Precise evaluation of the isotope shift (IS) factors for seven low-lying potassium (K) states is achieved using relativistic coupled-cluster (RCC) theory. The energies of these states are assessed and compared with experimental data to confirm the accuracy of the wave functions calculated at varying RCC theory approximations and highlight the significance of many-body and relativistic effects in determining the energies and IS factors of K. Various methods are used to compute the IS factors, with the finite-field (FF) approach yielding results that align with observed and semi-empirical data. This consistency is attributed to orbital relaxation effects that are naturally present in the FF method but emerge only through complex interactions in other techniques. Using the IS factors derived from FF, we review the mean square radius difference between \(^{38m}\)K and \(^{39}\)K. From this difference and muonic atom x-ray spectroscopy, we deduce the absolute radius of \(^{38m}K\) using an updated calculation of the nuclear polarizability effect. Finally, we evaluate the isospin symmetry breaking (ISB) in this isotriplet by integrating the radius of \(^{38m}\)K with an updated radius of \(^{38}\)Ca, concluding that the ISB is compatible with zero. This finding offers a stringent benchmark for nuclear model calculations of ISB corrections in nuclear beta decay, which play a key role in determining the \(V_{ud}\) matrix element.

We report the first study of the \(\mathcal{O}(\alpha)\) structure-dependent electromagnetic radiative corrections to unique first-forbidden nuclear beta decays. We show that the insertion of angular momentum into the nuclear matrix element by the virtual/real photon exchange opens up the decay at vanishing nuclear recoil momentum which was forbidden at tree level, leading to a dramatic change in the decay spectrum not anticipated in existing studies. We discuss its implications for precision tests on the Standard Model and searches for new physics.

In this work, we present the elastic electron scattering longitudinal form factors of A≤10 nuclei computed in a variational Monte Carlo approach. We employ the Norfolk family of local chiral interactions and a consistent electromagnetic charge operator. Our calculations are compared both to data and past theoretical evaluations. This work represents, to our knowledge, the first exact many-body calculation of longitudinal form factors in the 7≤A≤10 mass range. Finally, we identify 9Be and 10B as candidate targets for renewed experimental interest, as they exhibit the potential to provide more stringent constraints on the theoretical models. 

We present an ab initio study of the correlation between nuclear matrix elements of neutrinoless double-beta (0νββ) decay and nucleon-nucleon scattering phase shifts in the 1S0 channel. Starting from thirty-four statistically weighted interactions derived from chiral effective field theory, we apply the valence-space in-medium similarity renormalization group to calculate nuclear matrix elements in four key experimental isotopes. Comparing with the 1S0-channel phase shifts given from each interaction, in all cases we observe a strong correlation for scattering energies above 75 MeV. Furthermore, a global sensitivity analysis, enabled by newly developed machine-learning emulators, confirms that the nuclear matrix elements of the decay depend primarily on the C1S0 low-energy constant, which is associated with the phase shifts in that partial wave. These results provide the first clear correlation between 0νββ decay nuclear matrix elements and a measured observable and will therefore serve as a crucial component in ongoing and future refinements of ab initio uncertainty estimates.

We study the leading radiative correction to proton-proton fusion using the pionless effective field theory framework at leading order. We derive the relevant matrix elements and evaluate them using the method of regions. We benchmark the accuracy of our approximations by carrying out numerical computations of the full expressions. We show that the first order radiative corrections due to the exchange of a Coulomb photon between positron and proton-proton systems map onto the Sirlin function and the O(alpha) contribution from the Fermi function. We furthermore find that the nuclear structure dependent radiative correction omitted in the previous analysis by Kurylov and collaborators gives an up to 0.2 % correction to the pp fusion S-factor with its size ultimately depending on a two-nucleon counterterm that renormalizes the axial two-body current.

