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DOE OSTI2021

Coupled-Cluster Calculations of Neutrinoless Double- β Decay in Ca 48

We use coupled-cluster theory and nuclear interactions from chiral effective field theory to compute the nuclear matrix element for the neutrinoless double-$\beta$ decay of $^{48}$Ca. Benchmarks with the no-core shell model in several light nuclei inform us about the accuracy of our approach. For $^{48}$Ca we find a relatively small matrix element. We also compute the nuclear matrix element for the two-neutrino double-$\beta$ decay of $^{48}$Ca with a quenching factor deduced from two-body currents in recent ab initio calculation of the Ikeda sum rule in $^{48}$Ca [Gysbers et al., Nat. Phys. 15, 428 (2019)].

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Scattering using real-time path integrals

Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While imaginary time treatments of scattering are possible, imaginary time is not a natural framework for treating scattering problems. More importantly, quantum algorithms for calculating path integrals require real-time evolution. Purpose: Here, we test a recently introduced method for performing direct calculations of scattering observables using real-time path integrals in order to understand the challenges facing real-time path integral calculations of scattering observables. Method: The computations are based on a new interpretation of the path integral as the expectation value of a potential functional on cylinder sets of continuous paths with respect to a complex probability distribution. The method can in principle be applied to arbitrary short-range potentials. Results: The method is applied to compute matrix elements of Møller wave operators applied to narrow wave packets. These are used to calculate half-shell sharp-momentum transition matrix elements for one-dimensional potential scattering. The calculations for half-shell transition operator matrix elements converge to the numerical solution of the Lippmann-Schwinger equation. Conclusions: This work presents a proof in principle that scattering observables can be computed using real-time Feynman path integrals. While the computational method is not efficient, it can be improved. It provides a laboratory for studying quantum computational algorithms that are applicable to scattering problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Electroweak three-body decays in the presence of two- and three-body bound states

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

E2 rotational invariants of 0$^{+}_{1}$ and 2$^{+}_{1}$ states for 106 Cd: The emergence of collective rotation

The collective structure of 106 Cd is elucidated by multi-step Coulomb excitation of a 3.849 MeV/A beam of 106 Cd on a 1.1 mg/cm 2 208 Pb target using GRETINA-CHICO2 at ATLAS. Fourteen E2 matrix elements were obtained. The nucleus 106 Cd is a prime example of emergent collectivity that possesses a simple structure: it is free of complexity caused by shape coexistence and has a small, but collectively active number of valence nucleons. This work follows in a long and currently active quest to answer the fundamental question of the origin of nuclear collectivity and deformation, notably in the cadmium isotopes. The results are discussed in terms of phenomenological models, the shell model, and Kumar-Cline sums of E2 matrix elements. The < 0$^{+}_{2}$ ||E2||2$^{+}_{1}$ > matrix element is determined for the first time, providing a total, converged measure of the electric quadrupole strength, < Q 2 >, of the first-excited 2$^{+}_{1}$ level relative to the 0$^{+}_{1}$ ground state, which does not show an increase as expected of harmonic and anharmonic vibrations. Strong evidence for triaxial shapes in weakly collective nuclei is indicated; collective vibrations are excluded. This is contrary to the only other cadmium result of this kind in 114 Cd by C. Fahlander et al., Nucl. Phys. A485, 327 (1988), which is complicated by low-lying shape coexistence near midshell.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Quantum Monte Carlo calculation of 𝛿 NS in 10 C using an effective field theory approach

Here, we compute radiative corrections to the superallowed 𝛽 decay of 10 C in an effective field theory approach using nuclear matrix elements obtained from quantum Monte Carlo calculations. These corrections are an important ingredient in the extraction of the Cabibbo-Kobayashi-Masakawa quark mixing matrix element 𝑉 𝑢⁢𝑑 , and the role of this work is to illuminate the uncertainties arising from nuclear structure. Our results provide good agreement with both the traditional extraction of 𝑉 𝑢⁢𝑑 , as well as with a more recent evaluation performed using the no-core shell model and a dispersion formalism. The dominant uncertainty in this approach is the presence of two unknown low-energy constants that enter into the relevant nuclear matrix elements. Future determinations of these low-energy constants—either from QCD or modeling them with two nucleon amplitudes—would improve the precision of the extraction in this formalism.

