Some aspects of three-quark potentials. II

We continue our investigation of the effective string model for the triply heavy quark system, mimicking that in pure <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>3</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> gauge theory. We present analytical and numerical studies of the three-quark potential for isosceles and collinear geometries. In the general case, we derive the asymptotic expression of the potential in the infrared limit. Here we also demonstrate the universality of the string tension and interpret the transition between two distinct regimes, occurring when one of the triangle’s angles formed by the quarks is equal to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mfrac> <e:mn>2</e:mn> <e:mn>3</e:mn> </e:mfrac> <e:mi>π</e:mi> </e:math> , as a breaking of permutational symmetry. This symmetry breaking implies the emergence of a heavy quark dressed by gluons, transforming in the two-index antisymmetric representation. Additionally, we discuss various aspects of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>Y</g:mi> </g:math> - and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi mathvariant="normal">Δ</i:mi> </i:math> -laws, diquarks, and connections to lattice QCD.