 093002. https://doi.org/10.1088/ 1361-6471/aad3eb

  23. [23]

    Superallowed 0+ → 0+ nuclear β decays: 2014 critical survey, with precise results for Vud and CKM unitarity.Physical Review C2015,91, 025501

    Hardy, J.C.; Towner, I.S. Superallowed 0+ → 0+ nuclear β decays: 2014 critical survey, with precise results for Vud and CKM unitarity.Physical Review C2015,91, 025501. https://doi.org/10.1103/PhysRevC.91.025501

    work page doi:10.1103/physrevc.91.025501 2014

  24. [24]

    γW Box Inside Out: Nuclear Polarizabilities Distort the Beta Decay Spectrum.Physical Review Letters2019,123, 042503

    Gorchtein, M. γW Box Inside Out: Nuclear Polarizabilities Distort the Beta Decay Spectrum.Physical Review Letters2019,123, 042503. https://doi.org/10.1103/PhysRevLett.123.042503

    doi:10.1103/physrevlett.123.042503

  25. [25]

    Modern theory of nuclear forces.Rev

    Epelbaum, E.; Hammer, H.W.; Meißner, U.G. Modern theory of nuclear forces.Rev. Mod. Phys.2009, 81, 1773–1825. https://doi.org/10.1103/RevModPhys.81.1773

    doi:10.1103/revmodphys.81.1773 2009

  26. [26]

    Chiral effective field theory and nuclear forces.Physics Reports2011,503, 1 – 75

    Machleidt, R.; Entem, D. Chiral effective field theory and nuclear forces.Physics Reports2011,503, 1 – 75. https://doi.org/https://doi.org/10.1016/j.physrep.2011.02.001

    doi:10.1016/j.physrep.2011.02.001 2011

  27. [27]

    Nuclear effective field theory: Status and perspectives.Rev

    Hammer, H.W.; König, S.; van Kolck, U. Nuclear effective field theory: Status and perspectives.Rev. Mod. Phys.2020,92, 025004. https://doi.org/10.1103/RevModPhys.92.025004

    doi:10.1103/revmodphys.92.025004 2020

  28. [28]

    A Guided Tour of ab initio Nuclear Many-Body Theory.Frontiers in Physics2020,Volume 8 - 2020

    Hergert, H. A Guided Tour of ab initio Nuclear Many-Body Theory.Frontiers in Physics2020,Volume 8 - 2020. https://doi.org/10.3389/fphy.2020.00379

    arXiv 2020

  29. [29]

    Quantifying truncation errors in effective field theory

    Furnstahl, R.J.; Klco, N.; Phillips, D.R.; Wesolowski, S. Quantifying truncation errors in effective field theory. Phys. Rev. C2015,92, 024005. https://doi.org/10.1103/PhysRevC.92.024005

    work page doi:10.1103/physrevc.92.024005

  30. [30]

    Quantifying correlated truncation errors in effective field theory.Phys

    Melendez, J.A.; Furnstahl, R.J.; Phillips, D.R.; Pratola, M.T.; Wesolowski, S. Quantifying correlated truncation errors in effective field theory.Phys. Rev. C2019,100, 044001. https://doi.org/10.1103/PhysRevC.100.0440 01

    work page doi:10.1103/physrevc.100.0440

  31. [31]

    Ab Initio Strategy for Taming the Nuclear- Structure Dependence of Vud Extractions: The 10C → 10B Superallowed Transition.Physical Review Letters 2025,134, 012501

    Gennari, M.; Drissi, M.; Gorchtein, M.; Navrátil, P .; Seng, C.Y. Ab Initio Strategy for Taming the Nuclear- Structure Dependence of Vud Extractions: The 10C → 10B Superallowed Transition.Physical Review Letters 2025,134, 012501. https://doi.org/10.1103/PhysRevLett.134.012501

    doi:10.1103/physrevlett.134.012501 2025

  32. [32]

    Cabibbo-Kobayashi-Maskawa unitarity deficit reduction via finite nuclear size.Phys