beta decay↗
DOE OSTI2022

Developments in Performance and Portability for MadGraph5_aMC@NLO

Event generators simulate particle interactions using Monte Carlo techniques, providing the primary connection between experiment and theory in experimental high energy physics. These software packages, which are the first step in the simulation worflow of collider experiments, represent approximately 5 to 20% of the annual WLCG usage for the ATLAS and CMS experiments. With computing architectures becoming more heterogeneous, it is important to ensure that these key software frameworks can be run on future systems, large and small. In this contribution, recent progress on porting and speeding up the Madgraph5_aMC@NLO event generator on hybrid architectures, i.e. CPU with GPU accelerators, is discussed. The main focus of this work has been in the calculation of scattering amplitudes and "matrix elements", which is the computational bottleneck of an event generation application. For physics processes limited to QCD leading order, the code generation toolkit has been expanded to produce matrix element calculations using C++ vector instructions on CPUs and using CUDA for NVidia GPUs, as well as using Alpaka, Kokkos and SYCL for multiple CPU and GPU architectures. Performance is reported in terms of matrix element calculations per time on NVidia, Intel, and AMD devices. The status and outlook for the integration of this work into a production release usable by the LHC experiments, with the same functionalities and very similar user interfaces as the current Fortran version, is also described.

Valassi, Andrea↗
DOE OSTI2022

Statistical uncertainty of fission matrix eigenvalues using perturbation theory

Eigenvalue search of high dominance ratio systems may be slow to converge. The fission matrix element is defined by its element (FM){sub ij}, which are the probability for a neutron born in cell i to create a fission in cell j for a spatial mesh of n{sub i}*n{sub j} elements. Fission matrices are used in Monte Carlo criticality simulations to enhance computing speed, but also to find higher order eigenvalues. However, few studies have been made on the link between statistical uncertainties of fission matrix elements and eigenvalues uncertainties. Thus, dominance ratio statistical uncertainties remain unknown. This paper uses a new generalized perturbation theory (GPT) method to estimate sensitivities of eigenvalues to fission matrix elements and then to calculate dominance ratio uncertainties.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Two-neutrino double-𝛽 decay in pionless effective field theory from a Euclidean finite-volume correlation function

Two-neutrino double-β decay of certain nuclear isotopes is one of the rarest Standard Model processes observed in nature. Its neutrinoless counterpart is an exotic lepton-number nonconserving process that is widely searched to determine if the neutrinos are Majorana fermions. In order to connect the rate of these processes to the Standard Model and beyond the Standard Model interactions, it is essential that the corresponding nuclear matrix elements are constrained reliably from theory. Lattice quantum chromodynamics (LQCD) and low-energy effective field theories (EFTs) are expected to play an essential role in constraining the matrix element of the two-nucleon subprocess, which could in turn provide the input into ab initio nuclear-structure calculations in larger isotopes. Focusing on the two-neutrino process $nn\rightarrow pp(ee\bar{v}_{e}\bar{v}_e)$, the amplitude is constructed in this work in pionless EFT at next-to-leading order, demonstrating the emergence of a renormalization-scale independent amplitude and the absence of any new low-energy constant at this order beyond those present in the single-weak process. Most importantly, it is shown how a LQCD four-point correlation function in Euclidean and finite-volume spacetime can be used to constrain the Minkowski infinite-volume amplitude in the EFT. The same formalism is provided for the related single-weak process, which is an input to the double-β decay formalism. The LQCD-EFT matching procedure outlined for the double-weak amplitude paves the road toward constraining the two-nucleon matrix element entering the neutrinoless double-β decay amplitude with a light Majorana neutrino.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Gluon unpolarized, polarized, and transversity GPDs from lattice QCD: Lorentz-covariant parametrization