We present Quantum Monte Carlo calculations of magnetic moments, form factors, and densities of A≤10 nuclei within a chiral effective field theory approach. We use the Norfolk two- and three-body chiral potentials and their consistent electromagnetic one- and two-nucleon current operators. We find that two-body contributions to the magnetic moment can be large (up to ∼33% in A=9 systems). We study the model dependence of these observables and place particular emphasis on investigating their sensitivity to using different cutoffs to regulate the many-nucleon operators. Calculations of elastic magnetic form factors for A≤10 nuclei show excellent agreement with the data out to momentum transfers q≈3 fm−1.

The Short-Time approximation is a method introduced to evaluate electroweak nuclear response for systems with A≥12, extending the reach of first-principle many-body Quantum Monte Carlo calculations. Using realistic two- and three-body nuclear interactions and consistent one- and two-body electromagnetic currents, we calculate longitudinal and transverse response densities and response functions of 12C. We compare the resulting cross sections with experimental data for electron-nucleus scattering, finding good agreement.

We present Quantum Monte Carlo calculations of magnetic form factors in A=6−10 nuclei, based on Norfolk two- and three-nucleon interactions, and associated one- and two-body electromagnetic currents. Agreement with the available experimental data for 6Li, 7Li, 9Be and 10B up to values of momentum transfer q∼3 fm−1 is achieved when two-nucleon currents are accounted for. We present a set of predictions for the magnetic form factors of 7Be, 8Li, 9Li, and 9C. In these systems, two-body currents account for ∼40−60% of the total magnetic strength. Measurements in any of these radioactive systems would provide valuable insights on the nuclear magnetic structure emerging from the underlying many-nucleon dynamics. A particularly interesting case is that of 7Be, as it would enable investigations of the magnetic structure of mirror nuclei

We explore the impact of retaining three-body operators within the in-medium similarity renormalization group (IMSRG), as well as various approximations schemes. After studying two toy problems, idential fermions with a contact interaction and the Lipkin-Meshkov-Glick model, we employ the valence-space formulation of the IMSRG to investigate the even-A carbon isotopes with a chiral two-body potential. We find that retaining only those commutators expressions that scale as N7 provides an excellent approximation of the full three-body treatment.

We describe an approximation to the in-medium similarity renormalization group (IMSRG) method in which we include the effects of intermediate three-body operators arising within nested commutators. As an initial step, we present the relevant equations for two nested commutators, all of which can be factorized so that the method scales like the standard IMSRG(2) approximation, enabling large-scale calculations. We test the accuracy of this approximation scheme, and apply it to the isotopic chains of carbon, sulfur and nickel isotopic chains. We obtain an improved description of spectroscopy, and a reduced dependence on the choice of the valence space. In addition, we provide an explanation of the relative importance of the diagram topologies included, with an eye toward assessing the impact of remaining omitted terms.

We report the first \textit{ab initio} calculation of the nuclear-structure-dependent radiative correction \(\delta_{ \mathrm{NS} }\) to the \({}^{10}\mathrm{C} \rightarrow {}^{10}\mathrm{B}\) superallowed transition, computed with the no-core shell model and chiral effective field theory. We obtain \(\delta_{ \mathrm{NS} } = - 0.400 (29)_{ \mathrm{nuc} } (12)_{n,\mathrm{el} }\) with a \(1.7\)-times reduction in the nuclear uncertainty when compared to the current literature estimate based on the shell model and Fermi gas picture. This work paves the way for a precise determination of \(V_{ud}\) from superallowed beta decays.

The accuracy of Vud determinations from superallowed β decays critically hinges on control over radiative corrections. Recently, substantial progress has been made on the single-nucleon, universal corrections, while nucleus-dependent effects, typically parameterized by a quantity δNS, are much less well constrained. Here, we lay out a program to evaluate this correction from effective field theory (EFT), highlighting the dominant terms as predicted by the EFT power counting. Moreover, we compare the results to a dispersive representation of δNS and show that the expected momentum scaling applies even in the case of low-lying intermediate states. Our EFT framework paves the way towards ab-initio calculations of δNS and thereby addresses the dominant uncertainty in Vud.