    Gorchtein, M.; Katyal, V .; Ohayon, B.; Sahoo, B.K.; Seng, C.Y. Cabibbo-Kobayashi-Maskawa unitarity deficit reduction via finite nuclear size.Phys. Rev. Res.2025,7, L042002, [arXiv:nucl-th/2502.17070]. https://doi.org/10.1103/z8g6-9j25

    arXiv 2025

  33. [33]

    Towards Precision Muonic X-Ray Measurements of Charge Radii of Light Nuclei.Physics2024,6, 206–215

    Ohayon, B.; Abeln, A.; Bara, S.; Cocolios, T.E.; Eizenberg, O.; Fleischmann, A.; Gastaldo, L.; Godinho, C.; Heines, M.; Hengstler, D.; et al. Towards Precision Muonic X-Ray Measurements of Charge Radii of Light Nuclei.Physics2024,6, 206–215. https://doi.org/10.3390/physics6010015

    work page doi:10.3390/physics6010015

  34. [34]

    MMC Array to Study X-Ray Transitions in Muonic Atoms.J

    Unger, D.; Abeln, A.; Cocolios, T.E.; Eizenberg, O.; Enss, C.; Fleischmann, A.; Gastaldo, L.; Godinho, C.; Heines, M.; Hengstler, D.; et al. MMC Array to Study X-Ray Transitions in Muonic Atoms.J. Low Temp. Phys.2024,216, 344–351. https://doi.org/10.1007/s10909-024-03141-x

    work page doi:10.1007/s10909-024-03141-x 2024

  35. [35]

    Charge radii of Cl isotopes from x-ray spectroscopy of muonic atoms2026

    Beyer, K.A.; Cocolios, T.E.; Costache, C.; Demol, P .; Deseyn, M.; Doinaki, A.; Eizenberg, O.; Gorchtein, M.; Heines, M.; Herzá ˇ n, A.; et al. Charge radii of Cl isotopes from x-ray spectroscopy of muonic atoms2026. [arXiv:nucl-ex/2605.08413]

    Pith/arXiv arXiv

  36. [36]

    Nuclear Charge Radius of9Be from Muonic Atom Spectroscopy Using a Microcalorimeter

    Eizenberg, O.; et al. Nuclear Charge Radius of9Be from Muonic Atom Spectroscopy Using a Microcalorimeter

  37. [37]

    Higher-order proton structure corrections to the Lamb shift in muonic hydrogen.Phys

    Carlson, C.E.; Vanderhaeghen, M. Higher-order proton structure corrections to the Lamb shift in muonic hydrogen.Phys. Rev. A2011,84, 020102. https://doi.org/10.1103/PhysRevA.84.020102

    work page doi:10.1103/physreva.84.020102

  38. [38]

    The Proton Structure in and out of Muonic Hydrogen.Annual Review of Nuclear and Particle Science2022,72, 389–418, [https://doi.org/10.1146/annurev-nucl-101920- 024709]

    Antognini, A.; Hagelstein, F.; Pascalutsa, V . The Proton Structure in and out of Muonic Hydrogen.Annual Review of Nuclear and Particle Science2022,72, 389–418, [https://doi.org/10.1146/annurev-nucl-101920- 024709]. https://doi.org/10.1146/annurev-nucl-101920-024709

    work page doi:10.1146/annurev-nucl-101920-

  39. [39]

    Nuclear currents in chiral effective field theory.Eur

    Krebs, H. Nuclear currents in chiral effective field theory.Eur. Phys. J. A2020,56, 234. https://doi.org/10.1 140/epja/s10050-020-00230-9

  40. [40]

    https://doi.org/10.1142/ 5500

    Walecka, J.D.Theoretical Nuclear and Subnuclear Physics, 2nd ed.; CO-PUBLISHED WITH IMPERIAL COL- LEGE PRESS, 2004; [https://www.worldscientific.com/doi/pdf/10.1142/5500]. https://doi.org/10.1142/ 5500

    work page doi:10.1142/5500 2004

  41. [41]

