# Novel method for the precise determination of the QCD running coupling from event shape distributions in electron-positron annihilation

## Abstract

We present a novel method for precisely determining the running QCD coupling constant ${\alpha}_{s}\left({Q}^{2}\right)$ over a wide range of ${Q}^{2}$ from event shapes for electron-positron annihilation measured at a single annihilation energy $\sqrt{s}$. The renormalization scale ${Q}^{2}$ of the running coupling depends dynamically on the virtuality of the underlying quark and gluon subprocess and thus the specific kinematics of each event. The determination of the renormalization scale for event shape distributions is obtained by using the principle of maximum conformality (PMC), a rigorous scale-setting method for gauge theories which satisfies all the requirements of renormalization group invariance, including renormalization-scheme independence and consistency with Abelian theory in the ${N}_{C}\to 0$ limit. In this paper, we apply the PMC to two classic event shapes measured in ${e}^{+}{e}^{\u2013}$ annihilation: the thrust ( $T$) and C-parameter ( $C$). The PMC renormalization scale depends differentially on the values of $T$ and $C$. The application of PMC scale-setting determines the running coupling ${\alpha}_{s}\left({Q}^{2}\right)$ to high precision over a wide range of ${Q}^{2}$ from 10 to $250\text{}\text{}{\mathrm{GeV}}^{2}$ from measurements of the event shape distributions at the ${Z}^{0}$ peak. The extrapolation of the running coupling using pQCD evolution gives the value ${\alpha}_{s}\left({M}_{Z}^{2}\right)=0.1185\pm 0.0012$ from the thrust and ${\alpha}_{s}\left({M}_{Z}^{2}\right)=0.119{3}_{\u20130.0019}^{+0.0021}$ from the C-parameter in the $\overline{\mathrm{MS}}$ scheme. These determinations of ${\alpha}_{s}\left({M}_{Z}^{2}\right)$ are consistent with the world average and are more precise than the values obtained from analyses of event shapes currently used in the world average. The highly consistent results for the $T$ and $C$ event-shape distributions provide an additional verification of the applicability of the PMC to pQCD.

- Authors:

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE; Natural Science Foundation of China

- OSTI Identifier:
- 1573861

- Alternate Identifier(s):
- OSTI ID: 1596796

- Report Number(s):
- SLAC-PUB-17458; arXiv:1908.00060v2

Journal ID: ISSN 2470-0010; PRVDAQ; 094010

- Grant/Contract Number:
- AC02-76SF00515; SLAC-PUB-17458; 11625520; 11705033; 11847301; 11905056; KY[2016]028; KY[2017]067

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 9; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Wang, Sheng-Quan, Brodsky, Stanley J., Wu, Xing-Gang, Shen, Jian-Ming, and Di Giustino, Leonardo. Novel method for the precise determination of the QCD running coupling from event shape distributions in electron-positron annihilation. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.094010.
```

```
Wang, Sheng-Quan, Brodsky, Stanley J., Wu, Xing-Gang, Shen, Jian-Ming, & Di Giustino, Leonardo. Novel method for the precise determination of the QCD running coupling from event shape distributions in electron-positron annihilation. United States. doi:10.1103/PhysRevD.100.094010.
```

```
Wang, Sheng-Quan, Brodsky, Stanley J., Wu, Xing-Gang, Shen, Jian-Ming, and Di Giustino, Leonardo. Mon .
"Novel method for the precise determination of the QCD running coupling from event shape distributions in electron-positron annihilation". United States. doi:10.1103/PhysRevD.100.094010.
```

```
@article{osti_1573861,
```

title = {Novel method for the precise determination of the QCD running coupling from event shape distributions in electron-positron annihilation},

author = {Wang, Sheng-Quan and Brodsky, Stanley J. and Wu, Xing-Gang and Shen, Jian-Ming and Di Giustino, Leonardo},

abstractNote = {We present a novel method for precisely determining the running QCD coupling constant αs(Q2) over a wide range of Q2 from event shapes for electron-positron annihilation measured at a single annihilation energy s. The renormalization scale Q2 of the running coupling depends dynamically on the virtuality of the underlying quark and gluon subprocess and thus the specific kinematics of each event. The determination of the renormalization scale for event shape distributions is obtained by using the principle of maximum conformality (PMC), a rigorous scale-setting method for gauge theories which satisfies all the requirements of renormalization group invariance, including renormalization-scheme independence and consistency with Abelian theory in the NC→0 limit. In this paper, we apply the PMC to two classic event shapes measured in e+e– annihilation: the thrust (T) and C-parameter (C). The PMC renormalization scale depends differentially on the values of T and C. The application of PMC scale-setting determines the running coupling αs(Q2) to high precision over a wide range of Q2 from 10 to 250 GeV2 from measurements of the event shape distributions at the Z0 peak. The extrapolation of the running coupling using pQCD evolution gives the value αs(MZ2)=0.1185±0.0012 from the thrust and αs(MZ2)=0.1193–0.0019+0.0021 from the C-parameter in the MS¯ scheme. These determinations of αs(MZ2) are consistent with the world average and are more precise than the values obtained from analyses of event shapes currently used in the world average. The highly consistent results for the T and C event-shape distributions provide an additional verification of the applicability of the PMC to pQCD.},

doi = {10.1103/PhysRevD.100.094010},

journal = {Physical Review D},

number = 9,

volume = 100,

place = {United States},

year = {2019},

month = {11}

}

DOI: 10.1103/PhysRevD.100.094010

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