Renormalization Scheme Dependence in a QCD Cross Section

Abstract

The zero to four loop contribution to the cross section $R_{e^{+}{e}^{-}}$ for $e^{+}{e}^{-}⟶$ hadrons, when combined with the renormalization group equation, allows for summation of all leading-log ($LL$), next-to-leading-log $(NLL)\dots N^{3}LL$ perturbative contributions. It is also shown how all logarithmic contributions to $R_{e^{+}{e}^{-}}$ can be summed and that $R_{e^{+}{e}^{-}}$ can be expressed in terms of the log independent contributions, and once this is done the running coupling $a$ is evaluated at a point independent of the renormalization scale $\mu$. All explicit dependence of $R_{e^{+}{e}^{-}}$ on $\mu$ cancels against its implicit dependence on $\mu$ through the running coupling $a$ so that the ambiguity associated with the value of $\mu$ is shown to disappear. The renormalization scheme dependency of the "summed" cross section $R_{e^{+}{e}^{-}}$ is examined in three distinct renormalization schemes. In each case, $R_{e^{+}{e}^{-}}$ is expressible in terms of renormalization scheme independent parameters ${\tau }_i$ and is explicitly and implicitly independent of the renormalization scale $\mu$. Two of the forms are then compared graphically both with each other and with the purely perturbative results and the $RG$-summed $N^{3}LL$ results.

20 pages, 3 figures, LaTeX2e; accepted version to appear in Physical Review D

References in corpus (10)

• Hadronic Z- and tau-Decays in Order alpha_s^4
• Lattice tests of beyond Standard Model dynamics
• Towards the five-loop Beta function for a general gauge group
• Generalization of the Brodsky-Lepage-Mackenzie optimization within the $\{\beta \}$-expansion and the Principle of Maximal Conformality
• Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Fourth-order QCD renormalization group quantities in the {\rm{V}}-scheme and the relation of the $\beta$-function to the Gell-Mann--Low function in QED
• New Scheme Transformations and Application to Study Scheme Dependence of an Infrared Zero of the Beta Function in Gauge Theories
• Setting the Renormalization Scale in pQCD: Comparisons of the Principle of Maximum Conformality with the Sequential Extended Brodsky-Lepage-Mackenzie Approach
• Momentum subtraction and the R-ratio
• Renormalization Scheme Dependence with Renormalization Group Summation

Cited by in corpus (10)

• Renormalization Scheme Dependence and the Renormalization Group Beta Function
• Comparing optimized renormalization schemes for QCD observables
• Multiple Couplings and Renormalization Scheme Ambiguities
• Use of Lagrange multiplier fields to eliminate multiloop corrections
• Achieving effective renormalization scale and scheme independence via the Principle of Observable Effective Matching
• Renormalization Scheme Dependence of $\beta$-Functions In Lorentz-Violating Quantum Field Theory
• The Effectve Potential in Massless Theories
• On the analytically-improved running coupling in QCD
• The Renormalization Group and the Effective Potential in the Wess-Zumino model
• Renormalisation