https://doi.org/10.1140/epjc/s10052-021-08873-8
Regular Article – Theoretical Physics
Hyperspherical variables analysis of lattice QCD three-quark potentials: skewed Y-string as the mechanism of confinement?
1
University of St. Andrews, The Old Burgh School, Abbey Walk, St. Andrews, KY16 9LB, Fife, Scotland, UK
2
Thales, Reading, UK
3
Institute of Physics Belgrade, University of Belgrade, P.O. Box 57, Pregrevica 118, Zemun, 11080, Beograd, Serbia
4
Department of Health Sciences Research, Mayo Clinic, 200 First Street SW, 55905, Rochester, MN, USA
Received:
26
October
2020
Accepted:
13
January
2021
Published online:
24
January
2021
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 
-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).
© The Author(s) 2021
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