Related papers: A Scheme Independent Definition of $\Lambda_{\rm Q…
In this paper we show that the apparent failure of QCD lattice perturbation theory to account for Monte Carlo measurements of perturbative quantities results from choosing the bare lattice coupling constant as the expansion parameter. Using…
When calculating next-to-leading order QCD cross sections, divergences in intermediate steps of the calculation must be regularized. The final result is independent of the regularization scheme used, provided that it is unitary. In this…
Effective coupling constant in quantum electrodynamics is investigated. A pole appears in the effective coupling constant for the space-like momentum if it is calculated by perturbation. The pole can be eliminated by the analytic…
we show there exists a mathematically consistent framework in which the Renormalization Program can be understood in a natural manner. The framework does not require any violations of mathematical rigor usually associated with the…
We compute the flavorless running coupling constant of QCD from the three gluon vertex in the (regularisation independent) momentum subtraction renormalisation scheme. This is performed on the lattice with high statistics. The expected…
Recently, Dvali, Gomez, and Mukhanov have investigated a classical lambda phi^4 model with external source and without mass and they have clarified that there are underlying renormalization group structure, including the phenomenon of the…
In these lectures, we discuss different types of renormalization problems in QCD and their non-perturbative solution in the framework of the lattice formulation. In particular the recursive finite size methods to compute the…
New equations governing the scale transformation behaviors of a QFT with underlying structures are derived. These equations, with their several equivalent versions, can yield some new and significant insights and results that are difficult…
A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to…
A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale $\mu$ of the running coupling $\alpha_s(\mu^2).$ The purpose of the running coupling in any gauge theory is to sum all…
We discuss how the renormalisation scheme ambiguities in QCD can be fixed, when two observables are related, by requiring the coefficients in the perturbative expansion relating the two observables to have their conformal limit values, i.e.…
The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making…
A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the…
The renormalization scheme for the Wick expansion of a modified version of the perturbative QCD introduced in previous works is discussed. Massless QCD is considered, by implementing the usual multiplicative scaling of the gluon and quark…
The conventional approach to fixed-order perturbative QCD predictions is based on an arbitrary choice of the renormalization scale, together with an arbitrary range. This {\it ad hoc} assignment of the renormalization scale causes the…
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…
We reconsider the choice of renormalization schemes in a differential-equation approach to aid the discussion of the renormalization of the unstable particles and the CKM matrix in the Standard Model. Certain mass dependent schemes do not…
We briefly review how it is possible to derive some exact expressions for the renormalization constants for the MS-like renormalization prescriptions using the arguments based on the renormalization group. These expressions are obtained for…
Commensurate scale relations relate observables to observables and thus are independent of theoretical conventions, such as the choice of intermediate renormalization scheme. The physical quantities are related at commensurate scales which…
A key issue in making precise predictions in perturbative QCD is the uncertainty in setting the renormalization scale. If in principle, the entire perturbative series is void of this issue, in practice the perturbative corrections are known…