Measurements of the Λ b → pl −ν l and Λ b → Λ c l −ν l decay rates can be used to determine the magnitudes of the Cabibbo-Kobayashi-Maskawa matrix elements V ub and V cb , provided that the relevant hadronic form factors are known. Here we present a precise calculation of these form factors using lattice QCD with 2 þ 1 flavors of dynamical domain-wall fermions. The b and c quarks are implemented with relativistic heavy-quark actions, allowing us to work directly at the physical heavy-quark masses. The lattice computation is performed for six different pion masses and two different lattice spacings, using gauge-field configurations generated by the RBC and UKQCD Collaborations. The b → u and b → c currents are renormalized with a mostly nonperturbative method. We extrapolate the form factor results to the physical pion mass and the continuum limit, parametrizing the q 2 dependence using z expansions. The form factors are presented in such a way as to enable the correlated propagation of both statistical and systematic uncertainties into derived quantities such as differential decay rates and asymmetries. Using these form factors, we present predictions for the Λ b → pl −ν l and Λ b → Λ c l −ν l differential and integrated decay rates. Combined with experimental data, our results enable determinations of jV ub j, jV cb j, and jV ub =V cb j with theory uncertainties of 4.4%, 2.2%, and 4.9%, respectively.

A Ward-Takahashi identity preserving Bethe-Salpeter kernel can always be calculated explicitly from a dressed-quark-gluon vertex whose diagrammatic content is enumerable. We illustrate that fact using a vertex obtained via the complete resummation of dressed-gluon ladders. While this vertex is planar, the vertex-consistent kernel is nonplanar and that is true for any dressed vertex. In an exemplifying model the rainbow-ladder truncation of the gap and Bethe-Salpeter equations yields many results; e.g., pi- and rho-meson masses, that are changed little by including higher-order corrections. Repulsion generated by nonplanar diagrams in the vertex-consistent Bethe-Salpeter kernel for quark-quark scattering is sufficient to guarantee that diquark bound states do not exist.Comment: 16 pages, 12 figures, REVTEX

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Using (2 þ 1)-flavor lattice QCD, we compute the 10 form factors describing the Λ b → Λ matrix elements of the b → s vector, axial vector, and tensor currents. The calculation is based on gauge field ensembles generated by the RBC and UKQCD Collaborations with a domain-wall action for the u, d, and s quarks and the Iwasaki gauge action. The b quark is implemented using an anisotropic clover action, tuned nonperturbatively to the physical point, and the currents are renormalized with a mostly nonperturbative method. We perform simultaneous chiral, continuum, and kinematic extrapolations of the form factors through modified z expansions. Using our form factor results, we obtain precise predictions for the

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...