Hyperspherical variables analysis of lattice QCD three-quark potentials: skewed Y-string as the mechanism of confinement?

• Published in: The European physical journal. C, Particles and fields Vol. 81; no. 1; pp. 1 - 9
• Main Authors: Leech, James, Šuvakov, Milovan, Dmitrašinović, V.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2021; Springer; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Astronomy; Astrophysics and Cosmology; Benchmarks; Curves; Deviation; Elementary Particles; Flux density; Hadrons; Heavy Ions; Mathematical analysis; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Qualitative analysis; Quantum chromodynamics; Quantum confinement; Quantum Field Theories; Quantum Field Theory; Quarks; Regular Article – Theoretical Physics; String Theory; Strings; Triangles
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-021-08873-8

We have re-analysed the lattice QCD calculations of the 3-quark potentials by: (i) Sakumichi and Suganuma (Phys Rev D 92(3), 034511, 2015); and (ii) Koma and Koma (Phys Rev D 95(9), 094513, 2017) using hyperspherical variables. We find that: (1) the two sets of lattice results have only two common sets of 3-quark geometries: (a) the isosceles, and (b) the right-angled triangles; (2) both sets of results are subject to unaccounted for deviations from smooth curves that are largest near the equilateral triangle geometry and are function of the hyperradius – the deviations being much larger and extending further in the triangle shape space in Sakumichi and Suganuma’s than in Koma and Koma’s data; (3) the variation of Sakumichi and Suganuma’s results brackets, from above and below, the Koma and Koma’s ones; the latter will be used as the benchmark; (4) this benchmark result generally passes between the Y- and the Δ -string predictions, thus excluding both; (5) three pieces of elastic strings joined at a skewed junction, which lies on the Euler line, reproduce such a potential, within the region where the data sets agree, in qualitative agreement with the calculations of colour flux density by Bissey et al. (Phys Rev D 76, 114512, 2007).