Radiative corrections are essential for an accurate determination of Vud from superallowed β decays. In view of recent progress in the single-nucleon sector, the uncertainty is dominated by the theoretical description of nucleus-dependent effects, limiting the precision that can currently be achieved for Vud. In this work, we provide a detailed account of the electroweak corrections to superallowed β decays in effective field theory (EFT), including the power counting, potential and ultrasoft contributions, and factorization in the decay rate. We present a first numerical evaluation of the dominant corrections in light nuclei based on Quantum Monte Carlo methods, confirming the expectations from the EFT power counting. Finally, we discuss strategies how to extract from data the low-energy constants that parameterize short-distance contributions and whose values are not predicted by the EFT. Combined with advances in ab-initio nuclear-structure calculations, this EFT framework allows one to systematically address the dominant uncertainty in Vud, as illustrated in detail for the 14O →14N transition.

We compute ground-state and dynamical properties of 4He and 16O nuclei using as input high-resolution, phenomenological nucleon-nucleon and three-nucleon forces that are local in coordinate space. The nuclear Schrödinger equation for both nuclei is accurately solved employing the auxiliary-field diffusion Monte Carlo approach. For the 4He nucleus, detailed benchmarks are carried out with the hyperspherical harmonics method. In addition to presenting results for the binding energies and radii, we also analyze the momentum distributions of these nuclei and their Euclidean response function corresponding to the isoscalar density transition. The latter quantity is particularly relevant for lepton-nucleus scattering experiments, as it paves the way to quantum Monte Carlo calculations of electroweak response functions of 16O.

The Mu2e and COMET experiments are expected to improve existing limits on charged lepton flavor violation (CLFV) by roughly four orders of magnitude. Muon-to-electron conversion experiments are typically optimized for electrons produced without nuclear excitation, as this maximizes the electron energy and minimizes backgrounds from the free decay of the muon. Here we argue that Mu2e and COMET will be able to extract additional constraints on CLFV from inelastic muon-to-electron conversion, given the 27Al target they have chosen and backgrounds they anticipate. We describe CLFV scenarios in which inelastic CLFV can induce measurable distortions in the near-endpoint spectrum of conversion electrons, including cases where certain contributing operators cannot be probed in elastic muon-to-electron conversion. We extend the nonrelativistic EFT treatment of elastic μ→e conversion to include the new nuclear operators needed for the inelastic process, evaluate the associated nuclear response functions, and describe several new-physics scenarios where the inelastic process can provide additional information on CLFV.

To continue from our previous work \textit{Phys.Rev.D\textbf{109}(2024),073007}, we derive the full Standard Model prediction of the most general free neutron differential decay rate with all massive particles (neutron, proton and electron) polarized, including the \(\mathcal{O}(1/m_N)\) recoil corrections and \(\mathcal{O}(\alpha/\pi)\) radiative corrections. For the latter we adopt the newly-developed pseudo-neutrino formalism which is compatible to realistic experimental setups, in which neutrinos and photons are not detected. We also provide readily-executable \textit{Mathematica} notebooks to evaluate these corrections.

A fully generic treatment of electric dipole moments (EDMs) is presented in the CP-violating and flavor-conserving weak effective field theory (WET) with five flavors of quarks and three flavors of leptons. We systematically analyze leading contributions to EDMs originating from QCD and QED renormalization group running between the electroweak scale and low energy scales of about 2 GeV. We include the full one-loop anomalous dimension and a subset of two-loop corrections, as well as threshold corrections at the bottom, charm and tau masses. This allows us to derive master formulae in the space of generic WET for the neutron and proton EDMs, for EDMs of diamagnetic atoms, and the precession frequencies constrained in molecular EDM experiments, from which bounds on the electron EDM are extracted. In particular, our master formulae capture the contributions of WET CP-violating operators with heavy quark and lepton flavors. As an application, we study EDM constraints on the Yukawa couplings of the Higgs boson, in both the linear and non-linear realizations of electroweak symmetry breaking.

