In the paper, we analyze the $η_c$ decays into light hadrons at the next-to-leading order QCD corrections by applying the principle of maximum conformality (PMC). The relativistic correction at the ${\cal{O}}(α_s v^2)$-order level has been included in the discussion, which gives about $10\%$ contribution to the ratio $R$. The PMC, which satisfies the renormalization group invariance, is designed to obtain a scale-fixed and scheme-independent prediction at any fixed order. To avoid the confusion of treating $n_f$-terms, we transform the usual $\overline{\rm MS}$ pQCD series into the one under the minimal momentum space subtraction scheme. To compare with the prediction under conventional scale setting, $R_{\rm{Conv,mMOM}-r}= \left(4.12^{+0.30}_{-0.28}\right)\times10^3$, after applying the PMC, we obtain $R_{\rm PMC,mMOM-r}=\left(6.09^{+0.62}_{-0.55}\right) \times10^3$, where the errors are squared averages of the ones caused by $m_c$ and $Λ_{\rm mMOM}$. The PMC prediction agrees with the recent PDG value within errors, i.e. $R^{\rm exp}=\left(6.3\pm0.5\right)\times10^3$. Thus we think the mismatching of the prediction under conventional scale-setting with the data is due to improper choice of scale, which however can be solved by using the PMC.
In the paper, we study the properties of the $Z$-boson hadronic decay width by using the $\mathcal{O}(α_s^4)$-order quantum chromodynamics (QCD) corrections with the help of the principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an accurate renormalization scale-and-scheme independent perturbative QCD (pQCD) correction for the $Z$-boson hadronic decay width, which is independent to any choice of renormalization scale. After applying the PMC, a more convergent pQCD series has been obtained; and the contributions from the unknown $\mathcal{O}(α_s^5)$-order…
A complete calculation of the ${\cal O}(α_s^4)$ perturbative QCD corrections to the hadronic decay width of the $Z$-boson has recently been performed by Baikov et al.[1]. In their analysis, Baikov et al. relied on the conventional practice of simply guessing the renormalization scale and taking an arbitrary range to estimate the pQCD uncertainties. This procedure inevitably introduces an arbitrary, scheme-dependent theoretical systematic error in the predictions. In this paper, we show that the renormalization scale uncertainties for hadronic $Z$ decays can be greatly reduced by applying the p…
The principle of maximum conformality (PMC) provides a way to eliminate the conventional renormalization scale ambiguity in a systematic way. By applying the PMC scale setting, all non-conformal terms in perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed prediction at any finite order. In the paper, we make a detailed PMC analysis for the spin-singlet heavy quarkoniums decay (into light hadrons) at the next-to-leading order. After applying the PMC scale setting, the decay widths for all those cases are almost independent of the initial renormalizati…
In any calculation in perturbative Quantum Chromodynamics (QCD) a choice needs to be made for the unphysical renormalisation scale, $μ_R$. The Brodsky-Lepage-Mackenzie/Principle of Maximum Conformality (BLM/PMC) scale-setting procedure is one proposed method for selecting this scale. In this work we identify three ambiguities in the BLM/PMC procedure itself. Their numerical impact is studied using the example of the total cross-section for $t\bar{t}$ production through Next-to-Next-to-Leading Order in QCD. One ambiguity is the arbitrary choice of the value of the highest-order PMC scale. The n…
As a basic requirement of the renormalization group invariance, any physical observable must be independent of the choice of both the renormalization scheme and the initial renormalization scale. In this paper, we show that by using the newly suggested $C$-scheme coupling, one can obtain a demonstration that the {\it Principle of Maximum Conformality} prediction is scheme-independent to all-orders for any renormalization schemes, thus satisfying all of the conditions of the renormalization group invariance. We illustrate these features for the non-singlet Adler function and for $τ$ decay to $ν…
We present in detail a new systematic method which can be used to automatically eliminate the renormalization scheme and scale ambiguities in perturbative QCD predictions at all orders. We show that all of the nonconformal β-dependent terms in a QCD perturbative series can be readily identified by generalizing the conventional renormalization schemes based on dimensional regularization. We then demonstrate that the nonconformal series of pQCD at any order can be resummed systematically into the scale of the QCD coupling in a unique and unambiguous way due to a special degeneracy of the β-terms…
The next-to-next-to-leading order (NNLO) pQCD correction to the inclusive decays of the heavy quarkonium $η_Q$ ($Q$ being $c$ or $b$) has been done in the literature within the framework of nonrelativistic QCD. One may observe that the NNLO decay width still has large conventional renormalization scale dependence due to its weaker pQCD convergence, e.g. about $(^{+4\%}_{-34\%})$ for $η_c$ and $(^{+0.0}_{-9\%})$ for $η_b$, by varying the scale within the range of $[m_Q, 4m_Q]$. The principle of maximum conformality (PMC) provides a systematic way to fix the $α_s$-running behavior of the process…
