The scattering lengths and effective ranges that describe low-energy nucleon-nucleon scattering are calculated in the limit of SU(3)-flavor symmetry at the physical strange-quark mass with Lattice Quantum Chromodynamics. The calculations are performed with an isotropic clover discretization of the quark action in three volumes with spatial extents of L ∼ 3.4 fm, 4.5 fm and 6.7 fm, and with a lattice spacing of b ∼ 0.145 fm. With determinations of the energies of the two-nucleon systems (both of which contain bound states at these up and down quark masses) at rest and moving in the lattice volume, Lüscher's method is used to determine the low-energy phase shifts in each channel, from which the scattering length and effective range are obtained. The scattering parameters, in the 1 S 0 channel are found to be m π a ( 1 S 0 ) = 9.50 . These values are consistent with the two-nucleon system exhibiting Wigner's supermultiplet symmetry, which becomes exact in the limit of large-N c . In both spin channels, the phase shifts change sign at higher momentum, near the start of the t-channel cut, indicating that the nuclear interactions have a repulsive core even at the SU(3)-symmetric point.

The scalar strange-quark matrix element of the nucleon is computed with lattice QCD. A mixedaction scheme is used with domain-wall valence fermions computed on the staggered MILC seaquark configurations. The matrix element is determined by making use of the Feynman-Hellmann theorem which relates this strange matrix element to the change in the nucleon mass with respect to the strange-quark mass. The final result of this calculation is m s N |ss|N = 49 ± 10 ± 15 MeV and, correspondingly f s = m s N |ss|N /m N = 0.053 ± 0.011 ± 0.016.Given the lack of a quantitative comparison of this phenomenologically important quantity determined from various lattice QCD calculations, we take the opportunity to present such an average. The resulting conservative determination is f s = 0.043 ± 0.011.Typeset by REVT E X 1

We present the results of a lattice calculation of tetraquark states with quark contents q1q2QQ, q1, q2 ⊂ u, d, s, c and Q ≡ b, c in both spin zero (J = 0) and spin one (J = 1) sectors. This calculation is performed on three dynamical N f = 2 + 1 + 1 highly improved staggered quark ensembles at lattice spacings of about 0.12, 0.09 and 0.06 fm. We use the overlap action for light to charm quarks while a non-relativistic action with non-perturbatively improved coefficients with terms up to O(αsv 4 ) is employed for the bottom quark. While considering charm or bottom quarks as heavy, we calculate the energy levels of various four-quark configurations with light quark masses ranging from the physical strange quark mass to that of the corresponding physical pion mass. This enables us to explore the quark mass dependence of the extracted four-quark energy levels over a wide range of quark masses. The results of the spin one states show the presence of ground state energy levels which are below their respective thresholds for all the light flavor combinations. Further, we identify a trend that the energy splittings, defined as the energy difference between the ground state energy levels and their respective thresholds, increase with decreasing the light quark masses and are maximum at the physical point for all the spin one states. The rate of increase is however dependent on the light quark configuration of the particular spin one state. We also present a study of hadron mass relations involving tetraquarks, baryons and mesons arising in the limit of infinitely heavy quark and find that these relations are more compatible with the heavy quark limit in the bottom sector but deviate substantially in the charm sector. The ground state spectra of the spin zero tetraquark states with various flavor combinations are seen to lie above their respective thresholds.1 A diquark can be interpreted as a compact colored object inside a hadron and is made out of two quarks (or antiquarks) in the 3(3) or 6(6) irrep of SU(3) and can have spin zero (scalar) or spin one (vector). With this model one can build rich phenomenology for mesons, baryons, as well as multiquark states.

We present a lattice QCD spectroscopy study in the isospin singlet, strangeness −2 sectors relevant for the conjectured H dibaryon. We employ both local and bilocal interpolating operators to isolate the ground state in the rest frame and in moving frames. Calculations are performed using two flavors of O(a)-improved Wilson fermions and a quenched strange quark. Our initial point-source method for constructing correlators does not allow for bilocal operators at the source; nevertheless, results from using these operators at the sink indicate that they provide an improved overlap onto the ground state in comparison with the local operators. We also present results, in the rest frame, using a second method based on distillation to compute a hermitian matrix of correlators with bilocal operators at both the source and the sink. This method yields a much more precise and reliable determination of the ground-state energy. In the flavor-SU(3) symmetric case, we apply Lüscher's finite-volume quantization condition to the rest-frame and moving-frame energy levels to determine the S-wave scattering phase shift, near and below the two-particle threshold. For a pion mass of 960 MeV, we find that there exists a bound H dibaryon with binding energy ∆E = (19 ± 10) MeV. In the 27-plet (dineutron) sector, the finite-volume analysis suggests that the existence of a bound state is unlikely.

We present results from a lattice QCD study of nucleon matrix elements at zero momentum transfer for local and twist-2 isovector operator insertions. Computations are performed on gauge ensembles with non-perturbatively improved N f = 2 + 1 Wilson fermions, covering four values of the lattice spacing and pion masses down to Mπ ≈ 200 MeV. Several source-sink separations (typically ∼ 1.0 fm to ∼ 1.5 fm) allow us to assess excited-state contamination. Results on individual ensembles are obtained from simultaneous two-state fits across all observables and all available source-sink separations with the energy gap as a common fit parameter. Physical results are obtained from a combined chiral, continuum and finite-size extrapolation. For the nucleon isovector axial, scalar and tensor charges we find physical values of g u−d A = 1.242(25)stat( +00 −31 )sys, g u−d S = 1.13(11)stat( +07 −06 )sys and g u−d T = 0.965(38)stat( +13 −41 )sys, respectively, where individual systematic errors in each direction from the chiral, continuum and finite-size extrapolation have been added in quadrature. Our final results for the isovector average quark momentum fraction and the isovector helicity and transversity moments are given by x u−d = 0.180(25)stat( +14 −06 )sys, x ∆u−∆d = 0.221(25)stat( +10 −00 )sys and x δu−δd = 0.212(32)stat( +16 −10 )sys, respectively.