We introduce a useful framework for high-precision studies of the neutron beta decay by merging the current algebra description and the fixed-order effective field theory calculation of the electroweak radiative corrections to the neutron axial form factor. We discuss the advantages of this hybrid method and show that it only requires a minimal amount of lattice QCD inputs to achieve a \(10^{−4}\) theory accuracy for the Standard Model prediction of the neutron lifetime and the axial-to-vector coupling ratio \(\lambda\), both important to the search for physics beyond the Standard Model.

Built on the seminal works by Jackson-Treiman-Wyld and Ebel-Feldman, we derive the most general free neutron differential decay rate where all massive particles (neutron, proton, and electron) are polarized. This introduces 33 new correlations in addition to the 18 existing ones, which overconstrain the coupling constants in the low-energy effective field theory of charged weak interactions, and thus provides stringent tests of the validity of the theory framework itself. We classify the correlation coefficients in terms of their Standard Model limit and discrete symmetries, and study their expansion with respect to the new physics coupling strengths, supplemented by the experiment-independent \(\mathcal{O}(\alpha)\) virtual electromagnetic radiative corrections.

At leading order in weak and electromagnetic couplings, cross sections for (anti)neutrino-nucleon elastic scattering are determined by four nucleon form factors that depend on the momentum transfer Q2. Including radiative corrections in the Standard Model and potential new physics contributions beyond the Standard Model, eight invariant amplitudes are possible, depending on both Q2 and the (anti)neutrino energy Eν. We review the definition of these amplitudes and use them to compute both unpolarized and polarized observables including radiative corrections. We show that unpolarized accelerator neutrino cross-section measurements can probe new physics parameter space within the constraints inferred from precision beta decay measurements.

We compute the muon capture on deuteron in the doublet hyperfine state for a variety of nuclear interactions and consistent nuclear currents. Our analysis includes a detailed examination of the theoretical uncertainties coming from different sources: the single-nucleon axial form factor, the truncation of the interaction and current chiral expansion, and the model dependence. Moreover, we study the impact of the use of different power counting scheme for the electroweak currents on the truncation error. To estimate the truncation error of the chiral expansion of interactions and currents we use the most modern techniques based on Bayesian analysis. This method enables us to give a clear statistical interpretation of the computed theoretical uncertainties. Finally, we provide the differential capture rate as function of the kinetic energy of the outgoing neutron which may be measured in future experiments. Our recommended theoretical value for the total doublet capture rate is Γth=395±10 s−1 (68% confidence level). We calculated also the capture rate in the quartet hyperfine state, which turns out to be in the range [13.3−13.8] s−1 depending on the adopted nuclear interaction.

Interactions of charged leptons with nuclei and the naive tree-level kinematics of these processes are affected by radiation of photons induced by the QED nuclear medium. We evaluate cross-section modifications at leading orders of the number of correlated interactions inside the nucleus, known as the opacity expansion. We derive results for soft and collinear types of the bremsstrahlung at the first three orders in opacity and generalize them to higher orders. We present the leading in opacity energy spectra of soft and collinear photons and radiative energy loss inside the nucleus for experiments with lepton kinematics in the GeV energy range. At leading power of the Glauber soft-collinear effective field theory, the soft radiation is further resummed to all orders both in opacity and in the electromagnetic coupling constant. We find that the soft and collinear medium-induced radiation is vacuumlike, and additional corrections are power suppressed. Despite the negligible modification to the induced photon spectra, the nuclear medium-induced radiation sizably affects the broadening of charged leptons in the direction orthogonal to their propagation.

We discuss a novel approach based on machine learning (ML) regression models to reduce the computational cost of disconnected diagrams in lattice QCD calculations. This method creates a mapping between the results of fermionic loops computed at different quark masses and flow times. The ML model, trained with just a small fraction of the complete data set, provides similar predictions and uncertainties over the calculation done over the whole ensemble, resulting in a significant computational gain.

