The Search for Beauty-fully Bound Tetraquarks Using Lattice Non-Relativistic QCD

Motivated by multiple phenomenological considerations, we perform the first search for the existence of a $\bar{b}\bar{b}bb$ tetraquark bound state with a mass below the lowest non-interacting bottomonium-pair threshold using the first-principles lattice non-relativistic QCD methodology. We use a full $S$-wave colour/spin basis for the $\bar{b}\bar{b}bb$ operators in the three $0^{++}$, $1^{+-}$ and $2^{++}$ channels. We employ four gluon field ensembles at multiple lattice spacing values ranging from $a = 0.06 - 0.12$ 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 non-interacting thresholds in the channels studied.Comment: 24 Pages; 19 Figures; Accepted By PRD; Unaveraged Correlator Data Publicly Available in SQLite Databas

Simple fish-eye calibration method with accuracy evaluation

In this paper, a simple fish-eye radial distortion calibration procedure is described. This method avoids costly minimisation and optimisation algorithms, and is based on trivial concentricity of three extracted points. The results show that this simplicity is at the expense of increased deviation of results (and thus increased error). However, this deviation can be reduced significantly by the use of simple averaging, such that it is only marginally greater than the current state-of-the-art

Potential Energy Landscape of the Two-Dimensional XY Model: Higher-Index Stationary Points

The application of numerical techniques to the study of energy landscapes of large systems relies on sufficient sampling of the stationary points. Since the number of stationary points is believed to grow exponentially with system size, we can only sample a small fraction. We investigate the interplay between this restricted sample size and the physical features of the potential energy landscape for the two-dimensional $XY$ model in the absence of disorder with up to $N=100$ spins. Using an eigenvector-following technique, we numerically compute stationary points with a given Hessian index $I$ for all possible values of $I$. We investigate the number of stationary points, their energy and index distributions, and other related quantities, with particular focus on the scaling with $N$. The results are used to test a number of conjectures and approximate analytic results for the general properties of energy landscapes.Comment: 8 pages, 10 figures. Published in Journal of Chemical Physic