Related papers: Setting the Renormalization Scale in QCD: The Prin…
We use the BLM procedure to eliminate the renormalization scale ambiguity in the evolution equation for the non-singlet deep-inelastic structure function $F_2^{\text NS}(x,Q).$ The scale of the QCD coupling in the $\overline{\text{MS}}$…
We introduce the running coupling constant of QCD in the high temperature phase, $\tilde{g}^2(T)$, through a renormalization scheme where the dimensional reduction is optimal at the one-loop level. We then calculate the relevant scale…
Non-perturbative scale-dependent renormalization problems are ubiquitous in lattice QCD as they enter many relevant phenomenological applications. They require solving non-perturbatively the renormalization group equations for the QCD…
Analytic QCD models are those where the QCD running coupling has the physically correct analytic behavior, i.e., no Landau singularities in the Euclidean regime. We present a simple analytic QCD model in which the discontinuity function of…
In the paper, we study the $\Upsilon(1S)$ leptonic decay width $\Gamma(\Upsilon(1S)\to \ell^+\ell^-)$ by using the principle of maximum conformality (PMC) scale-setting approach. The PMC adopts the renormalization group equation to set the…
Recently, the QCD renormalization group (RG) equation at higher orders in MS-like renormalization schemes has been solved for the running coupling as a series expansion in powers of the exact 2-loop order coupling. In this work, we prove…
We derive commensurate scale relations which relate perturbatively calculable QCD observables to each other, including the annihilation ratio, the heavy quark potential, tau decay, and radiative corrections to structure function sum rules.…
Renormalization scheme uncertainties in the next-next-to-leading order QCD predictions are discussed. To obtain an estimate of these uncertainties it is proposed to compare predictions in all schemes that do not have unnaturally large…
We try to review the main current ideas and points of view on the running coupling constant in QCD. We begin by recalling briefly the classic analysis based on the Renormalization Group with some emphasis on the exact solutions of the RG…
The conventional definition of the running coupling $\alpha_{\bar{MS}}(\mu)$ in quantum chromodynamics is based on a solution to the renormalization group equations which treats quarks as either completely massless at a renormalization…
A pivotal task in quantum metrology, and quantum parameter estimation in general, is to de- sign schemes that achieve the highest precision with given resources. Standard models of quantum metrology usually assume the dynamics is fixed, the…
The QCD coupling, $\alpha_s$, is not a physical observable since it depends on conventions related to the renormalization procedure. Here we discuss a redefinition of the coupling where changes of scheme are parametrised by a single…
The perturbative QCD corrections to the semileptonic decay width of the tau lepton are evaluated in the next-next-to-leading order from the contour integral representation in various renormalization schemes, using numerical solution of the…
We use the BLM method to fix the renormalization scale of the QCD coupling in exclusive hadronic amplitudes such as the pion form factor and the photon-to-pion transition form factor at large momentum transfer.…
We compute the running QCD coupling on the lattice by evaluating two-point and three-point off-shell gluon Green's functions in a fixed gauge and imposing non-perturbative renormalisation conditions on them. Our exploratory study is…
A simple parametrization of the QCD running coupling at low scales is introduced and used to illustrate various schemes for the estimation of non-perturbative power corrections. The `infrared matching' scheme proposed earlier gives…
In this paper, we compute the total and differential cross sections for $e^+e^- \to J/\psi+c+\bar{c}$ at the $B$ factories up to next-to-leading order (NLO) corrections within the framework of nonrelativistic QCD factorization theory. 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…
Based on a simple but effective regularization-renormalization method (RRM), the running coupling constants (RCC) of fermions with masses in quantum electrodynamics (QED) and quantum chromodynamics (QCD) are calculated by renormalization…
The scheme and gauge dependence of the factorization property of the RG $\beta$-function in the $SU(N_c)$ QCD generalized Crewther relation (GCR), which connects the non-singlet contributions to the Adler and Bjorken polarized sum rule…