#
Experimental Determination of the QCD Effective Charge α_{g1}(Q)

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Extraction of ${\mathbf{\alpha}}_{{\mathbf{g}}_{\mathbf{1}}}$

**Figure 1.**Effective charge ${\alpha}_{{g}_{1}}\left(Q\right)/\pi $ obtained from JLab experiments E03006/E97110 [33] (solid stars), E03006/E05111 [33] (solid circles) and EG1dvcs [32] (solid triangles) and from COMPASS [31] (solid square). Inner error bars represent the statistical uncertainties, and outer ones represent the systematic and statistical uncertainties added quadratically. The open symbols show the older world data [27,28,29,30] with the error bars the quadratic sum of the systematic and statistical uncertainties. Also shown are the HLFQCD [24] (red line, using the HLFQCD scale $\kappa =0.534$ GeV [59]) and DSE [25] (magenta line and hatched band) parameter-free predictions of effective charges. The dashed line and hatched cyan band are ${\alpha}_{{g}_{1}}\left(Q\right)/\pi $ obtained from the GDH and Bjorken sum rules, respectively.

## 3. Summary and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Table 1.**Data on ${\alpha}_{{g}_{1}}\left(Q\right)$ from JLab experiments EG4 (top, from $Q=0.143$ GeV to 0.704 GeV), EG4/E97110 (middle, from $Q=0.187$ GeV to 0.490 GeV) and EG1dvcs (bottom, from $Q=0.775$ GeV to 2.177 GeV).

Q (GeV) | ${\mathit{\alpha}}_{{\mathit{g}}_{1}}\pm \mathbf{stat}.\pm \mathbf{syst}.$ |
---|---|

0.143 | 3.064 $\pm \phantom{\rule{3.33333pt}{0ex}}0.043\pm 0.018$ |

0.156 | 3.129 $\pm \phantom{\rule{3.33333pt}{0ex}}0.046\pm 0.019$ |

0.171 | 2.955 $\pm \phantom{\rule{3.33333pt}{0ex}}0.046\pm 0.023$ |

0.187 | 3.083 $\pm \phantom{\rule{3.33333pt}{0ex}}0.044\pm 0.024$ |

0.204 | 3.022 $\pm \phantom{\rule{3.33333pt}{0ex}}0.049\pm 0.024$ |

0.223 | 3.002 $\pm \phantom{\rule{3.33333pt}{0ex}}0.052\pm 0.027$ |

0.243 | 2.988 $\pm \phantom{\rule{3.33333pt}{0ex}}0.055\pm 0.031$ |

0.266 | 2.947 $\pm \phantom{\rule{3.33333pt}{0ex}}0.060\pm 0.035$ |

0.291 | 2.983 $\pm \phantom{\rule{3.33333pt}{0ex}}0.065\pm 0.035$ |

$\mathbf{Q}$(GeV) | ${\mathbf{\alpha}}_{{\mathbf{g}}_{\mathbf{1}}}\pm \mathbf{stat}\mathbf{.}\pm \mathbf{syst}\mathbf{.}$ |

0.317 | 2.961 $\pm \phantom{\rule{3.33333pt}{0ex}}0.062\pm 0.038$ |

0.347 | 2.730 $\pm \phantom{\rule{3.33333pt}{0ex}}0.070\pm 0.044$ |

0.379 | 2.853 $\pm \phantom{\rule{3.33333pt}{0ex}}0.077\pm 0.040$ |

0.414 | 2.745 $\pm \phantom{\rule{3.33333pt}{0ex}}0.076\pm 0.041$ |

0.452 | 2.779 $\pm \phantom{\rule{3.33333pt}{0ex}}0.090\pm 0.043$ |

0.494 | 2.451 $\pm \phantom{\rule{3.33333pt}{0ex}}0.094\pm 0.044$ |

0.540 | 2.397 $\pm \phantom{\rule{3.33333pt}{0ex}}0.092\pm 0.039$ |

0.590 | 2.349 $\pm \phantom{\rule{3.33333pt}{0ex}}0.101\pm 0.040$ |

0.645 | 2.431 $\pm \phantom{\rule{3.33333pt}{0ex}}0.109\pm 0.043$ |

0.704 | 1.996 $\pm \phantom{\rule{3.33333pt}{0ex}}0.131\pm 0.104$ |

$\mathbf{Q}$(GeV) | ${\mathbf{\alpha}}_{{\mathbf{g}}_{\mathbf{1}}}\pm \mathbf{stat}\mathbf{.}\pm \mathbf{syst}\mathbf{.}$ |

