Symmetries of the Three Heavy-Quark System and the Color-Singlet Static Energy at NNLL

Abstract

We study the symmetries of the three heavy-quark system under exchange of the quark fields within the effective field theory framework of potential non-relativistic QCD. The symmetries constrain the form of the matching coefficients in the effective theory. We then focus on the color-singlet sector and determine the so far unknown leading ultrasoft contribution to the static potential, which is of order alpha_s^4 ln(μ), and consequently to the static energy, which is of order alpha_s^4 ln(alpha_s). Finally, in the case of an equilateral geometry, we solve the renormalization group equations and resum the leading ultrasoft logarithms for the static potential of three quarks in a color singlet, octet and decuplet representation.

27 pages, 3 figures; matches journal version

References in corpus (4)

• The QCD static energy at NNNLL
• Heavy quark free energies for three quark systems at finite temperature
• Instantaneous Interquark Potential in Generalized Landau Gauge in SU(3) Lattice QCD: A Linkage between the Landau and the Coulomb Gauges
• Effective field theories for baryons with two- and three-heavy quarks

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