We identify the matrix elements necessary to determine the leading-twist gluon generalized parton distributions (GPDs) H g , E g , H ˜ g , E ˜ g , H g T , E g T , H ˜ g T , E ˜ g T in lattice QCD calculations. We present a method to achieve a Lorentz-covariant parameterization of the matrix elements in terms of a linearly independent basis of tensor structures. This parameterization is crucial for projecting lattice QCD matrix elements onto light cone distributions. For the first time, we determine the corresponding components that project onto the linear combinations of invariant amplitudes, which reduce to the different gluon GPDs in the light cone limit and enable their separation in a lattice QCD calculation for spin-0 and spin- 1 2 hadrons. Hence, this work lays the foundation for the numerical determination of the gluon GPDs from first-principle lattice QCD calculations, directly advancing our understanding of the mass and spin structures and mechanical properties of the nucleon, as well as the physics underlying deeply virtual Compton scattering and deeply virtual meson production in a range of experimental processes. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Toward the first gluon parton distribution from the LaMET

Abstract We present progress towards the first unpolarized gluon quasi-parton distribution function (PDF) from lattice quantum chromodynamics using high-statistics measurements for hadrons at two valence pion masses M π ≈ 310 and 690 MeV computed on an a ≈ 0.12 fm ensemble with 2 + 1 + 1-flavors of highly improved staggered quark generated by the MILC collaboration. In this study, we consider two gluon operators for which the hybrid-ratio renormalization matching kernels have been recently derived and a third operator that has been used in prior pseudo-PDF studies of the gluon PDFs. We compare the matrix elements for each operator for both the nucleon and pion, at both pion masses, and using two gauge-smearing techniques. Focusing on the more phenomenologically studied nucleon gluon PDF, we compare the ratio and hybrid-ratio renormalized matrix elements at both pion masses and both smearings to those reconstructed from the nucleon gluon PDF from the CT18 global analysis. We identify the best choice of operator to study the gluon PDF and present the first gluon quasi-PDF under some caveats. Additionally, we explore the recent idea of Coulomb gauge fixing to improve signal at large Wilson-line displacement and find it could be a major help in improving the signal in the gluon matrix elements. This work helps identify the best operator for studying the gluon quasi-PDF, shows higher hadron boost momentum is needed to implement hybrid-ratio renormalization reliably, and suggests the need to study more diverse set of operators with their corresponding perturbative calculations for hybrid-ratio renormalization to further gluon quasi-PDF study.

Good, William (ORCID:0000000184281003)↗
DOE OSTI2024

Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Axial-vector case

Recently, we made significant advancements in improving the computational efficiency of lattice QCD calculations for generalized parton distributions (GPDs). This progress was achieved by adopting calculations of matrix elements in asymmetric frames, deviating from the computationally-expensive symmetric frame typically used, and allowing freedom in the choice for the distribution of the momentum transfer between the initial and final states. A crucial aspect of this approach involves the adoption of a Lorentz covariant parametrization for the matrix elements, introducing Lorentz-invariant amplitudes. This approach also allows us to propose an alternative definition of quasi-GPDs, ensuring frame independence and potentially reduce power corrections in matching to light cone GPDs. In our previous work, we presented lattice QCD results for twist-2 unpolarized GPDs ( H and E ) of quarks obtained from calculations performed in asymmetric frames at zero skewness. Building upon this work, we now introduce a novel Lorentz covariant parametrization for the axial-vector matrix elements. We employ this parametrization to compute the axial-vector GPD H ˜ at zero skewness, using an N f = 2 + 1 + 1 ensemble of twisted mass fermions with clover improvement. The light-quark masses employed in our calculations correspond to a pion mass of approximately 260 MeV. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Lattice calculation of short-range contributions to neutrinoless double-beta decay 𝜋 − → 𝜋 + ⁢𝑒⁢𝑒 at physical pion mass

