Commensurate scale relations: Precise tests of quantum chromodynamics without scale or scheme ambiguity
- Stanford Linear Accelerator Center, Menlo Park, CA (United States)
- Maryland Univ., College Park, MD (United States). Dept. of Physics
We derive commensurate scale relations which relate perturbatively calculable QCD observables to each other, including the annihilation ratio R{sub e+}e{sup {minus}}, the heavy quark potential, {tau} decay, and radiative corrections to structure function sum rules. For each such observable one can define an effective charge, such as {alpha}{sub R}({radical}s)/{pi} {equivalent_to} R {sub e+}e{sup {minus}}({radical}s)/(3{Sigma}e{sub q}{sup 2}){minus}1. The commensurate scale relation connecting the effective charges for observables A and B has the form {alpha}{sub A}(Q{sub A}) {alpha}{sub B}(Q{sub B})(1 + r {sub A/B}{sub {pi}}/{sup {alpha}B} + {hor_ellipsis}), where the coefficient r{sub A/B} is independent of the number of flavors {integral} contributing to coupling renormalization, as in BLM scale-fixing. The ratio of scales Q{sub A}/Q{sub B} is unique at leading order and guarantees that the observables A and B pass through new quark thresholds at the same physical scale. In higher orders a different renormalization scale Q{sup n*} is assigned for each order n in the perturbative series such that the coefficients of the series are identical to that of a invariant theory. The commensurate scale relations and scales satisfy the renormalization group transitivity rule which ensures that predictions in PQCD are independent of the choice of an intermediate renormalization scheme C. In particular, scale-fixed predictions can be made without reference to theoretically constructed singular renormalization schemes such as MS. QCD can thus be tested in a new and precise way by checking that the effective charges of observables track both in their relative normalization and in their commensurate scale dependence. The commensurate scale relations which relate the radiative corrections to the annihilation ratio R{sub e{sup +}e{sup {minus}}} to the radiative corrections for the Bjorken and Gross-Llewellyn Smith sum rules are particularly elegant and interesting.
- Research Organization:
- Stanford Linear Accelerator Center, Menlo Park, CA (United States); Maryland Univ., College Park, MD (United States). Dept. of Physics
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC03-76SF00515; FG02-93ER40762
- OSTI ID:
- 10193662
- Report Number(s):
- SLAC-PUB-6683; CONF-9406273-2; ON: DE95002785; BR: KB0300000; TRN: 94:023925
- Resource Relation:
- Conference: Tennessee international symposium on radiative corrections,Gatlinburg, TN (United States),27 Jun - 1 Jul 1994; Other Information: PBD: Oct 1994
- Country of Publication:
- United States
- Language:
- English
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