    Donnelly, T.; Haxton, W. Multipole operators in semileptonic weak and electromagnetic interactions with nuclei: Harmonic oscillator single-particle matrix elements.Atomic Data and Nuclear Data Tables1979, 23, 103–176. https://doi.org/https://doi.org/10.1016/0092-640X(79)90003-2. 30 of 36

    work page doi:10.1016/0092-640x(79)90003-2

  42. [42]

    SevenOperators, a Mathematica script for harmonic oscillator nuclear matrix elements arising in semileptonic electroweak interactions.Computer Physics Communications2008,179, 345–

    Haxton, W.; Lunardini, C. SevenOperators, a Mathematica script for harmonic oscillator nuclear matrix elements arising in semileptonic electroweak interactions.Computer Physics Communications2008,179, 345–

  43. [43]

    Accurate nucleon-nucleon potential with charge-independence breaking.Phys

    Wiringa, R.B.; Stoks, V .G.J.; Schiavilla, R. Accurate nucleon-nucleon potential with charge-independence breaking.Phys. Rev. C1995,51, 38–51. https://doi.org/10.1103/PhysRevC.51.38

    doi:10.1103/physrevc.51.38

  44. [44]

    High-precision, charge-dependent Bonn nucleon-nucleon potential.Phys

    Machleidt, R. High-precision, charge-dependent Bonn nucleon-nucleon potential.Phys. Rev. C2001, 63, 024001. https://doi.org/10.1103/PhysRevC.63.024001

    doi:10.1103/physrevc.63.024001

  45. [45]

    Quantum Monte Carlo Calculations ofA ≤ 6 Nuclei.Phys

    Pudliner, B.S.; Pandharipande, V .R.; Carlson, J.; Wiringa, R.B. Quantum Monte Carlo Calculations ofA ≤ 6 Nuclei.Phys. Rev. Lett.1995,74, 4396–4399. https://doi.org/10.1103/PhysRevLett.74.4396

    doi:10.1103/physrevlett.74.4396 1995

  46. [46]

    Realistic models of pion-exchange three-nucleon interactions.Phys

    Pieper, S.C.; Pandharipande, V .R.; Wiringa, R.B.; Carlson, J. Realistic models of pion-exchange three-nucleon interactions.Phys. Rev. C2001,64, 014001. https://doi.org/10.1103/PhysRevC.64.014001

    doi:10.1103/physrevc.64.014001

  47. [47]

    Nuclear forces from chiral Lagrangians.Phys

    Weinberg, S. Nuclear forces from chiral Lagrangians.Phys. Lett. B1990,251, 288–292. https://doi.org/10.1 016/0370-2693(90)90938-3

  48. [48]

    Effective chiral Lagrangians for nucleon-pion interactions and nuclear forces.Nucl

    Weinberg, S. Effective chiral Lagrangians for nucleon-pion interactions and nuclear forces.Nucl. Phys. B 1991,363, 3–18. https://doi.org/10.1016/0550-3213(91)90231-L

    doi:10.1016/0550-3213(91)90231-l 1991

  49. [49]

    Three-body interactions among nucleons and pions.Phys

    Weinberg, S. Three-body interactions among nucleons and pions.Phys. Lett. B1992,295, 114–121. https://doi.org/10.1016/0370-2693(92)90099-P

    work page doi:10.1016/0370-2693(92)90099-p

  50. [50]

    Precision Nucleon-Nucleon Potential at Fifth Order in the Chiral Expansion.Phys

    Epelbaum, E.; Krebs, H.; Meißner, U.G. Precision Nucleon-Nucleon Potential at Fifth Order in the Chiral Expansion.Phys. Rev. Lett.2015,115, 122301. https://doi.org/10.1103/PhysRevLett.115.122301

    doi:10.1103/physrevlett.115.122301 2015

  51. [51]

    High-Precision Nuclear Forces From Chiral EFT: State-of-the-Art, Challenges, and Outlook.Front