Neutrinoless double-beta (0⁢𝜈⁢𝛽⁢𝛽) decays provide an excellent probe for determining whether neutrinos are Dirac or Majorana fermions. The short-range matrix elements associated with the 𝜋 − → 𝜋 + ⁢𝑒⁢𝑒 process contribute at leading order in the 0⁢𝜈⁢𝛽⁢𝛽 decay channel 𝑛⁢𝑛 → 𝑝⁢𝑝⁢𝑒⁢𝑒 through pion exchange between nucleons. However, current lattice calculations show notable discrepancies in predicting these short-range contributions. To address this issue, we perform a lattice QCD calculation of the 𝜋 − → 𝜋 + ⁢𝑒⁢𝑒 matrix elements using domain wall fermion ensembles at the physical pion mass generated by the RBC/UKQCD Collaboration. To mitigate contamination from around-the-world effects, we develop a new method to reconstruct and subtract them directly from lattice data. We then perform nonperturbative renormalization in the regularization-independent symmetric momentum-subtraction scheme (RI/SMOM), using the (𝛾 𝜇 , 𝛾 𝜇 ) and ($\not{𝑞}$, $\not{𝑞}$) projectors. Compared with previous studies, this work reduces the uncertainties in the matrix elements and provides an independent cross-check that helps to reconcile the discrepancies among previous lattice calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Tritium β decay and proton-proton fusion in pionless effective field theory

The Gamow-Teller and Fermi matrix elements, 〈 GT 〉 and 〈 F 〉 , respectively, for tritium β decay are calculated to next-to-leading order (NLO) in pionless effective field theory in the absence of Coulomb interactions and isospin violation giving the leading order predictions 〈 GT 〉 0 = 0.9807 and 〈 F 〉 0 = 1 . Using an experimentally determined value for the tritium β decay GT matrix element, the two-body axial current low energy constant is fixed at NLO yielding L 1 , A = 6.01 ± 2.08 fm 3 at the renormalization scale of the physical pion mass, which agrees with predictions based on naive dimensional analysis. The impact of L 1 , A on proton-proton fusion is also discussed. Finally, the consequences of Wigner-SU(4) spin-isospin symmetry are considered for the Gamow-Teller matrix element. Published by the American Physical Society 2024

Physics↗
DOE OSTI2026

FLAG review 2024

We review lattice results related to pion, kaon, 𝐷-meson, 𝐵-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor 𝑓+⁡(0) arising in the semileptonic 𝐾 → 𝜋 transition at zero momentum transfer, as well as the decay-constant ratio 𝑓 𝐾 ⁡/𝑓 𝜋 and its consequences for the Cabibbo–Kobayashi–Maskawa (CKM) matrix elements 𝑉 𝑢⁢𝑠 and 𝑉 𝑢⁢𝑑 . We review the determination of the 𝐵 𝐾 parameter of neutral kaon mixing as well as the additional four 𝐵 parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for 𝑚 𝑐 and 𝑚 𝑏 as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant 𝛼 𝑠 . We review the determinations of nucleon charges from the matrix elements of both isovector and flavor-diagonal axial, scalar and tensor local quark bilinears, and momentum fraction, helicity moment and the transversity moment from one-link quark bilinears. We also review determinations of scale-setting quantities. Finally, in this review we have added a new section on the general definition of the low-energy limit of the Standard Model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Neutrinoless Double-Beta Decay Investigations of 82Se Using Three Shell Model Hamiltonians

