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The bottom quark forward-backward asymmetry $A_{\rm{FB}}$ is a key observable in electron-positron collisions at the $Z^{0}$ peak. In this paper, we employ the Principle of Maximum Conformality (PMC) to fix the $\alpha_s$-running behavior…

High Energy Physics - Phenomenology · Physics 2020-08-26 Sheng-Quan Wang , Rui-Qing Meng , Xing-Gang Wu , Long Chen , Jian-Ming Shen

Correlations between the QCD coupling \alpha_s, the gluon condensate < \alpha_s G^2 >, and the c,b-quark running masses m_c,b in the MS-scheme are explicitly studied (for the first time) from the (axial-)vector and (pseudo)scalar charmonium…

High Energy Physics - Phenomenology · Physics 2018-12-04 Stephan Narison

We predict the rate for exclusive double-charmonium production in electron-positron annihilation $e^+ e^- \to J/\psi+\eta_c$ using perturbative quantum chromodynamics and the NRQCD framework for hard, heavy-quarkonium exclusive processes.…

High Energy Physics - Phenomenology · Physics 2018-11-07 Zhan Sun , Xing-Gang Wu , Yang Ma , Stanley J. Brodsky

Data from e+e- annihilation into hadrons collected by the JADE experiment at centre-of-mass energies between 14 GeV and 44 GeV were used to study moments of event shape distributions. The data were compared with Monte Carlo models and with…

High Energy Physics - Experiment · Physics 2007-05-23 C. Pahl , S. Kluth , S. Bethke , P. A. Movilla Fernandez , J. Schieck , the JADE Collaboration

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…

High Energy Physics - Phenomenology · Physics 2007-05-23 Guang-jiong Ni , Guo-hong Yang , Rong-tang Fu , Haibin Wang

A pedagogical review is given of precise tests of QCD in electron-positron annihilation. Emphasis is placed on measurements that have served to establish QCD as the correct theory of strong interactions, as well as measurements of the…

High Energy Physics - Experiment · Physics 2009-09-25 P. N. Burrows

NNLO QCD corrections for the pion electromagnetic form factor at large momentum transfer have been recently performed in [Phys. Rev. Lett. 132, 201901 (2024); Phys. Rev. Lett. 134, 221901 (2025)], revealing that the NLO and NNLO…

High Energy Physics - Phenomenology · Physics 2025-12-29 Sheng-Quan Wang , Zuo-Fen Liao , Jian-Ming Shen , Hua Zhou , Jia-Wei Zhang , Jiang Yan , Xing-Gang Wu , Leonardo Di Giustino

In this lecture, after recalling the basic definitions and facts about the running coupling in QCD, I present a critical discussion of the methods for measuring $\alpha_s$ and select those that appear to me as the most reliably precise

High Energy Physics - Phenomenology · Physics 2013-03-26 Guido Altarelli

We present the first fully analytic calculation of the Quantum Chromodynamics (QCD) event shape observable Energy-Energy Correlation in electron-positron annihilation at Next-To-Leading Order (NLO). This result sheds light on the analytic…

High Energy Physics - Phenomenology · Physics 2018-07-20 Lance J. Dixon , Ming-xing Luo , Vladyslav Shtabovenko , Tong-Zhi Yang , Hua Xing Zhu

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.…

High Energy Physics - Phenomenology · Physics 2008-11-26 S. J. Brodsky , C. -R. Ji , A. Pang , D. G. Robertson

A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme -- this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance…

High Energy Physics - Phenomenology · Physics 2018-05-16 Xing-Gang Wu , Yang Ma , Sheng-Quan Wang , Hai-Bing Fu , Hong-Hao Ma , Stanley J. Brodsky , Matin Mojaza

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…

High Energy Physics - Phenomenology · Physics 2007-05-23 B. A. Magradze

The strong coupling $\alpha_s$ is determined with high precision from fits to lattice QCD simulations on the static energy. Our theoretical setup relies on R-improving the three-loop fixed-order prediction for the static energy by removing…

High Energy Physics - Phenomenology · Physics 2026-02-04 Jose M. Mena-Valle , Vicent Mateu , Pablo G. Ortega

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…

High Energy Physics - Phenomenology · Physics 2014-04-09 Qiong-Lian Zhang , Xing-Gang Wu , Xu-Chang Zheng , Sheng-Quan Wang , Hai-Bing Fu , Zhen-Yun Fang

In addition to the evaluation of high-order loop contributions, the precision and predictive power of perturbative QCD (pQCD) predictions depends on two important issues: (1) how to achieve a reliable, convergent fixed-order series, and (2)…

High Energy Physics - Phenomenology · Physics 2023-05-01 Jian-Ming Shen , Zhi-Jian Zhou , Sheng-Quan Wang , Jiang Yan , Zhi-Fei Wu , Xing-Gang Wu , Stanley J. Brodsky

We consider the electron-positron annihilation process into hadrons $R_{e^+e^-}$ up to $\mathcal{O}(\alpha_{s}^{3})$ and we adopt the smearing method suggest by Poggio, Quinn and Weinberg to confront the experimental data with theory. As a…

High Energy Physics - Phenomenology · Physics 2016-02-03 J. D. Gomez , A. A. Natale

In this paper, we present a new analysis on the $P$-wave charmonium annihilation into two photons up to next-to-next-to-leading order (NNLO) QCD corrections by using the principle of maximum conformality (PMC). The conventional perturbative…

High Energy Physics - Phenomenology · Physics 2021-07-28 Hua Zhou , Qing Yu , Xu-Dong Huang , Xu-Chang Zheng , Xing-Gang Wu

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.…

High Energy Physics - Phenomenology · Physics 2007-05-23 Stanley J. Brodsky , Hung Lung Lu

Theoretical predictions for particle production cross sections and decays at colliders rely heavily on perturbative Quantum Chromodynamics (QCD) calculations, expressed as an expansion in powers of the strong coupling constant $\alpha_s$.…

We have applied so-called `optimised' perturbation theory to resolve the renormalisation-scale (mu) ambiguity of exact O(alpha_s^2) QCD calculations of event shape observables in e+e- --> hadrons. We fitted the optimised predictions for 15…

High Energy Physics - Phenomenology · Physics 2009-10-28 P. N. Burrows , H. Masuda , D. Muller , Y. Ohnishi