With the experimental observation of several credible candidates for multiquark hadrons, the latter states re-entered the focus of interest of theoretical strong-interaction physics. Proper treatment of hadronic bound states by quantum chromodynamics, QCD, the quantum field theory governing all strong interactions, necessitates a nonperturbative approach. A well-established framework of this kind is provided by QCD sum rules relating hadron features to the parameters of QCD. Conceptual reconsideration, however, reveals that, in order to really match the peculiarities of multiquarks, the long-s…
In contrast to the folklore that Technicolor (TC) is a "Higgsless theory", we shall discuss existence of a composite Higgs boson, Techni-Dilaton (TD), a pseudo-Nambu-Goldstone boson of the scale invariance in the Scale-invariant/Walking/Conformal TC (SWC TC) which generates a large anomalous dimension $γ_m \simeq 1$ in a wide region from the dynamical mass $m$ $= {\cal O}$ (TeV) of the techni-fermion all the way up to the intrinsic scale $Λ_{\rm TC}$ of the SWC TC (analogue of $Λ_{\rm QCD}$), where $Λ_{\rm TC} $ is taken typically as the scale of the Extended TC scale $Λ_{\rm ETC}$: $Λ_{\rm TC…
I discuss a number of novel tests of QCD at the LHC, measurements which can illuminate fundamental features of hadron physics. I also review the "Principle of Maximum Conformality" (PMC) which systematically sets the renormalization scale order-by-order in pQCD, eliminating an unnecessary theoretical uncertainty. The PMC allows LHC experiments to test QCD much more precisely, and the sensitivity of LHC measurements to physics beyond the Standard Model is increased.
We present improved pQCD predictions for Higgs boson hadroproduction at the Large Hadronic Collider (LHC) by applying the Principle of Maximum Conformality (PMC), a procedure which resums the pQCD series using the renormalization group (RG), thereby eliminating the dependence of the predictions on the choice of the renormalization scheme while minimizing sensitivity to the initial choice of the renormalization scale. In previous pQCD predictions for Higgs boson hadroproduction, it has been conventional to assume that the renormalization scale $μ_r$ of the QCD coupling $α_s(μ_r)$ is the Higgs m…
We describe a procedure to extend the light-front holographic approach to hadronic physics to include light-quark masses. The proposed framework allows us to extend the formalism of de Alfaro, Fubini and Furlan to the frame-independent light-front Hamiltonian theory in the approximation where the dynamics in the invariant transverse variable is unchanged to first order in the quark masses. The confinement potential follows from an effective theory which encodes the fundamental conformality of the classical QCD Lagrangian and leads to a semiclassical relativistic light-front wave equation for a…
I discuss several novel and unexpected aspects of quantum chromodynamics. These include: (a) the nonperturbative origin of intrinsic strange, charm and bottom quarks in the nucleon at large light-cone momenta x; the breakdown of pQCD factorization theorems due to the lensing effects of initial- and final-state interactions; (b) important corrections to pQCD scaling for inclusive reactions due to processes in which hadrons are created at high transverse momentum directly in the hard processes and their relation to the baryon anomaly in high-centrality heavy-ion collisions; and (c) the nonuniver…
Light-Front Quantization provides a physical, frame-independent formalism for hadron dynamics and structure. Observables such as structure functions, transverse momentum distributions, and distribution amplitudes are defined from the hadronic light-front wavefunctions. One obtains new insights into the hadronic spectrum, light-front wavefunctions, and the functional form of the QCD running coupling in the nonperturbative domain using light-front holography -- the duality between the front form and AdS$_5$, the space of isometries of the conformal group. In addition, superconformal algebra lead…
Heavy fermion pair production in $e^+e^-$ annihilation is a fundamental process in hadron physics and is of considerable interest for various phenomena. In this paper, we will apply the Principle of Maximum Conformality (PMC) to provide a comprehensive analysis of these processes. The PMC provides a systematic, unambiguous method for determining the renormalization scales of the QCD coupling constant for single-scale and multiple-scale applications. The resulting predictions eliminate any renormalization scheme-and-scale ambiguities, eliminate the factorial renormalon divergences, and are cons…
The predictive power of perturbative QCD (pQCD) depends on two important issues: (1) how to eliminate the renormalization scheme-and-scale ambiguities at fixed order, and (2) how to reliably estimate the contributions of unknown higher-order terms using information from the known pQCD series. The Principle of Maximum Conformality (PMC) satisfies all of the principles of the renormalization group and eliminates the scheme-and-scale ambiguities by the recursive use of the renormalization group equation to determine the scale of the QCD running coupling $α_s$ at each order. Moreover, the resultin…