0.187 | 3.016 $\pm \phantom{\rule{3.33333pt}{0ex}}0.009\pm 0.027$ |

0.239 | 2.973 $\pm \phantom{\rule{3.33333pt}{0ex}}0.015\pm 0.035$ |

0.281 | 2.952 $\pm \phantom{\rule{3.33333pt}{0ex}}0.021\pm 0.041$ |

0.316 | 2.929 $\pm \phantom{\rule{3.33333pt}{0ex}}0.017\pm 0.048$ |

0.387 | 2.815 $\pm \phantom{\rule{3.33333pt}{0ex}}0.021\pm 0.076$ |

0.447 | 2.704 $\pm \phantom{\rule{3.33333pt}{0ex}}0.025\pm 0.086$ |

0.490 | 2.575 $\pm \phantom{\rule{3.33333pt}{0ex}}0.031\pm 0.053$ |

0.775 | 1.743 $\pm \phantom{\rule{3.33333pt}{0ex}}0.007\pm 0.071$ |

0.835 | 1.571 $\pm \phantom{\rule{3.33333pt}{0ex}}0.007\pm 0.101$ |

0.917 | 1.419 $\pm \phantom{\rule{3.33333pt}{0ex}}0.009\pm 0.132$ |

0.986 | 1.341 $\pm \phantom{\rule{3.33333pt}{0ex}}0.010\pm 0.147$ |

1.088 | 1.272 $\pm \phantom{\rule{3.33333pt}{0ex}}0.010\pm 0.156$ |

1.167 | 1.121 $\pm \phantom{\rule{3.33333pt}{0ex}}0.013\pm 0.153$ |

1.261 | 0.955 $\pm \phantom{\rule{3.33333pt}{0ex}}0.016\pm 0.146$ |

1.384 | 0.874 $\pm \phantom{\rule{3.33333pt}{0ex}}0.016\pm 0.269$ |

1.522 | 0.730 $\pm \phantom{\rule{3.33333pt}{0ex}}0.012\pm 0.280$ |

1.645 | 0.708 $\pm \phantom{\rule{3.33333pt}{0ex}}0.009\pm 0.257$ |

1.795 | 0.617 $\pm \phantom{\rule{3.33333pt}{0ex}}0.007\pm 0.254$ |

1.967 | 0.581 $\pm \phantom{\rule{3.33333pt}{0ex}}0.006\pm 0.223$ |

2.177 | 0.636 $\pm \phantom{\rule{3.33333pt}{0ex}}0.003\pm 0.187$ |

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**MDPI and ACS Style**

Deur, A.; Burkert, V.; Chen, J.-P.; Korsch, W. Experimental Determination of the QCD Effective Charge *α*_{g1}(*Q*). *Particles* **2022**, *5*, 171-179.
https://doi.org/10.3390/particles5020015

**AMA Style**

Deur A, Burkert V, Chen J-P, Korsch W. Experimental Determination of the QCD Effective Charge *α*_{g1}(*Q*). *Particles*. 2022; 5(2):171-179.
https://doi.org/10.3390/particles5020015

**Chicago/Turabian Style**

Deur, Alexandre, Volker Burkert, Jian-Ping Chen, and Wolfgang Korsch. 2022. "Experimental Determination of the QCD Effective Charge *α*_{g1}(*Q*)" *Particles* 5, no. 2: 171-179.
https://doi.org/10.3390/particles5020015