    Epelbaum, E.; Krebs, H.; Reinert, P . High-Precision Nuclear Forces From Chiral EFT: State-of-the-Art, Challenges, and Outlook.Front. Phys.2020,8, 98. https://doi.org/10.3389/fphy.2020.00098

    arXiv 2020

  52. [52]

    Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including ∆ resonances.Phys

    Piarulli, M.; Girlanda, L.; Schiavilla, R.; Navarro Pérez, R.; Amaro, J.E.; Ruiz Arriola, E. Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including ∆ resonances.Phys. Rev. C2015, 91, 024003. https://doi.org/10.1103/PhysRevC.91.024003

    work page doi:10.1103/physrevc.91.024003

  53. [53]

    Perturbative calculations of light nuclei up to N3LO in chiral effective field theory.arXiv preprint arXiv:2604.149852026

    Thim, O.; Ekström, A.; Forssén, C. Perturbative calculations of light nuclei up to N3LO in chiral effective field theory.arXiv preprint arXiv:2604.149852026

    Pith/arXiv arXiv

  54. [54]

    Chiral Effective Field Theory with Partly Perturbative Pions Applied to the Few-Nucleon Sector

    Thim, O. Chiral Effective Field Theory with Partly Perturbative Pions Applied to the Few-Nucleon Sector. PhD thesis, Chalmers University of Technology, Gothenburg, Sweden, 2026. https://doi.org/10.63959 /chalmers.dt/5891

    2026

  55. [55]

    Local chiral effective field theory interactions and quantum Monte Carlo applications

    Gezerlis, A.; et al. Local chiral effective field theory interactions and quantum Monte Carlo applications. Phys. Rev. C2014,90, 054323. https://doi.org/10.1103/PhysRevC.90.054323

    doi:10.1103/physrevc.90.054323

  56. [56]

    Chiral Three-Nucleon Interactions in Light Nuclei, Neutron- α Scattering and Neutron Matter

    Lynn, J.; et al. Chiral Three-Nucleon Interactions in Light Nuclei, Neutron- α Scattering and Neutron Matter. Phys. Rev. Lett2016,116, 062501. https://doi.org/10.1103/PhysRevLett.116.062501

    doi:10.1103/physrevlett.116.062501

  57. [57]

    Local Nucleon-Nucleon and Three-Nucleon Interactions Within Chiral Effective Field Theory, and Neutron Matter.Front

    Piarulli, M.; Tews, I. Local Nucleon-Nucleon and Three-Nucleon Interactions Within Chiral Effective Field Theory, and Neutron Matter.Front. Phys.2020,7, 245. https://doi.org/10.3389/fphy.2019.00245

    arXiv 2020

  58. [58]

    Maximally local two-nucleon interactions at N3LO in ∆-less chiral effective field theory.Phys

    Somasundaram, R.; Lynn, J.E.; Huth, L.; Schwenk, A.; Tews, I. Maximally local two-nucleon interactions at N3LO in ∆-less chiral effective field theory.Phys. Rev. C2024,109, 034005. https://doi.org/10.1103/ PhysRevC.109.034005

  59. [59]

    Implementation of Local Chiral Interactions in the Hyperspherical Harmonics Formalism.Frontiers in Physics2021,9

    Li Muli, S.S.; Bacca, S.; Barnea, N. Implementation of Local Chiral Interactions in the Hyperspherical Harmonics Formalism.Frontiers in Physics2021,9. https://doi.org/10.3389/fphy.2021.671869

    arXiv 2021

  60. [60]

    Quantum Monte Carlo calculations of weak transitions in A= 6–10 nuclei.Phys

    Pastore, S.; Baroni, A.; Carlson, J.; Gandolfi, S.; Pieper, S.C.; Schiavilla, R.; Wiringa, R.B. Quantum Monte Carlo calculations of weak transitions in A= 6–10 nuclei.Phys. Rev. C2018,97, 022501. https://doi.org/10 .1103/PhysRevC.97.022501

  61. [61]

    Chiral effective field theory calculations of weak transitions in light nuclei.Phys