Neutrinoless double-beta decay is considered one of the most promising processes that would help clarify some of the symmetry-breaking problems in our understanding of the observable universe. Recent studies of neutrinoless double-beta decay matrix elements have employed statistical approaches based on modified shell model effective Hamiltonians for 48Ca (Phys. Rev. C 106, 054302 (2022)) and 136Xe (Phys. Rev. C 107, 045501 (2023)). The analyses rely on inducing perturbations in the starting effective Hamiltonians to observe the behavior of a wide range of observables, besides the 0νββ) NME, that are compared with experimental data. Following a Bayesian model averaging approach, the range of probable values for the neutrinoless double-beta decay matrix elements is presented. In this paper, we present a similar study for 82Se, which is described in the same model space as 76Ge that is under experimental observation. Due to its faster calculation time compared to 76Ge, 82Se can be used as an appropriate substitute in our complex statistical study. Using the calculations performed for the statistical analysis of the neutrinoless double-beta decay matrix elements, we also search for the correlations between the observables that we can compare to experimental data.

Science & Technology - Other Topics↗
DOE OSTI2022

Neutrinoless double-β decay: Combining quantum Monte Carlo and the nuclear shell model with the generalized contact formalism

Neutrinoless double beta decay searches can determine the Majorana nature of neutrinos, the absolute neutrino mass, and provide invaluable insights on the matter dominance of the universe. However, the uncertainty in the nuclear matrix elements that govern the decay limits the physics reach of these experiments. Here, we devise a novel framework based on the generalized contact formalism that combines the nuclear shell model and quantum Monte Carlo methods and compute the neutrinoless double-beta decay of nuclei used in the most advanced experiments, including 76 Ge, 130 Te, and 136 Xe. Our results cover all relevant terms, including the leading-order short-range operator recognized recently. We validate our method in light nuclei by comparing against accurate variational Monte Carlo results. On heavy systems we obtain reduced nuclear matrix elements compared with previous calculations due to additional correlations captured by quantum Monte Carlo and introduced within the generalized contact formalism, suggesting longer decay half-lives than previously considered. On the other hand, we find an enhancement of the nuclear matrix elements due to the new short-range operator.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

FLAG Review 2021

Abstract We review lattice results related to pion, kaon, D -meson, B -meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $$f_+(0)$$ f + ( 0 ) arising in the semileptonic $$K \rightarrow \pi $$ K → π transition at zero momentum transfer, as well as the decay constant ratio $$f_K/f_\pi $$ f K / f π and its consequences for the CKM matrix elements $$V_{us}$$ V us and $$V_{ud}$$ V ud . Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $$SU(2)_L\times SU(2)_R$$ S U ( 2 ) L × S U ( 2 ) R and $$SU(3)_L\times SU(3)_R$$ S U ( 3 ) L × S U ( 3 ) R Chiral Perturbation Theory. We review the determination of the $$B_K$$ B K parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $$m_c$$ m c and $$m_b$$ m b as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $$\alpha _s$$ α s . We consider nucleon matrix elements, and review the determinations of the axial, scalar and tensor bilinears, both isovector and flavor diagonal. Finally, in this review we have added a new section reviewing determinations of scale-setting quantities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Spin-orbit correlations in the nucleon in the large- N c limit

We study the twist-3 spin-orbit correlations of quarks described by the nucleon matrix elements of the parity-odd rank-2 tensor QCD operator (the parity-odd partner of the QCD energy-momentum tensor). Our treatment is based on the effective dynamics emerging from the spontaneous breaking of chiral symmetry and the mean-field picture of the nucleon in the large- N c limit. The twist-3 QCD operators are converted to effective operators, in which the QCD interactions are replaced by spin-flavor-dependent chiral interactions of the quarks with the pion field. We compute the nucleon matrix elements of the twist-3 effective operators and discuss the role of the chiral interactions in the spin-orbit correlations. We derive the first-quantized representation in the mean-field picture and develop a quantum-mechanical interpretation. The chiral interactions give rise to new spin-orbit couplings and qualitatively change the correlations compared to the quark model picture. We also derive the twist-3 matrix elements in the topological soliton picture where the quarks are integrated out (skyrmion). The methods used here can be extended to other QCD operators describing higher-twist nucleon structure and generalized parton distributions. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