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Pade Estimate of QCD's Infrared Boundary

F. A. Chishtie·V. Elias·T. G. Steele
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Abstract

A mass scale $μ_c$ representing the boundary between effective theories of strong interactions and perturbative QCD (infrared and ultraviolet regimes) exists when the $β$-function is characterized by a simple pole. This behaviour, which is known to occur in N=1 supersymmetric Yang-Mills theories, leads to an infrared attractor in the evolution of the coupling constant, with the mass scale $μ_c$ of the attractor providing a natural boundary between the infrared and ultraviolet regimes. It is demonstrated that [2|2], [3|1] and [1|3] Pade-approximant versions of the three-flavour QCD $β$-function each contain a simple pole corresponding to such an infrared attractor. All three approximants, separately considered, are seen to lead to nearly equivalent estimates for the mass scale $μ_c$.

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F. A. Chishtie, V. Elias, T. G. Steele. 2001-06-25. Pade Estimate of QCD's Infrared Boundary. https://doi.org/10.1016/s0370-2693(01)00788-2

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