We discuss a machine learning (ML) regression model to reduce the computational cost of disconnected diagrams in lattice QCD calculations. This method creates a mapping between the results of fermionic loops computed at different quark masses and flow times. The ML mapping, trained with just a small fraction of the complete data set, makes use of translational invariance and provides consistent result with comparable uncertainties over the calculation done over the whole ensemble, resulting in a significant computational gain.

We perform a loop-level analysis of charged-current (CC) processes involving light leptons and quarks within the Standard Model Effective Field Theory (SMEFT). This work is motivated by the high precision reached in experiment and Standard Model calculations for CC decays of mesons, neutron, and nuclei, and by a lingering tension in the Cabibbo universality test. We identify the SMEFT operators that induce the largest loop-level contributions to CC processes. These include four-quark and four-fermion semileptonic operators involving two third-generation quarks. We discuss the available constraints on the relevant effective couplings and along the way we derive new loop-level bounds from K→πνν¯ on four-quark operators involving two top quarks. We find that low-energy CC processes are quite competitive with other probes, set constraints that do not depend on flavor-symmetry assumptions, and probe operators involving third-generation quarks up to effective scales of Λ≃8 TeV. Finally, we briefly discuss single-field ultraviolet completions that could induce the relevant operators.

Nuclei will play a prominent role in searches for physics beyond the Standard Model as the active material in experiments. In order to reliably interpret new physics signals, one needs an accurate model of the underlying nuclear dynamics. In this review, we discuss recent progress made with quantum Monte Carlo approaches for calculating the electroweak structure of light nuclei. We place particular emphasis on recent β-decay, muon capture, 0νββ-decay, and electron scattering results.

Modeling lepton-nucleus scattering with the accuracy required to extract neutrino-oscillation pa- rameters from long- and short-baseline experiments necessitates retaining most quantum-mechanical effects. One such effect is the interference between one- and two-body current operators in the transition currents, which has been known to enhance the cross-sections, especially in transverse kinematics. In this work, we incorporate such interference in the spectral function formalism, which combines relativistic currents and kinematics with an accurate description of the initial target state. Our analysis of lepton-scattering off 12C demonstrates that interference effects appreciably enhance the transverse electromagnetic response functions and the flux-folded neutrino-nucleus cross section, in both cases, improving the agreement with experimental data. We discuss the impact on the neutrino-oscillation program and the determination of nucleon axial form factors.

The continued generation of N_f=2+1 quark flavor gauge configurations using stabilized Wilson fermions by the open lattice initiative (OpenLat) is reported. We present the status of our ongoing production and show updates on increasing statistics at the four lattice spacings a=0.12, 0.094, 0.077 and 0.064 fm. Aside from the SU(3) flavor symmetric point we discuss advancements in going towards physical pion masses. We show preliminary results of the pion decay constants, extending previous results, and discuss further validation observables on the available ensembles.

It is well-known that the traditional treatment of radiative corrections that utilizes the true'' neutrino momentum $\vec{p}_\nu$ in the differential decay rate formula could lead to a $\sim \alpha/\pi$ systematic error in certain observables due to the mistreatment of 4-body kinematics. I investigate the theory structure of one of the proposed solutions, the\(\nu'\)-formalism'', in the non-recoil limit appropriate for neutron and nuclear beta decays. I derive an elegant master formula for the 4-body phase space and use it to re-analyze the spectrum-dependent outer'' radiative corrections to the beta decay of a polarized spin-half nucleus; a complete set of analytic expressions is provided for readers to straightforwardly obtain the final numerical results. I compare it to therecoil formalism'' where the energy of the recoil nucleus is fixed.

The nonrelativistic effective field theory (NRET) is widely used in dark matter direct detection and charged-lepton flavor violation studies through 𝜇→𝑒 conversion. However, existing literature has not fully considered tensor couplings. This study fills this gap by utilizing an innovative tensor decomposition method, extending NRET to incorporate previously overlooked tensor interactions. This development is expected to have a significant impact on ongoing experiments seeking physics beyond the Standard Model and on our understanding of the new-physics interactions. Notably, we identify additional operators in 𝜇→𝑒 conversion that are absent in scalar and vector couplings. To support further research and experimental analyses, comprehensive tables featuring tensor matrix elements and their corresponding operators are provided.

