Pade-Summation Approach to QCD β-Function Infrared Properties

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概要

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• In view of the successful asymptotic Pade-approximant predictions for higher-loop terms within QCD and massive scalar field theory, we address whether Pade-summations of the <MS>^^^- QCD β-function for a given number of flavours exhibit an infrared-stable fixed point, or alternatively, an infrared attractor of a double valued couplant as noted by Kogan and Shifman for the case of supersymmetric gluodynamics. Below an approximant-dependent flavour threshold(6≤n_f≤8), we find that Pade-summation β-functions incorporating[2|1], [1|2], [2|2], [1|3], and [3|1]approximants whose Maclaurin expansions match known higher-than-one-loop contributions to the β-function series always exhibit a positive pole prior to the occurrence of their first positive zero, precluding any indentification of this first positive zero as an infrared-stable fixed point of the β-function. This result is shown to be true regardless of the magnitude of the presently-unknown five-loop β-function contribution explicitly appearing within Pade-summation β-functions incorporating [2|2], [1|3] and [3|1] approximants. Moreover, the pole in question suggests the occurrence of dynamics in which both a strong and an asymptotically-free phase share a common infrared attractor. We briefly discuss the possible relevance of infrared-attractor dynamics to the success of recent calculations of the glueball mass spectra in QCD with N_c →∞ via supergravity. As n_f increases above an approximant-dependent flavour threshold, Pade-summation β-functions incorporating [2|2], [1|3] and [3|1] approximants exhibit dynamics controlled by an infraredstable fixed point over a widening domain of the five-loop <MS>^^^- β-function parameter(β_4/β_0). Subsequent to the above-mentioned flavour threshold, all approximants considered exhibit infrared-stable fixed points that decrease in magnitude with increasing flavour number.

• 理論物理学刊行会の論文
• 2000-09-25

著者

• Elias V

  Department Of Applied Mathematics The University Of Western Ontario

• CHISHTIE F.A.

  Department of Applied Mathematics, The University of Western Ontario

• ELIAS V.

  Department of Applied Mathematics, The University of Western Ontario

• MIRANSKY V.A.

  Department of Applied Mathematics, The University of Western Ontario, Department of Physics, Nagoya

• STEELE T.G.

  Department of Physics & Engineering Physics, University of Saskatchewan Saskatoon

• Steele T.g.

  Department Of Physics & Engineering Physics University Of Saskatchewan Saskatoon

• Chishtie F.a.

  Department Of Applied Mathematics The University Of Western Ontario

• Miransky V

  Univ. Western Ontario Ontario Can

• Miransky V.a.

  Department Of Applied Mathematics University Of Western Ontario

• Miransky V.

  Department Of Applied Mathematics University Of Western Ontario:yukawa Institute For Theoretical Phy

• STEELE T.G.

  Department of Physics & Engineering Physics, University of Saskatchewan Saskatoon

• Chishtie F.

  Department of Applied Mathematics, The University of Western Ontario

関連論文

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