    King, G.B.; Andreoli, L.; Pastore, S.; Piarulli, M.; Schiavilla, R.; Wiringa, R.B.; Carlson, J.; Gandolfi, S. Chiral effective field theory calculations of weak transitions in light nuclei.Phys. Rev. C2020,102, 025501. https://doi.org/10.1103/PhysRevC.102.025501

    work page doi:10.1103/physrevc.102.025501

  62. [62]

    Role of Spin-Isospin Symmetries in Nuclear β-Decays

    Li Muli, S.S.; Djärv, T.R.; Forssén, C.; Phillips, D.R. Role of Spin-Isospin Symmetries in Nuclear β-Decays. Phys. Rev. Lett.2026,136, 242501. https://doi.org/10.1103/vk51-b476

    work page doi:10.1103/vk51-b476 2026

  63. [63]

    Quantum Monte Carlo methods for nuclear physics.Rev

    Carlson, J.; Gandolfi, S.; Pederiva, F.; Pieper, S.C.; Schiavilla, R.; Schmidt, K.E.; Wiringa, R.B. Quantum Monte Carlo methods for nuclear physics.Rev. Mod. Phys.2015,87, 1067–1118. https://doi.org/10.1103/ RevModPhys.87.1067

    2015

  64. [64]

    Quantum Monte Carlo calculations of light nuclei with local chiral two- and three-nucleon interactions.Phys

    Lynn, J.E.; Tews, I.; Carlson, J.; Gandolfi, S.; Gezerlis, A.; Schmidt, K.E.; Schwenk, A. Quantum Monte Carlo calculations of light nuclei with local chiral two- and three-nucleon interactions.Phys. Rev. C2017, 96, 054007. https://doi.org/10.1103/PhysRevC.96.054007. 31 of 36

    work page doi:10.1103/physrevc.96.054007

  65. [65]

    Auxiliary field diffusion Monte Carlo calculations of light and medium-mass nuclei with local chiral interactions.Phys

    Lonardoni, D.; et al. Auxiliary field diffusion Monte Carlo calculations of light and medium-mass nuclei with local chiral interactions.Phys. Rev. C2018,97, 044318. https://doi.org/10.1103/PhysRevC.97.044318

    doi:10.1103/physrevc.97.044318

  66. [66]

    Variational Calculation on A = 3 and 4 Nuclei with Non-Local Potentials.Few-Body Systems2006,39, 159–176

    Viviani, M.; Marcucci, L.E.; Rosati, S.; et al.. Variational Calculation on A = 3 and 4 Nuclei with Non-Local Potentials.Few-Body Systems2006,39, 159–176. https://doi.org/https://doi.org/10.1007/s00601-006-0158- y

    work page doi:10.1007/s00601-006-0158-

  67. [67]

    The hyperspherical harmonics method: a tool for testing and improving nuclear interaction models.Front

    Marcucci, L.E.; Dohet-Eraly, J.; Girlanda, L.; Gnech, A.; Kievsky, A.; Viviani, M. The hyperspherical harmonics method: a tool for testing and improving nuclear interaction models.Front. Phys.2020,8. https://doi.org/10.3389/fphy.2020.00069

    arXiv 2020

  68. [68]

    State dependent effective interaction for the hyperspherical formalism.Phys

    Barnea, N.; Leidemann, W.; Orlandini, G. State dependent effective interaction for the hyperspherical formalism.Phys. Rev. C2000,61, 054001. https://doi.org/10.1103/PhysRevC.61.054001

    doi:10.1103/physrevc.61.054001

  69. [69]

    Ab initio no core shell model.Progress in Particle and Nuclear Physics2013, 69, 131–181

    Barrett, B.R.; Navrátil, P .; Vary, J.P . Ab initio no core shell model.Progress in Particle and Nuclear Physics2013, 69, 131–181. https://doi.org/https://doi.org/10.1016/j.ppnp.2012.10.003

    doi:10.1016/j.ppnp.2012.10.003 2012

  70. [70]

