Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-01-16
Phys.Rev.D58:116006,1998
Physics
High Energy Physics
High Energy Physics - Phenomenology
Final version accepted for publication in Phys. Rev. D. New section with applications added comparing the analytic scheme with
Scientific paper
10.1103/PhysRevD.58.116006
The conventional definition of the running coupling $\alpha_{\bar{MS}}(\mu)$ 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 $\alpha_{\bar{MS}}(\mu)$ 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 $\alpha_{\bar{MS}}(\mu)$ 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 $\bar {MS}$ 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.
Brodsky Stanley J.
Gill Mandeep S.
Melles Michael
Rathsman Johan
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