An Analytic Extension of the $\overline{MS}$ Renormalizaton Scheme

Abstract

The conventional definition of the running coupling ${\alpha }_{\overline{MS}}(\mu )$ in quantum chromodynamics is based on a solution to the renormalization group equations which treats quarks as either completely massless at a renormalization scale $\mu$ above their thresholds or infinitely massive at a scale below them. The coupling is thus nonanalytic at these thresholds. In this paper we present an analytic extension of ${\alpha }_{\overline{MS}}(\mu )$ which incorporates the finite-mass quark threshold effects into the running of the coupling. This is achieved by using a commensurate scale relation to connect ${\alpha }_{\overline{MS}}(\mu )$ to the physical ${\alpha }_V$ scheme at specific scales, thus naturally including finite quark masses. The analytic-extension inherits the exact analyticity of the ${\alpha }_V$ scheme and matches the conventional $\overline{MS}$ scheme far above and below mass thresholds. Furthermore just as in ${\alpha }_V$ scheme, there is no renormalization scale ambiguity, since the position of the physical mass thresholds is unambiguous.

Final version accepted for publication in Phys. Rev. D. New section with applications added comparing the analytic scheme with the standard treatment of masses in the MSbar scheme. Conclusions updated accordingly. Main results unchanged

References in corpus (5)

• Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme
• Optimal Renormalization Scale and Scheme for Exclusive Processes
• ${\alpha }_s(m_Z)$ from tau decays with matching conditions at three loops
• Aspects of SU(N_c) Gauge Theories in the Limit of Small Number of Colors
• Analytic Perturbation Theory: A New Approach to the Analytic Continuation of the Strong Coupling Constant ${\alpha }_S$ into the Timelike Region

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