Recent developments in the Standard Model analysis of semileptonic charged-current processes involving light quarks have revealed ∼3σ tensions in Cabibbo universality tests involving meson, neutron, and nuclear beta decays. In this paper, we explore beyond the Standard Model explanations of this so-called Cabibbo Angle Anomaly in the framework of the Standard Model Effective Field Theory (SMEFT), including not only low-energy charged current processes (L'), but also electroweak precision observables (EW') and Drell-Yan collider processes (C') that probe the same underlying physics across a broad range of energy scales. The resultingCLEW' framework not only allows one to test explanations of the Cabibbo Angle Anomaly, but is set up to provide near model-independent analyses with minimal assumptions on the flavor structure of the SMEFT operators. Besides the global analysis, we consider a large number of simpler scenarios, each with a subset of SMEFT operators, and investigate how much they improve upon the Standard Model fit. We find that the most favored scenarios, as judged by the Akaike Information Criterion, are those that involve right-handed charged currents. Additional interactions, namely oblique operators, terms modifying the Fermi constant, and operators involving right-handed neutral currents, play a role if the CDF determination of the W mass is included in the analysis.

We describe a procedure to determine moments of parton distribution functions of any order in lattice QCD. The procedure is based on the gradient flow for fermion and gauge fields. The flowed matrix elements of twist-2 operators renormalize multiplicatively, and the matching with the physical matrix elements can be obtained using continuum symmetries and the irreducible representations of Euclidean 4-dimensional rotations. We calculate the matching coefficients at one-loop in perturbation theory for moments of any order in the flavor non-singlet case. We also give specific examples of operators that could be used in lattice QCD computations. It turns out that it is possible to choose operators with identical Lorentz indices and still have a multiplicative matching. One can thus use twist-2 operators exclusively with temporal indices, thus substantially improving the signal-to-noise ratio in the computation of the hadronic matrix elements.

For many decades, the main source of information on the top-left corner element of the Cabibbo-Kobayashi-Maskawa quark mixing matrix \(V_{ud}\) were superallowed nuclear beta decays with an impressive 0.01\% precision. This precision, apart from experimental data, relies on theoretical calculations in which nuclear structure-dependent effects and uncertainties play a prime role. This review is dedicated to a thorough reassessment of all ingredients that enter the extraction of the value of \(V_{ud}\) from experimental data. We tried to keep balance between historical retrospect and new developments, many of which occurred in just five past years. They have not yet been reviewed in a complete manner, not least because new results are a-coming. This review aims at filling this gap and offers an in-depth yet accessible summary of all recent developments.

Neutral meson mixing and meson lifetimes are theory-side parametrised in terms four-quark operators which can be determined by calculating weak decay matrix elements using lattice Quantum Chromodynamics.While calculations of meson mixing matrix elements are standard, determinations of lifetimes typically suffer from complications in renormalisation procedures because dimension-6 four-quark operators can mix with operators of lower mass dimension and, moreover, quark-line disconnected diagrams contribute.We present work detailing the idea to use fermionic gradient flow to non-perturbatively renormalise matrix elements describing meson mixing or lifetimes, and combining it with a perturbative calculation to match to the MSbar scheme using the short flow time expansion.

We present a comprehensive re-evaluation of the \(ft\) values in superallowed nuclear beta decays crucial for the precise determination of \(V_{ud}\) and low-energy tests of the electroweak Standard Model. It consists of the first, fully data-driven analysis of the nuclear beta decay form factor, that utilizes isospin relations to connect the nuclear charged weak distribution to the measurable charge distributions. This prescription supersedes previous shell-model estimations, and allows for a rigorous quantification of theory uncertainties in \(f\) which is absent in the existing literature. Our new evaluation shows an overall downward shift of the central values of \(f\) at the level of 0.01\%.

