The nuclear matrix element determining the pp → de þ ν fusion cross section and the Gamow-Teller matrix element contributing to tritium β decay are calculated with lattice quantum chromodynamics for the first time. Using a new implementation of the background field method, these quantities are calculated at the SU(3) flavor-symmetric value of the quark masses, corresponding to a pion mass of m π ∼ 806 MeV. The Gamow-Teller matrix element in tritium is found to be 0.979(03)(10) at these quark masses, which is within 2σ of the experimental value. Assuming that the short-distance correlated two-nucleon contributions to the matrix element (meson-exchange currents) depend only mildly on the quark masses, as seen for the analogous magnetic interactions, the calculated pp → de þ ν transition matrix element leads to a fusion cross section at the physical quark masses that is consistent with its currently accepted value. Moreover, the leading two-nucleon axial counterterm of pionless effective field theory is determined to be L 1;A ¼ 3.9ð0.2Þð1.0Þð0.4Þð0.9Þ fm 3 at a renormalization scale set by the physical pion mass, also agreeing within the accepted phenomenological range. This work concretely demonstrates that weak transition amplitudes in few-nucleon systems can be studied directly from the fundamental quark and gluon degrees of freedom and opens the way for subsequent investigations of many important quantities in nuclear physics. DOI: 10.1103/PhysRevLett.119.062002 Weak nuclear processes play a central role in many settings, from the instability of the neutron to the dynamics of core-collapse supernova. In this work, the results of the first lattice quantum chromodynamics (LQCD) calculations of two such processes are presented, namely, the pp → de þ ν e fusion process and tritium β decay. The pp → de þ ν process is centrally important in astrophysics as it is primarily responsible for initiating the proton-proton fusion chain reaction that provides the dominant energy production mechanism in stars like the Sun. Significant theoretical effort has been expended in refining calculations of the pp → de þ ν cross section at the energies relevant to solar burning, and progress continues to be made with a range of techniques [1][2][3][4][5][6][7][8][9][10], as summarized in Ref. [11]. This process is related to the νd → nne þ neutrino-induced deuteron-breakup reaction [12][13][14], relevant to the measurement of neutrino oscillations at the Sudbury Neutrino Observatory [15,16], and to the muon capture reaction μ − d → nnν μ , which is the focus of current investigation in the MuSun experiment [17]. The second process studied in this work, tritium β decay, is a powerful tool for investigating the weak interactions of the Standard Model and plays an important role in the search for new physics. The superallowed process 3 H → 3 He e − ν is theoretically clean and is the simplest semileptonic weak decay of a nuclear system. In contrast to pp fusion, this decay has been very precisely studied in the laboratory (see Ref.[18...

A lattice quantum chromodynamics (LQCD) calculation of the nuclear matrix element relevant to the nn → ppeeν e ν e transition is described in detail, expanding on the results presented in Ref.[1]. This matrix element, which involves two insertions of the weak axial current, is an important input for phenomenological determinations of double-β decay rates of nuclei. From this exploratory study, performed using unphysical values of the quark masses, the long-distance deuteron-pole contribution to the matrix element is separated from shorter-distance hadronic contributions. This polarizability, which is only accessible in double-weak processes, cannot be constrained from single-β decay of nuclei, and is found to be smaller than the long-distance contributions in this calculation, but non-negligible. In this work, technical aspects of the LQCD calculations, and of the relevant formalism in the pionless effective field theory, are described. Further calculations of the isotensor axial polarizability, in particular near and at the physical values of the light-quark masses, are required for precise determinations of both two-neutrino and neutrinoless double-β decay rates in heavy nuclei.

