Independent factorization and renormalization scales are inconsistent with simultaneously preserving RG invariance, Ward identities, and PDF sum rules in generalized pole subtraction schemes.
Complete Renormalization Group Improvement-Avoiding Factorization and Renormalization Scale Dependence in QCD Predictions
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abstract
For moments of leptoproduction structure functions we show that all dependence on the renormalization and factorization scales disappears, provided that all the ultraviolet logarithms involving the physical energy scale Q are completely resummed. The approach is closely related to Grunberg's method of Effective Charges. A direct and simple method for extracting the universal dimensional transmutation parameter of QCD from experimental data is advocated.
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What are the consequences of independent factorization and renormalization scales?
Independent factorization and renormalization scales are inconsistent with simultaneously preserving RG invariance, Ward identities, and PDF sum rules in generalized pole subtraction schemes.