Precision measurements of antineutrino elastic scattering on hydrogen from future neutrino experiments offer a unique opportunity to access the low-energy structure of protons and neutrons. We discuss the determination of the nucleon axial-vector form factor and radius from antineutrino interactions on hydrogen that can be collected at the future Long-Baseline Neutrino Facility and study the sources of theoretical and experimental uncertainties. The projected accuracy would improve existing measurements by 1 order of magnitude and be competitive with contemporary lattice-QCD determinations, potentially helping to resolve the corresponding tension with measurements from (anti)neutrino elastic scattering on deuterium. We find that the current knowledge of the nucleon vector form factors could be one of the dominant sources of uncertainty. We also evaluate the constraints that can be simultaneously obtained on the absolute flux normalization.

We present the first lattice QCD calculation of the universal axial \(\gamma W\)-box contribution \(\square{\gamma W}^{VA}\) to both superallowed nuclear and neutron beta decays. This contribution emerges as a significant component within the theoretical uncertainties surrounding the extraction of \(|V{ud}|\) from superallowed decays. Our calculation is conducted using two domain wall fermion ensembles at the physical pion mass. To construct the nucleon 4-point correlation functions, we employ the random sparsening field technique. Furthermore, we incorporate long-distance contributions to the hadronic function using the infinite-volume reconstruction method. Upon performing the continuum extrapolation, we arrive at \(\square{\gamma W}^{VA}=3.65(8){\mathrm{lat}}(1){\mathrm{PT}}\times10^{-3}\). Consequently, this yields a slightly higher value of \(|V{ud}|=0.97386(11){\mathrm{exp.}}(9){\mathrm{RC}}(27){\mathrm{NS}}\), reducing the previous \(2.1\sigma\) tension with the CKM unitarity to \(1.8\sigma\). Additionally, we calculate the vector \(\gamma W\)-box contribution to the axial charge \(gA\), denoted as \(\square{\gamma W}^{VV}\), and explore its potential implications.*

In pursuing the essential elements of nuclear binding, we compute ground-state properties of atomic nuclei with up to A=20 nucleons, using as input a leading order pionless effective field theory Hamiltonian. A variational Monte Carlo method based on a new, highly-expressive, neural-network quantum state ansatz is employed to solve the many-body Schrödinger equation in a systematically improvable fashion. In addition to binding energies and charge radii, we accurately evaluate the magnetic moments of these nuclei, as they reveal the self-emergence of the shell structure, which is not a priori encoded in the neural-network ansatz. To this aim, we introduce a novel computational protocol based on adding an external magnetic field to the nuclear Hamiltonian, which allows the neural network to learn the preferred polarization of the nucleus within the given magnetic field.

The calculation of the neutron electric dipole moment within effective field theories for physics beyond the Standard Model requires non-perturbative hadronic matrix elements of effective operators composed of quark and gluon fields. In order to use input from lattice computations, these matrix elements must be translated from a scheme suitable for lattice QCD to the minimal-subtraction scheme used in the effective-field-theory framework. The accuracy goal in the context of the neutron electric dipole moment necessitates at least a one-loop matching calculation. Here, we provide the one-loop matching coefficients for the CP-odd three-gluon operator between two different minimally subtracted 't Hooft–Veltman schemes and the gradient flow. This completes our program to obtain the one-loop gradient-flow matching coefficients for all CP-violating and flavor-conserving operators in the low-energy effective field theory up to dimension six.

