We use light-front dynamics to calculate the electromagnetic form-factor for the Hulthén model of the deuteron. For small momentum transfer Q 2 < 5 GeV 2 the relativistic effects are quite small. For Q 2 ∼ 11 GeV 2 there is ∼ 13% discrepancy between the relativistic and non-relativistic approaches. For asymptotically large momentum transfer, however, the light-front form factor, ∼ log Q 2 /Q 4 , markedly differs from the non-relativistic version, ∼ 1/Q 4 . This behavior is also present for any wave function, such as those obtained from realistic potential models, which can be represented as a sum of Yukawa functions. Furthermore, the asymptotic behavior is in disagreement with the Drell-Yan-West relation. We investigate precisely how to determine the asymptotic behavior and confront the problem underlying troublesome form factors on the light front.

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.

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...

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We present the results of lattice QCD calculations of the magnetic moments of the lightest nuclei, the deuteron, the triton, and 3 He, along with those of the neutron and proton. These calculations, performed at quark masses corresponding to m π ∼ 800 MeV, reveal that the structure of these nuclei at unphysically heavy quark masses closely resembles that at the physical quark masses. In particular, we find that the magnetic moment of 3 He differs only slightly from that of a free neutron, as is the case in nature, indicating that the shell-model configuration of two spin-paired protons and a valence neutron captures its dominant structure. Similarly a shell-model-like moment is found for the triton, μ3 H ∼ μ p . The deuteron magnetic moment is found to be equal to the nucleon isoscalar moment within the uncertainties of the calculations. Furthermore, deviations from the Schmidt limits are also found to be similar to those in nature for these nuclei. These findings suggest that at least some nuclei at these unphysical quark masses are describable by a phenomenological nuclear shell model. The electromagnetic interactions of nuclei have been used extensively to elucidate their structure and dynamics. In the early days of nuclear physics, the magnetic moments of the light nuclei helped to reveal that they behaved like a collection of "weakly" interacting nucleons that, to a very large degree, retained their identity, despite being bound together by the strong nuclear force. This feature, in part, led to the establishment of the nuclear shell model as a phenomenological tool with which to predict basic properties of nuclei throughout the periodic table. The success of the shell model is somewhat remarkable, given that nuclei are fundamentally bound states of quarks and gluons, the degrees of freedom of quantum chromodynamics (QCD). The strong nuclear force emerges from QCD as a byproduct of confinement and chiral symmetry breaking. The fact that, at the physical values of the quark masses, nuclei are not simply collections of quarks and gluons, defined by their global quantum numbers, but have the structure of interacting protons and neutrons, remains to be understood at a deep level. In this Letter, we continue our exploration of nuclei at unphysical quark masses, and calculate the magnetic moments of the lightest few nuclei using lattice QCD. We find that they are close to those found in nature, and also close to the sum of the constituent nucleon magnetic moments in the simplest shell model configuration. This second finding, in particular, is remarkable and suggests that a phenomenological nuclear shell model is applicable for at least some nuclei at these unphysical quark masses.Our lattice QCD calculations were performed on one ensemble of gauge-field configurations generated with a N f ¼ 3 clover-improved fermion action [1] and a Lüscher-Weisz gauge action [2]. The configurations have L ¼ 32 lattice sites in each spatial direction, T ¼ 48 sites in the temporal direction, and a lattice spacing of a ∼ 0.12 fm. ...

Lattice QCD calculations of two-nucleon systems are used to isolate the short-distance two-body electromagnetic contributions to the radiative capture process np → dγ, and the photo-disintegration processes γ ðÃÞ d → np. In nuclear potential models, such contributions are described by phenomenological meson-exchange currents, while in the present work, they are determined directly from the quark and gluon interactions of QCD. Calculations of neutron-proton energy levels in multiple background magnetic fields are performed at two values of the quark masses, corresponding to pion masses of m π ∼ 450 and 806 MeV, and are combined with pionless nuclear effective field theory to determine the amplitudes for these low-energy inelastic processes. At m π ∼ 806 MeV, using only lattice QCD inputs, a cross section σ 806 MeV ∼ 17 mb is found at an incident neutron speed of v ¼ 2; 200 m=s. Extrapolating the short-distance contribution to the physical pion mass and combining the result with phenomenological scattering information and one-body couplings, a cross section of σ lqcd ðnp → dγÞ ¼ 334.9ð þ5.2 −5.4 Þ mb is obtained at the same incident neutron speed, consistent with the experimental value of σ expt ðnp → dγÞ ¼ 334.2ð0.5Þ mb. The radiative capture process, np → dγ, plays a critical role in big bang nucleosynthesis (BBN) as it is the starting point for the chain of reactions that form most of the light nuclei in the cosmos. Studies of radiative capture [1][2][3], and the inverse processes of deuteron electro-and photodisintegration, γ ðÃÞ d → np [4][5][6][7], have constrained these cross sections and have also provided critical insights into the interactions between nucleons and photons. They conclusively show the importance of non-nucleonic degrees of freedom in nuclei, which arise from meson-exchange currents (MECs) in the context of nuclear potential models [8,9]. Nevertheless, in the energy range relevant for BBN, experimental investigations are challenging [10]. For the analogous weak interactions of multinucleon systems, considerably less is known from experiment but these processes are equally important. The weak two-nucleon interactions currently contribute the largest uncertainty in calculations of the rate for proton-proton fusion in the Sun [11][12][13][14][15][16][17], and in neutrino-disintegration of the deuteron [18], which is a critical process needed to disentangle solar neutrino oscillations. Given the phenomenological importance of electroweak interactions in light nuclei, direct determinations from the underlying theory of strong interaction, quantum chromodynamics (QCD), are fundamental to future theoretical progress. Such determinations are also of significant phenomenological importance for calibrating long-baseline neutrino experiments and for investigations of double beta decay in nuclei. In this Letter, we take the initial steps towards meeting this challenge and present the first lattice QCD (LQCD) calculations of the np → dγ process. The results are in good agreement with experiment and show...

We use two-flavor chiral perturbation theory to describe hyperons. We focus on the strangeness conserving sector, and, as an example, calculate hyperon masses. Convergence of this two-flavor chiral expansion for observables is improved over the three-flavor theory. The cost, however, is a larger number of low-energy constants that must be ultimately determined from lattice QCD data. A formula for the mass of the omega baryon is derived to sixth order in this expansion, and will aid lattice practitioners in scale setting or tuning the strange quark mass.

Charged and neutral, pion and kaon electric polarizabilities are extracted from lattice QCD using an ensemble of anisotropic gauge configurations with dynamical clover fermions. We utilize classical background fields to access the polarizabilities from two-point correlation functions. Uniform background fields are achieved by quantizing the electric field strength with the proper treatment of boundary flux. These external fields, however, are implemented only in the valence quark sector. A novel method to extract charge particle polarizabilities is successfully demonstrated for the first time.