No abstract

Motivated by multiple phenomenological considerations, we perform the first search for the existence of abbbb tetraquark bound state with a mass below the lowest noninteracting bottomonium-pair threshold using the first-principles lattice nonrelativistic QCD methodology. We use a full S-wave color/spin basis for thebbbb operators in the three 0 þþ , 1 þ− and 2 þþ channels. We employ four gluon field ensembles at multiple lattice spacing values ranging from a ¼ 0.06-0.12 fm, all of which include u, d, s and c quarks in the sea, and one ensemble which has physical light-quark masses. Additionally, we perform novel exploratory work with the objective of highlighting any signal of a near threshold tetraquark, if it existed, by adding an auxiliary potential into the QCD interactions. With our results we find no evidence of a QCD bound tetraquark below the lowest noninteracting thresholds in the channels studied.

In the modern formulation of lattice gauge-fixing, the gauge fixing condition is written in terms of the minima or stationary points (collectively called solutions) of a gauge-fixing functional. Due to the non-linearity of this functional, it usually has many solutions called Gribov copies. The dependence of the number of Gribov copies, n[U] on the different gauge orbits plays an important role in constructing the Faddeev-Popov procedure and hence in realising the BRST symmetry on the lattice. Here, we initiate a study of counting n[U] for different orbits using three complimentary methods: 1. analytical results in lower dimensions, and some lower bounds on n[U] in higher dimensions, 2. the numerical polynomial homotopy continuation method, which numerically finds all Gribov copies for a given orbit for small lattices, and 3. numerical minimisation ("brute force"), which finds many distinct Gribov copies, but not necessarily all. Because n for the coset SU(N_c)/U(1) of an SU(N_c) theory is orbit-independent, we concentrate on the residual compact U(1) case in this article and establish that n is orbit-dependent for the minimal lattice Landau gauge and orbit-independent for the absolute lattice Landau gauge. We also observe that contrary to a previous claim, n is not exponentially suppressed for the recently proposed stereographic lattice Landau gauge compared to the naive gauge in more than one dimension.Comment: 39 pages, 15 eps figures. Published version: minor changes onl

We determine the normalization of scalar and pseudoscalar current operators made from nonrelativistic b quarks and highly improved staggered light quarks in lattice quantum chromodynamics (QCD) through Oðα s Þ and Λ QCD =m b . We use matrix elements of these operators to extract B meson decay constants and form factors, and then compare to those obtained using the standard vector and axial-vector operators. This provides a test of systematic errors in the lattice QCD determination of the B meson decay constants and form factors. We provide a new value for the B and B s meson decay constants from lattice QCD calculations on ensembles that include u, d, s, and c quarks in the sea and those that have the u=d quark mass going down to its physical value. Our results are f B ¼ 0.196ð6Þ GeV, f B s ¼ 0.236ð7Þ GeV, and f B s =f B ¼ 1.207ð7Þ, agreeing well with earlier results using the temporal axial current. By combining with these previous results, we provide updated values of f B ¼ 0.190ð4Þ GeV, f B s ¼ 0.229ð5Þ GeV, and f B s =f B ¼ 1.206ð5Þ.