Related papers: Renormalization Scheme Dependence and Renormalizat…
We consider all radiative corrections to the total electron-positron cross section showing how the renormalization group equation can be used to sum the logarithmic contributions in two ways. First of all, one can sum leading-log etc.…
The zero to four loop contribution to the cross section $R_{e^{+}e^{-}}$ for $e^{+}e^{-} \longrightarrow$ hadrons, when combined with the renormalization group equation, allows for summation of all leading-log ($LL$), next-to-leading-log…
Using an approach developed in the context of zero-temperature QCD to systematically sum higher order effects whose form is fixed by the renormalization group equation, we sum to all orders the leading log (LL) and next-to-leading log (NLL)…
We employ renormalization group (RG) summation techniques to obtain portions of Laplace QCD sum rules for scalar gluon currents beyond the order to which they have been explicitly calculated. The first two of these sum rules are considered…
We demonstrate that in the mass independent renormalization scheme. the renormalization group equations associated with the unphysical parameters that characterize the renormalization scheme and the mass scale leads to summation that…
Invariance of the effective action under changes of the renormalization scale $\mu$ leads to relations between those (presumably calculated) terms independent of $\mu$ at a given order of perturbation theory and those higher order terms…
Based on the renormalization group summation method of McKeon ${\it et\; al.}$, it is shown that the renormalization group equation, while related to the radiatively mass scale $\mu$, would perform a summation over QCD perturbative terms.…
After reviewing how the renormalization group equation can be used to sum logarithmic corrections to the decay rate for the semi-leptonic process b->u when using minimal subtraction, we consider renormalization scheme dependence for this…
The renormalization group (RG) is known to provide information about radiative corrections beyond the order in perturbation theory to which one has calculated explicitly. We first demonstrate the effect of the renormalization scheme used on…
Conventionally, one adopts typical momentum flow of a physical observable as the renormalization scale for its perturbative QCD (pQCD) approximant. This simple treatment leads to renormalization scheme-and-scale ambiguities due to the…
The summation of logarithmic contributions to perturbative radiative corrections in physical processes through use of the renormalization group equation has proved to be a useful way of enhancing the information one can obtain from explicit…
We analyse approximate solutions to an exact renormalisation group equation with particular emphasis on their dependence on the regularisation scheme, which is kept arbitrary. Physical quantities related to the coarse-grained potential of…
We show that dimensionful renormalization scheme parameters such as the renormalization or factorization scale can be completely eliminated from perturbative QCD predictions provided that all the ultraviolet logarithms involving the…
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…
Two approaches to renormalization-group improvement are examined: the substitution of the solutions of running couplings, masses and fields into perturbatively computed quantities is compared with the systematic sum of all the leading log…
The general relation between the standard expansion coefficients and the beta function for the QCD coupling is exactly derived in a mathematically strict way. It is accordingly found that an infinite number of logarithmic terms are lost in…
The renormalization that relates a coupling "a" associated with a distinct renormalization group beta function in a given theory is considered. Dimensional regularization and mass independent renormalization schemes are used in this…
Given a renormalization scheme of QCD, one can define a mass scale $\Lambda_{\rm QCD}$ in terms of the beta function. Under a change of the renormalization scheme, however, $\Lambda_{\rm QCD}$ changes by a multiplicative constant. We…
QCD contributions to the $b \to u \ell^- \bar{\nu}_\ell$ decay rate, which are known to two-loop order in the $\bar{MS}$ scheme, exhibit sufficient dependence on the renormalization mass $\mu$ to compromise phenomenological predictions for…
Using renormalization-group methods, differential equations can be obtained for the all-orders summation of leading and subsequent non-leading logarithmic corrections to QCD perturbative series for a number of processes and correlation…