    Coupled-cluster computations of atomic nuclei

    Hagen, G.; Papenbrock, T.; Hjorth-Jensen, M.; Dean, D.J. Coupled-cluster computations of atomic nuclei. Reports on Progress in Physics2014,77, 096302. https://doi.org/10.1088/0034-4885/77/9/096302

    doi:10.1088/0034-4885/77/9/096302

  71. [71]

    The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei.Physics Reports2016,621, 165–222

    Hergert, H.; Bogner, S.; Morris, T.; Schwenk, A.; Tsukiyama, K. The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei.Physics Reports2016,621, 165–222. Memorial Volume in Honor of Gerald E. Brown, https://doi.org/https://doi.org/10.1016/j.physrep.2015.12.007

    doi:10.1016/j.physrep.2015.12.007 2015

  72. [72]

    An iteration method for the solution of the eigenvalue problem of linear differential and integral operators.Journal of Research of the National Bureau of Standards1950,45, 255–282

    Lanczos, C. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators.Journal of Research of the National Bureau of Standards1950,45, 255–282. https://doi.org/10.6028/ jres.045.026

  73. [73]

    Komzsik, L.The Lanczos method: evolution and application; SIAM, 2003

    2003

  74. [74]

    Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem.Linear Algebra and its Applications1980,34, 235–258

    Paige, C. Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem.Linear Algebra and its Applications1980,34, 235–258. https://doi.org/https://doi.org/10.1016/0024-3795(80)90167-6

    work page doi:10.1016/0024-3795(80)90167-6

  75. [75]

    Do we fully understand the symmetric Lanczos algorithm yet?, 1995

    Parlett, B. Do we fully understand the symmetric Lanczos algorithm yet?, 1995

    1995

  76. [76]

    The inverse of a linear operator.Journal of Physics A: Mathematical, Nuclear and General1974, 7, 2120

    Haydock, R. The inverse of a linear operator.Journal of Physics A: Mathematical, Nuclear and General1974, 7, 2120

  77. [77]

    The Recursive Solution of the Schrodinger Equation

    Haydock, R. The Recursive Solution of the Schrodinger Equation. InSolid State Physics; Ehrenreich, H.; Seitz, F.; Turnbull, D., Eds.; Academic Press, 1980; Vol. 35,Solid State Physics, pp. 215–294. https://doi.org/https: //doi.org/10.1016/S0081-1947(08)60505-6

    work page doi:10.1016/s0081-1947(08)60505-6 1980

  78. [78]

    Electronic Structure from the Point of View of the Local Atomic Environment

    Heine, V . Electronic Structure from the Point of View of the Local Atomic Environment. InSolid State Physics; Ehrenreich, H.; Seitz, F.; Turnbull, D., Eds.; Academic Press, 1980; Vol. 35,Solid State Physics, pp. 1–127. https://doi.org/https://doi.org/10.1016/S0081-1947(08)60503-2

    work page doi:10.1016/s0081-1947(08)60503-2 1980

  79. [79]

    Applications of the Recursion Method to the Electronic Structure from an Atomic Point of View

    Kelly, M. Applications of the Recursion Method to the Electronic Structure from an Atomic Point of View. InSolid State Physics; Ehrenreich, H.; Seitz, F.; Turnbull, D., Eds.; Academic Press, 1980; Vol. 35,Solid State Physics, pp. 295–383. https://doi.org/https://doi.org/10.1016/S0081-1947(08)60506-8

    work page doi:10.1016/s0081-1947(08)60506-8 1980

  80. [80]

    Electronic structure based on the local atomic environment for tight- binding bands.Journal of Physics C: Solid State Physics1972,5, 2845

    Haydock, R.; Heine, V .; Kelly, M.J. Electronic structure based on the local atomic environment for tight- binding bands.Journal of Physics C: Solid State Physics1972,5, 2845. https://doi.org/10.1088/0022-3719/5/ 20/004

    work page doi:10.1088/0022-3719/5/

Showing first 80 references.