We compare recent MINERvA antineutrino-hydrogen charged-current measurements to phenomenological predictions of the axial-vector form factor based on fits to all available electron scattering and deuterium bubble-chamber data and to representative lattice-QCD (LQCD) determination by the PNDME Collaboration. While there is 1--2σ agreement in the cross section with MINERvA data for each bin in Q2, we identify three regions with different relevance and opportunity for LQCD predictions. For Q2≲0.2 GeV2, the phenomenological extractions have large number of data points and LQCD is competitive, while MINERvA data have large errors. For 0.2 GeV2≲Q2≲1 GeV2, LQCD is competitive with the MINERvA determination, and both give values larger than from phenomenological extraction. For Q2>1 GeV2, the MINERvA data are the most precise. Our analysis indicates that with improving precision of MINERvA-like experiments and LQCD data, the uncertainty in the nucleon axial-vector form factor will be steadily reduced.

We review the status of the Standard Model theory of neutron beta decay. Particular emphasis is put on the recent developments in the electroweak radiative corrections. Given that some existing approaches give slightly different results, we thoroughly review the origin of discrepancies, and provide our recommended value for the radiative correction to the neutron and nuclear decay rates. The use of dispersion relation, lattice Quantum Chromodynamics and effective field theory framework allows for high-precision theory calculations at the level of \(10^{−4}\), turning neutron beta decay into a powerful tool to search for new physics, complementary to high-energy collider experiments. We offer an outlook to the future improvements.

It was recently estimated that the strong isospin-symmetry breaking (ISB) corrections to the Fermi matrix element in free neutron decay could be of the order \(10^{-4}\), one order of magnitude larger than the naïve estimate based on the Behrends-Sirlin-Ademollo-Gatto theorem. To investigate this claim, we derive a general expression of the leading ISB correction to hadronic Fermi matrix elements, which takes the form of a four-point correlation function in lattice gauge theory and is straightforward to compute from first principles. Our formalism paves the way for the first determination of such correction in the neutron sector with fully-controlled theory uncertainties.

In order to test the end-to-end operations of gallium solar neutrino experiments, intense electron-capture sources were fabricated to measure the responses of the radiochemical SAGE and GALLEX/GNO detectors to known fluxes of low-energy neutrinos. Such tests were viewed at the time as a cross-check, given the many tests of 71Ge recovery and counting that had been routinely performed, with excellent results. However, the four 51Cr and 37Ar source experiments yielded rates below expectations, a result commonly known as the Ga anomaly. As the intensity of the electron-capture sources can be measured to high precision, the neutrino lines they produce are fixed by known atomic and nuclear rates, and the neutrino absorption cross section on 71Ga is tightly constrained by the lifetime of 71Ge, no simple explanation for the anomaly has been found. To check these calibration experiments, a dedicated experiment BEST was performed, utilizing a neutrino source of unprecedented intensity and a detector optimized to increase statistics while providing some information on counting rate as a function of distance from the source. The results BEST obtained are consistent with the earlier solar neutrino calibration experiments, and when combined with those measurements, yield a Ga anomaly with a significance of approximately 4 sigma, under conservative assumptions. But BEST found no evidence of distance dependence and thus no explicit indication of new physics. In this review we describe the extensive campaigns carried out by SAGE, GALLEX/GNO, and BEST to demonstrate the reliability and precision of their experimental procedures, including 71Ge recovery, counting, and analysis. We also describe efforts to define uncertainties in the neutrino capture cross section. With the results from BEST, an anomaly remains.

We study radiative corrections to low-energy charged-current processes involving nucleons, such as neutron beta decay and (anti)neutrino-nucleon scattering within a top-down effective-field-theory approach. We first match the Standard Model to the low-energy effective theory valid below the weak scale and, using renormalization group equations with anomalous dimensions of O(α,ααs,α2), evolve the resulting effective coupling down to the hadronic scale. Here, we first match to heavy-baryon chiral perturbation theory and subsequently, below the pion-mass scale, to a pionless effective theory, evolving the effective vector coupling with anomalous dimensions of O(α,α2) all the way down to the scale of the electron mass, relevant for beta decays. We thus provide a new evaluation of the ``inner" radiative corrections to the vector coupling constant and to the neutron decay rate, discussing differences with the previous literature. Using our new result for the radiative corrections, we update the extraction of the Cabibbo-Kobayashi-Maskawa matrix element Vud from the neutron decay.