Lattice quantum chromodynamics is used to constrain the interactions of two octet baryons at the SUð3Þ flavor-symmetric point, with quark masses that are heavier than those in nature (equal to that of the physical strange quark mass and corresponding to a pion mass of ≈806 MeV). Specifically, the S-wave scattering phase shifts of two-baryon systems at low energies are obtained with the application of Lüscher's formalism, mapping the energy eigenvalues of two interacting baryons in a finite volume to the two-particle scattering amplitudes below the relevant inelastic thresholds. The leading-order low-energy scattering parameters in the two-nucleon systems that were previously obtained at these quark masses are determined with a refined analysis, and the scattering parameters in two other channels containing the Σ and Ξ baryons are constrained for the first time. It is found that the values of these parameters are consistent with an approximate SUð6Þ spin-flavor symmetry in the nuclear and hypernuclear forces that is predicted in the large-N c limit of QCD. The two distinct SUð6Þ-invariant interactions between two baryons are constrained for the first time at this value of the quark masses, and their values indicate an approximate accidental SUð16Þ symmetry. The SUð3Þ irreps containing the NNð 1 S 0 Þ, NNð 3 S 1 Þ and 1 ffiffi 2 p ðΞ 0 n þ Ξ − pÞð 3 S 1 Þ channels unambiguously exhibit a single bound state, while the irrep containing the Σ þ pð 3 S 1 Þ channel exhibits a state that is consistent with either a bound state or a scattering state close to threshold. These results are in agreement with the previous conclusions of the NPLQCD collaboration regarding the existence of twonucleon bound states at this value of the quark masses.

The potential importance of short-distance nuclear effects in double-β decay is assessed using a lattice QCD calculation of the nn → pp transition and effective field theory methods. At the unphysical quark masses used in the numerical computation, these effects, encoded in the isotensor axial polarizability, are found to be of similar magnitude to the nuclear modification of the single axial current, which phenomenologically is the quenching of the axial charge used in nuclear many-body calculations. This finding suggests that nuclear models for neutrinoful and neutrinoless double-β decays should incorporate this previously neglected contribution if they are to provide reliable guidance for next-generation neutrinoless double-β decay searches. The prospects of constraining the isotensor axial polarizabilities of nuclei using lattice QCD input into nuclear many-body calculations are discussed. DOI: 10.1103/PhysRevLett.119.062003 Double-β (ββ) decays of nuclei are of significant phenomenological interest; they probe fundamental symmetries of nature and admit both tests of the standard model (SM) and investigations of physics beyond it [1]. Consequently, these decays are the subject of intense experimental study, and next-generation ββ-decay experiments are currently being planned [2][3][4]. At present, both the robust prediction of the efficacy of different detector materials, necessary for optimal design sensitivity, and the robust interpretation of the highly sought-after neutrinoless ββ-decay (0νββ) mode are impeded by the lack of knowledge of second-order weak-interaction nuclear matrix elements. These quantities bear uncertainties from nuclear modeling that are both significant and difficult to quantify [5]. Controlling the nuclear uncertainties in ββ-decay matrix elements by connecting the nuclear many-body methods to the underlying parameters of the SM is a critical task for nuclear theory.In this Letter, lattice QCD and pionless effective field theory [EFTðπ Þ)] are used to investigate the strong-interaction uncertainties in the second-order weak transition of the two-nucleon system in the SM by determining the threshold transition matrix element for nn → pp. This matrix element receives long-distance contributions from the deuteron intermediate state whose size is governed by the squared magnitude of the hppjJ þ μ jdi matrix element of the axial current that has been recently calculated using lattice quantum chromodynamics (LQCD) [6]. In that work, the two-body contribution to the matrix element (i.e., that beyond the coupling of the axial current to a single nucleon) was constrained, quantifying the effective modification (quenching) of the axial charge of the nucleon from two-body effects. Here, it is highlighted that the nn → pp matrix element receives additional short-distance contributions beyond those in jhppjJ þ μ jdij 2 arising from the two axial currents being separated by r < Λ −1 ∼ m −1 π [where Λ is the cutoff scale of EFTðπ Þ], referred to herein as the isotensor axial polarizability. Usi...